%%% -*-BibTeX-*- %%% ==================================================================== %%% BibTeX-file{ %%% author = "Nelson H. F. Beebe", %%% version = "1.31", %%% date = "02 June 2023", %%% time = "09:54:10 MDT", %%% filename = "canjmath2010.bib", %%% address = "University of Utah %%% Department of Mathematics, 110 LCB %%% 155 S 1400 E RM 233 %%% Salt Lake City, UT 84112-0090 %%% USA", %%% telephone = "+1 801 581 5254", %%% FAX = "+1 801 581 4148", %%% URL = "https://www.math.utah.edu/~beebe", %%% checksum = "61416 19709 100843 949799", %%% email = "beebe at math.utah.edu, beebe at acm.org, %%% beebe at computer.org (Internet)", %%% codetable = "ISO/ASCII", %%% keywords = "bibliography, BibTeX, Canadian Journal of %%% Mathematics, Journal canadien de %%% math{\'e}matiques", %%% license = "public domain", %%% supported = "yes", %%% docstring = "This is a COMPLETE bibliography of the %%% Canadian Journal of Mathematics = Journal %%% canadien de math{\'e}matiques (CODEN CJMAAB, %%% ISSN 0008-414X (print), 1496-4279 %%% (electronic)), published by the Canadian %%% Mathematical Society = Soci{\'e}t{\'e} %%% canadienne de math{\'e}matiques for the %%% decade 2010--2019. %%% %%% Publication began with Volume 1, Number 1, in %%% 1949. The journal was published quarterly %%% from 1949 to 1964, and since then, appears %%% bimonthly in February, April, June, August, %%% October, and December. %%% %%% Articles may be published in either English %%% or French, and English abstracts are %%% sometimes provided for articles in French. %%% %%% The journal has World-Wide Web sites at %%% %%% http://cms.math.ca/cjm/ %%% http://math.ca/Journals/ %%% http://cms.math.ca/Publications/CJM-CMB.html %%% http://www.utpjournals.com/cjm/cjm.html %%% http://www.camel.math.ca/CMS/CJM/ %%% %%% Electronic full text of articles is available %%% to qualified subscribers, and for older %%% issues, to anyone. %%% %%% At version 1.31, the COMPLETE year coverage %%% looked like this: %%% %%% 2006 ( 1) 2012 ( 57) 2018 ( 50) %%% 2007 ( 0) 2013 ( 59) 2019 ( 61) %%% 2008 ( 0) 2014 ( 53) 2020 ( 1) %%% 2009 ( 1) 2015 ( 56) 2021 ( 1) %%% 2010 ( 69) 2016 ( 49) 2022 ( 1) %%% 2011 ( 56) 2017 ( 52) %%% %%% Article: 567 %%% %%% Total entries: 567 %%% %%% BibTeX citation tags are uniformly chosen as %%% name:year:abbrev, where name is the family %%% name of the first author or editor, year is a %%% 4-digit number, and abbrev is a 3-letter %%% condensation of important title %%% words. Citation tags are automatically %%% generated by software developed for the %%% BibNet Project. %%% %%% In this bibliography, entries are sorted in %%% publication order, using bibsort -byvolume. %%% The checksum field above contains a CRC-16 %%% checksum as the first value, followed by the %%% equivalent of the standard UNIX wc (word %%% count) utility output of lines, words, and %%% characters. This is produced by Robert %%% Solovay's checksum utility.", %%% } %%% ====================================================================

@Preamble{ "\input canjmath.sty" # "\ifx \undefined \frak \let \germ = \bf \else \let \germ = \frak \fi" # "\ifx \undefined \iindex \def \iindex#1{} \fi" # "\ifx \undefined \mathbb \def \mathbb #1{{\bf #1}} \fi" # "\ifx \undefined \mathcal \def \mathcal #1{{\cal #1}}\fi" # "\ifx \undefined \mathfrak \let \mathfrak = \mathcal \fi" # "\ifx \undefined \mathrm \def \mathrm #1{{\rm #1}}\fi" # "\ifx \undefined \refcno \def \refcno{Cno. } \fi" }

%%% ==================================================================== %%% Acknowledgement abbreviations:

@String{ack-nhfb= "Nelson H. F. Beebe, University of Utah, Department of Mathematics, 110 LCB, 155 S 1400 E RM 233, Salt Lake City, UT 84112-0090, USA, Tel: +1 801 581 5254, FAX: +1 801 581 4148, e-mail: \path|beebe@math.utah.edu|, \path|beebe@acm.org|, \path|beebe@computer.org| (Internet), URL: \path|https://www.math.utah.edu/~beebe/|"}

%%% ==================================================================== %%% Journal abbreviations:

@String{j-CAN-J-MATH= "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques"}

%%% ==================================================================== %%% Bibliography entries:

@Article{Chiang:2006:VDT, author = "Yik-Man Chiang and Mourad E. H. Ismail", title = "On Value Distribution Theory of Second Order Periodic {ODE}s, Special Functions and Orthogonal Polynomials", journal = j-CAN-J-MATH, volume = "58", number = "4", pages = "726--767", month = aug, year = "2006", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2006-030-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:13 MDT 2011", bibsource = "http://cms.math.ca/cjm/v58/; https://www.math.utah.edu/pub/tex/bib/canjmath2000.bib; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", note = "See \cite{Chiang:2010:EVD}.", abstract = "We show that the value distribution (complex oscillation) of solutions of certain periodic second order ordinary differential equations studied by Bank, Laine and Langley is closely related to confluent hypergeometric functions, Bessel functions and Bessel polynomials. As a result, we give a complete characterization of the zero-distribution in the sense of Nevanlinna theory of the solutions for two classes of the ODEs. Our approach uses special functions and their asymptotics. New results concerning finiteness of the number of zeros (finite-zeros) problem of Bessel and Coulomb wave functions with respect to the parameters are also obtained as a consequence. We demonstrate that the problem for the remaining class of ODEs not covered by the above {``special function approach''} can be described by a classical Heine problem for differential equations that admit polynomial solutions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bell:2009:MAI, author = "J. P. Bell and K. G. Hare", title = "On {$\mathbb{Z}$}-Modules of Algebraic Integers", journal = j-CAN-J-MATH, volume = "61", number = "??", pages = "264--281", month = "????", year = "2009", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2009-013-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:15 MDT 2011", bibsource = "http://cms.math.ca/cjm/v61/; https://www.math.utah.edu/pub/tex/bib/canjmath2000.bib; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", note = "See corrigendum \cite{Bell:2012:CMA}.", abstract = "Let $q$ be an algebraic integer of degree $d \geq 2$. Consider the rank of the multiplicative subgroup of ${\mathbb C}$^*$$ generated by the conjugates of $q$. We say $q$ is of $full rank$ if either the rank is $d - 1$ and $q$ has norm $pm 1$, or the rank is $d$. In this paper we study some properties of ${\mathbb Z}[q]$ where $q$ is an algebraic integer of full rank. The special cases of when $q$ is a Pisot number and when $q$ is a Pisot-cyclotomic number are also studied. There are four main results. (1) If $q$ is an algebraic integer of full rank and $n$ is a fixed positive integer, then there are only finitely many $m$ such that disc $({\mathbb Z}[q$^m$ ]) =$ disc $({\mathbb Z}[q$^n$ ])$. (2) If $q$ and $r$ are algebraic integers of degree $d$ of full rank and ${\mathbb Z][q$^n$ ] = {\mathbb Z}[r$^n$ ]$ for infinitely many $n$, then either $q = \omega r$^'$$ or $q =$ Norm $(r)$^{{2/d}}$ \omega/r$^{', where r '}$$ is some conjugate of $r$ and $\omega$ is some root of unity. (3) Let $r$ be an algebraic integer of degree at most 3. Then there are at most 40 Pisot numbers $q$ such that ${\mathbb Z}[q] = {\mathbb Z}[r]$. (4) There are only finitely many Pisot-cyclotomic numbers of any fixed order.??}", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Anchouche:2010:ABC, author = "Boudjem{\^a}a Anchouche", title = "On the asymptotic behavior of complete {K{\"a}hler} metrics of positive {Ricci} curvature", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "3--18", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-001-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "32Q15 (32Q40)", MRnumber = "2596939 (2011d:32034)", MRreviewer = "Jacopo Stoppa", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let ( X,g) be a complete noncompact K{\"a}hler manifold, of dimension n{\geq}2, with positive Ricci curvature and of standard type (see the definition below). N. Mok proved that $X$ can be compactified, i.e., $X$ is biholomorphic to a quasi-projective variety. The aim of this paper is to prove that the L$^2$ holomorphic sections of the line bundle K$_X^{-q}$ and the volume form of the metric $g$ have no essential singularities near the divisor at infinity. As a consequence we obtain a comparison between the volume forms of the K{\"a}hler metric $g$ and of the Fubini--Study metric induced on $X$. In the case of dim$_C$ X=2, we establish a relation between the number of components of the divisor $D$ and the dimension of the groups H$^i$ ( \overline{X}, \Omega$_{\overline{X}}^1$ ( log D)).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bouchekif:2010:SSE, author = "Mohammed Bouchekif and Yasmina Nasri", title = "Solutions for semilinear elliptic systems with critical {Sobolev} exponent and {Hardy} potential", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "19--33", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-002-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "35J57 (35B33 35J61)", MRnumber = "2596940 (2011a:35114)", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we consider an elliptic system with an inverse square potential and critical Sobolev exponent in a bounded domain of \mathbb{R}$^N$. By variational methods we study the existence results.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Campbell:2010:BRR, author = "Peter S. Campbell and Monica Nevins", title = "Branching Rules for Ramified Principal Series Representations of {$\mathrm{GL}(3)$} over a $p$-adic Field", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "34--51", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-003-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "20G25 (20G05 22E50)", MRnumber = "2597022 (2011a:20126)", MRreviewer = "Maarten Sander Solleveld", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We decompose the restriction of ramified principal series representations of the $p$-adic group GL(3,k) to its maximal compact subgroup K=GL(3, $R$). Its decomposition is dependent on the degree of ramification of the inducing characters and can be characterized in terms of filtrations of the Iwahori subgroup in $K$. We establish several irreducibility results and illustrate the decomposition with some examples.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Deng:2010:AAW, author = "Shaoqiang Deng", title = "An algebraic approach to weakly symmetric {Finsler} spaces", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "52--73", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-004-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "53C60 (22E60)", MRnumber = "2597023 (2011d:53181)", MRreviewer = "Mihai Anastasiei", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper, we introduce a new algebraic notion, weakly symmetric Lie algebras, to give an algebraic description of an interesting class of homogeneous Riemann--Finsler spaces, weakly symmetric Finsler spaces. Using this new definition, we are able to give a classification of weakly symmetric Finsler spaces with dimensions 2 and 3. Finally, we show that all the non-Riemannian reversible weakly symmetric Finsler spaces we find are non-Berwaldian and with vanishing S-curvature. This means that reversible non-Berwaldian Finsler spaces with vanishing S-curvature may exist at large. Hence the generalized volume comparison theorems due to Z. Shen are valid for a rather large class of Finsler spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ducrot:2010:PGE, author = "Arnaud Ducrot and Zhihua Liu and Pierre Magal", title = "Projectors on the generalized eigenspaces for neutral functional differential equations in {$L^p$} spaces", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "74--93", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-005-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "47N20 (47Gxx)", MRnumber = "2597024", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We present the explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues for linear neutral functional differential equations (NFDE) in $L^p$ spaces by using integrated semigroup theory. The analysis is based on the main result established elsewhere by the authors and results by Magal and Ruan on non-densely defined Cauchy problem. We formulate the NFDE as a non-densely defined Cauchy problem and obtain some spectral properties from which we then derive explicit formulas for the projectors on the generalized eigenspaces associated with some eigenvalues. Such explicit formulas are important in studying bifurcations in some semi-linear problems.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kuo:2010:LCG, author = "Wentang Kuo", title = "The {Langlands} correspondence on the generic irreducible constituents of principal series", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "94--108", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-006-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "22E50 (22E35)", MRnumber = "2597025 (2011b:22029)", MRreviewer = "Luis Alberto Lomel{\'\i}", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $G$ be a connected semisimple split group over a $p$-adic field. We establish the explicit link between principal nilpotent orbits and the irreducible constituents of principal series in terms of $L$-group objects.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Li:2010:SHM, author = "Chi-Kwong Li and Yiu-Tung Poon", title = "Sum of {Hermitian} matrices with given eigenvalues: inertia, rank, and multiple eigenvalues", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "109--132", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-007-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "15B57 (15A18)", MRnumber = "2597026 (2011b:15086)", MRreviewer = "Julio Ben{\'\i}tez", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $A$ and $B$ be n\times n complex Hermitian (or real symmetric) matrices with eigenvalues a$_1$ {\geq} {\ldots} {\geq} a$_n$ and b$_1$ {\geq} {\ldots} {\geq} b$_n$. All possible inertia values, ranks, and multiple eigenvalues of $A$ + $B$ are determined. Extension of the results to the sum of $k$ matrices with k > 2 and connections of the results to other subjects such as algebraic combinatorics are also discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Makarov:2010:SAP, author = "Konstantin A. Makarov and Anna Skripka", title = "Some applications of the perturbation determinant in finite {von Neumann} algebras", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "133--156", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-008-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "47A55 (46L10 47A53 47C15)", MRnumber = "2597027 (2011h:47022)", MRreviewer = "Oscar F. Bandtlow", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In the finite von Neumann algebra setting, we introduce the concept of a perturbation determinant associated with a pair of self-adjoint elements H$_0$ and $H$ in the algebra and relate it to the concept of the de la Harpe--Skandalis homotopy invariant determinant associated with piecewise C$^1$-paths of operators joining H$_0$ and $H$. We obtain an analog of Krein's formula that relates the perturbation determinant and the spectral shift function and, based on this relation, we derive subsequently (i) the Birman--Solomyak formula for a general non-linear perturbation, (ii) a universality of a spectral averaging, and (iii) a generalization of the Dixmier--Fuglede--Kadison differentiation formula.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Masri:2010:SVC, author = "Riad Masri", title = "Special values of class group {$L$}-functions for {CM} fields", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "157--181", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-009-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11R42 (11F41 11M36)", MRnumber = "2597028 (2011c:11169)", MRreviewer = "Siman Wong", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $H$ be the Hilbert class field of a CM number field $K$ with maximal totally real subfield $F$ of degree $n$ over Q. We evaluate the second term in the Taylor expansion at s=0 of the Galois-equivariant $L$-function $\Theta_{S \infty}(s)$ associated to the unramified abelian characters of Gal(H/K). This is an identity in the group ring C[Gal(H/K)] expressing $\Theta^{(n)}_{S \infty}(0)$ as essentially a linear combination of logarithms of special values ${\Psi(z_\sigma)}$, where $\Psi: H^n {\rightarrow} R$ is a Hilbert modular function for a congruence subgroup of $\SL_2(Gal{O}_F)$ and ${z_{\sigma}: \sigma {\in} Gal(H/K)}$ are CM points on a universal Hilbert modular variety. We apply this result to express the relative class number $h_H / h_K$ as a rational multiple of the determinant of an $(h_K - 1) \times (h_K - 1)$ matrix of logarithms of ratios of special values $\Psi(z_\sigma)$, thus giving rise to candidates for higher analogs of elliptic units. Finally, we obtain a product formula for $\Psi(z_\sigma)$ in terms of exponentials of special values of $L$-functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Prajs:2010:MAD, author = "Janusz R. Prajs", title = "Mutually aposyndetic decomposition of homogeneous continua", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "182--201", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-010-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "54F15 (54B15)", MRnumber = "2597029 (2011c:54037)", MRreviewer = "Leonard R. Rubin", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "A new decomposition, the $mutually aposyndetic decomposition$ of homogeneous continua into closed, homogeneous sets is introduced. This decomposition is respected by homeomorphisms and topologically unique. Its quotient is a mutually aposyndetic homogeneous continuum, and in all known examples, as well as in some general cases, the members of the decomposition are semi-indecomposable continua. As applications, we show that hereditarily decomposable homogeneous continua and path connected homogeneous continua are mutually aposyndetic. A class of new examples of homogeneous continua is defined. The mutually aposyndetic decomposition of each of these continua is non-trivial and different from Jones' aposyndetic decomposition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Tang:2010:IEP, author = "Lin Tang", title = "Interior $h^1$ estimates for parabolic equations with {$\LMO$} coefficients", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "202--217", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-011-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "35K20 (35B65 35R05)", MRnumber = "2597030 (2011a:35214)", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we establish $a priori$ h$^1$-estimates in a bounded domain for parabolic equations with vanishing LMO coefficients.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Xing:2010:GDC, author = "Yang Xing", title = "The general definition of the complex {Monge--Amp{\`e}re} operator on compact {K{\"a}hler} manifolds", journal = j-CAN-J-MATH, volume = "62", number = "1", pages = "218--239", month = feb, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-012-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "32W20 (32U05 32U20 35Q15)", MRnumber = "2597031 (2011b:32062)", MRreviewer = "Norman Levenberg", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We introduce a wide subclass $F(X, \omega)$ of quasi-plurisubharmonic functions in a compact K{\"a}hler manifold, on which the complex Monge--Amp{\`e}re operator is well defined and the convergence theorem is valid. We also prove that $F(X, \omega)$ is a convex cone and includes all quasi-plurisubharmonic functions that are in the Cegrell class.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Azagra:2010:SOS, author = "Daniel Azagra and Robb Fry", title = "A second order smooth variational principle on {Riemannian} manifolds", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "241--260", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-013-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "58E30 (47J30 49J52)", MRnumber = "2643041 (2011d:58040)", MRreviewer = "Salvatore A. Marano", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We establish a second order smooth variational principle valid for functions defined on (possibly infinite-dimensional) Riemannian manifolds which are uniformly locally convex and have a strictly positive injectivity radius and bounded sectional curvature.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chiang:2010:EVD, author = "Yik-Man Chiang and Mourad E. H. Ismail", title = "Erratum to: {On value distribution theory of second order periodic ODEs, special functions and orthogonal polynomials [\refcno 2245272]}", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "261--261", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-034-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "34M10 (30D35 33C15 33C47)", MRnumber = "2643042", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", note = "See \cite{Chiang:2006:VDT}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Goresky:2010:SEC, author = "Mark Goresky and Robert MacPherson", title = "On the Spectrum of the Equivariant Cohomology Ring", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "262--283", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-016-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14L30 (14F43 55N91)", MRnumber = "2643043 (2011f:14079)", MRreviewer = "Wenchuan Hu", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "If an algebraic torus $T$ acts on a complex projective algebraic variety $X$, then the affine scheme Spec $H_T^*(X; {\bf C})$ associated with the equivariant cohomology is often an arrangement of linear subspaces of the vector space ${\rm Spec} H_2^T(X; {\bf C})$. In many situations the ordinary cohomology ring of $X$ can be described in terms of this arrangement.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Grbic:2010:SML, author = "Jelena Grbi{\'c} and Stephen Theriault", title = "Self-Maps of Low Rank {Lie} Groups at Odd Primes", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "284--304", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-017-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "55P45 (55Q05 57T20)", MRnumber = "2643044 (2011f:55018)", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let G be a simple, compact, simply-connected Lie group localized at an odd prime $p$. We study the group of homotopy classes of self-maps [ $G$, $G$ ] when the rank of $G$ is low and in certain cases describe the set of homotopy classes of multiplicative self-maps $H$ [ $G$, $G$ ]. The low rank condition gives $G$ certain structural properties which make calculations accessible. Several examples and applications are given.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{He:2010:ASC, author = "Hua He and Yunbai Dong and Xianzhou Guo", title = "Approximation and Similarity Classification of Stably Finitely Strongly Irreducible Decomposable Operators", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "305--319", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-018-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "47A58 (46L80 47B40)", MRnumber = "2643045 (2011c:47028)", MRreviewer = "Chun Lan Jiang", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let {$ {\bf H} $} be a complex separable Hilbert space and {$ {\bf L}({\bf H}) $} denote the collection of bounded linear operators on {$ {\bf H} $}. In this paper, we show that for any operator {$ A \in {\bf L}({\bf H}) $}, there exists a stably finitely (SI) decomposable operator {$ A_\epsilon $}, such that {$ ||A - A_\epsilon || < \epsilon $} and {$ {\bf A^prime (A_\epsilon) / {\rm rad} {\bf A}^\prime } (A_\epsilon) $} is commutative, where {$ {\rm rad} {\bf A}^\prime (A_\epsilon) $} is the Jacobson radical of {$ {\bf A}^\prime (A_\epsilon) $}. Moreover, we give a similarity classification of the stably finitely decomposable operators that generalizes the result on similarity classification of Cowen-Douglas operators given by C. L. Jiang.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jerrard:2010:SRR, author = "Robert L. Jerrard", title = "Some rigidity results related to {Monge--Amp{\`e}re} functions", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "320--354", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-019-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "49Q15 (35J96 53C24)", MRnumber = "2643046 (2011c:49082)", MRreviewer = "David A. Hartenstine", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "The space of Monge-Amp{\`e}re functions, introduced by J. H. G. Fu, is a space of rather rough functions in which the map $u$ {\rightarrow} Det $D$$^2$ $u$ is well defined and weakly continuous with respect to a natural notion of weak convergence. We prove a rigidity theorem for Lagrangian integral currents that allows us to extend the original definition of Monge-Amp{\`e}re functions. We also prove that if a Monge-Amp{\`e}re function $u$ on a bounded set {\Omega} {\subset} {\bf R}$^2$ satisfies the equation Det $D$$^2$ $u$ = 0 in a particular weak sense, then the graph of $u$ is a developable surface, and moreover $u$ enjoys somewhat better regularity properties than an arbitrary Monge-Amp{\`e}re function of 2 variables.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kral:2010:CRS, author = "Daniel Kr{\'a}l and Edita M{\'a}{\v{c}}ajov{\'a} and Attila P{\'o}r and Jean-S{\'e}bastien Sereni", title = "Characterisation results for {Steiner} triple systems and their application to edge-colourings of cubic graphs", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "355--381", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-021-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "05B07 (05C15)", MRnumber = "2643047 (2011e:05038)", MRreviewer = "Landang Yuan", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "It is known that a Steiner triple system is projective if and only if it does not contain the four-triple configuration $C$$_{14}$. We find three configurations such that a Steiner triple system is affine if and only if it does not contain one of these configurations. Similarly, we characterise Hall triple systems using two forbidden configurations. Our characterisations have several interesting corollaries in the area of edge-colourings of graphs. A cubic graph $G$ is $S$-edge-colourable for a Steiner triple system $S$ if its edges can be coloured with points of $S$ in such a way that the points assigned to three edges sharing a vertex form a triple in $S$. Among others, we show that all cubic graphs are $S$-edge-colourable for every non-projective non-affine point-transitive Steiner triple system $S$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lu:2010:VMQ, author = "Rencai L{\"u} and Kaiming Zhao", title = "{Verma} Modules over Quantum Torus {Lie} Algebras", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "382--399", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-022-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "17B10 (17B67)", MRnumber = "2643048 (2011g:17020)", MRreviewer = "Shaobin Tan", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Representations of various one-dimensional central extensions of quantum tori (called quantum torus Lie algebras) were studied by several authors. Now we define a central extension of quantum tori so that all known representations can be regarded as representations of the new quantum torus Lie algebras $L$_q$$. The center of $L$_q$$ now is generally infinite dimensional. In this paper, {\bf Z} -graded Verma modules {\bf V} ( ${\phi}$) over $L$_q$$ and their corresponding irreducible highest weight modules $V$ ( ${\phi}$) are defined for some linear functions {\phi}. Necessary and sufficient conditions for $V$ ( ${\phi}$) to have all finite dimensional weight spaces are given. Also necessary and sufficient conditions for Verma modules {\bf V} ( ${\phi}$) to be irreducible are obtained.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Prasanna:2010:APC, author = "Kartik Prasanna", title = "On {$p$}-adic properties of central {$L$}-values of quadratic twists of an elliptic curve", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "400--414", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-023-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11G40 (11F67 11G05)", MRnumber = "2643049 (2011h:11071)", MRreviewer = "Amir Akbary", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We study $p$-indivisibility of the central values $L$ (1, $E$_d$$) of quadratic twists $E$_d$$ of a semi-stable elliptic curve $E$ of conductor $N$. A consideration of the conjecture of Birch and Swinnerton-Dyer shows that the set of quadratic discriminants $d$ splits naturally into several families {\bf F}$_S$, indexed by subsets $S$ of the primes dividing $N$. Let {\delta}$_S$ = gcd$_{d {\in} F S}$ $L$ (1, $E$_d$$)$^{alg}$, where $L$ (1, $E$_d$$)$^{alg}$ denotes the algebraic part of the central $L$-value, $L$ (1, $E$_d$$). Our main theorem relates the $p$-adic valuations of {\delta}$_S$ as $S$ varies. As a consequence we present an application to a refined version of a question of Kolyvagin. Finally we explain an intriguing (albeit speculative) relation between Waldspurger packets on {\bf SL$_2$} and congruences of modular forms of integral and half-integral weight. In this context, we formulate a conjecture on congruences of half-integral weight forms and explain its relevance to the problem of $p$-indivisibility of $L$-values of quadratic twists.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sun:2010:CRS, author = "Shunhua Sun and Dechao Zheng and Changyong Zhong", title = "Classification of reducing subspaces of a class of multiplication operators on the {Bergman} space via the {Hardy} space of the bidisk", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "415--438", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-026-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "47B38 (32A36 46E15 47A15 47B35)", MRnumber = "2643050 (2011e:47068)", MRreviewer = "Tomoko Osawa", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we obtain a complete description of nontrivial minimal reducing subspaces of the multiplication operator by a Blaschke product with four zeros on the Bergman space of the unit disk via the Hardy space of the bidisk.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sundhall:2010:HFH, author = "Marcus Sundh{\"a}ll and Edgar Tchoundja", title = "On {Hankel} forms of higher weights: the case of {Hardy} spaces", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "439--455", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-027-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "47B35 (32A35 42B30 46E15)", MRnumber = "2643051 (2011d:47070)", MRreviewer = "Richard Rochberg", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we study bilinear Hankel forms of higher weights on Hardy spaces in several dimensions. (The Schatten class Hankel forms of higher weights on weighted Bergman spaces have already been studied by Janson and Peetre for one dimension and by Sundh{\"a}ll for several dimensions). We get a full characterization of Schatten class Hankel forms in terms of conditions for the symbols to be in certain Besov spaces. Also, the Hankel forms are bounded and compact if and only if the symbols satisfy certain Carleson measure criteria and vanishing Carleson measure criteria, respectively.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yang:2010:CSF, author = "Tonghai Yang", title = "The {Chowla--Selberg} formula and the {Colmez} conjecture", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "456--472", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-028-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11G15 (11F41 11G50)", MRnumber = "2643052 (2011h:11066)", MRreviewer = "Philippe G. Michel", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper, we reinterpret the Colmez conjecture on the Faltings height of CM abelian varieties in terms of Hilbert (and Siegel) modular forms. We construct an elliptic modular form involving the Faltings height of a CM abelian surface and arithmetic intersection numbers, and prove that the Colmez conjecture for CM abelian surfaces is equivalent to the cuspidality of this modular form.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yun:2010:GMC, author = "Zhiwei Yun", title = "{Goresky--MacPherson} calculus for the affine flag varieties", journal = j-CAN-J-MATH, volume = "62", number = "2", pages = "473--480", month = apr, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-029-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14L30 (55N91)", MRnumber = "2643053 (2011d:14089)", MRreviewer = "Ada Boralevi", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We use the fixed point arrangement technique developed by Goresky and MacPherson to calculate the part of the equivariant cohomology of the affine flag variety {\bf Fl}$_G$ generated by degree 2. We use this result to show that the vertices of the moment map image of {\bf Fl}$_G$ lie on a paraboloid.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Casals-Ruiz:2010:EAG, author = "Montserrat Casals-Ruiz and Ilya V. Kazachkov", title = "Elements of algebraic geometry and the positive theory of partially commutative groups", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "481--519", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-035-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "20F10 (03C10 20F06)", MRnumber = "2666386 (2011f:20073)", MRreviewer = "Evgeny I. Timoshenko", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "The first main result of the paper is a criterion for a partially commutative group G to be a domain. It allows us to reduce the study of algebraic sets over G to the study of irreducible algebraic sets, and reduce the elementary theory of G (of a coordinate group over G) to the elementary theories of the direct factors of G (to the elementary theory of coordinate groups of irreducible algebraic sets). Then we establish normal forms for quantifier-free formulas over a non-abelian directly indecomposable partially commutative group H. Analogously to the case of free groups, we introduce the notion of a generalised equation and prove that the positive theory of H has quantifier elimination and that arbitrary first-order formulas lift from H to H* F, where F is a free group of finite rank. As a consequence, the positive theory of an arbitrary partially commutative group is decidable.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Eriksen:2010:CND, author = "Eivind Eriksen", title = "Computing noncommutative deformations of presheaves and sheaves of modules", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "520--542", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-015-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14D15 (13N10)", MRnumber = "2666387 (2011e:14016)", MRreviewer = "Thierry Dana-Picard", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We describe a noncommutative deformation theory for presheaves and sheaves of modules that generalizes the commutative deformation theory of these global algebraic structures and the noncommutative deformation theory of modules over algebras due to Laudal. In the first part of the paper, we describe a noncommutative deformation functor for presheaves of modules on a small category and an obstruction theory for this functor in terms of global Hochschild cohomology. An important feature of this obstruction theory is that it can be computed in concrete terms in many interesting cases. In the last part of the paper, we describe a noncommutative deformation functor for quasi-coherent sheaves of modules on a ringed space $(X, \mathcal{A})$. We show that for any good $\mathcal{A}$-affine open cover $\mathsf{U}$ of $X$, the forgetful functor $\mathsf{QCoh}\mathcal{A} \to \mathsf{PreSh}(\mathsf{U}, \mathcal{A})$ induces an isomorphism of noncommutative deformation functors. \emph{Applications.} We consider noncommutative deformations of quasi-coherent $\mathcal{A}$-modules on $X$ when $(X, \mathcal{A}) = (X, \mathcal{O}_X)$ is a scheme or $(X, \mathcal{A}) = (X, \mathcal{D})$ is a D-scheme in the sense of Beilinson and Bernstein. In these cases, we may use any open affine cover of $X$ closed under finite intersections to compute noncommutative deformations in concrete terms using presheaf methods. We compute the noncommutative deformations of the left $\sh D$_X$ $-module $\mathcal{D}$_X$ $ when $X$ is an elliptic curve as an example.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hare:2010:MVS, author = "Kevin G. Hare", title = "More variations on the {Sierpi{\'n}ski} sieve", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "543--562", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-036-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "28A80 (11R06 28A78)", MRnumber = "2666388 (2011f:28006)", MRreviewer = "Maria Moszy{\'n}ska", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "This paper answers a question of Broomhead, Montaldi and Sidorov about the existence of gaskets of a particular type related to the Sierpi{\'n}ski sieve. These gaskets are given by iterated function systems that do not satisfy the open set condition. We use the methods of Ngai and Wang to compute the dimension of these gaskets.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ishii:2010:WFR, author = "Taku Ishii", title = "{Whittaker} functions on real semisimple {Lie} groups of rank two", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "563--581", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-030-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11F70 (22E45)", MRnumber = "2666389 (2011e:11093)", MRreviewer = "Henry H. Kim", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We give explicit formulas for Whittaker functions on real semisimple Lie groups of real rank two belonging to the class one principal series representations. By using these formulas we compute certain archimedean zeta integrals.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Konyagin:2010:DP, author = "Sergei V. Konyagin and Carl Pomerance and Igor E. Shparlinski", title = "On the Distribution of Pseudopowers", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "582--594", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-020-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11N69 (11L07 11N36)", MRnumber = "2666390 (2011f:11128)", MRreviewer = "D. R. Heath-Brown", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "An $x$-pseudopower to base $g$ is a positive integer that is not a power of $g$, yet is so modulo $p$ for all primes $ple x$. We improve an upper bound for the least such number, due to E.~Bach, R.~Lukes, J.~Shallit, and H.~C.~Williams. The method is based on a combination of some bounds of exponential sums with new results about the average behaviour of the multiplicative order of $g$ modulo prime numbers.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Martinez:2010:LUR, author = "J. F. Mart{\'\i}nez and A. Molt{\'o} and J. Orihuela and S. Troyanski", title = "On locally uniformly rotund renormings in {$C(K)$} spaces", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "595--613", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-037-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46B03 (46B20)", MRnumber = "2666391 (2011g:46009)", MRreviewer = "Jarno Talponen", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "A characterization of the Banach spaces of type C(K) that admit an equivalent locally uniformly rotund norm is obtained, and a method to apply it to concrete spaces is developed. As an application the existence of such renorming is deduced when K is a Namioka--Phelps compact or for some particular class of Rosenthal compacta, results which were originally proved with ad hoc methods.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pronk:2010:TGO, author = "Dorette Pronk and Laura Scull", title = "Translation Groupoids and Orbifold Cohomology", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "614--645", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-024-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "55N32 (18D05 19L47 57R18 57S15)", MRnumber = "2666392 (2011h:55009)", MRreviewer = "Andr{\'e} G. Henriques", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", note = "See erratum \cite{Pronk:2017:ETG}.", abstract = "We show that the bicategory of (representable) orbifolds and good maps is equivalent to the bicategory of orbifold translation groupoids and generalized equivariant maps, giving a mechanism for transferring results from equivariant homotopy theory to the orbifold category. As an application, we use this result to define orbifold versions of a couple of equivariant cohomology theories: $K$-theory and Bredon cohomology for certain coefficient diagrams.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rupp:2010:R, author = "R. Rupp and A. Sasane", title = "Reducibility in {$A_\mathbb{R}(K)$}, {$C_\mathbb{R}(K)$}, and {$A(K)$}", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "646--667", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-025-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46J15 (19B10 30H80 93D15)", MRnumber = "2666393 (2011h:46069)", MRreviewer = "Jordi Pau", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $K$ denote a compact real symmetric subset of $\mC$ and let $A_{\mathbb R}(K)$ denote the real Banach algebra of all real symmetric continuous functions on $K$ that are analytic in the interior $K^\circ$ of $K$, endowed with the supremum norm. We characterize all unimodular pairs $(f,g)$ in $A_{\mathbb R}(K)$^2$ $ which are reducible. In addition, for an arbitrary compact $K$ in $\mathbb C$, we give a new proof (not relying on Banach algebra theory or elementary stable rank techniques) of the fact that the Bass stable rank of $A(K)$ is 1. Finally, we also characterize all compact real symmetric sets $K$ such that $A_{\mathbb R}(K)$, respectively $C_{\mathbb R}(K)$, has Bass stable rank 1.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Vollaard:2010:SLS, author = "Inken Vollaard", title = "The supersingular locus of the {Shimura} variety for {${\rm GU}(1,s)$}", journal = j-CAN-J-MATH, volume = "62", number = "3", pages = "668--720", month = jun, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-031-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14G35 (11G18)", MRnumber = "2666394 (2011j:14059)", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we study the supersingular locus of the reduction modulo $p$ of the Shimura variety for GU(1, $s$) in the case of an inert prime $p$. Using Dieudonn{\'e} theory we define a stratification of the corresponding moduli space of $p$-divisible groups. We describe the incidence relation of this stratification in terms of the Bruhat-Tits building of a unitary group. In the case of GU(1,2), we show that the supersingular locus is equidimensional of dimension 1 and is of complete intersection. We give an explicit description of the irreducible components and their intersection behaviour.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Boocher:2010:FFU, author = "Adam Boocher and Michael Daub and Ryan K. Johnson and H. Lindo and S. Loepp and Paul A. Woodard", title = "Formal Fibers of Unique Factorization Domains", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "721--736", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-014-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "13J10", MRnumber = "2674698", MRreviewer = "Tran Tuan Nam", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $(T,M)$ be a complete local (Noetherian) ring such that $\dim T\geq 2$ and $|T|=|T/M|$ and let $\{p$_i$ \} _{i \in \mathcal I}$ be a collection of elements of $T$ indexed by a set $\mathcal I$ so that $|\mathcal I | < |T|$. For each $i \in \mathcal{I}$, let $C_i :=\{Q_{i1}, \dots, Q_{in_i}\}$ be a set of nonmaximal prime ideals containing $p_i$ such that the $Q_{ij}$ are incomparable and $p_i \in Q_{jk}$ if and only if $i = j$. We provide necessary and sufficient conditions so that $T$ is the ${\bf m}$-adic completion of a local unique factorization domain $(A, {\bf m})$, and for each $i \in \mathcal I$, there exists a unit $t_i$ of $T$ so that $p_i t_i \in A$ and $C_i$ is the set of prime ideals $Q$ of $T$ that are maximal with respect to the condition that $Q \cap A = p_i t_i A$. We then use this result to construct a (nonexcellent) unique factorization domain containing many ideals for which tight closure and completion do not commute. As another application, we construct a unique factorization domain $A$ most of whose formal fibers are geometrically regular.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ditzian:2010:ADA, author = "Z. Ditzian and A. Prymak", title = "Approximation by dilated averages and {$K$}-functionals", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "737--757", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-040-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "41A30", MRnumber = "2674699 (2011h:41018)", MRreviewer = "Weiyi Su", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "For a positive finite measure $d{\mu}( {\bf u})$ on ${\bf R}^d$ normalized to satisfy ${f\int}_{R^d} d{\mu}( {\bf u}) = 1$, the dilated average of $f({\bf x})$ is given by $A_t f({\bf x})={\int}_{R^d} f({\bf x} {-}t {\bf u})d{\mu}( {\bf u})$. It will be shown that under some mild assumptions on d{\mu}( {\bf u}) one has the equivalence ||A$_t$ f - f||$_B$ \asymp inf{ (||f - g||$_B$ +t$^2$ ||P(D)g||$_B$): P(D)g {\in} B} for t > 0, where {\phi}(t) \asymp {\psi}(t) means $c^{ - 1}$ {\leq} {\phi}(t)/{\psi}(t) {\leq} c, B is a Banach space of functions for which translations are continuous isometries and P(D) is an elliptic differential operator induced by {\mu}. Many applications are given, notable among which is the averaging operator with d{\mu}( {\bf u}) = (1/m(S)){\chi}$_S$ ( {\bf u})d {\bf u}, where S is a bounded convex set in {\bf R}$^d$ with an interior point, m(S) is the Lebesgue measure of S, and {\chi}$_S$ ( {\bf u}) is the characteristic function of S. The rate of approximation by averages on the boundary of a convex set under more restrictive conditions is also shown to be equivalent to an appropriate K-functional.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dolinar:2010:GPQ, author = "Gregor Dolinar and Bojan Kuzma", title = "General Preservers of Quasi-Commutativity", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "758--786", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-041-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "06A99 (15A27 15A86)", MRnumber = "2674700 (2011f:06005)", MRreviewer = "Peter {\v{S}}emrl", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $M_n$ be the algebra of all $n \times n$ matrices over ${\bf C}$. We say that $A, B \in M_n$ quasi-commute if there exists a nonzero $\xi \in {\bf C}$ such that $AB = \xi BA$. In the paper we classify bijective not necessarily linear maps $\Phi: M_n \to M_n$ which preserve quasi-commutativity in both directions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Landquist:2010:ETC, author = "E. Landquist and P. Rozenhart and R. Scheidler and J. Webster and Q. Wu", title = "An explicit treatment of cubic function fields with applications", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "787--807", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-032-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14H05 (11G20 11R16 11R58 14H45)", MRnumber = "2674701 (2011f:14044)", MRreviewer = "Valmecir A. Bayer", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We give an explicit treatment of cubic function fields of characteristic at least five. This includes an efficient technique for converting such a field into standard form, formulae for the field discriminant and the genus, simple necessary and sufficient criteria for non-singularity of the defining curve, and a characterization of all triangular integral bases. Our main result is a description of the signature of any rational place in a cubic extension that involves only the defining curve and the order of the base field. All these quantities only require simple polynomial arithmetic as well as a few square-free polynomial factorizations and, in some cases, square and cube root extraction modulo an irreducible polynomial. We also illustrate why and how signature computation plays an important role in computing the class number of the function field. This in turn has applications to the study of zeros of zeta functions of function fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Legendre:2010:ELE, author = "Eveline Legendre", title = "Extrema of low eigenvalues of the {Dirichlet--Neumann Laplacian} on a disk", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "808--826", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-042-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "35P15 (35B05 35J25)", MRnumber = "2674702 (2011f:35239)", MRreviewer = "Sui Sun Cheng", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We study extrema of the first and the second mixed eigenvalues of the Laplacian on the disk among some families of Dirichlet--Neumann boundary conditions. We show that the minimizer of the second eigenvalue among all mixed boundary conditions lies in a compact 1-parameter family for which an explicit description is given. Moreover, we prove that among all partitions of the boundary with bounded number of parts on which Dirichlet and Neumann conditions are imposed alternately, the first eigenvalue is maximized by the uniformly distributed partition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ouyang:2010:BFC, author = "Caiheng Ouyang and Quanhua Xu", title = "{BMO} functions and {Carleson} measures with values in uniformly convex spaces", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "827--844", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-043-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46E40 (42B25 46B20)", MRnumber = "2674703 (2011e:46062)", MRreviewer = "Tuomas P. Hyt{\"o}nen", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "This paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let $dA$ and $dm$ denote Lebesgue measures on the unit disc $D$ and the unit circle ${\bf T}$, respectively. For $1 < q < \infty$ and a Banach space $B$, we prove that there exists a positive constant $c$ such that $\sup_{z 0} \in D \int_D (1 - |z|)^{q - 1} ||\nablaf(z)||^q P_{z 0} (z) dA(z) \leq c^q \sup_{z 0} \in D \int_T ||f(z) - f(z_0)||^q P_{z 0} (z) dm(z)$ holds for all trigonometric polynomials f with coefficients in B if and only if B admits an equivalent norm which is q-uniformly convex, where P$_{z 0}$ (z)=1 - |z$_0$ |$^2$ /|1 - z$_0^*$ z|$^2$. The validity of the converse inequality is equivalent to the existence of an equivalent q-uniformly smooth norm.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Samei:2010:BPA, author = "Ebrahim Samei and Nico Spronk and Ross Stokke", title = "Biflatness and pseudo-amenability of {Segal} algebras", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "845--869", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-044-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "43A20 (43A30 46H25 46L07)", MRnumber = "2674704 (2011h:43002)", MRreviewer = "Krishnan Parthasarathy", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We investigate generalized amenability and biflatness properties of various (operator) Segal algebras in both the group algebra, L$^1$ (G), and the Fourier algebra, A(G), of a locally compact group G.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Valdimarsson:2010:BLP, author = "Stef{\'a}n Ingi Valdimarsson", title = "The {Brascamp--Lieb} polyhedron", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "870--888", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-045-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "26D15 (44A35)", MRnumber = "2674705", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "A set of necessary and sufficient conditions for the Brascamp-Lieb inequality to hold has recently been found by Bennett, Carbery, Christ, and Tao. We present an analysis of these conditions. This analysis allows us to give a concise description of the set where the inequality holds in the case where each of the linear maps involved has co-rank 1. This complements the result of Barthe concerning the case where the linear maps all have rank 1. Pushing our analysis further, we describe the case where the maps have either rank 1 or rank 2. A separate but related problem is to give a list of the finite number of conditions necessary and sufficient for the Brascamp-Lieb inequality to hold. We present an algorithm which generates such a list.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Xia:2010:SIO, author = "Jingbo Xia", title = "Singular integral operators and essential commutativity on the sphere", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "889--913", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-038-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "47G10 (32A55 42B25 46L05 47B35 47L80)", MRnumber = "2674706 (2011g:47110)", MRreviewer = "Edgar Tchoundja", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $T$ be the $C$^*$$-algebra generated by the Toeplitz operators {$T$_{{\phi}}$$: ${\phi}$ {\in} $L$$^{\infty}$ ( $S$, $d{\sigma}$)} on the Hardy space $H$$^2$ ( $S$) of the unit sphere in {\bf C}$^n$. It is well known that $T$ is contained in the essential commutant of {$T$_{{\phi}}$$: ${\phi}$ {\in} VMO{\cap} $L$$^{\infty}$ ( $S$, $d{\sigma}$)}. We show that the essential commutant of {$T$_{{\phi}}$$: ${\phi}$ {\in} VMO{\cap} $L$$^{\infty}$ ( $S$, $d{\sigma}$)} is strictly larger than $T$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Zorn:2010:RPS, author = "Christian Zorn", title = "Reducibility of the principal series for {$\widetilde{\rm Sp}_2(F)$} over a {$p$}-adic field", journal = j-CAN-J-MATH, volume = "62", number = "4", pages = "914--960", month = aug, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-046-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "22E50 (11F70)", MRnumber = "2674707 (2011e:22026)", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $G_n = \Sp_n(F)$ be the rank $n$ symplectic group with entries in a nondyadic $p$-adic field $F$. We further let $G^{\texttt{~}}_n$ be the metaplectic extension of $G_n$ by ${\bf C}^1 = z \in {\bf C}^\times | |z| = 1$ defined using the Leray cocycle. In this paper, we aim to demonstrate the complete list of reducibility points of the genuine principal series of $G^{\texttt{~}}_2$. In most cases, we will use some techniques developed by Tadi{\'c} that analyze the Jacquet modules with respect to all of the parabolics containing a fixed Borel. The exceptional cases involve representations induced from unitary characters $\chi$ with $\chi^2 = 1$. Because such representations $\pi$ are unitary, to show the irreducibility of $\pi$, it suffices to show that ${\rm dim}_C {\rm Hom}_{G^{\texttt{~}}}(\pi, \pi) = 1$. We will accomplish this by examining the poles of certain intertwining operators associated to simple roots. Then some results of Shahidi and Ban decompose arbitrary intertwining operators into a composition of operators corresponding to the simple roots of $G^{\texttt{~}}_2$. We will then be able to show that all such operators have poles at principal series representations induced from quadratic characters and therefore such operators do not extend to operators in ${\rm Hom}_G^{\texttt{~}} 2(\pi, \pi)$ for the $\pi$ in question.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Aleman:2010:MII, author = "Alexandru Aleman and Peter Duren and Mar{\'\i}a J. Mart{\'\i}n and Dragan Vukoti{\'c}", title = "Multiplicative isometries and isometric zero-divisors", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "961--974", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-048-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46E15 (30H05)", MRnumber = "2730350", MRreviewer = "Oscar Blasco", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "For some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bjorndahl:2010:RTN, author = "Christina Bjorndahl and Yael Karshon", title = "Revisiting {Tietze--Nakajima}: local and global convexity for maps", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "975--993", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-052-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "53Dxx (52Bxx)", MRnumber = "2730351", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "A theorem of Tietze and Nakajima, from 1928, asserts that if a subset X of {\bf R}$^n$ is closed, connected, and locally convex, then it is convex. We give an analogous {``local to global convexity''} theorem when the inclusion map of X to {\bf R}$^n$ is replaced by a map from a topological space X to {\bf R}$^n$ that satisfies certain local properties. Our motivation comes from the Condevaux-Dazord-Molino proof of the Atiyah-Guillemin-Sternberg convexity theorem in symplectic geometry.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Breslin:2010:CBS, author = "William Breslin", title = "Curvature bounds for surfaces in hyperbolic 3-manifolds", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "994--1010", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-056-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "57M50", MRnumber = "2730352 (2011i:57020)", MRreviewer = "Baris Coskunuzer", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "A triangulation of a hyperbolic 3-manifold is L-thick if each tetrahedron having all vertices in the thick part of M is L-bilipschitz diffeomorphic to the standard Euclidean tetrahedron. We show that there exists a fixed constant L such that every complete hyperbolic 3-manifold has an L-thick geodesic triangulation. We use this to prove the existence of universal bounds on the principal curvatures of {\pi}$_1$-injective surfaces and strongly irreducible Heegaard surfaces in hyperbolic 3-manifolds.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Buckingham:2010:FCF, author = "Paul Buckingham and Victor Snaith", title = "Functoriality of the canonical fractional {Galois} ideal", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1011--1036", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-054-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11R42 (11R23 11R70)", MRnumber = "2730353", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "The fractional Galois ideal is a conjectural improvement on the higher Stickelberger ideals defined at negative integers, and is expected to provide non-trivial annihilators for higher K-groups of rings of integers of number fields. In this article, we extend the definition of the fractional Galois ideal to arbitrary (possibly infinite and non-abelian) Galois extensions of number fields under the assumption of Stark's conjectures and prove naturality properties under canonical changes of extension. We discuss applications of this to the construction of ideals in non-commutative Iwasawa algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Calvino-Louzao:2010:RET, author = "E. Calvi{\~n}o-Louzao and E. Garc{\'\i}a-R{\'\i}o and R. V{\'a}zquez-Lorenzo", title = "{Riemann} extensions of torsion-free connections with degenerate {Ricci} tensor", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1037--1057", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-059-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "53C50", MRnumber = "2730354", MRreviewer = "Miguel Brozos-V{\'a}zquez", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "{Correspondence} between torsion-free connections with {nilpotent skew-symmetric curvature operator} and IP Riemann extensions is shown. Some consequences are derived in the study of four-dimensional IP metrics and locally homogeneous affine surfaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2010:CS, author = "Yichao Chen and Yanpei Liu", title = "On a Conjecture of {S. Stahl}", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1058--1059", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-058-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "05C10 (05C31)", MRnumber = "2730355 (2011g:05068)", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "S. Stahl conjectured that the zeros of genus polynomials are real. In this note, we disprove this conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Darmon:2010:HPT, author = "Henri Darmon and Ye Tian", title = "{Heegner} Points over {Towers of Kummer} Extensions", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1060--1081", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-039-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11G40 (11F46 11G05 11R23)", MRnumber = "2730356", MRreviewer = "Jeremy T. Teitelbaum", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let E be an elliptic curve, and let L$_n$ be the Kummer extension generated by a primitive p$^n$-th root of unity and a p$^n$-th root of a for a fixed a {\in} {\bf Q}$^\times$ - {{\pm}1}. A detailed case study by Coates, Fukaya, Kato and Sujatha and V. Dokchitser has led these authors to predict unbounded and strikingly regular growth for the rank of E over L$_n$ in certain cases. The aim of this note is to explain how some of these predictions might be accounted for by Heegner points arising from a varying collection of Shimura curve parametrisations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Godinho:2010:FGM, author = "Leonor Godinho and M. E. Sousa-Dias", title = "The Fundamental Group of {$S^1$}-manifolds", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1082--1098", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-053-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "53D20 (37J15 55Q05)", MRnumber = "2730357 (2011i:53134)", MRreviewer = "Eduardo A. Gonzalez", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We address the problem of computing the fundamental group of a symplectic S$^1$-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian S$^1$-action. Several examples are presented to illustrate our main results.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Goldmakher:2010:CSS, author = "Leo Goldmakher", title = "Character Sums to Smooth Moduli are Small", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1099--1115", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-047-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11L40", MRnumber = "2730358", MRreviewer = "Moubariz Z. Garaev", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Recently, Granville and Soundararajan have made fundamental breakthroughs in the study of character sums. Building on their work and using estimates on short character sums developed by Graham--Ringrose and Iwaniec, we improve the P{\'o}lya--Vinogradov inequality for characters with smooth conductor.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jin:2010:DLO, author = "Yongyang Jin and Genkai Zhang", title = "Degenerate $p$-{Laplacian} Operators and {Hardy} Type Inequalities on {$H$}-Type Groups", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1116--1130", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-033-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "22E25 (22E30 26D10)", MRnumber = "2730359 (2011j:22015)", MRreviewer = "Luca Capogna", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $\mathbb G$ be a step-two nilpotent group of H-type with Lie algebra $\mathfrak G=V\oplus \mathfrak t$. We define a class of vector fields $X={X_j}$ on $\mathbb G$ depending on a real parameter $k\ge 1$, and we consider the corresponding $p$-Laplacian operator $L_{p,k} u= div_X (|\nabla_{X} u|^{p-2} \nabla_X u)$. For $k=1$ the vector fields $X=\{X_j\}$ are the left invariant vector fields corresponding to an orthonormal basis of $V$; for $\mathbb G$ being the Heisenberg group the vector fields are the Greiner fields. In this paper we obtain the fundamental solution for the operator $L_{p,k}$ and as an application, we get a Hardy type inequality associated with $X$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kleppe:2010:MSR, author = "Jan O. Kleppe", title = "Moduli spaces of reflexive sheaves of rank $2$", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1131--1154", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-057-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14F05 (14Dxx)", MRnumber = "2730360", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $F$ be a coherent rank 2 sheaf on a scheme Y {\subset} {\bf P}$^n$ of dimension at least two and let X {\subset} Y be the zero set of a section {\sigma} {\in} H$^0$ ( $F$). In this paper, we study the relationship between the functor that deforms the pair ( $F$,{\sigma}) and the two functors that deform $F$ on Y, and X in Y, respectively. By imposing some conditions on two forgetful maps between the functors, we prove that the scheme structure of e.g., the moduli scheme M $_Y$ (P) of stable sheaves on a threefold Y at ( $F$), and the scheme structure at (X) of the Hilbert scheme of curves on Y become closely related. Using this relationship, we get criteria for the dimension and smoothness of M $_Y$ (P) at ( $F$), without assuming Ext$^2$ ( $F$, $F$) = 0. For reflexive sheaves on Y= {\bf P}$^3$ whose deficiency module M = H$_*^1$ ( $F$) satisfies$_0$ Ext$^2$ (M,M) = 0 ( e.g., of diameter at most 2), we get necessary and sufficient conditions of unobstructedness that coincide in the diameter one case. The conditions are further equivalent to the vanishing of certain graded Betti numbers of the free graded minimal resolution of $H_*^0(F)$. Moreover, we show that every irreducible component of $M_P^3(P)$ containing a reflexive sheaf of diameter one is reduced (generically smooth) and we compute its dimension. We also determine a good lower bound for the dimension of any component of $M_P^3(P)$ that contains a reflexive stable sheaf with ``small'' deficiency module $M$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Young:2010:MCV, author = "Matthew P. Young", title = "Moments of the critical values of families of elliptic curves, with applications", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1155--1181", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-049-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11M50 (11G40)", MRnumber = "2730361 (2011h:11101)", MRreviewer = "Steven Joel Miller", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We make conjectures on the moments of the central values of the family of all elliptic curves and on the moments of the first derivative of the central values of a large family of positive rank curves. In both cases the order of magnitude is the same as that of the moments of the central values of an orthogonal family of L-functions. Notably, we predict that the critical values of all rank 1 elliptic curves is logarithmically larger than the rank 1 curves in the positive rank family. Furthermore, as arithmetical applications, we make a conjecture on the distribution of a$_p$ 's amongst all rank 2 elliptic curves and show how the Riemann hypothesis can be deduced from sufficient knowledge of the first moment of the positive rank family (based on an idea of Iwaniec).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yue:2010:FFR, author = "Hong Yue", title = "A fractal function related to the {John--Nirenberg} inequality for {$Q_\alpha(\mathbb{R}^n)$}", journal = j-CAN-J-MATH, volume = "62", number = "5", pages = "1182--1200", month = oct, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-055-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "42B35 (28A80 35A23 42C10)", MRnumber = "2730362 (2011j:42043)", MRreviewer = "Yong Lin", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "A borderline case function f for Q$_{{\alpha}}$ ( {\bf R}$^n$) spaces is defined as a Haar wavelet decomposition, with the coefficients depending on a fixed parameter {\beta} > 0. On its support I$_0$ =[0,1]$^n$, f(x) can be expressed by the binary expansions of the coordinates of x. In particular, f=f$_{{\beta}}$ {\in} Q$_{{\alpha}}$ ( {\bf R}$^n$) if and only if {\alpha} < {\beta} < n/2, while for {\beta} = {\alpha}, it was shown by Yue and Dafni that f satisfies a John-Nirenberg inequality for Q$_{{\alpha}}$ ( {\bf R}$^n$). When {\beta} {\not=} 1, f is a self-affine function. It is continuous almost everywhere and discontinuous at all dyadic points inside I$_0$. In addition, it is not monotone along any coordinate direction in any small cube. When the parameter {\beta} {\in} (0, 1), f is onto from $I_0$ to $[-1/(1 - 2^{-\beta}), 1 / (1 - 2^{-\beta})]$, and the graph of $f$ has a non-integer fractal dimension $n + 1 \beta$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Alzati:2010:CVA, author = "Alberto Alzati and Gian Mario Besana", title = "Criteria for very ampleness of rank two vector bundles over ruled surfaces", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1201--1227", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-066-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14J60", MRnumber = "2760655", bibdate = "Wed Sep 7 18:49:51 2011", bibsource = "https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ardila:2010:VMP, author = "Federico Ardila and Alex Fink and Felipe Rinc{\'o}n", title = "Valuations for Matroid Polytope Subdivisions", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1228--1245", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-064-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "05B35", MRnumber = "2760656", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chaput:2010:QCM, author = "P. E. Chaput and L. Manivel and N. Perrin", title = "Quantum cohomology of minuscule homogeneous spaces {III}. {Semi-simplicity} and consequences", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1246--1263", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-050-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14N35 (14M15)", MRnumber = "2760657", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We prove that the quantum cohomology ring of any minuscule or cominuscule homogeneous space, specialized at q=1, is semisimple. This implies that complex conjugation defines an algebra automorphism of the quantum cohomology ring localized at the quantum parameter. We check that this involution coincides with the strange duality defined in our previous article. We deduce Vafa-Intriligator type formulas for the Gromov-Witten invariants.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2010:HVM, author = "Jingyi Chen and Ailana Fraser", title = "Holomorphic variations of minimal disks with boundary on a {Lagrangian} surface", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1264--1275", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-068-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "58Exx (53Cxx 53Dxx)", MRnumber = "2760658", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let L be an oriented Lagrangian submanifold in an $n$-dimensional K{\"a}hler manifold $M$. Let $u: D \to M$ be a minimal immersion from a disk $D$ with $u(\partial D) \subset L$ such that $u(D)$ meets $L$ orthogonally along $u( \partial D)$. Then the real dimension of the space of admissible holomorphic variations is at least $n + \mu (E,F)$, where $\mu (E,F)$ is a boundary Maslov index; the minimal disk is holomorphic if there exist $n$ admissible holomorphic variations that are linearly independent over ${\bf R}$ at some point $p \in \partial D$; if $M = {\bf C} P^n$ and $u$ intersects $L$ positively, then $u$ is holomorphic if it is stable, and its Morse index is at least $n + \mu (E,F)$ if $u$ is unstable.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{ElWassouli:2010:GPT, author = "Fouzia {El Wassouli}", title = "A generalized {Poisson} transform of an {$L^p$}-function over the {Shilov} boundary of the {$n$}-dimensional {Lie} ball", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1276--1292", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-069-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "32A50 (31B10 31B25 32A45 32M15 46F15)", MRnumber = "2760659", MRreviewer = "Jacques Faraut", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $D$ be the n-dimensional Lie ball and let $\mathfrak B(S)$ be the space of hyperfunctions on the Shilov boundary $S$ of $D$. The aim of this paper is to give a necessary and sufficient condition on the generalized Poisson transform $P_{l,{\lambda}} f$ of an element $f$ in the space $\mathfrak B(S)$ for $f$ to be in $L^p (S), 1 < p < \infty$. Namely, if $F$ is the Poisson transform of some $f \in \mathfrak B(S)$ (i.e., $F = P_{l, \lambda} f$), then for any $l \in {\bf Z}$ and $\lambda \in {\bf C}$ such that $R e[i \lambda] > \frac{n}{2 - 1}$, we show that $f \in L^p (S)$ if and only if $f$ satisfies the growth condition $||F||_{\lambda,p} = \sup 0 \leq r < 1 (1 - r^2)^{R e[i \lambda]} - \frac{n}{2+l}$ \SGMLentity{"23a1} \SGMLentity{"23a3} \SGMLentity{8992} \SGMLentity{8993} S |F(ru)|$^p$ du \SGMLentity{"23a4} \SGMLentity{"23a6} $\frac 1 p < +\infty$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kasprzyk:2010:CTF, author = "Alexander M. Kasprzyk", title = "Canonical Toric {Fano} Threefolds", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1293--1309", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-070-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14J45 (14J30)", MRnumber = "2760660", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "An inductive approach to classifying all toric Fano varieties is given. As an application of this technique, we present a classification of the toric Fano threefolds with at worst canonical singularities. Up to isomorphism, there are 674,688 such varieties.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lee:2010:IHA, author = "Kyu-Hwan Lee", title = "{Iwahori--Hecke} Algebras of {${\rm SL}_2$} over $2$-Dimensional Local Fields", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1310--1324", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-072-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "20Gxx", MRnumber = "2760661", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we construct an analogue of Iwahori-Hecke algebras of SL$_2$ over 2-dimensional local fields. After considering coset decompositions of double cosets of a Iwahori subgroup, we define a convolution product on the space of certain functions on SL$_2$, and prove that the product is well-defined, obtaining a Hecke algebra. Then we investigate the structure of the Hecke algebra. We determine the center of the Hecke algebra and consider Iwahori-Matsumoto type relations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mo:2010:SEC, author = "Xiaohuan Mo and Changtao Yu", title = "On some explicit constructions of {Finsler} metrics with scalar flag curvature", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1325--1339", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-051-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "53C60", MRnumber = "2760662", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We give an explicit construction of polynomial ( of arbitrary degree) ({\alpha},{\beta})-metrics with scalar flag curvature and determine their scalar flag curvature. These Finsler metrics contain all non-trivial projectively flat ({\alpha},{\beta})-metrics of constant flag curvature.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Moeglin:2010:HOE, author = "C. M{\oe}glin", title = "Holomorphie des op{\'e}rateurs d'entrelacement normalis{\'e}s {\`a} l'aide des param{\`e}tres d'{Arthur}. ({French}) [{Holomorphism} of normalized interlacing operators with the help of {Arthur} parameters]", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1340--1386", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-074-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "22Exx", MRnumber = "2760663", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we prove holomorphy for certain intertwining operators arising from the theory of Eisenstein series. To do that we need to normalize using the Langlands-Shahidi's normalization arising from the twisted endoscopy and the associated representations of the general linear group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Pamuk:2010:HSE, author = "Mehmetcik Pamuk", title = "Homotopy self-equivalences of $4$-manifolds with free fundamental group", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1387--1403", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-061-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "57N13 (55P10 57R80)", MRnumber = "2760664 (2011i:57026)", MRreviewer = "Terry Lawson", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We calculate the group of homotopy classes of homotopy self-equivalences of 4-manifolds with free fundamental group and obtain a classification of such 4-manifolds up to s-cobordism.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Saroglou:2010:CES, author = "Christos Saroglou", title = "Characterizations of extremals for some functionals on convex bodies", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1404--1418", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-062-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "52A40 (52A22)", MRnumber = "2760665", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We investigate equality cases in inequalities for Sylvester-type functionals. Namely, it was proven by Campi, Colesanti, and Gronchi that the quantity {\int}$_{x 0}$ {\in} K {\ldots}{\int}$_{x n}$ {\in} K [V(conv{x$_0$,...,x$_n$})]$^p$ dx$_0$ {\ldots}dx$_n$, n {\geq} d, p {\geq} 1 is maximized by triangles among all planar convex bodies K (parallelograms in the symmetric case). We show that these are the only maximizers, a fact proven by Giannopoulos for p=1. Moreover, if h\from {\bf R}$_+$ {\rightarrow} {\bf R}$_+$ is a strictly increasing function and W$_j$ is the j-th quermassintegral in {\bf R}$^d$, we prove that the functional {\int}$_{x 0}$ {\in} K$_0$ {\ldots}{\int}$_{x n}$ {\in} K$_n$ h(W$_j$ (conv{x$_0$,...,x$_n$}))dx$_0$ {\ldots}dx$_n$, n {\geq} d is minimized among the (n+1)-tuples of convex bodies of fixed volumes if and only if K$_0$,...,K$_n$ are homothetic ellipsoids when j=0 (extending a result of Groemer) and Euclidean balls with the same center when j > 0 (extending a result of Hartzoulaki and Paouris).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Yang:2010:BEM, author = "Dachun Yang and Dongyong Yang", title = "{BMO}-estimates for maximal operators via approximations of the identity with non-doubling measures", journal = j-CAN-J-MATH, volume = "62", number = "6", pages = "1419--1434", month = dec, year = "2010", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-065-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "42B25 (42B30 43A99 47B38)", MRnumber = "2760666 (2011j:42034)", MRreviewer = "Yasuo Komori", bibdate = "Sat Sep 10 15:39:16 MDT 2011", bibsource = "http://cms.math.ca/cjm/v62/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let $\mu$ be a nonnegative Radon measure on $\mathbb{R}^d$ that satisfies the growth condition that there exist constants $C_0 > 0$ and $n \in (0,d]$ such that for all $x \in \mathbb{R}^d$ and $r > 0$, $\mu(B(x,r)) \leq C_0 r^n$, where $B(x,r)$ is the open ball centered at $x$ and having radius $r$. In this paper, the authors prove that if $f$ belongs to the BMO-type space RBMO($\mu$) of Tolsa, then the homogeneous maximal function $\cdot M_S(f)$ (when $\mathbb{R}^d$ is not an initial cube) and the inhomogeneous maximal function $M_S(f)$ (when $\mathbb{R}^d$ is an initial cube) associated with a given approximation of the identity $S$ of Tolsa are either infinite everywhere or finite almost everywhere, and in the latter case, ${\cdot} M_S$ and $M_S$ are bounded from RBMO($\mu$) to the BLO-type space RBLO($\mu$). The authors also prove that the inhomogeneous maximal operator $M_S$ is bounded from the local BMO-type space rbmo($\mu$) to the local BLO-type space rblo($\mu$).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Banica:2011:FBL, author = "T. Banica and S. T. Belinschi and M. Capitaine and B. Collins", title = "Free {Bessel} Laws", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "3--37", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-060-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46L54", MRnumber = "2779129", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We introduce and study a remarkable family of real probability measures ${\pi}_{st}$ that we call free Bessel laws. These are related to the free Poisson law {\pi} via the formulae ${\pi}_{s1} ={\pi}^{\boxtimes s}$ and ${\pi}_{1t} = \pi^{\boxplus t}$. Our study includes definition and basic properties, analytic aspects (supports, atoms, densities), combinatorial aspects (functional transforms, moments, partitions), and a discussion of the relation with random matrices and quantum groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Brudern:2011:AFP, author = "J{\"o}rg Br{\"u}dern and Trevor D. Wooley", title = "Asymptotic formulae for pairs of diagonal cubic equations", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "38--54", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-067-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11D72 (11P55)", MRnumber = "2779130", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We investigate the number of integral solutions possessed by a pair of diagonal cubic equations in a large box. Provided that the number of variables in the system is at least fourteen, and in addition the number of variables in any non-trivial linear combination of the underlying forms is at least eight, we obtain an asymptotic formula for the number of integral solutions consistent with the product of local densities associated with the system.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chau:2011:PRF, author = "Albert Chau and Luen-Fai Tam and Chengjie Yu", title = "Pseudolocality for the {Ricci} Flow and Applications", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "55--85", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-076-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "53C44", MRnumber = "2779131", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Perelman established a differential Li-Yau-Hamilton (LYH) type inequality for fundamental solutions of the conjugate heat equation corresponding to the Ricci flow on compact manifolds. As an application of the LYH inequality, Perelman proved a pseudolocality result for the Ricci flow on compact manifolds. In this article we provide the details for the proofs of these results in the case of a complete noncompact Riemannian manifold. Using these results we prove that under certain conditions, a finite time singularity of the Ricci flow must form within a compact set. The conditions are satisfied by asymptotically flat manifolds. We also prove a long time existence result for the K{\"a}hler-Ricci flow on complete nonnegatively curved K{\"a}hler manifolds.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2011:VC, author = "Xi Chen", title = "On {Vojta}'s {$1 + \epsilon$} conjecture", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "86--103", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-073-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "14G40 (14H15)", MRnumber = "2779132", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We give another proof of Vojta's 1+{\epsilon} conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", xxtitle = "On {Vojta}'s $1 + \varepsilon$ Conjecture", } @Article{Feng:2011:RIF, author = "Shui Feng and Byron Schmuland and Jean Vaillancourt and Xiaowen Zhou", title = "Reversibility of interacting {Fleming--Viot} processes with mutation, selection, and recombination", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "104--122", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-071-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "60K35 (60J70)", MRnumber = "2779133", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Reversibility of the Fleming-Viot process with mutation, selection, and recombination is well understood. In this paper, we study the reversibility of a system of Fleming-Viot processes that live on a countable number of colonies interacting with each other through migrations between the colonies. It is shown that reversibility fails when both migration and mutation are non-trivial.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Granirer:2011:SES, author = "Edmond E. Granirer", title = "Strong and Extremely Strong {Ditkin} sets for the {Banach} Algebras {$A_p^r(G) = {A_p\cap} L^r(G)$}", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "123--135", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-077-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "43A15 (43A10 46J10)", MRnumber = "2779134", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let A$_p$ (G) be the Figa-Talamanca, Herz Banach Algebra on G; thus A$_2$ (G) is the Fourier algebra. Strong Ditkin (SD) and Extremely Strong Ditkin (ESD) sets for the Banach algebras A$_p^r$ (G) are investigated for abelian and nonabelian locally compact groups G. It is shown that SD and ESD sets for A$_p$ (G) remain SD and ESD sets for A$_p^r$ (G), with strict inclusion for ESD sets. The case for the strict inclusion of SD sets is left open. A result on the weak sequential completeness of A$_2$ (F) for ESD sets F is proved and used to show that Varopoulos, Helson, and Sidon sets are not ESD sets for A$_2$ (G), yet they are such for A$_2^r$ (G) for discrete groups G, for any 1 {\leq} r {\leq} 2. A result is given on the equivalence of the sequential and the net definitions of SD or ESD sets for {\sigma}-compact groups. The above results are new even if G is abelian.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gun:2011:TNS, author = "Sanoli Gun and M. Ram Murty and Purusottam Rath", title = "Transcendental nature of special values of {$L$}-functions", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "136--152", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-078-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11J81 (11J86 11J91)", MRnumber = "2779135", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper, we study the non-vanishing and transcendence of special values of a varying class of L-functions and their derivatives. This allows us to investigate the transcendence of Petersson norms of certain weight one modular forms.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hambly:2011:AFA, author = "B. M. Hambly", title = "Asymptotics for functions associated with heat flow on the {Sierpinski} carpet", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "153--180", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-079-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "35Kxx (28A80 60J65)", MRnumber = "2779136", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We establish the asymptotic behaviour of the partition function, the heat content, the integrated eigenvalue counting function, and, for certain points, the on-diagonal heat kernel of generalized Sierpinski carpets. For all these functions the leading term is of the form x$^{{\gamma}}$ $\varphi$(logx) for a suitable exponent {\gamma} and $\varphi$ a periodic function. We also discuss similar results for the heat content of affine nested fractals.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ismail:2011:CCD, author = "Mourad E. H. Ismail and Josef Obermaier", title = "Characterizations of continuous and discrete {$q$}-ultraspherical polynomials", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "181--199", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-080-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "42C05 (33D45)", MRnumber = "2779137", MRreviewer = "Ilona Iglewska-Nowak", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We characterize the continuous q-ultraspherical polynomials in terms of the special form of the coefficients in the expansion $D$$_q$ P$_n$ (x) in the basis {P$_n$ (x)}, $D$$_q$ being the Askey--Wilson divided difference operator. The polynomials are assumed to be symmetric, and the connection coefficients are multiples of the reciprocal of the square of the L$^2$ norm of the polynomials. A similar characterization is given for the discrete q-ultraspherical polynomials. A new proof of the evaluation of the connection coefficients for big q-Jacobi polynomials is given.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rahman:2011:EPE, author = "Mizan Rahman", title = "An explicit polynomial expression for a $q$-analogue of the $9$-$j$ symbols", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "200--221", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-081-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "33D45 (33D50)", MRnumber = "2779138", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Using standard transformation and summation formulas for basic hypergeometric series we obtain an explicit polynomial form of the q-analogue of the 9-j symbols, introduced by the author in a recent publication. We also consider a limiting case in which the 9-j symbol factors into two Hahn polynomials. The same factorization occurs in another limit case of the corresponding q-analogue.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Wang:2011:LTA, author = "Jiun-Chau Wang", title = "Limit theorems for additive conditionally free convolution", journal = j-CAN-J-MATH, volume = "63", number = "1", pages = "222--240", month = feb, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-075-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46L54 (60F05)", MRnumber = "2779139", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we determine the limiting distributional behavior for sums of infinitesimal conditionally free random variables. We show that the weak convergence of classical convolution and that of conditionally free convolution are equivalent for measures in an infinitesimal triangular array, where the measures may have unbounded support. Moreover, we use these limit theorems to study the conditionally free infinite divisibility. These results are obtained by complex analytic methods without reference to the combinatorics of c-free convolution.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Essouabri:2011:MZF, author = "Driss Essouabri and Kohji Matsumoto and Hirofumi Tsumura", title = "Multiple zeta-functions associated with linear recurrence sequences and the vectorial sum formula", journal = j-CAN-J-MATH, volume = "63", number = "2", pages = "241--276", month = apr, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-085-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11M32 (11B39 40B05)", MRnumber = "2809056", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We prove the holomorphic continuation of certain multi-variable multiple zeta-functions whose coefficients satisfy a suitable recurrence condition. In fact, we introduce more general vectorial zeta-functions and prove their holomorphic continuation. Moreover, we show a vectorial sum formula among those vectorial zeta-functions from which some generalizations of the classical sum formula can be deduced.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ghate:2011:LIG, author = "Eknath Ghate and Vinayak Vatsal", title = "Locally Indecomposable {Galois} Representations", journal = j-CAN-J-MATH, volume = "63", number = "2", pages = "277--297", month = apr, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-084-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11F80", MRnumber = "2809057", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In a previous paper the authors showed that, under some technical conditions, the local Galois representations attached to the members of a non-CM family of ordinary cusp forms are indecomposable for all except possibly finitely many members of the family. In this paper we use deformation theoretic methods to give examples of non-CM families for which every classical member of weight at least two has a locally indecomposable Galois representation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gun:2011:VLC, author = "Sanoli Gun and V. Kumar Murty", title = "A variant of {Lehmer}'s conjecture, {II}: the {CM}-case", journal = j-CAN-J-MATH, volume = "63", number = "2", pages = "298--326", month = apr, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-002-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "11F11 (11F30)", MRnumber = "2809058", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let f be a normalized Hecke eigenform with rational integer Fourier coefficients. It is an interesting question to know how often an integer n has a factor common with the n-th Fourier coefficient of f. It has been shown in previous papers that this happens very often. In this paper, we give an asymptotic formula for the number of integers n for which (n, a(n)) = 1, where a(n) is the n-th Fourier coefficient of a normalized Hecke eigenform f of weight 2 with rational integer Fourier coefficients and having complex multiplication.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jantzen:2011:DSA, author = "Chris Jantzen", title = "Discrete series for $p$-adic {${\rm SO}(2 n)$} and restrictions of representations of {${\rm O}(2 n)$}", journal = j-CAN-J-MATH, volume = "63", number = "2", pages = "327--380", month = apr, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-003-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "22Exx", MRnumber = "2809059", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "In this paper we give a classification of discrete series for SO(2n,F), F p-adic, similar to that of Moeglin-Tadi{\'c} for the other classical groups. This is obtained by taking the Moeglin-Tadi{\'c} classification for O(2n,F) and studying how the representations restrict to SO(2n,F). We then extend this to an analysis of how admissible representations of O(2n,F) restrict.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ji:2011:CCA, author = "Kui Ji and Chunlan Jiang", title = "A complete classification of {AI} algebras with the ideal property", journal = j-CAN-J-MATH, volume = "63", number = "2", pages = "381--412", month = apr, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-005-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46L35 (19K14 46L05 46L08)", MRnumber = "2809060", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let A be an AI algebra; that is, A is the C$^*$-algebra inductive limit of a sequence A$_1$ $\varphi$$_{1,2}$ {\rightarrow} A$_2$ $\varphi$$_{2,3}$ {\rightarrow} A$_3$ {\rightarrow}{\ldots}{\rightarrow} A$_n$ {\rightarrow}{\ldots}, where A$_n$ ={\oplus}$_{i=1}^{k n}$ M$_{[n,i]}$ (C(X$^i_n$)), X$^i_n$ are [0,1], k$_n$, and [n,i] are positive integers. Suppose that A has the ideal property: each closed two-sided ideal of A is generated by the projections inside the ideal, as a closed two-sided ideal. In this article, we give a complete classification of AI algebras with the ideal property.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Konvalinka:2011:GFH, author = "Matja{\v{z}} Konvalinka and Mark Skandera", title = "Generating Functions for {Hecke} Algebra Characters", journal = j-CAN-J-MATH, volume = "63", number = "2", pages = "413--435", month = apr, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-082-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "20C08", MRnumber = "2809061", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Certain polynomials in $n^2$ variables that serve as generating functions for symmetric group characters are sometimes called ($S_n$) character immanants. We point out a close connection between the identities of Littlewood--Merris--Watkins and Goulden--Jackson, which relate $S_n$ character immanants to the determinant, the permanent and MacMahon's Master Theorem. From these results we obtain a generalization of Muir's identity. Working with the quantum polynomial ring and the Hecke algebra $H_n(q)$, we define quantum immanants that are generating functions for Hecke algebra characters. We then prove quantum analogs of the Littlewood--Merris--Watkins identities and selected Goulden--Jackson identities that relate $H_n(q)$ character immanants to the quantum determinant, quantum permanent, and quantum Master Theorem of Garoufalidis--L{\^e}--Zeilberger. We also obtain a generalization of Zhang's quantization of Muir's identity.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mine:2011:SCO, author = "Kotaro Mine and Katsuro Sakai", title = "Simplicial complexes and open subsets of non-separable {LF}-spaces", journal = j-CAN-J-MATH, volume = "63", number = "2", pages = "436--459", month = apr, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2010-083-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "57N20 (46Axx 46Txx 57Q40)", MRnumber = "2809062", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "Let F be a non-separable LF-space homeomorphic to the direct sum $\sum_{n {\in} N} l_2 (\tau_n)$, where $\aleph_0 < \tau_1 < \tau_2 < \ldots$. It is proved that every open subset U of F is homeomorphic to the product |K| \times F for some locally finite-dimensional simplicial complex K such that every vertex v {\in} K$^{(0)}$ has the star St(v,K) with card St(v,K)$^{(0)}$ < {\tau} = sup{\tau}$_n$ (and card K$^{(0)}$ {\leq} {\tau}), and, conversely, if K is such a simplicial complex, then the product |K| \times F can be embedded in F as an open set, where |K| is the polyhedron of K with the metric topology.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pavlicek:2011:MCM, author = "Libor Pavl{\'\i}{\v{c}}ek", title = "Monotonically Controlled Mappings", journal = j-CAN-J-MATH, volume = "63", number = "2", pages = "460--480", month = apr, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-004-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", MRclass = "46Gxx (26B05 46Bxx)", MRnumber = "2809063", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; MathSciNet database", abstract = "We study classes of mappings between finite and infinite dimensional Banach spaces that are monotone and mappings which are differences of monotone mappings (DM). We prove a Rad{\'o}-Reichelderfer estimate for monotone mappings in finite dimensional spaces that remains valid for DM mappings. This provides an alternative proof of the Fr{\'e}chet differentiability a.e. of DM mappings. We establish a Morrey-type estimate for the distributional derivative of monotone mappings. We prove that a locally DM mapping between finite dimensional spaces is also globally DM. We introduce and study a new class of the so-called UDM mappings between Banach spaces, which generalizes the concept of curves of finite variation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Baragar:2011:ACK, author = "Arthur Baragar", title = "The Ample Cone for a {K3} Surface", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "481--499", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-006-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we give several pictorial fractal representations of the ample or K{\"a}hler cone for surfaces in a certain class of K3 surfaces. The class includes surfaces described by smooth (2,2,2) forms in {\bf P}$^1$ \times {\bf P}$^1$ \times {\bf P}$^1$ defined over a sufficiently large number field K that have a line parallel to one of the axes and have Picard number four. We relate the Hausdorff dimension of this fractal to the asymptotic growth of orbits of curves under the action of the surface's group of automorphisms. We experimentally estimate the Hausdorff dimension of the fractal to be 1.296 {\pm}.010.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dadarlat:2011:OPC, author = "Marius Dadarlat and George A. Elliott and Zhuang Niu", title = "One-Parameter Continuous Fields of {Kirchberg} Algebras. {II}", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "500--532", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-001-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Parallel to the first two authors' earlier classification of separable, unita one-parameter, continuous fields of Kirchberg algebras with torsion free K -groups supported in one dimension, one-parameterble, unital, continuous fields of AF-algebras are classified by their ordered K $_0$-sheaves. Effros-Handelman-Shen type are proved for separable unital one-parameter continuous fields of AF-algebras and Kirchberg algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Espinola:2011:BPP, author = "Rafa Esp{\'\i}nola and Aurora Fern{\'a}ndez-Le{\'o}n", title = "On Best Proximity Points in Metric and {Banach} Spaces", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "533--550", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-007-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we study the existence and uniqueness of best proximity points of cyclic contractions as well as the convergence of iterates to such proximity points. We take two different approaches, each one leading to different results that complete, if not improve, other similar results in the theory. Results in this paper stand for Banach spaces, geodesic metric spaces and metric spaces. We also include an appendix on CAT(0) spaces where we study the particular behavior of these spaces regarding the problems we are concerned with.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hadwin:2011:TFE, author = "Don Hadwin and Qihui Li and Junhao Shen", title = "Topological Free Entropy Dimensions in Nuclear {C}$^*$-algebras and in Full Free Products of Unital {C}$^*$-algebras", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "551--590", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-014-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In the paper, we introduce a new concept, topological orbit dimension of an n-tuple of elements in a unital C$^{{\ast}}$-algebra. Using this concept, we conclude that Voiculescu's topological free entropy dimension of every finite family of self-adjoint generators of a nuclear C$^{{\ast}}$-algebra is less than or equal to 1. We also show that the Voiculescu's topological free entropy dimension is additive in the full free product of some unital C$^{{\ast}}$-algebras. We show that the unital full free product of Blackadar and Kirchberg's unital MF algebras is also an MF algebra. As an application, we obtain that Ext(C$_r^{{\ast}}$ (F$_2$){\ast}$_C$ C$_r^{{\ast}}$ (F$_2$)) is not a group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hanzer:2011:ROR, author = "Marcela Hanzer and Goran Mui{\'c}", title = "Rank One Reducibility for Metaplectic Groups via Theta Correspondence", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "591--615", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-015-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We calculate reducibility for the representations of metaplectic groups induced from cuspidal representations of maximal parabolic subgroups via theta correspondence, in terms of the analogous representations of the odd orthogonal groups. We also describe the lifts of all relevant subquotients.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lee:2011:MQC, author = "Edward Lee", title = "A Modular Quintic {Calabi--Yau} Threefold of Level $55$", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "616--633", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-016-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi--Yau threefold that is modular, in the sense that the L-function of its middle-dimensional cohomology is associated with a classical modular form of weight 4 and level 55.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lu:2011:HMF, author = "Guangshi L{\"u}", title = "On Higher Moments of {Fourier} Coefficients of Holomorphic Cusp Forms", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "634--647", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-010-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let S$_k$ ({\Gamma}) be the space of holomorphic cusp forms of even integral weight k for the full modular group. Let {\lambda}$_f$ (n) and {\lambda}$_g$ (n) be the n-th normalized Fourier coefficients of two holomorphic Hecke eigencuspforms f(z), g(z) {\in} S$_k$ ({\Gamma}), respectively. In this paper we are able to show the following results about higher moments of Fourier coefficients of holomorphic cusp forms. (i) For any {\epsilon} > 0, we have \sum n {\leq} x {\lambda}$_f^5$ (n) < < $_{f,{\epsilon}}$ x$^{(15/16)+{\epsilon}}$ and \sum n {\leq} x {\lambda}$_f^7$ (n) < < $_{f,{\epsilon}}$ x$^{(63/64)+{\epsilon}}$. (ii) If sym$^3$ {\pi}$_f$ \ncong sym$^3$ {\pi}$_g$, then for any {\epsilon} > 0, we have \sum n {\leq} x {\lambda}$_f^3$ (n){\lambda}$_g^3$ (n) < < $_{f,{\epsilon}}$ x$^{(31/32) +{\epsilon}}$; If sym$^2$ {\pi}$_f$ \ncong sym$^2$ {\pi}$_g$, then for any {\epsilon} > 0, we have \sum n {\leq} x {\lambda}$_f^4$ (n){\lambda}$_g^2$ (n)=cxlogx +c{\prime}x+O$_{f,{\epsilon}}$ (x$^{(31/32)+{\epsilon}}$); If sym$^2$ {\pi}$_f$ \ncong sym$^2$ {\pi}$_g$ and sym$^4$ {\pi}$_f$ \ncong sym$^4$ {\pi}$_g$, then for any {\epsilon} > 0, we have \sum n {\leq} x {\lambda}$_f^4$ (n){\lambda}$_g^4$ (n)=xP(logx)+ O$_{f,{\epsilon}}$ ( x$^{(127/128)+{\epsilon}}$), where P(x) is a polynomial of degree 3.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ngai:2011:SAL, author = "Sze-Man Ngai", title = "Spectral Asymptotics of {Laplacians} Associated with One-dimensional Iterated Function Systems with Overlaps", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "648--688", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-011-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We set up a framework for computing the spectral dimension of a class of one-dimensional self-similar measures that are defined by iterated function systems with overlaps and satisfy a family of second-order self-similar identities. As applications of our result we obtain the spectral dimension of important measures such as the infinite Bernoulli convolution associated with the golden ratio and convolutions of Cantor-type measures. The main novelty of our result is that the iterated function systems we consider are not post-critically finite and do not satisfy the well-known open set condition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Olphert:2011:HRW, author = "Sean Olphert and Stephen C. Power", title = "Higher Rank Wavelets", journal = j-CAN-J-MATH, volume = "63", number = "3", pages = "689--720", month = jun, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-012-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A theory of higher rank multiresolution analysis is given in the setting of abelian multiscalings. This theory enables the construction, from a higher rank MRA, of finite wavelet sets whose multidilations have translates forming an orthonormal basis in $L^2(R^d)$. While tensor products of uniscaled MRAs provide simple examples we construct many nonseparable higher rank wavelets. In particular we construct $Latin square wavelets$ as rank 2 variants of Haar wavelets. Also we construct nonseparable scaling functions for rank 2 variants of Meyer wavelet scaling functions, and we construct the associated nonseparable wavelets with compactly supported Fourier transforms. On the other hand we show that compactly supported scaling functions for biscaled MRAs are necessarily separable.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Autin:2011:ICV, author = "Aymeric Autin", title = "Isoresonant Complex-valued Potentials and Symmetries", journal = j-CAN-J-MATH, volume = "63", number = "4", pages = "721--754", month = aug, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-031-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $X$ be a connected Riemannian manifold such that the resolvent of the free Laplacian $(\Delta-z)^{-1}$, $z\in\mathbb{C} \setminus \mathbb{R}^+$, has a meromorphic continuation through $\mathbb{R}^+$. The poles of this continuation are called resonances. When $X$ has some symmetries, we construct complex-valued potentials, $V$, such that the resolvent of $\Delta+V$, which has also a meromorphic continuation, has the same resonances with multiplicities as the free Laplacian.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chu:2011:GMS, author = "Kenneth C. K. Chu", title = "On the Geometry of the Moduli Space of Real Binary Octics", journal = j-CAN-J-MATH, volume = "63", number = "4", pages = "755--797", month = aug, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-026-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The moduli space of smooth real binary octics has five connected components. They parametrize the real binary octics whose defining equations have 0,...,4 complex-conjugate pairs of roots respectively. We show that each of these five components has a real hyperbolic structure in the sense that each is isomorphic as a real-analytic manifold to the quotient of an open dense subset of 5-dimensional real hyperbolic space {\bf RH}$^5$ by the action of an arithmetic subgroup of Isom( {\bf RH}$^5$). These subgroups are commensurable to discrete hyperbolic reflection groups, and the Vinberg diagrams of the latter are computed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Daws:2011:RMF, author = "Matthew Daws", title = "Representing Multipliers of the {Fourier} Algebra on Non-Commutative {$L^p$} Spaces", journal = j-CAN-J-MATH, volume = "63", number = "4", pages = "798--825", month = aug, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-020-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We show that the multiplier algebra of the Fourier algebra on a locally compact group G can be isometrically represented on a direct sum on non-commutative L$^p$ spaces associated with the right von Neumann algebra of G. The resulting image is the idealiser of the image of the Fourier algebra. If these spaces are given their canonical operator space structure, then we get a completely isometric representation of the completely bounded multiplier algebra. We make a careful study of the non-commutative L$^p$ spaces we construct and show that they are completely isometric to those considered recently by Forrest, Lee, and Samei. We improve a result of theirs about module homomorphisms. We suggest a definition of a Figa-Talamanca-Herz algebra built out of these non-commutative L$^p$ spaces, say A$_p$ ( {\wedge} G). It is shown that A$_2$ ( {\wedge} G) is isometric to L$^1$ (G), generalising the abelian situation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Errthum:2011:SMS, author = "Eric Errthum", title = "Singular Moduli of {Shimura} Curves", journal = j-CAN-J-MATH, volume = "63", number = "4", pages = "826--861", month = aug, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-023-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The j-function acts as a parametrization of the classical modular curve. Its values at complex multiplication (CM) points are called singular moduli and are algebraic integers. A Shimura curve is a generalization of the modular curve and, if the Shimura curve has genus 0, a rational parameterizing function exists and when evaluated at a CM point is again algebraic over {\bf Q}. This paper shows that the coordinate maps given by N. Elkies for the Shimura curves associated to the quaternion algebras with discriminants 6 and 10 are Borcherds lifts of vector-valued modular forms. This property is then used to explicitly compute the rational norms of singular moduli on these curves. This method not only verifies conjectural values for the rational CM points, but also provides a way of algebraically calculating the norms of CM points with arbitrarily large negative discriminant.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hosokawa:2011:LCC, author = "Takuya Hosokawa and Pekka J. Nieminen and Sh{\^u}ichi Ohno", title = "Linear Combinations of Composition Operators on the {Bloch} Spaces", journal = j-CAN-J-MATH, volume = "63", number = "4", pages = "862--877", month = aug, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-008-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We characterize the compactness of linear combinations of analytic composition operators on the Bloch space. We also study their boundedness and compactness on the little Bloch space.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Howard:2011:TGT, author = "Benjamin Howard and Christopher Manon and John Millson", title = "The Toric Geometry of Triangulated Polygons in {Euclidean} Space", journal = j-CAN-J-MATH, volume = "63", number = "4", pages = "878--937", month = aug, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-021-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Speyer and Sturmfels associated Gr{\"o}bner toric degenerations Gr $_2$ ( {\bf C}$^n$)$^T$ of Gr $_2$ ( {\bf C}$^n$) with each trivalent tree $T$ having n leaves. These degenerations induce toric degenerations M$_r^T$ of M$_r$, the space of n ordered, weighted (by {\bf r}) points on the projective line. Our goal in this paper is to give a geometric (Euclidean polygon) description of the toric fibers and describe the action of the compact part of the torus as {``bendings of polygons''}. We prove the conjecture of Foth and Hu that the toric fibers are homeomorphic to the spaces defined by Kamiyama and Yoshida.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Li-Bland:2011:ACA, author = "David Li-Bland", title = "{AV--Courant} Algebroids and Generalized {CR} Structures", journal = j-CAN-J-MATH, volume = "63", number = "4", pages = "938--960", month = aug, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-009-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 10 15:39:17 MDT 2011", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We construct a generalization of Courant algebroids that are classified by the third cohomology group H$^3$ (A,V), where A is a Lie Algebroid, and V is an A-module. We see that both Courant algebroids and $E$$^1$ (M) structures are examples of them. Finally we introduce generalized CR structures on a manifold, which are a generalization of generalized complex structures, and show that every CR structure and contact structure is an example of a generalized CR structure.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bouclet:2011:LFE, author = "Jean-Marc Bouclet", title = "Low Frequency Estimates for Long Range Perturbations in Divergence Form", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "961--991", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-022-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove a uniform control as $z \rightarrow 0$ for the resolvent $(P-z)^{-1}$ of long range perturbations $P$ of the Euclidean Laplacian in divergence form by combining positive commutator estimates and properties of Riesz transforms. These estimates hold in dimension $d \geq 3$ when $P$ is defined on ${\bf R}^d$ and in dimension $d \geq 2$ when $P$ is defined outside a compact obstacle with Dirichlet boundary conditions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bruin:2011:AGT, author = "Nils Bruin and Kevin Doerksen", title = "The Arithmetic of Genus Two Curves with $(4,4)$-Split {Jacobians}", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "992--1024", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-039-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we study genus $2$ curves whose Jacobians admit a polarized $(4,4)$-isogeny to a product of elliptic curves. We consider base fields of characteristic different from $2$ and $3$, which we do not assume to be algebraically closed. We obtain a full classification of all principally polarized abelian surfaces that can arise from gluing two elliptic curves along their $4$-torsion, and we derive the relation their absolute invariants satisfy. As an intermediate step, we give a general description of Richelot isogenies between Jacobians of genus $2$ curves, where previously only Richelot isogenies with kernels that are pointwise defined over the base field were considered. Our main tool is a Galois theoretic characterization of genus $2$ curves admitting multiple Richelot isogenies.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Clouatre:2011:USR, author = "Rapha{\"e}l Clou{\^a}tre", title = "Universal Series on a {Riemann} Surface", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "1025--1037", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-013-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Every holomorphic function on a compact subset of a Riemann surface can be uniformly approximated by partial sums of a given series of functions. Those functions behave locally like the classical fundamental solutions of the Cauchy--Riemann operator in the plane.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cohen:2011:CPR, author = "D. Cohen and G. Denham and M. Falk and A. Varchenko", title = "Critical Points and Resonance of Hyperplane Arrangements", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "1038--1057", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-028-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "If {\Phi}$_{{\lambda}}$ is a master function corresponding to a hyperplane arrangement $A$ and a collection of weights {\lambda}, we investigate the relationship between the critical set of {\Phi}$_{{\lambda}}$, the variety defined by the vanishing of the one-form {\omega}$_{{\lambda}}$ = d log{\Phi}$_{{\lambda}}$, and the resonance of {\lambda}. For arrangements satisfying certain conditions, we show that if {\lambda} is resonant in dimension p, then the critical set of {\Phi}$_{{\lambda}}$ has codimension at most p. These include all free arrangements and all rank 3 arrangements.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Easton:2011:CS, author = "Robert W. Easton", title = "{$S_3$}-covers of Schemes", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "1058--1082", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-045-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We analyze flat $S_3$-covers of schemes, attempting to create structures parallel to those found in the abelian and triple cover theories. We use an initial local analysis as a guide in finding a global description.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kaletha:2011:DSI, author = "Tasho Kaletha", title = "Decomposition of Splitting Invariants in Split Real Groups", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "1083--1106", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-024-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For a maximal torus in a quasi-split semi-simple simply-connected group over a local field of characteristic 0, Langlands and Shelstad constructed a cohomological invariant called the splitting invariant, which is an important component of their endoscopic transfer factors. We study this invariant in the case of a split real group and prove a decomposition theorem which expresses this invariant for a general torus as a product of the corresponding invariants for simple tori. We also show how this reduction formula allows for the comparison of splitting invariants between different tori in the given real group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Liu:2011:GRP, author = "Baiying Liu", title = "Genericity of Representations of $p$-Adic {${\rm Sp}_{2 n}$} and Local {Langlands} Parameters", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "1107--1136", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-017-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let G be the F-rational points of the symplectic group Sp$_{2n}$, where F is a non-Archimedean local field of characteristic 0. Cogdell, Kim, Piatetski-Shapiro, and Shahidi constructed local Langlands functorial lifting from irreducible generic representations of G to irreducible representations of GL$_{2n+1}$ (F). Jiang and Soudry constructed the descent map from irreducible supercuspidal representations of GL$_{2n+1}$ (F) to those of G, showing that the local Langlands functorial lifting from the irreducible supercuspidal generic representations is surjective. In this paper, based on above results, using the same descent method of studying SO$_{2n+1}$ as Jiang and Soudry, we will show the rest of local Langlands functorial lifting is also surjective, and for any local Langlands parameter {\SGMLvarphi} {\in} {\Phi}(G), we construct a representation {\sigma} such that {\SGMLvarphi} and {\sigma} have the same twisted local factors. As one application, we prove the G-case of a conjecture of Gross-Prasad and Rallis, that is, a local Langlands parameter {\SGMLvarphi} {\in} {\Phi}(G) is generic, i.e., the representation attached to {\SGMLvarphi} is generic, if and only if the adjoint L-function of {\SGMLvarphi} is holomorphic at s=1. As another application, we prove for each Arthur parameter {\psi}, and the corresponding local Langlands parameter {\SGMLvarphi}$_{{\psi}}$, the representation attached to {\SGMLvarphi}$_{{\psi}}$ is generic if and only if {\SGMLvarphi}$_{{\psi}}$ is tempered.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Moy:2011:DAP, author = "Allen Moy", title = "Distribution Algebras on $p$-adic Groups and {Lie} Algebras", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "1137--1160", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-025-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "When F is a p-adic field, and G= {\bf G} (F) is the group of F-rational points of a connected algebraic F-group, the complex vector space $H$ (G) of compactly supported locally constant distributions on G has a natural convolution product that makes it into a {\bf C} -algebra (without an identity) called the Hecke algebra. The Hecke algebra is a partial analogue for p-adic groups of the enveloping algebra of a Lie group. However, $H$ (G) has drawbacks such as the lack of an identity element, and the process G {\rightarrow} $H$ (G) is not a functor. Bernstein introduced an enlargement $H$ {\wedge} (G) of $H$ (G). The algebra $H$ {\wedge} (G) consists of the distributions that are left essentially compact. We show that the process G {\rightarrow} $H$ {\wedge} (G) is a functor. If {\tau}: G {\rightarrow}H is a morphism of p-adic groups, let F({\tau}) : $H$ {\wedge} (G) {\rightarrow} $H$ {\wedge} (H) be the morphism of {\bf C} -algebras. We identify the kernel of F({\tau}) in terms of Ker({\tau}). In the setting of p-adic Lie algebras, with {\bf g} a reductive Lie algebra, {\bf m} a Levi, and {\tau}: {\bf g} {\rightarrow} {\bf m} the natural projection, we show that F({\tau}) maps G-invariant distributions on $G$ to N$_G$ ( {\bf m} )-invariant distributions on {\bf m}. Finally, we exhibit a natural family of G-invariant essentially compact distributions on {\bf g} associated with a G-invariant non-degenerate symmetric bilinear form on {\bf g} and in the case of SL(2) show how certain members of the family can be moved to the group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Neuwirth:2011:TFM, author = "Stefan Neuwirth and {\'E}ric Ricard", title = "Transfer of {Fourier} Multipliers into {Schur} Multipliers and Sumsets in a Discrete Group", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "1161--1187", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-053-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue-Orlicz spaces of a discrete group $\varGamma$ and relative Toeplitz-Schur multipliers on Schatten-von-Neumann-Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum $\varLambda\subseteq\varGamma$, the norm of the Hilbert transform and the Riesz projection on Schatten-von-Neumann classes with exponent a power of 2, and the norm of Toeplitz Schur multipliers on Schatten-von-Neumann classes with exponent less than 1.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sliwa:2011:CSN, author = "Wies{\l}aw {\'S}liwa and Agnieszka Ziemkowska", title = "On Complemented Subspaces of Non-{Archimedean} Power Series Spaces", journal = j-CAN-J-MATH, volume = "63", number = "5", pages = "1188--1200", month = oct, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-018-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The non-archimedean power series spaces, A$_1$ (a) and A$_{{\infty}}$ (b), are the best known and most important examples of non-archimedean nuclear Fr{\'e}chet spaces. We prove that the range of every continuous linear map from A$_p$ (a) to A$_q$ (b) has a Schauder basis if either p=1 or p={\infty} and the set M$_{b,a}$ of all bounded limit points of the double sequence (b$_i$ /a$_j$ )$_{i,j {\in} N}$ is bounded. It follows that every complemented subspace of a power series space A$_p$ (a) has a Schauder basis if either p=1 or p={\infty} and the set M$_{a,a}$ is bounded.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Salem:2011:RTF, author = "Walid K. Abou Salem and Catherine Sulem", title = "Resonant Tunneling of Fast Solitons through Large Potential Barriers", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1201--1219", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-029-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We rigorously study the resonant tunneling of fast solitons through large potential barriers for the nonlinear Schr{\"o}dinger equation in one dimension. Our approach covers the case of general nonlinearities, both local and Hartree (nonlocal).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Baake:2011:SSP, author = "Michael Baake and Rudolf Scharlau and Peter Zeiner", title = "Similar Sublattices of Planar Lattices", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1220--1237", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-019-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The similar sublattices of a planar lattice can be classified via its multiplier ring. The latter is the ring of rational integers in the generic case, and an order in an imaginary quadratic field otherwise. Several classes of examples are discussed, with special emphasis on concrete results. In particular, we derive Dirichlet series generating functions for the number of distinct similar sublattices of a given index, and relate them to zeta functions of orders in imaginary quadratic fields.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bump:2011:CBI, author = "Daniel Bump and Maki Nakasuji", title = "{Casselman}'s Basis of {Iwahori} Vectors and the {Bruhat} Order", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1238--1253", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-042-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "W. Casselman defined a basis $f_u$ of Iwahori fixed vectors of a spherical representation $(\pi, V)$ of a split semisimple $p$-adic group $G$ over a nonarchimedean local field $F$ by the condition that it be dual to the intertwining operators, indexed by elements $u$ of the Weyl group $W$. On the other hand, there is a natural basis $\psi_u$, and one seeks to find the transition matrices between the two bases. Thus, let $f_u = \sum_v \tilde{m} (u, v) \psi_v$ and $\psi_u = \sum_v m (u, v) f_v$. Using the Iwahori-Hecke algebra we prove that if a combinatorial condition is satisfied, then $m (u, v) = \prod_{\alpha} \frac{1 - q^{- 1} \mathbf{z}^{\alpha}}{1 -\mathbf{z}^{\alpha}}$, where $\mathbf z$ are the Langlands parameters for the representation and $\alpha$ runs through the set $S (u, v)$ of positive coroots $\alpha \in \hat{\Phi}$ (the dual root system of $G$) such that $u \leqslant v r_\alpha < v$ with $r_{\alpha}$ the reflection corresponding to $\alpha$. The condition is conjecturally always satisfied if $G$ is simply-laced and the Kazhdan--Lusztig polynomial $P_{w_0 v, w_0 u} = 1$ with $w_0$ the long Weyl group element. There is a similar formula for $\tilde{m}$ conjecturally satisfied if $P_{u, v} = 1$. This leads to various combinatorial conjectures.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{DAzevedo:2011:CCP, author = "Antonio Breda D'Azevedo and Gareth A. Jones and Egon Schulte", title = "Constructions of Chiral Polytopes of Small Rank", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1254--1283", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-033-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "An abstract polytope of rank $n$ is said to be chiral if its automorphism group has precisely two orbits on the flags, such that adjacent flags belong to distinct orbits. This paper describes a general method for deriving new finite chiral polytopes from old finite chiral polytopes of the same rank. In particular, the technique is used to construct many new examples in ranks $3$, $4$, and $5$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dewar:2011:NER, author = "Michael Dewar", title = "Non-Existence of {Ramanujan} Congruences in Modular Forms of Level Four", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1284--1306", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-027-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Ramanujan famously found congruences like p(5n+4) {\equiv} 0 mod 5 for the partition function. We provide a method to find all simple congruences of this type in the coefficients of the inverse of a modular form on {\Gamma}$_1$ (4) that is non-vanishing on the upper half plane. This is applied to answer open questions about the (non)-existence of congruences in the generating functions for overpartitions, crank differences, and 2-colored F-partitions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dimitrov:2011:BBW, author = "Ivan Dimitrov and Ivan Penkov", title = "A {Bott--Borel--Weil} Theorem for Diagonal Ind-groups", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1307--1327", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-032-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A diagonal ind-group is a direct limit of classical affine algebraic groups of growing rank under a class of inclusions that contains the inclusion SL(n)\to SL(2n), \quad M\mapsto \begin{pmatrix}M {\&} 0 \\ 0 {\&} M \end{pmatrix} as a typical special case. If $G$ is a diagonal ind-group and $B\subset G$ is a Borel ind-subgroup, we consider the ind-variety $G/B$ and compute the cohomology $H^\ell(G/B,\mathcal{O}_{-\lambda})$ of any $G$-equivariant line bundle $\mathcal{O}_{-\lambda}$ on $G/B$. It has been known that, for a generic $\lambda$, all cohomology groups of $\mathcal{O}_{-\lambda}$ vanish, and that a non-generic equivariant line bundle $\mathcal{O}_{-\lambda}$ has at most one nonzero cohomology group. The new result of this paper is a precise description of when $H^j(G/B,\mathcal{O}_{-\lambda})$ is nonzero and the proof of the fact that, whenever nonzero, $H^j(G/B, \mathcal{O}_{-\lambda})$ is a $G$-module dual to a highest weight module. The main difficulty is in defining an appropriate analog $W_B$ of the Weyl group, so that the action of $W_B$ on weights of $G$ is compatible with the analog of the Demazure ``action'' of the Weyl group on the cohomology of line bundles. The highest weight corresponding to $H^j(G/B, \mathcal{O}_{-\lambda})$ is then computed by a procedure similar to that in the classical Bott-Borel--Weil theorem.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gun:2011:CCM, author = "Sanoli Gun and M. Ram Murty and Purusottam Rath", title = "On a Conjecture of {Chowla} and {Milnor}", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1328--1344", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-034-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we investigate a conjecture due to S. and P. Chowla and its generalization by Milnor. These are related to the delicate question of non-vanishing of $L$-functions associated to periodic functions at integers greater than $1$. We report on some progress in relation to these conjectures. In a different vein, we link them to a conjecture of Zagier on multiple zeta values and also to linear independence of polylogarithms.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jardine:2011:PT, author = "J. F. Jardine", title = "Pointed Torsors", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1345--1363", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-058-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This paper gives a characterization of homotopy fibres of inverse image maps on groupoids of torsors that are induced by geometric morphisms, in terms of both pointed torsors and pointed cocycles, suitably defined. Cocycle techniques are used to give a complete description of such fibres, when the underlying geometric morphism is the canonical stalk on the classifying topos of a profinite group $G$. If the torsors in question are defined with respect to a constant group $H$, then the path components of the fibre can be identified with the set of continuous maps from the profinite group $G$ to the group $H$. More generally, when $H$ is not constant, this set of path components is the set of continuous maps from a pro-object in sheaves of groupoids to $H$, which pro-object can be viewed as a ``Grothendieck fundamental groupoid''.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Meinrenken:2011:CDO, author = "Eckhard Meinrenken", title = "The Cubic {Dirac} Operator for Infinite-Dimensonal {Lie} Algebras", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1364--1387", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-036-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $\mathfrak{g}=\bigoplus_{i\in\mathbb{Z}} \mathfrak{g}_i$ be an infinite-dimensional graded Lie algebra, with $\dim\mathfrak{g}_i < \infty$, equipped with a non-degenerate symmetric bilinear form $B$ of degree $0$. The quantum Weil algebra $\widehat{\mathcal{W}}\mathfrak{g}$ is a completion of the tensor product of the enveloping and Clifford algebras of $\mathfrak{g}$. Provided that the Kac-Peterson class of $\mathfrak{g}$ vanishes, one can construct a cubic Dirac operator $\mathcal{D}\in\widehat{\mathcal{W}}(\mathfrak{g})$, whose square is a quadratic Casimir element. We show that this condition holds for symmetrizable Kac--Moody algebras. Extending Kostant's arguments, one obtains generalized Weyl-Kac character formulas for suitable ``equal rank'' Lie subalgebras of Kac--Moody algebras. These extend the formulas of G. Landweber for affine Lie algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Misamore:2011:NEV, author = "Michael D. Misamore", title = "Nonabelian {$H^1$} and the {{\'E}tale Van Kampen Theorem}", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1388--1415", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-030-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Generalized {\'e}tale homotopy pro-groups {\pi}$_1^{{\'e}t}$ (C, x) associated with pointed, connected, small Grothendieck sites (C, x) are defined, and their relationship to Galois theory and the theory of pointed torsors for discrete groups is explained. Applications include new rigorous proofs of some folklore results around {\pi}$_1^{{\'e}t}$ ({\'e}t(X), x), a description of Grothendieck's short exact sequence for Galois descent in terms of pointed torsor trivializations, and a new {\'e}tale van Kampen theorem that gives a simple statement about a pushout square of pro-groups that works for covering families that do not necessarily consist exclusively of monomorphisms. A corresponding van Kampen result for Grothendieck's profinite groups {\pi}$_1^{Gal}$ immediately follows.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Shelah:2011:MSF, author = "Saharon Shelah", title = "{MAD} Saturated Families and {SANE} Player", journal = j-CAN-J-MATH, volume = "63", number = "6", pages = "1416--??", month = dec, year = "2011", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-057-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:39 MST 2012", bibsource = "http://cms.math.ca/cjm/v63/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We throw some light on the question: is there a MAD family (a maximal family of infinite subsets of $\mathbb{N}$, the intersection of any two is finite) that is saturated (completely separable \emph{i.e.}, any $X \subseteq \mathbb{N}$ is included in a finite union of members of the family \emph{or} includes a member (and even continuum many members) of the family). We prove that it is hard to prove the consistency of the negation: (i) if $2^{\aleph_0} \lt \aleph_\omega$, then there is such a family; (ii) if there is no such family, then some situation related to pcf holds whose consistency is large (and if ${\mathfrak a}_* \gt \aleph_1$ even unknown); (iii) if, \emph{e.g.}, there is no inner model with measurables, \emph{then} there is such a family.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Boissiere:2012:ANE, author = "Samuel Boissi{\`e}re", title = "Automorphismes naturels de l'espace de {Douady} de points sur une surface. ({French}). [{Natural} isomorphisms on the points in a surface in {Douady} space]", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "3--23", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-041-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "On {\'e}tablit quelques r{\'e}sultats g{\'e}n{\'e}raux relatifs {\`a} la taille du groupe d'automorphismes de l'espace de Douady de points sur une surface, puis on {\'e}tudie quelques propri{\'e}t{\'e}s des automorphismes provenant d'un automorphisme de la surface, en particulier leur action sur la cohomologie et la classification de leurs points fixes.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Borodachov:2012:LOT, author = "S. V. Borodachov", title = "Lower Order Terms of the Discrete Minimal {Riesz} Energy on Smooth Closed Curves", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "24--43", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-038-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider the problem of minimizing the energy of $N$ points repelling each other on curves in $\mathbb{R}^d$ with the potential $|x-y|^{-s}$, $s\geq 1$, where $|\, \cdot\, |$ is the Euclidean norm. For a sufficiently smooth, simple, closed, regular curve, we find the next order term in the asymptotics of the minimal $s$-energy. On our way, we also prove that at least for $s\geq 2$, the minimal pairwise distance in optimal configurations asymptotically equals $L/N$, $N\to\infty$, where $L$ is the length of the curve.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Carvalho:2012:SRC, author = "T. M. M. Carvalho and H. N. Moreira and K. Tenenblat", title = "Surfaces of Rotation with Constant Mean Curvature in the Direction of a Unitary Normal Vector Field in a {Randers} Space", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "44--80", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-047-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider the Randers space $(V^n,F_b)$ obtained by perturbing the Euclidean metric by a translation, $F_b=\alpha+\beta$, where $\alpha$ is the Euclidean metric and $\beta$ is a $1$-form with norm $b$, $0\leq b\lt 1$. We introduce the concept of a hypersurface with constant mean curvature in the direction of a unitary normal vector field. We obtain the ordinary differential equation that characterizes the rotational surfaces $(V^3,F_b)$ of constant mean curvature (cmc) in the direction of a unitary normal vector field. These equations reduce to the classical equation of the rotational cmc surfaces in Euclidean space, when $b=0$. It also reduces to the equation that characterizes the minimal rotational surfaces in $(V^3,F_b)$ when $H=0$, obtained by M. Souza and K. Tenenblat. Although the differential equation depends on the choice of the normal direction, we show that both equations determine the same rotational surface, up to a reflection. We also show that the round cylinders are cmc surfaces in the direction of the unitary normal field. They are generated by the constant solution of the differential equation. By considering the equation as a nonlinear dynamical system, we provide a qualitative analysis, for $0\lt b\lt \frac{\sqrt{3}}{3}$. Using the concept of stability and considering the linearization around the single equilibrium point (the constant solution), we verify that the solutions are locally asymptotically stable spirals. This is proved by constructing a Lyapunov function for the dynamical system and by determining the basin of stability of the equilibrium point. The surfaces of rotation generated by such solutions tend asymptotically to one end of the cylinder.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{David:2012:PRE, author = "C. David and J. Wu", title = "Pseudoprime Reductions of Elliptic Curves", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "81--101", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-044-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $E$ be an elliptic curve over $\mathbb Q$ without complex multiplication, and for each prime $p$ of good reduction, let $n_E(p) = | E(\mathbb F_p) |$. For any integer $b$, we consider elliptic pseudoprimes to the base $b$. More precisely, let $Q_{E,b}(x)$ be the number of primes $p \leq x$ such that $b^{n_E(p)} \equiv b\,({\rm mod}\,n_E(p))$, and let $\pi_{E, b}^{\operatorname{pseu}}(x)$ be the number of compositive $n_E(p)$ such that $b^{n_E(p)} \equiv b\,({\rm mod}\,n_E(p))$ (also called elliptic curve pseudoprimes). Motivated by cryptography applications, we address the problem of finding upper bounds for $Q_{E,b}(x)$ and $\pi_{E, b}^{\operatorname{pseu}}(x)$, generalising some of the literature for the classical pseudoprimes to this new setting.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ishii:2012:QCI, author = "Atsushi Ishii and Masahide Iwakiri", title = "{Quandle} Cocycle Invariants for Spatial Graphs and Knotted Handlebodies", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "102--122", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-035-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We introduce a flow of a spatial graph and see how invariants for spatial graphs and handlebody-links are derived from those for flowed spatial graphs. We define a new quandle (co)homology by introducing a subcomplex of the rack chain complex. Then we define quandle colorings and quandle cocycle invariants for spatial graphs and handlebody-links.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lee:2012:GPP, author = "Jae-Hyouk Lee", title = "{Gosset} Polytopes in {Picard} Groups of {del Pezzo} Surfaces", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "123--150", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-063-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this article, we study the correspondence between the geometry of del Pezzo surfaces $S_{r}$ and the geometry of the $r$-dimensional Gosset polytopes $(r-4)_{21}$. We construct Gosset polytopes $(r-4)_{21}$ in $\operatorname{Pic} S_{r}\otimes\mathbb{Q}$ whose vertices are lines, and we identify divisor classes in $\operatorname{Pic} S_{r}$ corresponding to $(a-1)$-simplexes ($a\leq r$), $(r-1)$-simplexes and $(r-1)$-crosspolytopes of the polytope $(r-4)_{21}$. Then we explain how these classes correspond to skew $a$-lines($a\leq r$), exceptional systems, and rulings, respectively. As an application, we work on the monoidal transform for lines to study the local geometry of the polytope $(r-4)_{21}$. And we show that the Gieser transformation and the Bertini transformation induce a symmetry of polytopes $3_{21}$ and $4_{21}$, respectively.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Miller:2012:MRE, author = "Steven J. Miller and Siman Wong", title = "Moments of the Rank of Elliptic Curves", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "151--182", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-037-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Fix an elliptic curve $E/\mathbb{Q}$ and assume the Riemann Hypothesis for the $L$-function $L(E_D, s)$ for every quadratic twist $E_D$ of $E$ by $D\in\mathbb{Z}$. We combine Weil's explicit formula with techniques of Heath-Brown to derive an asymptotic upper bound for the weighted moments of the analytic rank of $E_D$. We derive from this an upper bound for the density of low-lying zeros of $L(E_D, s)$ that is compatible with the random matrix models of Katz and Sarnak. We also show that for any unbounded increasing function $f$ on $\mathbb{R}$, the analytic rank and (assuming in addition the Birch and Swinnerton-Dyer conjecture) the number of integral points of $E_D$ are less than $f(D)$ for almost all $D$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nowak:2012:NPL, author = "Adam Nowak and Krzysztof Stempak", title = "Negative Powers of {Laguerre} Operators", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "183--216", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-040-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study negative powers of Laguerre differential operators in $\mathbb{R}^d$, $d\ge1$. For these operators we prove two-weight $L^p-L^q$ estimates with ranges of $q$ depending on $p$. The case of the harmonic oscillator (Hermite operator) has recently been treated by Bongioanni and Torrea by using a straightforward approach of kernel estimates. Here these results are applied in certain Laguerre settings. The procedure is fairly direct for Laguerre function expansions of Hermite type, due to some monotonicity properties of the kernels involved. The case of Laguerre function expansions of convolution type is less straightforward. For half-integer type indices $\alpha$ we transfer the desired results from the Hermite setting and then apply an interpolation argument based on a device we call the convexity principle to cover the continuous range of $\alpha \in [-1/2, \infty)^d$. Finally, we investigate negative powers of the Dunkl harmonic oscillator in the context of a finite reflection group acting on $\mathbb{R}^d$ and isomorphic to $\mathbb Z^d_2$. The two weight $L^p-L^q$ estimates we obtain in this setting are essentially consequences of those for Laguerre function expansions of convolution type.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Tang:2012:SCD, author = "Lin Tang", title = "{$W_\omega^2, p$}-Solvability of the {Cauchy--Dirichlet} Problem for Nondivergence Parabolic Equations with {BMO} Coefficients", journal = j-CAN-J-MATH, volume = "64", number = "1", pages = "217--??", month = feb, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-054-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Feb 4 10:03:45 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we establish the regularity of strong solutions to nondivergence parabolic equations with BMO coefficients in nondoubling weighted spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Allcock:2012:TBS, author = "Daniel Allcock", title = "Triangles of {Baumslag--Solitar} Groups", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "241--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-062-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Our main result is that many triangles of Baumslag--Solitar groups collapse to finite groups, generalizing a famous example of Hirsch and other examples due to several authors. A triangle of Baumslag--Solitar groups means a group with three generators, cyclically ordered, with each generator conjugating some power of the previous one to another power. There are six parameters, occurring in pairs, and we show that the triangle fails to be developable whenever one of the parameters divides its partner, except for a few special cases. Furthermore, under fairly general conditions, the group turns out to be finite and solvable of derived length $\leq 3$. We obtain a lot of information about finite quotients, even when we cannot determine developability.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bell:2012:CMA, author = "Jason P. Bell and Kevin G. Hare", title = "Corrigendum to {``On {$\mathbb{Z}$}-modules of Algebraic Integers''}", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "254--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-072-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", note = "See \cite{Bell:2009:MAI}.", abstract = "We fix a mistake in the proof of Theorem 1.6 in the paper in the title.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2012:CCS, author = "Yanping Chen and Yong Ding and Xinxia Wang", title = "Compactness of Commutators for Singular Integrals on {Morrey} Spaces", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "257--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-043-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we characterize the compactness of the commutator $[b,T]$ for the singular integral operator on the Morrey spaces $L^{p,\lambda}(\mathbb R^n)$. More precisely, we prove that if $b\in \operatorname{VMO}(\mathbb R^n)$, the $\operatorname {BMO} (\mathbb R^n)$-closure of $C_c^\infty(\mathbb R^n)$, then $[b,T]$ is a compact operator on the Morrey spaces $L^{p,\lambda}(\mathbb R^n)$ for $1\lt p\lt \infty$ and $0\lt \lambda\lt n$. Conversely, if $b\in \operatorname{BMO}(\mathbb R^n)$ and $[b,T]$ is a compact operator on the $L^{p,\,\lambda}(\mathbb R^n)$ for some $p\ (1\lt p\lt \infty)$, then $b\in \operatorname {VMO}(\mathbb R^n)$. Moreover, the boundedness of a rough singular integral operator $T$ and its commutator $[b,T]$ on $L^{p,\,\lambda}(\mathbb R^n)$ are also given. We obtain a sufficient condition for a subset in Morrey space to be a strongly pre-compact set, which has interest in its own right.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Dahmen:2012:LLM, author = "Sander R. Dahmen and Soroosh Yazdani", title = "Level Lowering Modulo Prime Powers and Twisted {Fermat} Equations", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "282--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-059-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We discuss a clean level lowering theorem modulo prime powers for weight $2$ cusp forms. Furthermore, we illustrate how this can be used to completely solve certain twisted Fermat equations $ax^n+by^n+cz^n=0$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hurlburt:2012:HCF, author = "Chris Hurlburt and Jeffrey Lin Thunder", title = "{Hermite}'s Constant for Function Fields", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "301--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-046-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We formulate an analog of Hermite's constant for function fields over a finite field and state a conjectural value for this analog. We prove our conjecture in many cases, and prove slightly weaker results in all other cases.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ingram:2012:CPP, author = "Patrick Ingram", title = "Cubic Polynomials with Periodic Cycles of a Specified Multiplier", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "318--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-093-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider cubic polynomials $f(z) = z^3 + a z + b$ defined over $\mathbb{C}(\lambda)$, with a marked point of period $N$ and multiplier $\lambda$. In the case $N = 1$, there are infinitely many such objects, and in the case $N \geq 3$, only finitely many (subject to a mild assumption). The case $N = 2$ has particularly rich structure, and we are able to describe all such cubic polynomials defined over the field $\bigcup_{n\geq 1}\mathbb{C}(\lambda^{1/n})$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{McKee:2012:SNP, author = "James McKee and Chris Smyth", title = "{Salem} Numbers and {Pisot} Numbers via Interlacing", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "345--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-051-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We present a general construction of Salem numbers via rational functions whose zeros and poles mostly lie on the unit circle and satisfy an interlacing condition. This extends and unifies earlier work. We then consider the ``obvious'' limit points of the set of Salem numbers produced by our theorems and show that these are all Pisot numbers, in support of a conjecture of Boyd. We then show that all Pisot numbers arise in this way. Combining this with a theorem of Boyd, we produce all Salem numbers via an interlacing construction.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Meyer:2012:ATS, author = "Ralf Meyer and Ryszard Nest", title = "{$C^*$}-Algebras over Topological Spaces: Filtrated {$K$}-Theory", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "368--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-061-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We define the filtrated K-theory of a $\mathrm{C}^*$-algebra over a finite topological space \(X\) and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over \(X\) in terms of filtrated K-theory. For finite spaces with a totally ordered lattice of open subsets, this spectral sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe two $\mathrm{C}^*$-algebras over a space \(X\) with four points that have isomorphic filtrated K-theory without being $\mathrm{KK}(X)$-equivalent. For this space \(X\), we enrich filtrated K-theory by another K-theory functor to a complete invariant up to $\mathrm{KK}(X)$-equivalence that satisfies a Universal Coefficient Theorem.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rainer:2012:LQM, author = "Armin Rainer", title = "Lifting Quasianalytic Mappings over Invariants", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "409--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-049-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $\rho \colon G \to \operatorname{GL}(V)$ be a rational finite dimensional complex representation of a reductive linear algebraic group $G$, and let $\sigma_1,\dots,\sigma_n$ be a system of generators of the algebra of invariant polynomials $\mathbb C[V]^G$. We study the problem of lifting mappings $f\colon \mathbb R^q \supseteq U \to \sigma(V) \subseteq \mathbb C^n$ over the mapping of invariants $\sigma=(\sigma_1,\dots,\sigma_n) \colon V \to \sigma(V)$. Note that $\sigma(V)$ can be identified with the categorical quotient $V /\!\!/ G$ and its points correspond bijectively to the closed orbits in $V$. We prove that if $f$ belongs to a quasianalytic subclass $\mathcal C \subseteq C^\infty$ satisfying some mild closedness properties that guarantee resolution of singularities in $\mathcal C$, e.g., the real analytic class, then $f$ admits a lift of the same class $\mathcal C$ after desingularization by local blow-ups and local power substitutions. As a consequence we show that $f$ itself allows for a lift that belongs to $\operatorname{SBV}_{\operatorname{loc}}$, i.e., special functions of bounded variation. If $\rho$ is a real representation of a compact Lie group, we obtain stronger versions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Shafikov:2012:HMB, author = "Rasul Shafikov and Kaushal Verma", title = "Holomorphic Mappings between Domains in {$\mathbb C^2$}", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "429--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-056-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "An extension theorem for holomorphic mappings between two domains in $\mathbb C^2$ is proved under purely local hypotheses.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sherman:2012:CIG, author = "David Sherman", title = "On Cardinal Invariants and Generators for {von Neumann} Algebras", journal = j-CAN-J-MATH, volume = "64", number = "2", pages = "455--??", month = apr, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-048-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Apr 9 15:20:54 MDT 2012", bibsource = "http://cms.math.ca/cjm/v64/; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We demonstrate how most common cardinal invariants associated with a von Neumann algebra $\mathcal M$ can be computed from the decomposability number, $\operatorname{dens}(\mathcal M)$, and the minimal cardinality of a generating set, $\operatorname{gen}(\mathcal M)$. Applications include the equivalence of the well-known generator problem, ``Is every separably-acting von Neumann algebra singly-generated?'', with the formally stronger questions, ``Is every countably-generated von Neumann algebra singly-generated?'' and ``Is the $\operatorname{gen}$ invariant monotone?'' Modulo the generator problem, we determine the range of the invariant $\bigl( \operatorname{gen}(\mathcal M), \operatorname{dens}(\mathcal M) \bigr)$, which is mostly governed by the inequality $\operatorname{dens}(\mathcal M) \leq \mathfrak C^{\operatorname{gen}(\mathcal M)}$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chamorro:2012:SFI, author = "Diego Chamorro", title = "Some Functional Inequalities on Polynomial Volume Growth {Lie} Groups", journal = j-CAN-J-MATH, volume = "64", number = "3", pages = "481--??", month = jun, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-050-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:29 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this article we study some Sobolev-type inequalities on polynomial volume growth Lie groups. We show in particular that improved Sobolev inequalities can be extended to this general framework without the use of the Littlewood--Paley decomposition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Li:2012:LFP, author = "Wen-Wei Li", title = "Le lemme fondamental pond{\'e}r{\'e} pour le groupe m{\'e}taplectique", journal = j-CAN-J-MATH, volume = "64", number = "3", pages = "497--??", month = jun, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-088-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:29 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Dans cet article, on {\'e}nonce une variante du lemme fondamental pond{\'e}r{\'e} d'Arthur pour le groupe m{\'e}taplectique de Weil, qui sera un ingr{\'e}dient indispensable de la stabilisation de la formule des traces. Pour un corps de caract{\'e}ristique r{\'e}siduelle suffisamment grande, on en donne une d{\'e}monstration {\`a} l'aide de la m{\'e}thode de descente, qui est conditionnelle: on admet le lemme fondamental pond{\'e}r{\'e} non standard sur les alg{\`e}bres de Lie. Vu les travaux de Chaudouard et Laumon, on s'attend {\`a} ce que cette condition soit ult{\'e}rieurement v{\'e}rifi{\'e}e.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Li:2012:SIL, author = "Zhiqiang Li", title = "On the Simple Inductive Limits of Splitting Interval Algebras with Dimension Drops", journal = j-CAN-J-MATH, volume = "64", number = "3", pages = "544--??", month = jun, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-060-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:29 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A K-theoretic classification is given of the simple inductive limits of finite direct sums of the type I $C^*$-algebras known as splitting interval algebras with dimension drops. (These are the subhomogeneous $C^*$-algebras, each having spectrum a finite union of points and an open interval, and torsion $\textrm{K}_1$-group.)", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nawata:2012:FGS, author = "Norio Nawata", title = "Fundamental Group of Simple {$C^*$}-algebras with Unique Trace {III}", journal = j-CAN-J-MATH, volume = "64", number = "3", pages = "573--??", month = jun, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-052-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:29 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We introduce the fundamental group ${\mathcal F}(A)$ of a simple $\sigma$-unital $C^*$-algebra $A$ with unique (up to scalar multiple) densely defined lower semicontinuous trace. This is a generalization of ``Fundamental Group of Simple $C^*$-algebras with Unique Trace I and II'' by Nawata and Watatani. Our definition in this paper makes sense for stably projectionless $C^*$-algebras. We show that there exist separable stably projectionless $C^*$-algebras such that their fundamental groups are equal to $\mathbb{R}_+^\times$ by using the classification theorem of Razak and Tsang. This is a contrast to the unital case in Nawata and Watatani. This study is motivated by the work of Kishimoto and Kumjian.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nekovar:2012:LRA, author = "Jan Nekov{\'a}r", title = "Level Raising and Anticyclotomic {Selmer} Groups for {Hilbert} Modular Forms of Weight Two", journal = j-CAN-J-MATH, volume = "64", number = "3", pages = "588--??", month = jun, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-077-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:29 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this article we refine the method of Bertolini and Darmon and prove several finiteness results for anticyclotomic Selmer groups of Hilbert modular forms of parallel weight two.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Pantano:2012:GOR, author = "Alessandra Pantano and Annegret Paul and Susana A. Salamanca-Riba", title = "The Genuine Omega-regular Unitary Dual of the Metaplectic Group", journal = j-CAN-J-MATH, volume = "64", number = "3", pages = "669--??", month = jun, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-075-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:29 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We classify all genuine unitary representations of the metaplectic group whose infinitesimal character is real and at least as regular as that of the oscillator representation. In a previous paper we exhibited a certain family of representations satisfying these conditions, obtained by cohomological induction from the tensor product of a one-dimensional representation and an oscillator representation. Our main theorem asserts that this family exhausts the genuine omega-regular unitary dual of the metaplectic group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Thomsen:2012:PIC, author = "Klaus Thomsen", title = "Pure Infiniteness of the Crossed Product of an {AH}-Algebra by an Endomorphism", journal = j-CAN-J-MATH, volume = "64", number = "3", pages = "705--??", month = jun, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-081-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:29 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "It is shown that simplicity of the crossed product of a unital AH-algebra with slow dimension growth by an endomorphism implies that the algebra is also purely infinite, provided only that the endomorphism leaves no trace state invariant and takes the unit to a full projection.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Achab:2012:ABK, author = "Dehbia Achab and Jacques Faraut", title = "Analysis of the {Brylinski--Kostant} Model for Spherical Minimal Representations", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "721--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-011-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We revisit with another view point the construction by R. Brylinski and B. Kostant of minimal representations of simple Lie groups. We start from a pair $(V,Q)$, where $V$ is a complex vector space and $Q$ a homogeneous polynomial of degree 4 on $V$. The manifold $\Xi $ is an orbit of a covering of ${\rm Conf}(V,Q)$, the conformal group of the pair $(V,Q)$, in a finite dimensional representation space. By a generalized Kantor-Koecher-Tits construction we obtain a complex simple Lie algebra $\mathfrak g$, and furthermore a real form ${\mathfrak g}_{\mathbb R}$. The connected and simply connected Lie group $G_{\mathbb R}$ with ${\rm Lie}(G_{\mathbb R})={\mathfrak g}_{\mathbb R}$ acts unitarily on a Hilbert space of holomorphic functions defined on the manifold $\Xi $.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Brown:2012:HCP, author = "Lawrence G. Brown and Hyun Ho Lee", title = "Homotopy Classification of Projections in the {Corona} Algebra of a Non-simple {$C^*$}-algebra", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "755--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-092-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study projections in the corona algebra of $C(X)\otimes K$, where K is the $C^*$-algebra of compact operators on a separable infinite dimensional Hilbert space and $X=[0,1],[0,\infty),(-\infty,\infty)$, or $[0,1]/\{ 0,1 \}$. Using BDF's essential codimension, we determine conditions for a projection in the corona algebra to be liftable to a projection in the multiplier algebra. We also determine the conditions for two projections to be equal in $K_0$, Murray-von Neumann equivalent, unitarily equivalent, or homotopic. In light of these characterizations, we construct examples showing that the equivalence notions above are all distinct.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Calvaruso:2012:RSG, author = "Giovanni Calvaruso and Anna Fino", title = "{Ricci} Solitons and Geometry of Four-dimensional Non-reductive Homogeneous Spaces", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "778--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-091-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the geometry of non-reductive $4$-dimensional homogeneous spaces. In particular, after describing their Levi-Civita connection and curvature properties, we classify homogeneous Ricci solitons on these spaces, proving the existence of shrinking, expanding and steady examples. For all the non-trivial examples we find, the Ricci operator is diagonalizable.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chapon:2012:QRW, author = "Fran{\c{c}}ois Chapon and Manon Defosseux", title = "Quantum Random Walks and Minors of {Hermitian} {Brownian} Motion", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "805--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-064-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Considering quantum random walks, we construct discrete-time approximations of the eigenvalues processes of minors of Hermitian Brownian motion. It has been recently proved by Adler, Nordenstam, and van Moerbeke that the process of eigenvalues of two consecutive minors of a Hermitian Brownian motion is a Markov process; whereas, if one considers more than two consecutive minors, the Markov property fails. We show that there are analog results in the noncommutative counterpart and establish the Markov property of eigenvalues of some particular submatrices of Hermitian Brownian motion.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Haglund:2012:CSC, author = "J. Haglund and J. Morse and M. Zabrocki", title = "A Compositional Shuffle Conjecture Specifying Touch Points of the {Dyck} Path", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "822--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-078-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We introduce a $q,t$-enumeration of Dyck paths that are forced to touch the main diagonal at specific points and forbidden to touch elsewhere and conjecture that it describes the action of the Macdonald theory $\nabla$ operator applied to a Hall--Littlewood polynomial. Our conjecture refines several earlier conjectures concerning the space of diagonal harmonics including the ``shuffle conjecture{\SGMLquot} (Duke J. Math. $\mathbf {126}$ ($2005$), 195-232) for $\nabla e_n[X]$. We bring to light that certain generalized Hall--Littlewood polynomials indexed by compositions are the building blocks for the algebraic combinatorial theory of $q,t$-Catalan sequences, and we prove a number of identities involving these functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Helm:2012:MFT, author = "David Helm and Eric Katz", title = "Monodromy Filtrations and the Topology of Tropical Varieties", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "845--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-067-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the topology of tropical varieties that arise from a certain natural class of varieties. We use the theory of tropical degenerations to construct a natural, ``multiplicity-free'' parameterization of $\operatorname{Trop}(X)$ by a topological space $\Gamma_X$ and give a geometric interpretation of the cohomology of $\Gamma_X$ in terms of the action of a monodromy operator on the cohomology of $X$. This gives bounds on the Betti numbers of $\Gamma_X$ in terms of the Betti numbers of $X$ which constrain the topology of $\operatorname{Trop}(X)$. We also obtain a description of the top power of the monodromy operator acting on middle cohomology of $X$ in terms of the volume pairing on $\Gamma_X$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hu:2012:BSD, author = "Ze-Chun Hu and Wei Sun", title = "Balayage of Semi-{Dirichlet} Forms", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "869--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-055-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we study the balayage of semi-Dirichlet forms. We present new results on balayaged functions and balayaged measures of semi-Dirichlet forms. Some of the results are new even in the Dirichlet forms setting.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hytonen:2012:BCZ, author = "Tuomas Hyt{\"o}nen and Suile Liu and Dachun Yang and Dongong Yang", title = "Boundedness of {Calder{\'o}n--Zygmund} Operators on Non-homogeneous Metric Measure Spaces", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "892--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-065-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $({\mathcal X}, d, \mu)$ be a separable metric measure space satisfying the known upper doubling condition, the geometrical doubling condition, and the non-atomic condition that $\mu(\{x\})=0$ for all $x\in{\mathcal X}$. In this paper, we show that the boundedness of a Calder{\'o}n-Zygmund operator $T$ on $L^2(\mu)$ is equivalent to that of $T$ on $L^p(\mu)$ for some $p\in (1, \infty)$, and that of $T$ from $L^1(\mu)$ to $L^{1,\,\infty}(\mu).$ As an application, we prove that if $T$ is a Calder{\'o}n-Zygmund operator bounded on $L^2(\mu)$, then its maximal operator is bounded on $L^p(\mu)$ for all $p\in (1, \infty)$ and from the space of all complex-valued Borel measures on ${\mathcal X}$ to $L^{1,\,\infty}(\mu)$. All these results generalize the corresponding results of Nazarov et al. on metric spaces with measures satisfying the so-called polynomial growth condition.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{McCann:2012:ROT, author = "Robert J. McCann and Brendan Pass and Micah Warren", title = "Rectifiability of Optimal Transportation Plans", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "924--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-080-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The regularity of solutions to optimal transportation problems has become a hot topic in current research. It is well known by now that the optimal measure may not be concentrated on the graph of a continuous mapping unless both the transportation cost and the masses transported satisfy very restrictive hypotheses (including sign conditions on the mixed fourth-order derivatives of the cost function). The purpose of this note is to show that in spite of this, the optimal measure is supported on a Lipschitz manifold, provided only that the cost is $C^{2}$ with non-singular mixed second derivative. We use this result to provide a simple proof that solutions to Monge's optimal transportation problem satisfy a change of variables equation almost everywhere.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{McIntosh:2012:HKF, author = "Richard J. McIntosh", title = "The {$H$} and {$K$} Families of Mock Theta Functions", journal = j-CAN-J-MATH, volume = "64", number = "4", pages = "935--??", month = aug, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-066-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Nov 5 09:42:30 MST 2012", bibsource = "http://cms.math.ca/cjm/v64/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In his last letter to Hardy, Ramanujan defined 17 functions $F(q)$, $|q|\lt 1$, which he called mock $\theta$-functions. He observed that as $q$ radially approaches any root of unity $\zeta$ at which $F(q)$ has an exponential singularity, there is a $\theta$-function $T_\zeta(q)$ with $F(q)-T_\zeta(q)=O(1)$. Since then, other functions have been found that possess this property. These functions are related to a function $H(x,q)$, where $x$ is usually $q^r$ or $e^{2\pi i r}$ for some rational number $r$. For this reason we refer to $H$ as a ``universal'' mock $\theta$-function. Modular transformations of $H$ give rise to the functions $K$, $K_1$, $K_2$. The functions $K$ and $K_1$ appear in Ramanujan's lost notebook. We prove various linear relations between these functions using Appell-Lerch sums (also called generalized Lambert series). Some relations (mock theta ``conjectures'') involving mock $\theta$-functions of even order and $H$ are listed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Borwein:2012:DSU, author = "Jonathan M. Borwein and Armin Straub and James Wan and Wadim Zudilin", title = "Densities of Short Uniform Random Walks", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "961--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-079-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the densities of uniform random walks in the plane. A special focus is on the case of short walks with three or four steps and less completely those with five steps. As one of the main results, we obtain a hypergeometric representation of the density for four steps, which complements the classical elliptic representation in the case of three steps. It appears unrealistic to expect similar results for more than five steps. New results are also presented concerning the moments of uniform random walks and, in particular, their derivatives. Relations with Mahler measures are discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Damianou:2012:PBP, author = "Pantelis A. Damianou and Fani Petalidou", title = "{Poisson} Brackets with Prescribed {Casimirs}", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "991--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-082-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider the problem of constructing Poisson brackets on smooth manifolds {$M$} with prescribed Casimir functions. If {$M$} is of even dimension, we achieve our construction by considering a suitable almost symplectic structure on {$M$}, while, in the case where {$M$} is of odd dimension, our objective is achieved by using a convenient almost cosymplectic structure. Several examples and applications are presented.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fiorilli:2012:TBF, author = "Daniel Fiorilli", title = "On a Theorem of {Bombieri}, {Friedlander}, and {Iwaniec}", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "1019--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-005-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this article, we show to which extent one can improve a theorem of Bombieri, Friedlander and Iwaniec by using Hooley's variant of the divisor switching technique. We also give an application of the theorem in question, which is a Bombieri-Vinogradov type theorem for the Tichmarsh divisor problem in arithmetic progressions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Koh:2012:HAR, author = "Doowon Koh and Chun-Yen Shen", title = "Harmonic Analysis Related to Homogeneous Varieties in Three Dimensional Vector Spaces over Finite Fields", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "1036--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-089-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we study the extension problem, the averaging problem, and the generalized Erd{\SGMLquot}os-Falconer distance problem associated with arbitrary homogeneous varieties in three dimensional vector spaces over finite fields. In the case when the varieties do not contain any plane passing through the origin, we obtain the best possible results on the aforementioned three problems. In particular, our result on the extension problem modestly generalizes the result by Mockenhaupt and Tao who studied the particular conical extension problem. In addition, investigating the Fourier decay on homogeneous varieties enables us to give complete mapping properties of averaging operators. Moreover, we improve the size condition on a set such that the cardinality of its distance set is nontrivial.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Plakhov:2012:ORC, author = "Alexander Plakhov", title = "Optimal Roughening of Convex Bodies", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "1058--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-070-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A body moves in a rarefied medium composed of point particles at rest. The particles make elastic reflections when colliding with the body surface, and do not interact with each other. We consider a generalization of Newton's minimal resistance problem: given two bounded convex bodies {$ C_1 $} and {$ C_2 $} such that {$ C_1 \subset C_2 \subset \mathbb {R}^3 $} and {$ \partial C_1 \cap \partial C_2 = \emptyset $}, minimize the resistance in the class of connected bodies {$B$} such that {$ C_1 \subset B \subset C_2 $}. We prove that the infimum of resistance is zero; that is, there exist {\SGMLquot}almost perfectly streamlined{\SGMLquot} bodies.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Raja:2012:SDE, author = "Chandiraraj Robinson Edward Raja", title = "A Stochastic Difference Equation with Stationary Noise on Groups", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "1075--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-094-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider the stochastic difference equation \eta _k = \xi _k \phi (\eta _{k-1}), \quad k \in \mathbb Z on a locally compact group {$G$} where $ \phi $ is an automorphism of {$G$}, $ \xi_k $ are given {$G$}-valued random variables and $ \eta_k $ are unknown {$G$}-valued random variables. This equation was considered by Tsirelson and Yor on one-dimensional torus. We consider the case when $ \xi_k $ have a common law $ \mu $ and prove that if {$G$} is a distal group and $ \phi $ is a distal automorphism of {$G$} and if the equation has a solution, then extremal solutions of the equation are in one-one correspondence with points on the coset space {$ K \backslash G $} for some compact subgroup {$K$} of {$G$} such that $ \mu $ is supported on {$ K z = z \phi (K) $} for any $z$ in the support of $ \mu $. We also provide a necessary and sufficient condition for the existence of solutions to the equation.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rosso:2012:CMR, author = "Daniele Rosso", title = "Classic and Mirabolic {Robinson--Schensted--Knuth} Correspondence for Partial Flags", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "1090--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-071-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we first generalize to the case of partial flags a result proved both by Spaltenstein and by Steinberg that relates the relative position of two complete flags and the irreducible components of the flag variety in which they lie, using the Robinson-Schensted-Knuth correspondence. Then we use this result to generalize the mirabolic Robinson-Schensted-Knuth correspondence defined by Travkin, to the case of two partial flags and a line.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Seveso:2012:AFR, author = "Marco Adamo Seveso", title = "$p$-adic {$L$}-functions and the Rationality of {Darmon} Cycles", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "1122--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-076-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Darmon cycles are a higher weight analogue of Stark--Heegner points. They yield local cohomology classes in the Deligne representation associated with a cuspidal form on {$ \Gamma_0 (N) $} of even weight $ k_0 \geq 2 $. They are conjectured to be the restriction of global cohomology classes in the Bloch--Kato Selmer group defined over narrow ring class fields attached to a real quadratic field. We show that suitable linear combinations of them obtained by genus characters satisfy these conjectures. We also prove $p$-adic Gross--Zagier type formulas, relating the derivatives of $p$-adic {$L$}-functions of the weight variable attached to imaginary (resp. real) quadratic fields to Heegner cycles (resp. Darmon cycles). Finally we express the second derivative of the Mazur--Kitagawa $p$-adic {$L$}-function of the weight variable in terms of a global cycle defined over a quadratic extension of {$ \mathbb {Q} $}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Tall:2012:PMM, author = "Franklin D. Tall", title = "{$ {\rm PFA}(S)[S] $}: More Mutually Consistent Topological Consequences of {$ P F A $} and {$ V = L $}", journal = j-CAN-J-MATH, volume = "64", number = "5", pages = "1182--??", month = oct, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-010-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:29 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Extending the work of Larson and Todorcevic, we show there is a model of set theory in which normal spaces are collectionwise Hausdorff if they are either first countable or locally compact, and yet there are no first countable {$L$}-spaces or compact {$S$}-spaces. The model is one of the form {PFA$ (S)[S] $}, where {$S$} is a coherent Souslin tree.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Aistleitner:2012:CLT, author = "Christoph Aistleitner and Christian Elsholtz", title = "The {Central Limit Theorem for} Subsequences in Probabilistic Number Theory", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1201--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-074-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ (n_k)_{k \geq 1} $ be an increasing sequence of positive integers, and let $ f(x) $ be a real function satisfying \begin{equation} \tag{1} f(x+1)=f(x), \qquad \int_0^1 f(x) ~dx=0,\qquad \operatorname{Var_{[0,1]}} f \lt \infty. \end{equation} If $ \lim_{k \to \infty } \frac {n_{k + 1}n_k} = \infty $ the distribution of \begin{equation} \tag{2} \frac{\sum_{k=1}^N f(n_k x)}{\sqrt{N}} \end{equation} converges to a Gaussian distribution. In the case 1 \lt \liminf_{k \to \infty} \frac{n_{k+1}}{n_k}, \qquad \limsup_{k \to \infty} \frac{n_{k+1}}{n_k} \lt \infty there is a complex interplay between the analytic properties of the function $f$, the number-theoretic properties of $ (n_k)_{k \geq 1} $, and the limit distribution of (2). In this paper we prove that any sequence $ (n_k)_{k \geq 1} $ satisfying $ \limsup_{k \to \infty } \frac {n_{k + 1}n_k} = 1 $ contains a nontrivial subsequence $ (m_k)_{k \geq 1} $ such that for any function satisfying (1) the distribution of \frac{\sum_{k=1}^N f(m_k x)}{\sqrt{N}} converges to a Gaussian distribution. This result is best possible: for any $ \varepsilon \gt 0 $ there exists a sequence $ (n_k)_{k \geq 1} $ satisfying $ \limsup_{k \to \infty } \frac {n_{k + 1}n_k} \leq 1 + \varepsilon $ such that for every nontrivial subsequence $ (m_k)_{k \geq 1} $ of $ (n_k)_{k \geq 1} $ the distribution of (2) does not converge to a Gaussian distribution for some $f$. Our result can be viewed as a Ramsey type result: a sufficiently dense increasing integer sequence contains a subsequence having a certain requested number-theoretic property.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bobinski:2012:NMO, author = "Grzegorz Bobi{\'n}ski", title = "Normality of Maximal Orbit Closures for {Euclidean} Quivers", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1222--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-012-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let {$ \Delta $} be an Euclidean quiver. We prove that the closures of the maximal orbits in the varieties of representations of {$ \Delta $} are normal and Cohen--Macaulay (even complete intersections). Moreover, we give a generalization of this result for the tame concealed-canonical algebras.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gartner:2012:DPQ, author = "J{\'e}r{\^o}me G{\"a}rtner", title = "{Darmon}'s Points and Quaternionic {Shimura} Varieties", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1248--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-086-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we generalize a conjecture due to Darmon and Logan in an adelic setting. We study the relation between our construction and Kudla's works on cycles on orthogonal Shimura varieties. This relation allows us to conjecture a Gross-Kohnen-Zagier theorem for Darmon's points.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Gomes:2012:SWC, author = "Diogo Gomes and Ant{\'o}nio Serra", title = "Systems of Weakly Coupled {Hamilton--Jacobi} Equations with Implicit Obstacles", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1289--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-085-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we study systems of weakly coupled Hamilton--Jacobi equations with implicit obstacles that arise in optimal switching problems. Inspired by methods from the theory of viscosity solutions and weak KAM theory, we extend the notion of Aubry set for these systems. This enables us to prove a new result on existence and uniqueness of solutions for the Dirichlet problem, answering a question of F. Camilli, P. Loreti and N. Yamada.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Harutyunyan:2012:UCD, author = "Ararat Harutyunyan and P. Mark Kayll and Bojan Mohar and Liam Rafferty", title = "Uniquely {$D$}-colourable Digraphs with Large Girth", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1310--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-084-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let {$C$} and {$D$} be digraphs. A mapping {$ f \colon V(D) \to V(C) $} is a {$C$}-colouring if for every arc $ u v $ of {$D$}, either $ f(u)f(v) $ is an arc of {$C$} or $ f(u) = f(v) $, and the preimage of every vertex of {$C$} induces an acyclic subdigraph in {$D$}. We say that {$D$} is {$C$}-colourable if it admits a {$C$}-colouring and that {$D$} is uniquely {$C$}-colourable if it is surjectively {$C$}-colourable and any two {$C$}-colourings of {$D$} differ by an automorphism of {$C$}. We prove that if a digraph {$D$} is not {$C$}-colourable, then there exist digraphs of arbitrarily large girth that are {$D$}-colourable but not {$C$}-colourable. Moreover, for every digraph {$D$} that is uniquely {$D$}-colourable, there exists a uniquely {$D$}-colourable digraph of arbitrarily large girth. In particular, this implies that for every rational number $ r \geq 1 $, there are uniquely circularly $r$-colourable digraphs with arbitrarily large girth.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Izuchi:2012:COI, author = "Kei Ji Izuchi and Quang Dieu Nguyen and Sh{\^u}ichi Ohno", title = "Composition Operators Induced by Analytic Maps to the Polydisk", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1329--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-073-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study properties of composition operators induced by symbols acting from the unit disk to the polydisk. This result will be involved in the investigation of weighted composition operators on the Hardy space on the unit disk and moreover be concerned with composition operators acting from the Bergman space to the Hardy space on the unit disk.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Killough:2012:BMH, author = "D. B. Killough and I. F. Putnam", title = "{Bowen} Measure From Heteroclinic Points", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1341--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-083-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to another: heteroclinic points. The spirit of the construction is similar to Bowen's construction from periodic points, though the techniques are very different. We also prove results about the growth rate of certain sets of heteroclinic points, and about the stable and unstable components of the Bowen measure. The approach we take is to prove results through direct computation for the case of a Shift of Finite type, and then use resolving factor maps to extend the results to more general Smale spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Nozaki:2012:NCF, author = "Hiroshi Nozaki and Masanori Sawa", title = "Note on Cubature Formulae and Designs Obtained from Group Orbits", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1359--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-069-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In 1960, Sobolev proved that for a finite reflection group {$G$}, a {$G$}-invariant cubature formula is of degree $t$ if and only if it is exact for all {$G$}-invariant polynomials of degree at most $t$. In this paper, we find some observations on invariant cubature formulas and Euclidean designs in connection with the Sobolev theorem. First, we give an alternative proof of theorems by Xu (1998) on necessary and sufficient conditions for the existence of cubature formulas with some strong symmetry. The new proof is shorter and simpler compared to the original one by Xu, and moreover gives a general interpretation of the analytically-written conditions of Xu's theorems. Second, we extend a theorem by Neumaier and Seidel (1988) on Euclidean designs to invariant Euclidean designs, and thereby classify tight Euclidean designs obtained from unions of the orbits of the corner vectors. This result generalizes a theorem of Bajnok (2007) which classifies tight Euclidean designs invariant under the Weyl group of type {$B$} to other finite reflection groups.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Raghavan:2012:WTF, author = "Dilip Raghavan and Juris Steprans", title = "On Weakly Tight Families", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1378--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-017-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Using ideas from Shelah's recent proof that a completely separable maximal almost disjoint family exists when $ \mathfrak {c} \lt {\aleph }_{\omega } $, we construct a weakly tight family under the hypothesis $ \mathfrak {s} \leq \mathfrak {b} \lt {\aleph }_{\omega } $. The case when $ \mathfrak {s} \lt \mathfrak {b} $ is handled in {$ \mathrm {ZFC} $} and does not require $ \mathfrak {b} \lt {\aleph }_{\omega } $, while an additional PCF type hypothesis, which holds when $ \mathfrak {b} \lt {\aleph }_{\omega } $ is used to treat the case $ \mathfrak {s} = \mathfrak {b} $. The notion of a weakly tight family is a natural weakening of the well studied notion of a Cohen indestructible maximal almost disjoint family. It was introduced by Hrus{\'a}k and Garc{\'\i}a Ferreira, who applied it to the Kat{\'e}tov order on almost disjoint families.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rodney:2012:EWS, author = "Scott Rodney", title = "Existence of Weak Solutions of Linear Subelliptic {Dirichlet} Problems With Rough Coefficients", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1395--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-029-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This article gives an existence theory for weak solutions of second order non-elliptic linear Dirichlet problems of the form \begin{align*} \nabla'P(x)\nabla u +{\bf HR}u+{\bf S'G}u +Fu {\&}= f+{\bf T'g} \text{ in }\Theta \\ u{\&}=\varphi\text{ on }\partial \Theta. \end{align*} The principal part {$ \xi 'P(x) \xi $} of the above equation is assumed to be comparable to a quadratic form {$ {\mathcal Q}(x, \xi) = \xi 'Q(x) \xi $} that may vanish for non-zero {$ \xi \in \mathbb {R}^n $}. This is achieved using techniques of functional analysis applied to the degenerate Sobolev spaces {$ Q H^1 (\Theta) = W^{1, 2}(\Theta, Q) $} and {$ Q H^1_0 (\Theta) = W^{1, 2}_0 (\Theta, Q) $} as defined in previous works. Sawyer and Wheeden give a regularity theory for a subset of the class of equations dealt with here.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Selmi:2012:GWP, author = "Ridha Selmi", title = "Global Well-Posedness and Convergence Results for {3D}-Regularized {Boussinesq} System", journal = j-CAN-J-MATH, volume = "64", number = "6", pages = "1415--??", month = dec, year = "2012", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-013-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:31 MDT 2013", bibsource = "http://cms.math.ca/cjm/v64/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Analytical study to the regularization of the Boussinesq system is performed in frequency space using Fourier theory. Existence and uniqueness of weak solution with minimum regularity requirement are proved. Convergence results of the unique weak solution of the regularized Boussinesq system to a weak Leray-Hopf solution of the Boussinesq system are established as the regularizing parameter $ \alpha $ vanishes. The proofs are done in the frequency space and use energy methods, Arsel{\`a}-Ascoli compactness theorem and a Friedrichs like approximation scheme.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Barto:2013:FRA, author = "Libor Barto", title = "Finitely Related Algebras in Congruence Distributive Varieties Have Near Unanimity Terms", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "3--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-087-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We show that every finite, finitely related algebra in a congruence distributive variety has a near unanimity term operation. As a consequence we solve the near unanimity problem for relational structures: it is decidable whether a given finite set of relations on a finite set admits a compatible near unanimity operation. This consequence also implies that it is decidable whether a given finite constraint language defines a constraint satisfaction problem of bounded strict width.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Blomer:2013:NVF, author = "Valentin Blomer and Farrell Brumley", title = "Non-vanishing of {$L$}-functions, the {Ramanujan} Conjecture, and Families of {Hecke} Characters", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "22--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-068-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove a non-vanishing result for families of {$ \operatorname {GL}_n \times \operatorname {GL}_n $} Rankin-Selberg {$L$}-functions in the critical strip, as one factor runs over twists by Hecke characters. As an application, we simplify the proof, due to Luo, Rudnick, and Sarnak, of the best known bounds towards the Generalized Ramanujan Conjecture at the infinite places for cusp forms on {$ \operatorname {GL}_n $}. A key ingredient is the regularization of the units in residue classes by the use of an Arakelov ray class group.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Christensen:2013:ANC, author = "Erik Christensen and Allan M. Sinclair and Roger R. Smith and Stuart White", title = "{$ C^* $}-algebras Nearly Contained in Type {$ \mathrm {I} $} Algebras", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "52--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-001-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we consider near inclusions {$ A \subseteq_\gamma B $} of C$^*$-algebras. We show that if {$B$} is a separable type {$ \mathrm {I} $} C$^*$-algebra and {$A$} satisfies Kadison's similarity problem, then {$A$} is also type {$ \mathrm {I} $} and use this to obtain an embedding of {$A$} into {$B$}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Deng:2013:FCH, author = "Shaoqiang Deng and Zhiguang Hu", title = "On Flag Curvature of Homogeneous {Randers} Spaces", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "66--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-004-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we give an explicit formula for the flag curvature of homogeneous Randers spaces of Douglas type and apply this formula to obtain some interesting results. We first deduce an explicit formula for the flag curvature of an arbitrary left invariant Randers metric on a two-step nilpotent Lie group. Then we obtain a classification of negatively curved homogeneous Randers spaces of Douglas type. This results, in particular, in many examples of homogeneous non-Riemannian Finsler spaces with negative flag curvature. Finally, we prove a rigidity result that a homogeneous Randers space of Berwald type whose flag curvature is everywhere nonzero must be Riemannian.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Felix:2013:RHG, author = "Yves F{\'e}lix and Steve Halperin and Jean-Claude Thomas", title = "The Ranks of the Homotopy Groups of a Finite Dimensional Complex", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "82--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-050-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let {$X$} be an $n$-dimensional, finite, simply connected CW complex and set {$ \alpha_X = \limsup_i \frac {\log \mbox { rank} \, \pi_i(X)}{i} $}. When {$ 0 \lt \alpha_X \lt \infty $}, we give upper and lower bound for {$ \sum_{i = k + 2}^{k + n} \textrm {rank} \, \pi_i(X) $} for $k$ sufficiently large. We show also for any $r$ that {$ \alpha_X $} can be estimated from the integers {rk$ \, \pi_i(X) $}, $ i \leq n r $ with an error bound depending explicitly on $r$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Francois:2013:UFR, author = "Georges Fran{\c{c}}ois and Simon Hampe", title = "Universal Families of Rational Tropical Curves", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "120--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-097-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We introduce the notion of families of $n$-marked smooth rational tropical curves over smooth tropical varieties and establish a one-to-one correspondence between (equivalence classes of) these families and morphisms from smooth tropical varieties into the moduli space of $n$-marked abstract rational tropical curves {$ \mathcal {M}_n $}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kellendonk:2013:EDD, author = "Johannes Kellendonk and Daniel Lenz", title = "Equicontinuous {Delone} Dynamical Systems", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "149--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-090-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with finite local complexity, the only equicontinuous systems are then shown to be the crystallographic ones. On the other hand, within the class without finite local complexity, we exhibit examples of equicontinuous minimal Delone dynamical systems that are not crystallographic. Our results solve the problem posed by Lagarias as to whether a Delone set whose Dirac comb is strongly almost periodic must be crystallographic.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lyall:2013:OPR, author = "Neil Lyall and {\'A}kos Magyar", title = "Optimal Polynomial Recurrence", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "171--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-003-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let {$ P \in \mathbb Z[n] $} with {$ P(0) = 0 $} and $ \varepsilon \gt 0 $. We show, using Fourier analytic techniques, that if {$ N \geq \exp \exp (C \varepsilon^{-1} \log \varepsilon^{-1}) $} and {$ A \subseteq \{ 1, \dots, N \} $}, then there must exist {$ n \in \mathbb N $} such that \[\frac{|A\cap (A+P(n))|}{N}\gt \left(\frac{|A|}{N}\right)^2-\varepsilon.\] In addition to this we also show, using the same Fourier analytic methods, that if {$ A \subseteq \mathbb N $}, then the set of $ \varepsilon $-optimal return times \[R(A,P,\varepsilon)=\left\{n\in \mathbb N \,:\,\delta(A\cap(A+P(n)))\gt \delta(A)^2-\varepsilon\right\}\] is syndetic for every $ \varepsilon \gt 0 $. Moreover, we show that {$ R(A, P, \varepsilon) $} is dense in every sufficiently long interval, in particular we show that there exists an {$ L = L(\varepsilon, P, A) $} such that \[\left|R(A,P,\varepsilon)\cap I\right| \geq c(\varepsilon,P)|I|\] for all intervals {$I$} of natural numbers with {$ |I| \geq L $} and {$ c(\varepsilon, P) = \exp \exp ( - C \, \varepsilon^{-1} \log \varepsilon^{-1}) $}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Penegini:2013:SAM, author = "Matteo Penegini and Francesco Polizzi", title = "Surfaces with $ p_g = q = 2 $, {$ K^2 = 6 $}, and {Albanese} Map of Degree $2$", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "195--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-007-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We classify minimal surfaces of general type with $ p_g = q = 2 $ and {$ K^2 = 6 $} whose Albanese map is a generically finite double cover. We show that the corresponding moduli space is the disjoint union of three generically smooth irreducible components {$ \mathcal {M}_{Ia} $}, {$ \mathcal {M}_{Ib} $}, {$ \mathcal {M}_{II} $} of dimension $4$, $4$, $3$, respectively.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sauer:2013:DSU, author = "N. W. Sauer", title = "Distance Sets of {Urysohn} Metric Spaces", journal = j-CAN-J-MATH, volume = "65", number = "1", pages = "222--??", month = feb, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-022-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:33 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A metric space {$ \mathrm {M} = (M; \operatorname {d}) $} is {\em homogeneous} if for every isometry $f$ of a finite subspace of {$ \mathrm {M} $} to a subspace of {$ \mathrm {M} $} there exists an isometry of {$ \mathrm {M} $} onto {$ \mathrm {M} $} extending $f$. The space {$ \mathrm {M} $} is {\em universal} if it isometrically embeds every finite metric space {$ \mathrm {F} $} with {$ \operatorname {dist}(\mathrm {F}) \subseteq \operatorname {dist}(\mathrm {M}) $}. (With {$ \operatorname {dist}(\mathrm {M}) $} being the set of distances between points in {$ \mathrm {M} $}.) A metric space {$ \boldsymbol {U} $} is an {\em Urysohn} metric space if it is homogeneous, universal, separable and complete. (It is not difficult to deduce that an Urysohn metric space {$ \boldsymbol {U} $} isometrically embeds every separable metric space {$ \mathrm {M} $} with {$ \operatorname {dist}(\mathrm {M}) \subseteq \operatorname {dist}(\boldsymbol {U}) $}.) The main results are: (1) A characterization of the sets {$ \operatorname {dist}(\boldsymbol {U}) $} for Urysohn metric spaces {$ \boldsymbol {U} $}. (2) If {$R$} is the distance set of an Urysohn metric space and {$ \mathrm {M} $} and {$ \mathrm {N} $} are two metric spaces, of any cardinality with distances in {$R$}, then they amalgamate disjointly to a metric space with distances in {$R$}. (3) The completion of every homogeneous, universal, separable metric space {$ \mathrm {M} $} is homogeneous.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Aguiar:2013:LTH, author = "Marcelo Aguiar and Aaron Lauve", title = "{Lagrange}'s Theorem for {Hopf} Monoids in Species", journal = j-CAN-J-MATH, volume = "65", number = "2", pages = "241--??", month = apr, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-098-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:35 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Following Radford's proof of Lagrange's theorem for pointed Hopf algebras, we prove Lagrange's theorem for Hopf monoids in the category of connected species. As a corollary, we obtain necessary conditions for a given subspecies $ \mathbf k $ of a Hopf monoid $ \mathbf h $ to be a Hopf submonoid: the quotient of any one of the generating series of $ \mathbf h $ by the corresponding generating series of $ \mathbf k $ must have nonnegative coefficients. Other corollaries include a necessary condition for a sequence of nonnegative integers to be the dimension sequence of a Hopf monoid in the form of certain polynomial inequalities, and of a set-theoretic Hopf monoid in the form of certain linear inequalities. The latter express that the binomial transform of the sequence must be nonnegative.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Berard:2013:ACH, author = "Vincent B{\'e}rard", title = "Les applications conforme-harmoniques. ({French}) [Conformal-harmonic applications]", journal = j-CAN-J-MATH, volume = "65", number = "2", pages = "266--??", month = apr, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-034-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:35 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Sur une surface de Riemann, l'{\'e}nergie d'une application {\`a} valeurs dans une vari{\'e}t{\'e} riemannienne est une fonctionnelle invariante conforme, ses points critiques sont les applications harmoniques. Nous proposons ici un analogue en dimension sup{\'e}rieure, en construisant une fonctionnelle invariante conforme pour les applications entre deux vari{\'e}t{\'e}s riemanniennes, dont la vari{\'e}t{\'e} de d{\'e}part est de dimension $n$ paire. Ses points critiques satisfont une EDP elliptique d'ordre $n$ non-lin{\'e}aire qui est covariante conforme par rapport {\`a} la vari{\'e}t{\'e} de d{\'e}part, on les appelle les applications conforme-harmoniques. Dans le cas des fonctions, on retrouve l'op{\'e}rateur GJMS, dont le terme principal est une puissance $ n / 2 $ du laplacien. Quand $n$ est impaire, les m{\^e}mes id{\'e}es permettent de montrer que le terme constant dans le d{\'e}veloppement asymptotique de l'{\'e}nergie d'une application asymptotiquement harmonique sur une vari{\'e}t{\'e} AHE est ind{\'e}pendant du choix du repr{\'e}sentant de l'infini conforme.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Grafakos:2013:MFM, author = "Loukas Grafakos and Akihiko Miyachi and Naohito Tomita", title = "On Multilinear {Fourier} Multipliers of Limited Smoothness", journal = j-CAN-J-MATH, volume = "65", number = "2", pages = "299--??", month = apr, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-025-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:35 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we prove certain {$ L^2 $}-estimate for multilinear Fourier multiplier operators with multipliers of limited smoothness. As a result, we extend the result of Calder{\'o}n and Torchinsky in the linear theory to the multilinear case. The sharpness of our results and some related estimates in Hardy spaces are also discussed.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kadets:2013:LNI, author = "Vladimir Kadets and Miguel Mart{\'\i}n and Javier Mer{\'\i} and Dirk Werner", title = "Lushness, Numerical Index 1 and the Daugavet Property in Rearrangement Invariant Spaces", journal = j-CAN-J-MATH, volume = "65", number = "2", pages = "331--??", month = apr, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-096-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:35 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We show that for spaces with 1-unconditional bases lushness, the alternative Daugavet property and numerical index 1 are equivalent. In the class of rearrangement invariant (r.i.) sequence spaces the only examples of spaces with these properties are $ c_0 $, $ \ell_1 $ and $ \ell_\infty $. The only lush r.i. separable function space on $ [0, 1] $ is {$ L_1 [0, 1] $}; the same space is the only r.i. separable function space on $ [0, 1] $ with the Daugavet property over the reals.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Muller:2013:EPR, author = "Peter M{\"u}ller and Christoph Richard", title = "Ergodic Properties of Randomly Coloured Point Sets", journal = j-CAN-J-MATH, volume = "65", number = "2", pages = "349--??", month = apr, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-009-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:35 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We provide a framework for studying randomly coloured point sets in a locally compact, second-countable space on which a metrisable unimodular group acts continuously and properly. We first construct and describe an appropriate dynamical system for uniformly discrete uncoloured point sets. For point sets of finite local complexity, we characterise ergodicity geometrically in terms of pattern frequencies. The general framework allows to incorporate a random colouring of the point sets. We derive an ergodic theorem for randomly coloured point sets with finite-range dependencies. Special attention is paid to the exclusion of exceptional instances for uniquely ergodic systems. The setup allows for a straightforward application to randomly coloured graphs.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{VanOrder:2013:DMC, author = "Jeanine {Van Order}", title = "On the Dihedral Main Conjectures of {Iwasawa} Theory for {Hilbert} Modular Eigenforms", journal = j-CAN-J-MATH, volume = "65", number = "2", pages = "403--??", month = apr, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-002-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:35 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We construct a bipartite Euler system in the sense of Howard for Hilbert modular eigenforms of parallel weight two over totally real fields, generalizing works of Bertolini-Darmon, Longo, Nekovar, Pollack-Weston and others. The construction has direct applications to Iwasawa main conjectures. For instance, it implies in many cases one divisibility of the associated dihedral or anticyclotomic main conjecture, at the same time reducing the other divisibility to a certain nonvanishing criterion for the associated $p$-adic {$L$}-functions. It also has applications to cyclotomic main conjectures for Hilbert modular forms over CM fields via the technique of Skinner and Urban.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Wilson:2013:QFC, author = "Glen Wilson and Christopher T. Woodward", title = "Quasimap {Floer} Cohomology for Varying Symplectic Quotients", journal = j-CAN-J-MATH, volume = "65", number = "2", pages = "467--??", month = apr, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-008-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:35 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We show that quasimap Floer cohomology for varying symplectic quotients resolves several puzzles regarding displaceability of toric moment fibers. For example, we (i) present a compact Hamiltonian torus action containing an open subset of non-displaceable orbits and a codimension four singular set, partly answering a question of McDuff, and (ii) determine displaceability for most of the moment fibers of a symplectic ellipsoid.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Ara:2013:CPS, author = "Pere Ara and Kenneth J. Dykema and Mikael R{\o}rdam", title = "Correction of Proofs in {``Purely Infinite Simple $ C^* $-algebras Arising from Free Product Constructions''} and a Subsequent Paper", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "481--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-018-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The proofs of Theorem 2.2 of K. J. Dykema and M. R{\o}rdam, Purely infinite simple {$ C^* $}-algebras arising from free product {constructions??}, Canad. J. Math. 50 (1998), 323--341 and of Theorem 3.1 of K. J. Dykema, Purely infinite simple {$ C^* $}-algebras arising from free product constructions, II, Math. Scand. 90 (2002), 73--86 are corrected.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bice:2013:FCA, author = "Tristan Matthew Bice", title = "Filters in {C$^*$}-Algebras", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "485--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2011-095-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we analyze states on C*-algebras and their relationship to filter-like structures of projections and positive elements in the unit ball. After developing the basic theory we use this to investigate the Kadison-Singer conjecture, proving its equivalence to an apparently quite weak paving conjecture and the existence of unique maximal centred extensions of projections coming from ultrafilters on the natural numbers. We then prove that Reid's positive answer to this for q-points in fact also holds for rapid p-points, and that maximal centred filters are obtained in this case. We then show that consistently such maximal centred filters do not exist at all meaning that, for every pure state on the Calkin algebra, there exists a pair of projections on which the state is 1, even though the state is bounded strictly below 1 for projections below this pair. Lastly we investigate towers, using cardinal invariant equalities to construct towers on the natural numbers that do and do not remain towers when canonically embedded into the Calkin algebra. Finally we show that consistently all towers on the natural numbers remain towers under this embedding.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{delaCruz:2013:TVV, author = "Oscar Blasco de la Cruz and Paco Villarroya Alvarez", title = "Transference of vector-valued multipliers on weighted {$ L^p $}-spaces", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "510--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-041-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove restriction and extension of multipliers between weighted Lebesgue spaces with two different weights, which belong to a class more general than periodic weights, and two different exponents of integrability which can be below one. We also develop some ad-hoc methods which apply to weights defined by the product of periodic weights with functions of power type. Our vector-valued approach allow us to extend results to transference of maximal multipliers and provide transference of Littlewood--Paley inequalities.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Deitmar:2013:IIH, author = "Anton Deitmar and Ivan Horozov", title = "Iterated Integrals and Higher Order Invariants", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "544--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-020-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We show that higher order invariants of smooth functions can be written as linear combinations of full invariants times iterated integrals. The non-uniqueness of such a presentation is captured in the kernel of the ensuing map from the tensor product. This kernel is computed explicitly. As a consequence, it turns out that higher order invariants are a free module of the algebra of full invariants.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Godinho:2013:AES, author = "Leonor Godinho and M. E. Sousa-Dias", title = "Addendum and Erratum to {``The Fundamental Group of $ S^1 $-manifolds''}", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "553--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-024-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This paper provides an addendum and erratum to L. Godinho and M. E. Sousa-Dias, {\SGMLquot}The Fundamental Group of {$ S^1 $}-manifolds{\SGMLquot}. Canad. J. Math. 62(2010), no. 5, 1082--1098.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Helemskii:2013:EVP, author = "A. Ya. Helemskii", title = "Extreme Version of Projectivity for Normed Modules Over Sequence Algebras", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "559--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-006-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We define and study the so-called extreme version of the notion of a projective normed module. The relevant definition takes into account the exact value of the norm of the module in question, in contrast with the standard known definition that is formulated in terms of norm topology. After the discussion of the case where our normed algebra {$A$} is just {$ \mathbb {C} $}, we concentrate on the case of the next degree of complication, where {$A$} is a sequence algebra, satisfying some natural conditions. The main results give a full characterization of extremely projective objects within the subcategory of the category of non-degenerate normed {$A$}--modules, consisting of the so-called homogeneous modules. We consider two cases, `non-complete' and `complete', and the respective answers turn out to be essentially different. In particular, all Banach non-degenerate homogeneous modules, consisting of sequences, are extremely projective within the category of Banach non-degenerate homogeneous modules. However, neither of them, provided it is infinite-dimensional, is extremely projective within the category of all normed non-degenerate homogeneous modules. On the other hand, submodules of these modules, consisting of finite sequences, are extremely projective within the latter category.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kallel:2013:GFG, author = "Sadok Kallel and Walid Taamallah", title = "The Geometry and Fundamental Group of Permutation Products and Fat Diagonals", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "575--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-028-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Permutation products and their various ``fat diagonal'' subspaces are studied from the topological and geometric point of view. We describe in detail the stabilizer and orbit stratifications related to the permutation action, producing a sharp upper bound for its depth and then paying particular attention to the geometry of the diagonal stratum. We write down an expression for the fundamental group of any permutation product of a connected space {$X$} having the homotopy type of a CW complex in terms of {$ \pi_1 (X) $} and {$ H_1 (X; \mathbb {Z}) $}. We then prove that the fundamental group of the configuration space of $n$-points on {$X$}, of which multiplicities do not exceed $ n / 2 $, coincides with {$ H_1 (X; \mathbb {Z}) $}. Further results consist in giving conditions for when fat diagonal subspaces of manifolds can be manifolds again. Various examples and homological calculations are included.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kroo:2013:CFU, author = "A. Kro{\'o} and D. S. Lubinsky", title = "{Christoffel} Functions and Universality in the Bulk for Multivariate Orthogonal Polynomials", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "600--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-016-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We establish asymptotics for Christoffel functions associated with multivariate orthogonal polynomials. The underlying measures are assumed to be regular on a suitable domain - in particular this is true if they are positive a.e. on a compact set that admits analytic parametrization. As a consequence, we obtain asymptotics for Christoffel functions for measures on the ball and simplex, under far more general conditions than previously known. As another consequence, we establish universality type limits in the bulk in a variety of settings.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Lee:2013:STD, author = "Paul W. Y. Lee", title = "On Surfaces in Three Dimensional Contact Manifolds", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "621--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-027-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we introduce two notions on a surface in a contact manifold. The first one is called degree of transversality (DOT) which measures the transversality between the tangent spaces of a surface and the contact planes. The second quantity, called curvature of transversality (COT), is designed to give a comparison principle for DOT along characteristic curves under bounds on COT. In particular, this gives estimates on lengths of characteristic curves assuming COT is bounded below by a positive constant. We show that surfaces with constant COT exist and we classify all graphs in the Heisenberg group with vanishing COT. This is accomplished by showing that the equation for graphs with zero COT can be decomposed into two first order PDEs, one of which is the backward invisicid Burgers' equation. Finally we show that the p-minimal graph equation in the Heisenberg group also has such a decomposition. Moreover, we can use this decomposition to write down an explicit formula of a solution near a regular point.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mezzetti:2013:LEW, author = "Emilia Mezzetti and Rosa M. Mir{\'o}-Roig and Giorgio Ottaviani", title = "{Laplace} Equations and the Weak {Lefschetz} Property", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "634--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-033-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove that $r$ independent homogeneous polynomials of the same degree $d$ become dependent when restricted to any hyperplane if and only if their inverse system parameterizes a variety whose $ (d - 1) $-osculating spaces have dimension smaller than expected. This gives an equivalence between an algebraic notion (called Weak Lefschetz Property) and a differential geometric notion, concerning varieties which satisfy certain Laplace equations. In the toric case, some relevant examples are classified and as byproduct we provide counterexamples to Ilardi's conjecture.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Shemyakova:2013:PCD, author = "E. Shemyakova", title = "Proof of the Completeness of {Darboux} {Wronskian} Formulae for Order Two", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "655--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-026-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Darboux Wronskian formulas allow to construct Darboux transformations, but Laplace transformations, which are Darboux transformations of order one cannot be represented this way. It has been a long standing problem on what are other exceptions. In our previous work we proved that among transformations of total order one there are no other exceptions. Here we prove that for transformations of total order two there are no exceptions at all. We also obtain a simple explicit invariant description of all possible Darboux Transformations of total order two.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Strungaru:2013:BDS, author = "Nicolae Strungaru", title = "On the {Bragg} Diffraction Spectra of a {Meyer} Set", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "675--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-032-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Meyer sets have a relatively dense set of Bragg peaks and for this reason they may be considered as basic mathematical examples of (aperiodic) crystals. In this paper we investigate the pure point part of the diffraction of Meyer sets in more detail. The results are of two kinds. First we show that given a Meyer set and any positive intensity $a$ less than the maximum intensity of its Bragg peaks, the set of Bragg peaks whose intensity exceeds $a$ is itself a Meyer set (in the Fourier space). Second we show that if a Meyer set is modified by addition and removal of points in such a way that its density is not altered too much (the allowable amount being given explicitly as a proportion of the original density) then the newly obtained set still has a relatively dense set of Bragg peaks.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Taylor:2013:RSW, author = "Michael Taylor", title = "Regularity of Standing Waves on {Lipschitz} Domains", journal = j-CAN-J-MATH, volume = "65", number = "3", pages = "702--??", month = jun, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-014-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Apr 30 16:47:37 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We analyze the regularity of standing wave solutions to nonlinear Schr{\"o}dinger equations of power type on bounded domains, concentrating on Lipschitz domains. We establish optimal regularity results in this setting, in Besov spaces and in H{\"o}lder spaces.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Adamus:2013:TCD, author = "Janusz Adamus and Serge Randriambololona and Rasul Shafikov", title = "Tameness of Complex Dimension in a Real Analytic Set", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "721--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-019-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Given a real analytic set {$X$} in a complex manifold and a positive integer $d$, denote by {$ \mathcal A^d $} the set of points $p$ in {$X$} at which there exists a germ of a complex analytic set of dimension $d$ contained in {$X$}. It is proved that {$ \mathcal A^d $} is a closed semianalytic subset of {$X$}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bernard:2013:RSD, author = "P. Bernard and M. Zavidovique", title = "Regularization of Subsolutions in Discrete Weak {KAM} Theory", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "740--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-059-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We expose different methods of regularizations of subsolutions in the context of discrete weak KAM theory. They allow to prove the existence and the density of {$ C^{1, 1} $} subsolutions. Moreover, these subsolutions can be made strict and smooth outside of the Aubry set.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Delanoe:2013:PCR, author = "Philippe Delano{\"e} and Fran{\c{c}}ois Rouvi{\`e}re", title = "Positively Curved {Riemannian} Locally Symmetric Spaces are Positively Squared Distance Curved", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "757--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-015-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The squared distance curvature is a kind of two-point curvature the sign of which turned out crucial for the smoothness of optimal transportation maps on Riemannian manifolds. Positivity properties of that new curvature have been established recently for all the simply connected compact rank one symmetric spaces, except the Cayley plane. Direct proofs were given for the sphere, (an indirect one via the Hopf fibrations) for the complex and quaternionic projective spaces. Here, we present a direct proof of a property implying all the preceding ones, valid on every positively curved Riemannian locally symmetric space.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Fuller:2013:NAS, author = "Adam Hanley Fuller", title = "Nonself-adjoint Semicrossed Products by {Abelian} Semigroups", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "768--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-051-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let {$ \mathcal {S} $} be the semigroup {$ \mathcal {S} = \sum^{\oplus k}_{i = 1} \mathcal {S}_i $}, where for each {$ i \in I $}, {$ \mathcal {S}_i $} is a countable subsemigroup of the additive semigroup {$ \mathbb {R}_+ $} containing $0$. We consider representations of {$ \mathcal {S} $} as contractions {$ \{ T_s \}_{s \in \mathcal {S}} $} on a Hilbert space with the Nica-covariance property: {$ T_s^*T_t = T_t T_s^* $} whenever $ t \wedge s = 0 $. We show that all such representations have a unique minimal isometric Nica-covariant dilation. This result is used to help analyse the nonself-adjoint semicrossed product algebras formed from Nica-covariant representations of the action of {$ \mathcal {S} $} on an operator algebra {$ \mathcal {A} $} by completely contractive endomorphisms. We conclude by calculating the {$ C^* $}-envelope of the isometric nonself-adjoint semicrossed product algebra (in the sense of Kakariadis and Katsoulis).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Garces:2013:GTH, author = "Jorge J. Garc{\'e}s and Antonio M. Peralta", title = "Generalised Triple Homomorphisms and Derivations", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "783--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-043-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We introduce generalised triple homomorphism between Jordan Banach triple systems as a concept which extends the notion of generalised homomorphism between Banach algebras given by K. Jarosz and B.E. Johnson in 1985 and 1987, respectively. We prove that every generalised triple homomorphism between JB$^*$-triples is automatically continuous. When particularised to C$^*$-algebras, we rediscover one of the main theorems established by B.E. Johnson. We shall also consider generalised triple derivations from a Jordan Banach triple {$E$} into a Jordan Banach triple {$E$}-module, proving that every generalised triple derivation from a JB$^*$-triple {$E$} into itself or into {$ E^* $} is automatically continuous.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Grandjean:2013:HLD, author = "Vincent Grandjean", title = "On {Hessian} Limit Directions along Gradient Trajectories", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "808--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-021-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Given a non-oscillating gradient trajectory $ | \gamma | $ of a real analytic function $f$, we show that the limit $ \nu $ of the secants at the limit point $ \mathbf {0} $ of $ | \gamma | $ along the trajectory $ | \gamma | $ is an eigen-vector of the limit of the direction of the Hessian matrix {$ \operatorname {Hess} (f) $} at $ \mathbf {0} $ along $ | \gamma | $. The same holds true at infinity if the function is globally sub-analytic. We also deduce some interesting estimates along the trajectory. Away from the ends of the ambient space, this property is of metric nature and still holds in a general Riemannian analytic setting.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Guardo:2013:SPV, author = "Elena Guardo and Brian Harbourne and Adam {Van Tuyl}", title = "Symbolic Powers Versus Regular Powers of Ideals of General Points in {$ \mathbb {P}^1 \times \mathbb {P}^1 $}", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "823--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-045-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Recent work of Ein-Lazarsfeld-Smith and Hochster-Huneke raised the problem of which symbolic powers of an ideal are contained in a given ordinary power of the ideal. Bocci-Harbourne developed methods to address this problem, which involve asymptotic numerical characters of symbolic powers of the ideals. Most of the work done up to now has been done for ideals defining 0-dimensional subschemes of projective space. Here we focus on certain subschemes given by a union of lines in {$ \mathbb {P}^3 $} which can also be viewed as points in {$ \mathbb {P}^1 \times \mathbb {P}^1 $}. We also obtain results on the closely related problem, studied by Hochster and by Li-Swanson, of determining situations for which each symbolic power of an ideal is an ordinary power.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Jonsson:2013:THC, author = "Jakob Jonsson", title = "$3$-torsion in the Homology of Complexes of Graphs of Bounded Degree", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "843--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-008-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For $ \delta \ge 1 $ and $ n \ge 1 $, consider the simplicial complex of graphs on $n$ vertices in which each vertex has degree at most $ \delta $; we identify a given graph with its edge set and admit one loop at each vertex. This complex is of some importance in the theory of semigroup algebras. When $ \delta = 1 $, we obtain the matching complex, for which it is known that there is $3$-torsion in degree $d$ of the homology whenever $ \frac {n - 43} \le d \le \frac {n - 62} $. This paper establishes similar bounds for $ \delta \ge 2 $. Specifically, there is $3$-torsion in degree $d$ whenever $ \frac {(3 \delta - 1)n - 86} \le d \le \frac {\delta (n - 1) - 42} $. The procedure for detecting torsion is to construct an explicit cycle $z$ that is easily seen to have the property that $ 3 z $ is a boundary. Defining a homomorphism that sends $z$ to a non-boundary element in the chain complex of a certain matching complex, we obtain that $z$ itself is a non-boundary. In particular, the homology class of $z$ has order $3$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Josuat-Verges:2013:CSL, author = "Matthieu Josuat-Verg{\`e}s", title = "Cumulants of the $q$-semicircular Law, {Tutte} Polynomials, and Heaps", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "863--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-042-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The $q$-semicircular distribution is a probability law that interpolates between the Gaussian law and the semicircular law. There is a combinatorial interpretation of its moments in terms of matchings where $q$ follows the number of crossings, whereas for the free cumulants one has to restrict the enumeration to connected matchings. The purpose of this article is to describe combinatorial properties of the classical cumulants. We show that like the free cumulants, they are obtained by an enumeration of connected matchings, the weight being now an evaluation of the Tutte polynomial of a so-called crossing graph. The case $ q = 0 $ of these cumulants was studied by Lassalle using symmetric functions and hypergeometric series. We show that the underlying combinatorics is explained through the theory of heaps, which is Viennot's geometric interpretation of the Cartier-Foata monoid. This method also gives a general formula for the cumulants in terms of free cumulants.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kawabe:2013:SHM, author = "Hiroko Kawabe", title = "A Space of Harmonic Maps from the Sphere into the Complex Projective Space", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "879--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-052-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Guest-Ohnita and Crawford have shown the path-connectedness of the space of harmonic maps from {$ S^2 $} to {$ \mathbf {C} P^n $} of a fixed degree and energy.It is well-known that the $ \partial $ transform is defined on this space. In this paper,we will show that the space is decomposed into mutually disjoint connected subspaces on which $ \partial $ is homeomorphic.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Thompson:2013:EMT, author = "Alan Thompson", title = "Explicit Models for Threefolds Fibred by {K3} Surfaces of Degree Two", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "905--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-037-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider threefolds that admit a fibration by K3 surfaces over a nonsingular curve, equipped with a divisorial sheaf that defines a polarisation of degree two on the general fibre. Under certain assumptions on the threefold we show that its relative log canonical model exists and can be explicitly reconstructed from a small set of data determined by the original fibration. Finally we prove a converse to the above statement: under certain assumptions, any such set of data determines a threefold that arises as the relative log canonical model of a threefold admitting a fibration by K3 surfaces of degree two.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Wang:2013:IMS, author = "Liping Wang and Chunyi Zhao", title = "Infinitely Many Solutions for the Prescribed Boundary Mean Curvature Problem in {$ \mathbb B^N $}", journal = j-CAN-J-MATH, volume = "65", number = "4", pages = "927--??", month = aug, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-054-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jun 22 17:13:28 MDT 2013", bibsource = "http://cms.math.ca/cjm/v65/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider the following prescribed boundary mean curvature problem in {$ \mathbb B^N $} with the Euclidean metric: \[ \begin{cases} \displaystyle -\Delta u =0,\quad u\gt 0 {\&}\text{in }\mathbb B^N, \\[2ex] \displaystyle \frac{\partial u}{\partial\nu} + \frac{N-2}{2} u =\frac{N-2}{2} \widetilde K(x) u^{2^\#-1} \quad {\&} \text{on }\mathbb S^{N-1}, \end{cases} \] where {$ \widetilde K(x) $} is positive and rotationally symmetric on {$ \mathbb S^{N - 1}, 2^\# = \frac {2(N - 1)N - 2} $}. We show that if {$ \widetilde K(x) $} has a local maximum point, then the above problem has infinitely many positive solutions that are not rotationally symmetric on {$ \mathbb S^{N - 1} $}.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Aholt:2013:HSC, author = "Chris Aholt and Bernd Sturmfels and Rekha Thomas", title = "A {Hilbert} Scheme in Computer Vision", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "961--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-023-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Multiview geometry is the study of two-dimensional images of three-dimensional scenes, a foundational subject in computer vision. We determine a universal Gr{\"o}bner basis for the multiview ideal of $n$ generic cameras. As the cameras move, the multiview varieties vary in a family of dimension $ 11 n - 15 $. This family is the distinguished component of a multigraded Hilbert scheme with a unique Borel-fixed point. We present a combinatorial study of ideals lying on that Hilbert scheme.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Chu:2013:ACH, author = "C-H. Chu and M. V. Velasco", title = "Automatic Continuity of Homomorphisms in Non-associative {Banach} Algebras", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "989--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-049-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We introduce the concept of a rare element in a non-associative normed algebra and show that the existence of such element is the only obstruction to continuity of a surjective homomorphism from a non-associative Banach algebra to a unital normed algebra with simple completion. Unital associative algebras do not admit any rare element and hence automatic continuity holds.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Forrest:2013:UCF, author = "Brian Forrest and Tianxuan Miao", title = "Uniformly Continuous Functionals and {$M$}-Weakly Amenable Groups", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "1005--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-019-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $G$ be a locally compact group. Let $ A_M(G) $ ($ A_0 (G) $ )denote the closure of $ A(G) $, the Fourier algebra of $G$ in the space of bounded (completely bounded) multipliers of $ A(G) $. We call a locally compact group M-weakly amenable if $ A_M(G) $ has a bounded approximate identity. We will show that when $G$ is M-weakly amenable, the algebras $ A_M(G) $ and $ A_0 (G) $ have properties that are characteristic of the Fourier algebra of an amenable group. Along the way we show that the sets of tolopolically invariant means associated with these algebras have the same cardinality as those of the Fourier algebra.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Goulden:2013:MHN, author = "I. P. Goulden and Mathieu Guay-Paquet and Jonathan Novak", title = "Monotone {Hurwitz} Numbers in Genus Zero", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "1020--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-038-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Hurwitz numbers count branched covers of the Riemann sphere with specified ramification data, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of these branched covers related to the expansion of complete symmetric functions in the Jucys-Murphy elements, and have arisen in recent work on the asymptotic expansion of the Harish-Chandra-Itzykson--Zuber integral. In this paper we begin a detailed study of monotone Hurwitz numbers. We prove two results that are reminiscent of those for classical Hurwitz numbers. The first is the monotone join-cut equation, a partial differential equation with initial conditions that characterizes the generating function for monotone Hurwitz numbers in arbitrary genus. The second is our main result, in which we give an explicit formula for monotone Hurwitz numbers in genus zero.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hu:2013:CTC, author = "Zhiguo Hu and Matthias Neufang and Zhong-Jin Ruan", title = "Convolution of Trace Class Operators over Locally Compact Quantum Groups", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "1043--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-030-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study locally compact quantum groups $ \mathbb {G} $ through the convolution algebras $ L_1 (\mathbb {G}) $ and $ (T(L_2 (\mathbb {G})), \triangleright) $. We prove that the reduced quantum group $ C^* $-algebra $ C_0 (\mathbb {G}) $ can be recovered from the convolution $ \triangleright $ by showing that the right $ T(L_2 (\mathbb {G})) $-module $ \langle K(L_2 (\mathbb {G}) \triangleright T(L_2 (\mathbb {G})) \rangle $ is equal to $ C_0 (\mathbb {G}) $. On the other hand, we show that the left $ T(L_2 (\mathbb {G})) $-module $ \langle T(L_2 (\mathbb {G})) \triangleright K(L_2 (\mathbb {G}) \rangle $ is isomorphic to the reduced crossed product $ C_0 (\widehat {\mathbb {G}}) \,_r \! \ltimes C_0 (\mathbb {G}) $, and hence is a much larger $ C^* $-subalgebra of $ B(L_2 (\mathbb {G})) $. We establish a natural isomorphism between the completely bounded right multiplier algebras of $ L_1 (\mathbb {G}) $ and $ (T(L_2 (\mathbb {G})), \triangleright) $, and settle two invariance problems associated with the representation theorem of Junge-Neufang-Ruan (2009). We characterize regularity and discreteness of the quantum group $ \mathbb {G} $ in terms of continuity properties of the convolution $ \triangleright $ on $ T(L_2 (\mathbb {G})) $. We prove that if $ \mathbb {G} $ is semi-regular, then the space $ \langle T(L_2 (\mathbb {G})) \triangleright B(L_2 (\mathbb {G})) \rangle $ of right $ \mathbb {G} $-continuous operators on $ L_2 (\mathbb {G}) $, which was introduced by Bekka (1990) for $ L_{\infty }(G) $, is a unital $ C^* $-subalgebra of $ B(L_2 (\mathbb {G})) $. In the representation framework formulated by Neufang-Ruan-Spronk (2008) and Junge-Neufang-Ruan, we show that the dual properties of compactness and discreteness can be characterized simultaneously via automatic normality of quantum group bimodule maps on $ B(L_2 (\mathbb {G})) $. We also characterize some commutation relations of completely bounded multipliers of $ (T(L_2 (\mathbb {G})), \triangleright) $ over $ B(L_2 (\mathbb {G})) $.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kalantar:2013:QGG, author = "Mehrdad Kalantar and Matthias Neufang", title = "From Quantum Groups to Groups", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "1073--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-047-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we use the recent developments in the representation theory of locally compact quantum groups, to assign, to each locally compact quantum group $ \mathbb {G} $, a locally compact group $ \tilde {\mathbb {G}} $ which is the quantum version of point-masses, and is an invariant for the latter. We show that ``quantum point-masses{\SGMLquot} can be identified with several other locally compact groups that can be naturally assigned to the quantum group $ \mathbb {G} $. This assignment preserves compactness as well as discreteness (hence also finiteness), and for large classes of quantum groups, amenability. We calculate this invariant for some of the most well-known examples of non-classical quantum groups. Also, we show that several structural properties of $ \mathbb {G} $ are encoded by $ \tilde {\mathbb {G}} $: the latter, despite being a simpler object, can carry very important information about $ \mathbb {G} $.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Sambou:2013:RPS, author = "Diomba Sambou", title = "{R{\'e}sonances} pr{\`e}s de seuils d'op{\'e}rateurs magn{\'e}tiques de {Pauli} et de {Dirac}. ({French}) [Resonances near the thresholds of magnetic operators of {Pauli} and {Dirac}]", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "1095--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-057-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Nous consid{\'e}rons les perturbations $ H := H_0 + V $ et $ D := D_0 + V $ des Hamiltoniens libres $ H_0 $ de Pauli et $ D_0 $ de Dirac en dimension 3 avec champ magn{\'e}tique non constant, $V$ {\'e}tant un potentiel {\'e}lectrique qui d{\'e}cro{\^\i}t super-exponentiellement dans la direction du champ magn{\'e}tique. Nous montrons que dans des espaces de Banach appropri{\'e}s, les r{\'e}solvantes de $H$ et $D$ d{\'e}finies sur le demi-plan sup{\'e}rieur admettent des prolongements m{\'e}romorphes. Nous d{\'e}finissons les r{\'e}sonances de $H$ et $D$ comme {\'e}tant les p{\^o}les de ces extensions m{\'e}romorphes. D'une part, nous {\'e}tudions la r{\'e}partition des r{\'e}sonances de $H$ pr{\`e}s de l'origine $0$ et d'autre part, celle des r{\'e}sonances de $D$ pr{\`e}s de $ \pm m $ o{\`u} $m$ est la masse d'une particule. Dans les deux cas, nous obtenons d'abord des majorations du nombre de r{\'e}sonances dans de petits domaines au voisinage de $0$ et $ \pm m $. Sous des hypoth{\`e}ses suppl{\'e}mentaires, nous obtenons des d{\'e}veloppements asymptotiques du nombre de r{\'e}sonances qui entra{\^\i}nent leur accumulation pr{\`e}s des seuils $0$ et $ \pm m $. En particulier, pour une perturbation $V$ de signe d{\'e}fini, nous obtenons des informations sur la r{\'e}partition des valeurs propres de $H$ et $D$ pr{\`e}s de $0$ et $ \pm m $ respectivement.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Vandenbergen:2013:GSS, author = "Nicolas Vandenbergen", title = "On the Global Structure of Special Cycles on Unitary {Shimura} Varieties", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "1125--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-004-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we study the reduced loci of special cycles on local models of the Shimura variety for $ \operatorname {GU}(1, n - 1) $. Those special cycles are defined by Kudla and Rapoport. We explicitly compute the irreducible components of the reduced locus of a single special cycle, as well as of an arbitrary intersection of special cycles, and their intersection behaviour in terms of Bruhat-Tits theory. Furthermore, as an application of our results, we prove the connectedness of arbitrary intersections of special cycles, as conjectured by Kudla and Rapoport.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Vitagliano:2013:PDH, author = "Luca Vitagliano", title = "Partial Differential {Hamiltonian} Systems", journal = j-CAN-J-MATH, volume = "65", number = "5", pages = "1164--??", month = oct, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-055-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:37 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We define partial differential (PD in the following), i.e., field theoretic analogues of Hamiltonian systems on abstract symplectic manifolds and study their main properties, namely, PD Hamilton equations, PD Noether theorem, PD Poisson bracket, etc.. Unlike in standard multisymplectic approach to Hamiltonian field theory, in our formalism, the geometric structure (kinematics) and the dynamical information on the ``phase space'' appear as just different components of one single geometric object.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cho:2013:ASA, author = "Peter J. Cho and Henry H. Kim", title = "Application of the Strong {Artin} Conjecture to the Class Number Problem", journal = j-CAN-J-MATH, volume = "65", number = "6", pages = "1201--??", month = dec, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-031-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:38 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We construct unconditionally several families of number fields with the largest possible class numbers. They are number fields of degree 4 and 5 whose Galois closures have the Galois group $ A_4, S_4 $ and $ S_5 $. We first construct families of number fields with smallest regulators, and by using the strong Artin conjecture and applying zero density result of Kowalski-Michel, we choose subfamilies of $L$-functions which are zero free close to 1. For these subfamilies, the $L$-functions have the extremal value at $ s = 1 $, and by the class number formula, we obtain the extreme class numbers.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Cruz:2013:BEC, author = "Victor Cruz and Joan Mateu and Joan Orobitg", title = "{Beltrami} Equation with Coefficient in {Sobolev} and {Besov} Spaces", journal = j-CAN-J-MATH, volume = "65", number = "6", pages = "1217--??", month = dec, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-001-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:38 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Our goal in this work is to present some function spaces on the complex plane $ \mathbb C $, $ X(\mathbb C) $, for which the quasiregular solutions of the Beltrami equation, $ \overline \partial f (z) = \mu (z) \partial f (z) $, have first derivatives locally in $ X(\mathbb C) $, provided that the Beltrami coefficient $ \mu $ belongs to $ X(\mathbb C) $.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{DeBernardi:2013:HCP, author = "Carlo Alberto {De Bernardi}", title = "Higher Connectedness Properties of Support Points and Functionals of Convex Sets", journal = j-CAN-J-MATH, volume = "65", number = "6", pages = "1236--??", month = dec, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-048-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:38 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove that the set of all support points of a nonempty closed convex bounded set $C$ in a real infinite-dimensional Banach space $X$ is $ \mathrm {AR}(\sigma - \mathrm {compact}) $ and contractible. Under suitable conditions, similar results are proved also for the set of all support functionals of $C$ and for the domain, the graph and the range of the subdifferential map of a proper convex l.s.c. function on $X$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Iglesias-Zemmour:2013:VID, author = "Patrick Iglesias-Zemmour", title = "Variations of Integrals in Diffeology", journal = j-CAN-J-MATH, volume = "65", number = "6", pages = "1255--??", month = dec, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-044-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:38 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We establish the formula for the variation of integrals of differential forms on cubic chains, in the context of diffeological spaces. Then, we establish the diffeological version of Stoke's theorem, and we apply that to get the diffeological variant of the Cartan-Lie formula. Still in the context of Cartan-De-Rham calculus in diffeology, we construct a Chain-Homotopy Operator $ \mathbf K $ we apply it here to get the homotopic invariance of De Rham cohomology for diffeological spaces. This is the Chain-Homotopy Operator which used in symplectic diffeology to construct the Moment Map.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Reihani:2013:TFT, author = "Kamran Reihani", title = "{$K$}-theory of {Furstenberg} Transformation Group {$ C^* $}-algebras", journal = j-CAN-J-MATH, volume = "65", number = "6", pages = "1287--??", month = dec, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-022-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:38 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The paper studies the $K$-theoretic invariants of the crossed product $ C^* $-algebras associated with an important family of homeomorphisms of the tori $ \mathbb {T}^n $ called Furstenberg transformations. Using the Pimsner-Voiculescu theorem, we prove that given $n$, the $K$-groups of those crossed products, whose corresponding $ n \times n $ integer matrices are unipotent of maximal degree, always have the same rank $ a_n $. We show using the theory developed here that a claim made in the literature about the torsion subgroups of these $K$-groups is false. Using the representation theory of the simple Lie algebra $ \frak {sl}(2, \mathbb {C}) $, we show that, remarkably, $ a_n $ has a combinatorial significance. For example, every $ a_{2n + 1} $ is just the number of ways that $0$ can be represented as a sum of integers between $ - n $ and $n$ (with no repetitions). By adapting an argument of van Lint (in which he answered a question of Erd{\SGMLquot}os), a simple, explicit formula for the asymptotic behavior of the sequence $ \{ a_n \} $ is given. Finally, we describe the order structure of the $ K_0 $-groups of an important class of Furstenberg crossed products, obtaining their complete Elliott invariant using classification results of H. Lin and N. C. Phillips.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Taniguchi:2013:OFS, author = "Takashi Taniguchi and Frank Thorne", title = "Orbital {$L$}-functions for the Space of Binary Cubic Forms", journal = j-CAN-J-MATH, volume = "65", number = "6", pages = "1320--??", month = dec, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-027-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:38 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We introduce the notion of orbital $L$-functions for the space of binary cubic forms and investigate their analytic properties. We study their functional equations and residue formulas in some detail. Aside from their intrinsic interest, the results from this paper are used to prove the existence of secondary terms in counting functions for cubic fields. This is worked out in a companion paper.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Wright:2013:EHD, author = "Paul Wright", title = "Estimates of {Hausdorff} Dimension for Non-wandering Sets of Higher Dimensional Open Billiards", journal = j-CAN-J-MATH, volume = "65", number = "6", pages = "1384--??", month = dec, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-030-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:38 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This article concerns a class of open billiards consisting of a finite number of strictly convex, non-eclipsing obstacles $K$. The non-wandering set $ M_0 $ of the billiard ball map is a topological Cantor set and its Hausdorff dimension has been previously estimated for billiards in $ \mathbb {R}^2 $, using well-known techniques. We extend these estimates to billiards in $ \mathbb {R}^n $, and make various refinements to the estimates. These refinements also allow improvements to other results. We also show that in many cases, the non-wandering set is confined to a particular subset of $ \mathbb {R}^n $ formed by the convex hull of points determined by period 2 orbits. This allows more accurate bounds on the constants used in estimating Hausdorff dimension.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhao:2013:UVC, author = "Wei Zhao and Yibing Shen", title = "A Universal Volume Comparison Theorem for {Finsler} Manifolds and Related Results", journal = j-CAN-J-MATH, volume = "65", number = "6", pages = "1401--??", month = dec, year = "2013", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-053-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:40:38 MST 2014", bibsource = "http://cms.math.ca/cjm/v65/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we establish a universal volume comparison theorem for Finsler manifolds and give the Berger-Kazdan inequality and Santal{\'o}'s formula in Finsler geometry. Being based on these, we derive a Berger-Kazdan type comparison theorem and a Croke type isoperimetric inequality for Finsler manifolds.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Abdesselam:2014:HC, author = "Abdelmalek Abdesselam and Jaydeep Chipalkatti", title = "On {Hilbert} Covariants", journal = j-CAN-J-MATH, volume = "66", number = "1", pages = "3--??", month = feb, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-046-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:34 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $F$ denote a binary form of order $d$ over the complex numbers. If $r$ is a divisor of $d$, then the Hilbert covariant $ \mathcal {H}_{r, d}(F) $ vanishes exactly when $F$ is the perfect power of an order $r$ form. In geometric terms, the coefficients of $ \mathcal {H} $ give defining equations for the image variety $X$ of an embedding $ \mathbf {P}^r \hookrightarrow \mathbf {P}^d $. In this paper we describe a new construction of the Hilbert covariant; and simultaneously situate it into a wider class of covariants called the G{\"o}ttingen covariants, all of which vanish on $X$. We prove that the ideal generated by the coefficients of $ \mathcal {H} $ defines $X$ as a scheme. Finally, we exhibit a generalisation of the G{\"o}ttingen covariants to $n$-ary forms using the classical Clebsch transfer principle.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bailey:2014:SFG, author = "Michael Bailey", title = "Symplectic Foliations and Generalized Complex Structures", journal = j-CAN-J-MATH, volume = "66", number = "1", pages = "31--??", month = feb, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-007-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:34 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We answer the natural question: when is a transversely holomorphic symplectic foliation induced by a generalized complex structure? The leafwise symplectic form and transverse complex structure determine an obstruction class in a certain cohomology, which vanishes if and only if our question has an affirmative answer. We first study a component of this obstruction, which gives the condition that the leafwise cohomology class of the symplectic form must be transversely pluriharmonic. As a consequence, under certain topological hypotheses, we infer that we actually have a symplectic fibre bundle over a complex base. We then show how to compute the full obstruction via a spectral sequence. We give various concrete necessary and sufficient conditions for the vanishing of the obstruction. Throughout, we give examples to test the sharpness of these conditions, including a symplectic fibre bundle over a complex base which does not come from a generalized complex structure, and a regular generalized complex structure which is very unlike a symplectic fibre bundle, i.e., for which nearby leaves are not symplectomorphic.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Bezuglyi:2014:POF, author = "S. Bezuglyi and J. Kwiatkowski and R. Yassawi", title = "Perfect Orderings on Finite Rank {Bratteli} Diagrams", journal = j-CAN-J-MATH, volume = "66", number = "1", pages = "57--??", month = feb, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-041-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:34 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Given a Bratteli diagram $B$, we study the set $ \mathcal O_B $ of all possible orderings on $B$ and its subset $ \mathcal P_B $ consisting of perfect orderings that produce Bratteli-Vershik topological dynamical systems (Vershik maps). We give necessary and sufficient conditions for the ordering $ \omega $ to be perfect. On the other hand, a wide class of non-simple Bratteli diagrams that do not admit Vershik maps is explicitly described. In the case of finite rank Bratteli diagrams, we show that the existence of perfect orderings with a prescribed number of extreme paths constrains significantly the values of the entries of the incidence matrices and the structure of the diagram $B$. Our proofs are based on the new notions of skeletons and associated graphs, defined and studied in the paper. For a Bratteli diagram $B$ of rank $k$, we endow the set $ \mathcal O_B $ with product measure $ \mu $ and prove that there is some $ 1 \leq j \leq k $ such that $ \mu $-almost all orderings on $B$ have $j$ maximal and $j$ minimal paths. If $j$ is strictly greater than the number of minimal components that $B$ has, then $ \mu $-almost all orderings are imperfect.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Birth:2014:CCT, author = "Lidia Birth and Helge Gl{\"o}ckner", title = "Continuity of convolution of test functions on {Lie} groups", journal = j-CAN-J-MATH, volume = "66", number = "1", pages = "102--??", month = feb, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-035-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:34 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For a Lie group $G$, we show that the map $ C^\infty_c(G) \times C^\infty_c(G) \to C^\infty_c(G) $, $ (\gamma, \eta) \mapsto \gamma * \eta $ taking a pair of test functions to their convolution is continuous if and only if $G$ is $ \sigma $-compact. More generally, consider $ r, s, t \in \mathbb {N}_0 \cup \{ \infty \} $ with $ t \leq r + s $, locally convex spaces $ E_1 $, $ E_2 $ and a continuous bilinear map $ b \colon E_1 \times E_2 \to F $ to a complete locally convex space $F$. Let $ \beta \colon C^r_c(G, E_1) \times C^s_c(G, E_2) \to C^t_c(G, F) $, $ (\gamma, \eta) \mapsto \gamma *_b \eta $ be the associated convolution map. The main result is a characterization of those $ (G, r, s, t, b) $ for which $ \beta $ is continuous. Convolution of compactly supported continuous functions on a locally compact group is also discussed, as well as convolution of compactly supported $ L^1 $-functions and convolution of compactly supported Radon measures.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Caillat-Gibert:2014:ETF, author = "Shanti Caillat-Gibert and Daniel Matignon", title = "Existence of Taut Foliations on {Seifert} Fibered Homology $3$-spheres", journal = j-CAN-J-MATH, volume = "66", number = "1", pages = "141--??", month = feb, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-011-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:34 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This paper concerns the problem of existence of taut foliations among $3$-manifolds. Since the contribution of David Gabai, we know that closed $3$-manifolds with non-trivial second homology group admit a taut foliation. The essential part of this paper focuses on Seifert fibered homology $3$-spheres. The result is quite different if they are integral or rational but non-integral homology $3$-spheres. Concerning integral homology $3$-spheres, we can see that all but the $3$-sphere and the Poincar{\'e} $3$-sphere admit a taut foliation. Concerning non-integral homology $3$-spheres, we prove there are infinitely many which admit a taut foliation, and infinitely many without taut foliation. Moreover, we show that the geometries do not determine the existence of taut foliations on non-integral Seifert fibered homology $3$-spheres.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Guitart:2014:MAV, author = "Xavier Guitart and Jordi Quer", title = "Modular {Abelian} Varieties Over Number Fields", journal = j-CAN-J-MATH, volume = "66", number = "1", pages = "170--??", month = feb, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-040-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:34 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The main result of this paper is a characterization of the abelian varieties $ B / K $ defined over Galois number fields with the property that the $L$-function $ L(B / K; s) $ is a product of $L$-functions of non-CM newforms over $ \mathbb Q $ for congruence subgroups of the form $ \Gamma_1 (N) $. The characterization involves the structure of $ \operatorname {End}(B) $, isogenies between the Galois conjugates of $B$, and a Galois cohomology class attached to $ B / K $. We call the varieties having this property strongly modular. The last section is devoted to the study of a family of abelian surfaces with quaternionic multiplication. As an illustration of the ways in which the general results of the paper can be applied we prove the strong modularity of some particular abelian surfaces belonging to that family, and we show how to find nontrivial examples of strongly modular varieties by twisting.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Harris:2014:HDS, author = "Adam Harris and Martin Kol{\'a}r", title = "On Hyperbolicity of Domains with Strictly Pseudoconvex Ends", journal = j-CAN-J-MATH, volume = "66", number = "1", pages = "197--??", month = feb, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-036-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:34 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This article establishes a sufficient condition for Kobayashi hyperbolicity of unbounded domains in terms of curvature. Specifically, when $ \Omega \subset {\mathbb C}^n $ corresponds to a sub-level set of a smooth, real-valued function $ \Psi $, such that the form $ \omega = {\bf i} \partial \bar {\partial } \Psi $ is K{\"a}hler and has bounded curvature outside a bounded subset, then this domain admits a Hermitian metric of strictly negative holomorphic sectional curvature.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Iovanov:2014:GFA, author = "Miodrag Cristian Iovanov", title = "Generalized {Frobenius} Algebras and {Hopf} Algebras", journal = j-CAN-J-MATH, volume = "66", number = "1", pages = "205--??", month = feb, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-060-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:34 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "{\SGMLquot}Co-Frobenius{\SGMLquot} coalgebras were introduced as dualizations of Frobenius algebras. We previously showed that they admit left-right symmetric characterizations analogue to those of Frobenius algebras. We consider the more general quasi-co-Frobenius (QcF) coalgebras; the first main result in this paper is that these also admit symmetric characterizations: a coalgebra is QcF if it is weakly isomorphic to its (left, or right) rational dual $ R a t(C^*) $, in the sense that certain coproduct or product powers of these objects are isomorphic. Fundamental results of Hopf algebras, such as the equivalent characterizations of Hopf algebras with nonzero integrals as left (or right) co-Frobenius, QcF, semiperfect or with nonzero rational dual, as well as the uniqueness of integrals and a short proof of the bijectivity of the antipode for such Hopf algebras all follow as a consequence of these results. This gives a purely representation theoretic approach to many of the basic fundamental results in the theory of Hopf algebras. Furthermore, we introduce a general concept of Frobenius algebra, which makes sense for infinite dimensional and for topological algebras, and specializes to the classical notion in the finite case. This will be a topological algebra $A$ that is isomorphic to its complete topological dual $ A^\vee $. We show that $A$ is a (quasi)Frobenius algebra if and only if $A$ is the dual $ C^* $ of a (quasi)co-Frobenius coalgebra $C$. We give many examples of co-Frobenius coalgebras and Hopf algebras connected to category theory, homological algebra and the newer q-homological algebra, topology or graph theory, showing the importance of the concept.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Broussous:2014:TDP, author = "P. Broussous", title = "Transfert du pseudo-coefficient de {Kottwitz} et formules de caract{\`e}re pour la s{\'e}rie discr{\`e}te de {$ \mathrm {GL}(N) $} sur un corps local. ({French}) [{Transfer} of {Kottwitz}'s pseudo-coefficient and character formulars for the discrete series of {$ \mathrm {GL}(N) $} on a local body]", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "241--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-010-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Soit $G$ le groupe $ \mathrm {GL}(N, F) $, o{\`u} $F$ est un corps localement compact et non archim{\'e}dien. En utilisant la th{\'e}orie des types simples de Bushnell et Kutzko, ainsi qu'une id{\'e}e originale d'Henniart, nous construisons des pseudo-coefficients explicites pour les repr{\'e}sentations de la s{\'e}rie discr{\`e}te de $G$. Comme application, nous en d{\'e}duisons des formules in{\'e}dites pour la valeur du charact{\`e}re d'Harish-Chandra de certaines telles repr{\'e}sentations en certains {\'e}l{\'e}ments elliptiques r{\'e}guliers.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Eikrem:2014:RHF, author = "Kjersti Solberg Eikrem", title = "Random Harmonic Functions in Growth Spaces and {Bloch}-type Spaces", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "284--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-029-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ h^\infty_v(\mathbf D) $ and $ h^\infty_v(\mathbf B) $ be the spaces of harmonic functions in the unit disk and multi-dimensional unit ball which admit a two-sided radial majorant $ v(r) $. We consider functions $v$ that fulfill a doubling condition. In the two-dimensional case let $ u (r e^{i \theta }, \xi) = \sum_{j = 0}^\infty (a_{j0} \xi_{j0} r^j \cos j \theta + a_{j1} \xi_{j1} r^j \sin j \theta) $ where $ \xi = \{ \xi_{ji} \} $ is a sequence of random subnormal variables and $ a_{ji} $ are real; in higher dimensions we consider series of spherical harmonics. We will obtain conditions on the coefficients $ a_{ji} $ which imply that $u$ is in $ h^\infty_v(\mathbf B) $ almost surely. Our estimate improves previous results by Bennett, Stegenga and Timoney, and we prove that the estimate is sharp. The results for growth spaces can easily be applied to Bloch-type spaces, and we obtain a similar characterization for these spaces, which generalizes results by Anderson, Clunie and Pommerenke and by Guo and Liu.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Elekes:2014:HNS, author = "M{\'a}rton Elekes and Juris Steprans", title = "{Haar} Null Sets and the Consistent Reflection of Non-meagreness", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "303--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-058-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A subset $X$ of a Polish group $G$ is called Haar null if there exists a Borel set $ B \supset X $ and Borel probability measure $ \mu $ on $G$ such that $ \mu (g B h) = 0 $ for every $ g, h \in G $. We prove that there exist a set $ X \subset \mathbb R $ that is not Lebesgue null and a Borel probability measure $ \mu $ such that $ \mu (X + t) = 0 $ for every $ t \in \mathbb R $. This answers a question from David Fremlin's problem list by showing that one cannot simplify the definition of a Haar null set by leaving out the Borel set $B$. (The answer was already known assuming the Continuum Hypothesis.) This result motivates the following Baire category analogue. It is consistent with $ Z F C $ that there exist an abelian Polish group $G$ and a Cantor set $ C \subset G $ such that for every non-meagre set $ X \subset G $ there exists a $ t \in G $ such that $ C \cap (X + t) $ is relatively non-meagre in $C$. This essentially generalises results of Bartoszy{\'n}ski and Burke-Miller.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Hohlweg:2014:ABR, author = "Christophe Hohlweg and Jean-Philippe Labb{\'e} and Vivien Ripoll", title = "Asymptotical behaviour of roots of infinite {Coxeter} groups", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "323--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-024-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $W$ be an infinite Coxeter group. We initiate the study of the set $E$ of limit points of ``normalized'' roots (representing the directions of the roots) of W. We show that $E$ is contained in the isotropic cone $Q$ of the bilinear form $B$ associated to a geometric representation, and illustrate this property with numerous examples and pictures in rank $3$ and $4$. We also define a natural geometric action of $W$ on $E$, and then we exhibit a countable subset of $E$, formed by limit points for the dihedral reflection subgroups of $W$. We explain how this subset is built from the intersection with $Q$ of the lines passing through two positive roots, and finally we establish that it is dense in $E$.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kellerhals:2014:MGR, author = "Ruth Kellerhals and Alexander Kolpakov", title = "The Minimal Growth Rate of Cocompact {Coxeter} Groups in Hyperbolic $3$-space", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "354--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-062-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Due to work of W. Parry it is known that the growth rate of a hyperbolic Coxeter group acting cocompactly on $ {\mathbb H^3} $ is a Salem number. This being the arithmetic situation, we prove that the simplex group (3,5,3) has smallest growth rate among all cocompact hyperbolic Coxeter groups, and that it is as such unique. Our approach provides a different proof for the analog situation in $ {\mathbb H^2} $ where E. Hironaka identified Lehmer's number as the minimal growth rate among all cocompact planar hyperbolic Coxeter groups and showed that it is (uniquely) achieved by the Coxeter triangle group (3,7).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Kim:2014:UCB, author = "Sun Kwang Kim and Han Ju Lee", title = "Uniform Convexity and {Bishop--Phelps--Bollob{\'a}s} Property", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "373--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-009-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A new characterization of the uniform convexity of Banach space is obtained in the sense of Bishop--Phelps--Bollob{\'a}s theorem. It is also proved that the couple of Banach spaces $ (X, Y) $ has the Bishop--Phelps--Bollob{\'a}s property for every Banach space $y$ when $X$ is uniformly convex. As a corollary, we show that the Bishop--Phelps--Bollob{\'a}s theorem holds for bilinear forms on $ \ell_p \times \ell_q $ ($ 1 \lt p, q \lt \infty $ ).", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mashreghi:2014:CIF, author = "J. Mashreghi and M. Shabankhah", title = "Composition of Inner Functions", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "387--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-002-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the image of the model subspace $ K_\theta $ under the composition operator $ C_\varphi $, where $ \varphi $ and $ \theta $ are inner functions, and find the smallest model subspace which contains the linear manifold $ C_\varphi K_\theta $. Then we characterize the case when $ C_\varphi $ maps $ K_\theta $ into itself. This case leads to the study of the inner functions $ \varphi $ and $ \psi $ such that the composition $ \psi \circ \varphi $ is a divisor of $ \psi $ in the family of inner functions.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Mendonca:2014:US, author = "Bruno Mendon{\c{c}}a and Ruy Tojeiro", title = "Umbilical Submanifolds of {$ \mathbb {S}^n \times \mathbb {R} $}", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "400--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-003-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We give a complete classification of umbilical submanifolds of arbitrary dimension and codimension of $ \mathbb {S}^n \times \mathbb {R} $, extending the classification of umbilical surfaces in $ \mathbb {S}^2 \times \mathbb {R} $ by Souam and Toubiana as well as the local description of umbilical hypersurfaces in $ \mathbb {S}^n \times \mathbb {R} $ by Van der Veken and Vrancken. We prove that, besides small spheres in a slice, up to isometries of the ambient space they come in a two-parameter family of rotational submanifolds whose substantial codimension is either one or two and whose profile is a curve in a totally geodesic $ \mathbb {S}^1 \times \mathbb {R} $ or $ \mathbb {S}^2 \times \mathbb {R} $, respectively, the former case arising in a one-parameter family. All of them are diffeomorphic to a sphere, except for a single element that is diffeomorphic to Euclidean space. We obtain explicit parametrizations of all such submanifolds. We also study more general classes of submanifolds of $ \mathbb {S}^n \times \mathbb {R} $ and $ \mathbb {H}^n \times \mathbb {R} $. In particular, we give a complete description of all submanifolds in those product spaces for which the tangent component of a unit vector field spanning the factor $ \mathbb {R} $ is an eigenvector of all shape operators. We show that surfaces with parallel mean curvature vector in $ \mathbb {S}^n \times \mathbb {R} $ and $ \mathbb {H}^n \times \mathbb {R} $ having this property are rotational surfaces, and use this fact to improve some recent results by Alencar, do Carmo, and Tribuzy. We also obtain a Dajczer-type reduction of codimension theorem for submanifolds of $ \mathbb {S}^n \times \mathbb {R} $ and $ \mathbb {H}^n \times \mathbb {R} $.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Rivera-Noriega:2014:PSI, author = "Jorge Rivera-Noriega", title = "Perturbation and Solvability of Initial {$ L^p $} {Dirichlet} Problems for Parabolic Equations over Non-cylindrical Domains", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "429--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-028-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For parabolic linear operators $L$ of second order in divergence form, we prove that the solvability of initial $ L^p $ Dirichlet problems for the whole range $ 1 \lt p \lt \infty $ is preserved under appropriate small perturbations of the coefficients of the operators involved. We also prove that if the coefficients of $L$ satisfy a suitable controlled oscillation in the form of Carleson measure conditions, then for certain values of $ p \gt 1 $, the initial $ L^p $ Dirichlet problem associated to $ L u = 0 $ over non-cylindrical domains is solvable. The results are adequate adaptations of the corresponding results for elliptic equations.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Vaz:2014:RBA, author = "Pedro Vaz and Emmanuel Wagner", title = "A Remark on {BMW} algebra, $q$-{Schur} Algebras and Categorification", journal = j-CAN-J-MATH, volume = "66", number = "2", pages = "453--??", month = apr, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-018-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Mar 4 07:38:35 MST 2014", bibsource = "http://cms.math.ca/cjm/v66/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove that the 2-variable BMW algebra embeds into an algebra constructed from the HOMFLY-PT polynomial. We also prove that the $ \mathfrak {so}_{2N} $-BMW algebra embeds in the $q$-Schur algebra of type $A$. We use these results to suggest a schema providing categorifications of the $ \mathfrak {so}_{2N} $-BMW algebra.", acknowledgement = ack-nhfb, fjournal = "Canadian Journal of Mathematics = Journal canadien de math{\'e}matiques", journal-URL = "http://cms.math.ca/cjm/", } @Article{Aguiar:2014:HPH, author = "Marcelo Aguiar and Swapneel Mahajan", title = "On the {Hadamard} Product of {Hopf} Monoids", journal = j-CAN-J-MATH, volume = "66", number = "3", pages = "481--??", month = jun, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-005-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 12 08:34:05 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Combinatorial structures that compose and decompose give rise to Hopf monoids in Joyal's category of species. The Hadamard product of two Hopf monoids is another Hopf monoid. We prove two main results regarding freeness of Hadamard products. The first one states that if one factor is connected and the other is free as a monoid, their Hadamard product is free (and connected). The second provides an explicit basis for the Hadamard product when both factors are free. The first main result is obtained by showing the existence of a one-parameter deformation of the comonoid structure and appealing to a rigidity result of Loday and Ronco that applies when the parameter is set to zero. To obtain the second result, we introduce an operation on species that is intertwined by the free monoid functor with the Hadamard product. As an application of the first result, we deduce that the Boolean transform of the dimension sequence of a connected Hopf monoid is nonnegative.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Arapura:2014:HTC, author = "Donu Arapura", title = "{Hodge} Theory of Cyclic Covers Branched over a Union of Hyperplanes", journal = j-CAN-J-MATH, volume = "66", number = "3", pages = "505--??", month = jun, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-040-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 12 08:34:05 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Suppose that $Y$ is a cyclic cover of projective space branched over a hyperplane arrangement $D$, and that $U$ is the complement of the ramification locus in $Y$. The first theorem implies that the Beilinson-Hodge conjecture holds for $U$ if certain multiplicities of $D$ are coprime to the degree of the cover. For instance this applies when $D$ is reduced with normal crossings. The second theorem shows that when $D$ has normal crossings and the degree of the cover is a prime number, the generalized Hodge conjecture holds for any toroidal resolution of $Y$. The last section contains some partial extensions to more general nonabelian covers.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Berg:2014:LSH, author = "Chris Berg and Nantel Bergeron and Franco Saliola and Luis Serrano and Mike Zabrocki", title = "A Lift of the {Schur} and {Hall--Littlewood} Bases to Non-commutative Symmetric Functions", journal = j-CAN-J-MATH, volume = "66", number = "3", pages = "525--??", month = jun, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-013-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 12 08:34:05 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We introduce a new basis of the algebra of non-commutative symmetric functions whose images under the forgetful map are Schur functions when indexed by a partition. Dually, we build a basis of the quasi-symmetric functions which expand positively in the fundamental quasi-symmetric functions. We then use the basis to construct a non-commutative lift of the Hall--Littlewood symmetric functions with similar properties to their commutative counterparts.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Choiy:2014:TPM, author = "Kwangho Choiy", title = "Transfer of {Plancherel} Measures for Unitary Supercuspidal Representations between $p$-adic Inner Forms", journal = j-CAN-J-MATH, volume = "66", number = "3", pages = "566--??", month = jun, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-063-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 12 08:34:05 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $F$ be a $p$-adic field of characteristic $0$, and let $M$ be an $F$-Levi subgroup of a connected reductive $F$-split group such that $ \Pi_{i = 1}^r S L_{n_i} \subseteq M \subseteq \Pi_{i = 1}^r G L_{n_i}$ for positive integers $r$ and $ n_i$. We prove that the Plancherel measure for any unitary supercuspidal representation of $ M(F)$ is identically transferred under the local Jacquet-Langlands type correspondence between $M$ and its $F$-inner forms, assuming a working hypothesis that Plancherel measures are invariant on a certain set. This work extends the result of Mui{\'c} and Savin (2000) for Siegel Levi subgroups of the groups $ S O_{4n}$ and $ S p_{4n}$ under the local Jacquet-Langlands correspondence. It can be applied to a simply connected simple $F$-group of type $ E_6$ or $ E_7$, and a connected reductive $F$-group of type $ A_n$, $ B_n$, $ C_n$ or $ D_n$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Eilers:2014:OTF, author = "S{\o}ren Eilers and Gunnar Restorff and Efren Ruiz", title = "The Ordered {$K$}-theory of a Full Extension", journal = j-CAN-J-MATH, volume = "66", number = "3", pages = "596--??", month = jun, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-015-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 12 08:34:05 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathfrak {A} $ be a $ C^*$-algebra with real rank zero which has the stable weak cancellation property. Let $ \mathfrak {I}$ be an ideal of $ \mathfrak {A}$ such that $ \mathfrak {I}$ is stable and satisfies the corona factorization property. We prove that $ 0 \to \mathfrak {I} \to \mathfrak {A} \to \mathfrak {A} / \mathfrak {I} \to 0 $ is a full extension if and only if the extension is stenotic and $K$-lexicographic. {As an immediate application, we extend the classification result for graph $ C^*$-algebras obtained by Tomforde and the first named author to the general non-unital case. In combination with recent results by Katsura, Tomforde, West and the first author, our result may also be used to give a purely $K$-theoretical description of when an essential extension of two simple and stable graph $ C^*$-algebras is again a graph $ C^*$-algebra.}", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Giambruno:2014:CMV, author = "Antonio Giambruno and Daniela {La Mattina} and Mikhail Zaicev", title = "Classifying the Minimal Varieties of Polynomial Growth", journal = j-CAN-J-MATH, volume = "66", number = "3", pages = "625--??", month = jun, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-016-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 12 08:34:05 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathcal {V} $ be a variety of associative algebras generated by an algebra with $1$ over a field of characteristic zero. This paper is devoted to the classification of the varieties $ \mathcal {V}$ which are minimal of polynomial growth (i.e., their sequence of codimensions growth like $ n^k$ but any proper subvariety grows like $ n^t$ with $ t \lt k$). These varieties are the building blocks of general varieties of polynomial growth. It turns out that for $ k \le 4$ there are only a finite number of varieties of polynomial growth $ n^k$, but for each $ k \gt 4$, the number of minimal varieties is at least $ |F|$, the cardinality of the base field and we give a recipe of how to construct them.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Grigoryan:2014:HKG, author = "Alexander Grigor'yan and Jiaxin Hu", title = "Heat Kernels and {Green} Functions on Metric Measure Spaces", journal = j-CAN-J-MATH, volume = "66", number = "3", pages = "641--??", month = jun, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-061-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 12 08:34:05 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove that, in a setting of local Dirichlet forms on metric measure spaces, a two-sided sub-Gaussian estimate of the heat kernel is equivalent to the conjunction of the volume doubling propety, the elliptic Harnack inequality and a certain estimate of the capacity between concentric balls. The main technical tool is the equivalence between the capacity estimate and the estimate of a mean exit time in a ball, that uses two-sided estimates of a Green function in a ball.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{He:2014:IRT, author = "Jianxun He and Jinsen Xiao", title = "Inversion of the {Radon} Transform on the Free Nilpotent {Lie} Group of Step Two", journal = j-CAN-J-MATH, volume = "66", number = "3", pages = "700--??", month = jun, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-056-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 12 08:34:05 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ F_{2n, 2} $ be the free nilpotent Lie group of step two on $ 2 n $ generators, and let $ \mathbf P $ denote the affine automorphism group of $ F_{2n, 2} $. In this article the theory of continuous wavelet transform on $ F_{2n, 2} $ associated with $ \mathbf P $ is developed, and then a type of radial wavelets is constructed. Secondly, the Radon transform on $ F_{2n, 2} $ is studied and two equivalent characterizations of the range for Radon transform are given. Several kinds of inversion Radon transform formulae are established. One is obtained from the Euclidean Fourier transform, the others are from group Fourier transform. By using wavelet transform we deduce an inversion formula of the Radon transform, which does not require the smoothness of functions if the wavelet satisfies the differentiability property. Specially, if $ n = 1 $, $ F_{2, 2} $ is the $3$-dimensional Heisenberg group $ H^1$, the inversion formula of the Radon transform is valid which is associated with the sub-Laplacian on $ F_{2, 2}$. This result cannot be extended to the case $ n \geq 2$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Durand-Cartagena:2014:WTC, author = "E. Durand-Cartagena and L. Ihnatsyeva and R. Korte and M. Szuma{\'n}ska", title = "On {Whitney}-type Characterization of Approximate Differentiability on Metric Measure Spaces", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "721--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-064-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study approximately differentiable functions on metric measure spaces admitting a Cheeger differentiable structure. The main result is a Whitney-type characterization of approximately differentiable functions in this setting. As an application, we prove a Stepanov-type theorem and consider approximate differentiability of Sobolev, $ B V $ and maximal functions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Hrusak:2014:NCD, author = "Michael Hrus{\'a}k and Jan van Mill", title = "Nearly Countable Dense Homogeneous Spaces", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "743--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-006-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", note = "See addendum \cite{Hrusak:2014:AT}.", abstract = "We study separable metric spaces with few types of countable dense sets. We present a structure theorem for locally compact spaces having precisely $n$ types of countable dense sets: such a space contains a subset $S$ of size at most $ n{-}1$ such that $S$ is invariant under all homeomorphisms of $X$ and $ X \setminus S$ is countable dense homogeneous. We prove that every Borel space having fewer than $ \mathfrak {c}$ types of countable dense sets is Polish. The natural question of whether every Polish space has either countably many or $ \mathfrak {c}$ many types of countable dense sets, is shown to be closely related to Topological Vaught's Conjecture.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Hrusak:2014:AT, author = "Michael Hrus{\'a}k and Jan van Mill", title = "Addendum to {`Nearly Countable Dense Homogeneous Spaces'}", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "759--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-045-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", note = "See \cite{Hrusak:2014:NCD}.", abstract = "This paper provides an addendum to M. Hrus{\'a}k and J. van Mill ``Nearly countable dense homogeneous spaces.'' Canad. J. Math., published online 2013-03-08 https://doi.org/10.4153/CJM-2013-006-8.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Hu:2014:RKP, author = "Shengda Hu and Manuele Santoprete", title = "Regularization of the {Kepler} Problem on the Three-sphere", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "760--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2012-039-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we regularize the Kepler problem on $ S^3 $ in several different ways. First, we perform a Moser-type regularization. Then, we adapt the Ligon-Schaaf regularization to our problem. Finally, we show that the Moser regularization and the Ligon-Schaaf map we obtained can be understood as the composition of the corresponding maps for the Kepler problem in Euclidean space and the gnomonic transformation.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Izmestiev:2014:IRC, author = "Ivan Izmestiev", title = "Infinitesimal Rigidity of Convex Polyhedra through the Second Derivative of the {Hilbert--Einstein} Functional", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "783--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-031-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The paper is centered around a new proof of the infinitesimal rigidity of convex polyhedra. The proof is based on studying derivatives of the discrete Hilbert-Einstein functional on the space of {"warped} {polyhedra"} with a fixed metric on the boundary. The situation is in a sense dual to using derivatives of the volume in order to prove the Gauss infinitesimal rigidity of convex polyhedra. This latter kind of rigidity is related to the Minkowski theorem on the existence and uniqueness of a polyhedron with prescribed face normals and face areas. In the spherical and in the hyperbolic-de Sitter space, there is a perfect duality between the Hilbert-Einstein functional and the volume, as well as between both kinds of rigidity. We review some of the related work and discuss directions for future research.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kim:2014:SSG, author = "Byoung Du Kim", title = "Signed-{Selmer} Groups over the {$ \mathbb {Z}_p^2 $}-extension of an Imaginary Quadratic Field", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "826--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-043-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $E$ be an elliptic curve over $ \mathbb Q$ which has good supersingular reduction at $ p \gt 3$. We construct what we call the $ \pm / \pm $-Selmer groups of $E$ over the $ \mathbb Z_p^2$-extension of an imaginary quadratic field $K$ when the prime $p$ splits completely over $ K / \mathbb Q$, and prove they enjoy a property analogous to Mazur's control theorem. Furthermore, we propose a conjectural connection between the $ \pm / \pm $-Selmer groups and Loeffler's two-variable $ \pm / \pm $-$p$-adic $L$-functions of elliptic curves.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kuo:2014:MVT, author = "Wentang Kuo and Yu-Ru Liu and Xiaomei Zhao", title = "Multidimensional {Vinogradov}-type Estimates in Function Fields", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "844--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-014-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathbb {F}_q[t] $ denote the polynomial ring over the finite field $ \mathbb {F}_q $. We employ Wooley's new efficient congruencing method to prove certain multidimensional Vinogradov-type estimates in $ \mathbb {F}_q[t] $. These results allow us to apply a variant of the circle method to obtain asymptotic formulas for a system connected to the problem about linear spaces lying on hypersurfaces defined over $ \mathbb {F}_q[t] $.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Levandovskyy:2014:QDH, author = "Viktor Levandovskyy and Anne V. Shepler", title = "Quantum {Drinfeld} {Hecke} Algebras", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "874--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-012-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", note = "See corrigendum \cite{Levandovskyy:2014:CEI}.", abstract = "We consider finite groups acting on quantum (or skew) polynomial rings. Deformations of the semidirect product of the quantum polynomial ring with the acting group extend symplectic reflection algebras and graded Hecke algebras to the quantum setting over a field of arbitrary characteristic. We give necessary and sufficient conditions for such algebras to satisfy a Poincar{\'e}-Birkhoff-Witt property using the theory of noncommutative Gr{\"o}bner bases. We include applications to the case of abelian groups and the case of groups acting on coordinate rings of quantum planes. In addition, we classify graded automorphisms of the coordinate ring of quantum 3-space. In characteristic zero, Hochschild cohomology gives an elegant description of the PBW conditions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Levandovskyy:2014:CEI, author = "Viktor Levandovskyy and Anne V. Shepler", title = "Corrigendum to Example in {``Quantum Drinfeld Hecke Algebras''}", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "902--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-004-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", note = "See \cite{Levandovskyy:2014:QDH}.", abstract = "The last example of the article contains an error which we correct. We also indicate some indices in Theorem 11.1 that were accidently transposed.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Sargsyan:2014:NTM, author = "Grigor Sargsyan and Nam Trang", title = "Non-tame Mice from Tame Failures of the Unique Branch Hypothesis", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "903--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-036-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we show that the failure of the unique branch hypothesis (UBH) for tame trees implies that in some homogeneous generic extension of $V$ there is a transitive model $M$ containing $ O r d \cup \mathbb {R}$ such that $ M \vDash \mathsf {AD}^+ + \Theta \gt \theta_0$. In particular, this implies the existence (in $V$) of a non-tame mouse. The results of this paper significantly extend J. R. Steel's earlier results for tame trees.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Stankewicz:2014:TSC, author = "James Stankewicz", title = "Twists of {Shimura} Curves", journal = j-CAN-J-MATH, volume = "66", number = "4", pages = "924--??", month = aug, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-023-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:06 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Consider a Shimura curve $ X^D_0 (N) $ over the rational numbers. We determine criteria for the twist by an Atkin-Lehner involution to have points over a local field. As a corollary we give a new proof of the theorem of Jordan-Livn{\'e} on $ \mathbf {Q}_p $ points when $ p \mid D $ and for the first time give criteria for $ \mathbf {Q}_p $ points when $ p \mid N $. We also give congruence conditions for roots modulo $p$ of Hilbert class polynomials.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Baird:2014:MSV, author = "Thomas Baird", title = "Moduli Spaces of Vector Bundles over a Real Curve: {$ \mathbb Z / 2$--Betti} Numbers", journal = j-CAN-J-MATH, volume = "66", number = "5", pages = "961--??", month = oct, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-049-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:08 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Moduli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi-stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah-Bott's ``Yang--Mills over a Riemann Surface'' to compute $ \mathbb Z / 2$-Betti numbers of these spaces.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Beuzart-Plessis:2014:EFE, author = "Rapha{\"e}l Beuzart-Plessis", title = "Expression d'un facteur epsilon de paire par une formule int{\'e}grale. ({French}) [{Expression} of a pair-epsilon factor by an integral formula]", journal = j-CAN-J-MATH, volume = "66", number = "5", pages = "993--??", month = oct, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-042-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:08 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ E / F $ be a quadratic extension of $p$-adic fields and let $d$, $m$ be nonnegative integers of distinct parities. Fix admissible irreducible tempered representations $ \pi $ and $ \sigma $ of $ G L_d(E)$ and $ G L_m(E)$ respectively. We assume that $ \pi $ and $ \sigma $ are conjugate-dual. That is to say $ \pi \simeq \pi^{\vee, c}$ and $ \sigma \simeq \sigma^{\vee, c}$ where $c$ is the non trivial $F$-automorphism of $E$. This implies, we can extend $ \pi $ to an unitary representation $ \tilde {\pi }$ of a nonconnected group $ G L_d(E) \rtimes \{ 1, \theta \} $. Define $ \tilde {\sigma }$ the same way. We state and prove an integral formula for $ \epsilon (1 / 2, \pi \times \sigma, \psi_E)$ involving the characters of $ \tilde {\pi }$ and $ \tilde {\sigma }$. This formula is related to the local Gan-Gross-Prasad conjecture for unitary groups.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Holmes:2014:RWD, author = "Mark Holmes and Thomas S. Salisbury", title = "Random Walks in Degenerate Random Environments", journal = j-CAN-J-MATH, volume = "66", number = "5", pages = "1050--??", month = oct, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-017-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:08 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the asymptotic behaviour of random walks in i.i.d. random environments on $ \mathbb {Z}^d $. The environments need not be elliptic, so some steps may not be available to the random walker. We prove a monotonicity result for the velocity (when it exists) for any 2-valued environment, and show that this does not hold for 3-valued environments without additional assumptions. We give a proof of directional transience and the existence of positive speeds under strong, but non-trivial conditions on the distribution of the environment. Our results include generalisations (to the non-elliptic setting) of 0-1 laws for directional transience, and in 2-dimensions the existence of a deterministic limiting velocity.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Lanphier:2014:VTT, author = "Dominic Lanphier and Howard Skogman", title = "Values of Twisted Tensor {$L$}-functions of Automorphic Forms Over Imaginary Quadratic Fields", journal = j-CAN-J-MATH, volume = "66", number = "5", pages = "1078--??", month = oct, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-047-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:08 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $K$ be a complex quadratic extension of $ \mathbb {Q}$ and let $ \mathbb {A}_K$ denote the adeles of $K$. We find special values at all of the critical points of twisted tensor $L$-functions attached to cohomological cuspforms on $ G L_2 (\mathbb {A}_K)$, and establish Galois equivariance of the values. To investigate the values, we determine the archimedean factors of a class of integral representations of these $L$-functions, thus proving a conjecture due to Ghate. We also investigate analytic properties of these $L$-functions, such as their functional equations.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Li:2014:DED, author = "Dong Li and Guixiang Xu and Xiaoyi Zhang", title = "On the Dispersive Estimate for the {Dirichlet} {Schr{\"o}dinger} Propagator and Applications to Energy Critical {NLS}", journal = j-CAN-J-MATH, volume = "66", number = "5", pages = "1110--??", month = oct, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-002-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:08 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider the obstacle problem for the Schr{\"o}dinger evolution in the exterior of the unit ball with Dirichlet boundary condition. Under the radial symmetry we compute explicitly the fundamental solution for the linear Dirichlet Schr{\"o}dinger propagator $ e^{it \Delta_D} $ and give a robust algorithm to prove sharp $ L^1 \rightarrow L^{\infty } $ dispersive estimates. We showcase the analysis in dimensions $ n = 5, 7 $. As an application, we obtain global well-posedness and scattering for defocusing energy-critical NLS on $ \Omega = \mathbb {R}^n \backslash \overline {B(0, 1)} $ with Dirichlet boundary condition and radial data in these dimensions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Plevnik:2014:MPC, author = "Lucijan Plevnik and Peter Semrl", title = "Maps Preserving Complementarity of Closed Subspaces of a {Hilbert} Space", journal = j-CAN-J-MATH, volume = "66", number = "5", pages = "1143--??", month = oct, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-025-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:08 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathcal {H} $ and $ \mathcal {K} $ be infinite-dimensional separable Hilbert spaces and $ {\rm Lat} \, \mathcal {H} $ the lattice of all closed subspaces oh $ \mathcal {H} $. We describe the general form of pairs of bijective maps $ \phi, \psi : {\rm Lat} \, \mathcal {H} \to {\rm Lat} \, \mathcal {K} $ having the property that for every pair $ U, V \in {\rm Lat} \, \mathcal {H} $ we have $ \mathcal {H} = U \oplus V \iff \mathcal {K} = \phi (U) \oplus \psi (V) $. Then we reformulate this theorem as a description of bijective image equality and kernel equality preserving maps acting on bounded linear idempotent operators. Several known structural results for maps on idempotents are easy consequences.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Rotger:2014:GRF, author = "Victor Rotger and Carlos {de Vera-Piquero}", title = "{Galois} Representations Over Fields of Moduli and Rational Points on {Shimura} Curves", journal = j-CAN-J-MATH, volume = "66", number = "5", pages = "1167--??", month = oct, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-020-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Sep 13 12:48:08 MDT 2014", bibsource = "http://cms.math.ca/cjm/v66/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The purpose of this note is introducing a method for proving the existence of no rational points on a coarse moduli space $X$ of abelian varieties over a given number field $K$, in cases where the moduli problem is not fine and points in $ X(K)$ may not be represented by an abelian variety (with additional structure) admitting a model over the field $K$. This is typically the case when the abelian varieties that are being classified have even dimension. The main idea, inspired on the work of Ellenberg and Skinner on the modularity of $ \mathbb {Q}$-curves, is that to a point $ P = [A] \in X(K)$ represented by an abelian variety $ A / \bar K$ one may still attach a Galois representation of $ \operatorname {Gal}(\bar K / K)$ with values in the quotient group $ \operatorname {GL}(T_\ell (A)) / \operatorname {Aut}(A)$, provided $ \operatorname {Aut}(A)$ lies in the centre of $ \operatorname {GL}(T_\ell (A))$. We exemplify our method in the cases where $X$ is a Shimura curve over an imaginary quadratic field or an Atkin-Lehner quotient over $ \mathbb {Q}$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Adler:2014:LRF, author = "Jeffrey D. Adler and Joshua M. Lansky", title = "Lifting Representations of Finite Reductive Groups {I}: Semisimple Conjugacy Classes", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1201--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-013-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Suppose that $ \tilde {G} $ is a connected reductive group defined over a field $k$, and $ \Gamma $ is a finite group acting via $k$-automorphisms of $ \tilde {G}$ satisfying a certain quasi-semisimplicity condition. Then the identity component of the group of $ \Gamma $-fixed points in $ \tilde {G}$ is reductive. We axiomatize the main features of the relationship between this fixed-point group and the pair $ (\tilde {G}, \Gamma)$, and consider any group $G$ satisfying the axioms. If both $ \tilde {G}$ and $G$ are $k$-quasisplit, then we can consider their duals $ \tilde {G}^*$ and $ G^*$. We show the existence of and give an explicit formula for a natural map from the set of semisimple stable conjugacy classes in $ G^*(k)$ to the analogous set for $ \tilde {G}^*(k)$. If $k$ is finite, then our groups are automatically quasisplit, and our result specializes to give a map of semisimple conjugacy classes. Since such classes parametrize packets of irreducible representations of $ G(k)$ and $ \tilde {G}(k)$, one obtains a mapping of such packets.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Benitez:2014:MGD, author = "Teresa Cortadellas Ben{\'\i}tez and Carlos D'Andrea", title = "Minimal Generators of the Defining Ideal of the {Rees} Algebra Associated with a Rational Plane Parametrization with $ \mu = 2 $", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1225--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-035-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We exhibit a set of minimal generators of the defining ideal of the Rees Algebra associated with the ideal of three bivariate homogeneous polynomials parametrizing a proper rational curve in projective plane, having a minimal syzygy of degree 2.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Feigin:2014:SDF, author = "Evgeny Feigin and Michael Finkelberg and Peter Littelmann", title = "Symplectic Degenerate Flag Varieties", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1250--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-038-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A simple finite dimensional module $ V_\lambda $ of a simple complex algebraic group $G$ is naturally endowed with a filtration induced by the PBW-filtration of $ U(\mathrm {Lie} \, G)$. The associated graded space $ V_\lambda^a$ is a module for the group $ G^a$, which can be roughly described as a semi-direct product of a Borel subgroup of $G$ and a large commutative unipotent group $ \mathbb {G}_a^M$. In analogy to the flag variety $ \mathcal {F}_\lambda = G.[v_\lambda] \subset \mathbb {P}(V_\lambda)$, we call the closure $ \overline {G^a.[v_\lambda]} \subset \mathbb {P}(V_\lambda^a)$ of the $ G^a$-orbit through the highest weight line the degenerate flag variety $ \mathcal {F}^a_\lambda $. In general this is a singular variety, but we conjecture that it has many nice properties similar to that of Schubert varieties. In this paper we consider the case of $G$ being the symplectic group. The symplectic case is important for the conjecture because it is the first known case where even for fundamental weights $ \omega $ the varieties $ \mathcal {F}^a_\omega $ differ from $ \mathcal {F}_\omega $. We give an explicit construction of the varieties $ S p \mathcal {F}^a_\lambda $ and construct desingularizations, similar to the Bott-Samelson resolutions in the classical case. We prove that $ S p \mathcal {F}^a_\lambda $ are normal locally complete intersections with terminal and rational singularities. We also show that these varieties are Frobenius split. Using the above mentioned results, we prove an analogue of the Borel--Weil theorem and obtain a $q$-character formula for the characters of irreducible $ S p_{2n}$-modules via the Atiyah-Bott-Lefschetz fixed points formula.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Henniart:2014:TC, author = "Guy Henniart and Vincent S{\'e}cherre", title = "Types et contragr{\'e}dientes. ({French}) [{Types} and contragredients]", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1287--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-032-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Soit $ \mathrm {G} $ un groupe r{\'e}ductif $p$-adique, et soit $ \mathrm {R}$ un corps alg{\'e}briquement clos. Soit $ \pi $ une repr{\'e}sentation lisse de $ \mathrm {G}$ dans un espace vectoriel $ \mathrm {V}$ sur $ \mathrm {R}$. Fixons un sous-groupe ouvert et compact $ \mathrm {K}$ de $ \mathrm {G}$ et une repr{\'e}sentation lisse irr{\'e}ductible $ \tau $ de $ \mathrm {K}$ dans un espace vectoriel $ \mathrm {W}$ de dimension finie sur $ \mathrm {R}$. Sur l'espace $ \mathrm {Hom}_{\mathrm {K}(\mathrm {W}, \mathrm {V})}$ agit l'alg{\`e}bre d'entrelacement $ \mathscr {H}(\mathrm {G}, \mathrm {K}, \mathrm {W})$. Nous examinons la compatibilit{\'e} de ces constructions avec le passage aux repr{\'e}sentations contragr{\'e}dientes $ \mathrm {V}^e e$ et $ \mathrm {W}^e e$, et donnons en particulier des conditions sur $ \mathrm {W}$ ou sur la caract{\'e}ristique de $ \mathrm {R}$ pour que le comportement soit semblable au cas des repr{\'e}sentations complexes. Nous prenons un point de vue abstrait, n'utilisant que des propri{\'e}t{\'e}s g{\'e}n{\'e}rales de $ \mathrm {G}$. Nous terminons par une application {\`a} la th{\'e}orie des types pour le groupe $ \mathrm {GL}_n$ et ses formes int{\'e}rieures sur un corps local non archim{\'e}dien.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Koskivirta:2014:CRS, author = "Jean-Stefan Koskivirta", title = "Congruence Relations for {Shimura} Varieties Associated with {$ {\rm GU}(n - 1, 1) $}", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1305--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-037-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove the congruence relation for the mod-$p$ reduction of Shimura varieties associated to a unitary similitude group $ G U(n - 1, 1)$ over $ \mathbb {Q}$, when $p$ is inert and $n$ odd. The case when $n$ is even was obtained by T. Wedhorn and O. B?ltel, as a special case of a result of B. Moonen, when the $ \mu $-ordinary locus of the $p$-isogeny space is dense. This condition fails in our case. We show that every supersingular irreducible component of the special fiber of $ p \textrm {-} \mathscr {I}s o g$ is annihilated by a degree one polynomial in the Frobenius element $F$, which implies the congruence relation.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Mohar:2014:OCT, author = "Bojan Mohar and Petr Skoda", title = "Obstructions of Connectivity Two for Embedding Graphs into the Torus", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1327--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-025-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The complete set of minimal obstructions for embedding graphs into the torus is still not determined. In this paper, we present all obstructions for the torus of connectivity 2. Furthermore, we describe the building blocks of obstructions of connectivity 2 for any orientable surface.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Osekowski:2014:SLI, author = "Adam Osekowski", title = "Sharp Localized Inequalities for {Fourier} Multipliers", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1358--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-050-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In the paper we study sharp localized $ L^q \colon L^p $ estimates for Fourier multipliers resulting from modulation of the jumps of L{\'e}vy processes. The proofs of these estimates rest on probabilistic methods and exploit related sharp bounds for differentially subordinated martingales, which are of independent interest. The lower bounds for the constants involve the analysis of laminates, a family of certain special probability measures on $ 2 \times 2 $ matrices. As an application, we obtain new sharp bounds for the real and imaginary parts of the Beurling-Ahlfors operator .", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Wu:2014:WCM, author = "Xinfeng Wu", title = "Weighted {Carleson} Measure Spaces Associated with Different Homogeneities", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1382--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-021-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we introduce weighted Carleson measure spaces associated with different homogeneities and prove that these spaces are the dual spaces of weighted Hardy spaces studied in a forthcoming paper. As an application, we establish the boundedness of composition of two Calder{\'o}n-Zygmund operators with different homogeneities on the weighted Carleson measure spaces; this, in particular, provides the weighted endpoint estimates for the operators studied by Phong-Stein.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhang:2014:GKE, author = "Xi Zhang and Xiangwen Zhang", title = "Generalized {K{\"a}hler--Einstein} Metrics and Energy Functionals", journal = j-CAN-J-MATH, volume = "66", number = "6", pages = "1413--??", month = dec, year = "2014", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-034-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v66/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we consider a generalized K{\"a}hler-Einstein equation on K{\"a}hler manifold $M$. Using the twisted $ \mathcal K$-energy introduced by Song and Tian, we show that the existence of generalized K{\"a}hler-Einstein metrics with semi-positive twisting $ (1, 1)$-form $ \theta $ is also closely related to the properness of the twisted $ \mathcal K$-energy functional. Under the condition that the twisting form $ \theta $ is strictly positive at a point or $M$ admits no nontrivial Hamiltonian holomorphic vector field, we prove that the existence of generalized K{\"a}hler-Einstein metric implies a Moser-Trudinger type inequality.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Alfonseca:2015:LCI, author = "M. Angeles Alfonseca and Jaegil Kim", title = "On the Local Convexity of Intersection Bodies of Revolution", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "3--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-039-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "One of the fundamental results in Convex Geometry is Busemann's theorem, which states that the intersection body of a symmetric convex body is convex. Thus, it is only natural to ask if there is a quantitative version of Busemann's theorem, i.e., if the intersection body operation actually improves convexity. In this paper we concentrate on the symmetric bodies of revolution to provide several results on the (strict) improvement of convexity under the intersection body operation. It is shown that the intersection body of a symmetric convex body of revolution has the same asymptotic behavior near the equator as the Euclidean ball. We apply this result to show that in sufficiently high dimension the double intersection body of a symmetric convex body of revolution is very close to an ellipsoid in the Banach-Mazur distance. We also prove results on the local convexity at the equator of intersection bodies in the class of star bodies of revolution.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Asadollahi:2015:BDC, author = "Javad Asadollahi and Rasool Hafezi and Razieh Vahed", title = "Bounded Derived Categories of Infinite Quivers: {Grothendieck} Duality, Reflection Functor", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "28--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-018-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study bounded derived categories of the category of representations of infinite quivers over a ring $R$. In case $R$ is a commutative noetherian ring with a dualising complex, we investigate an equivalence similar to Grothendieck duality for these categories, while a notion of dualising complex does not apply to them. The quivers we consider are left, resp. right, rooted quivers that are either noetherian or their opposite are noetherian. We also consider reflection functor and generalize a result of Happel to noetherian rings of finite global dimension, instead of fields.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Barron:2015:VLA, author = "Tatyana Barron and Dmitry Kerner and Marina Tvalavadze", title = "On Varieties of {Lie} Algebras of Maximal Class", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "55--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-008-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study complex projective varieties that parametrize (finite-dimensional) filiform Lie algebras over $ {\mathbb C} $, using equations derived by Millionshchikov. In the infinite-dimensional case we concentrate our attention on $ {\mathbb N}$-graded Lie algebras of maximal class. As shown by A. Fialowski there are only three isomorphism types of $ \mathbb {N}$-graded Lie algebras $ L = \oplus^{\infty }_{i = 1} L_i$ of maximal class generated by $ L_1$ and $ L_2$, $ L = \langle L_1, L_2 \rangle $. Vergne described the structure of these algebras with the property $ L = \langle L_1 \rangle $. In this paper we study those generated by the first and $q$-th components where $ q \gt 2$, $ L = \langle L_1, L_q \rangle $. Under some technical condition, there can only be one isomorphism type of such algebras. For $ q = 3$ we fully classify them. This gives a partial answer to a question posed by Millionshchikov.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bousch:2015:PDC, author = "Thierry Bousch", title = "Une propri{\'e}t{\'e} de domination convexe pour les orbites sturmiennes. ({French}) [{A} property of convex domination for {Sturmian} orbits]", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "90--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-009-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ {\bf x} = (x_0, x_1, \ldots) $ be a $N$-periodic sequence of integers ($ N \ge 1$), and $ {\bf s}$ a sturmian sequence with the same barycenter (and also $N$-periodic, consequently). It is shown that, for affine functions $ \alpha : \mathbb R^\mathbb N_{(N)} \to \mathbb R$ which are increasing relatively to some order $ \le_2$ on $ \mathbb R^\mathbb N_{(N)}$ (the space of all $N$-periodic sequences), the average of $ | \alpha |$ on the orbit of $ {\bf x}$ is greater than its average on the orbit of $ {\bf s}$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Chang:2015:WPN, author = "Jui-En Chang and Ling Xiao", title = "The {Weyl} Problem With Nonnegative {Gauss} Curvature In Hyperbolic Space", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "107--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-046-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we discuss the isometric embedding problem in hyperbolic space with nonnegative extrinsic curvature. We prove a priori bounds for the trace of the second fundamental form $H$ and extend the result to $n$-dimensions. We also obtain an estimate for the gradient of the smaller principal curvature in 2 dimensions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Clouatre:2015:UES, author = "Rapha{\"e}l Clou{\^a}tre", title = "Unitary Equivalence and Similarity to {Jordan} Models for Weak Contractions of Class {$ C_0 $}", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "132--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-044-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We obtain results on the unitary equivalence of weak contractions of class $ C_0 $ to their Jordan models under an assumption on their commutants. In particular, our work addresses the case of arbitrary finite multiplicity. The main tool is the theory of boundary representations due to Arveson. We also generalize and improve previously known results concerning unitary equivalence and similarity to Jordan models when the minimal function is a Blaschke product.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Lescop:2015:HIC, author = "Christine Lescop", title = "On Homotopy Invariants of Combings of Three-manifolds", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "152--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-031-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Combings of compact, oriented $3$-dimensional manifolds $M$ are homotopy classes of nowhere vanishing vector fields. The Euler class of the normal bundle is an invariant of the combing, and it only depends on the underlying Spin$^c$-structure. A combing is called torsion if this Euler class is a torsion element of $ H^2 (M; \mathbb Z)$. Gompf introduced a $ \mathbb Q$-valued invariant $ \theta_G$ of torsion combings on closed $3$-manifolds, and he showed that $ \theta_G$ distinguishes all torsion combings with the same Spin$^c$-structure. We give an alternative definition for $ \theta_G$ and we express its variation as a linking number. We define a similar invariant $ p_1$ of combings for manifolds bounded by $ S^2$. We relate $ p_1$ to the $ \Theta $-invariant, which is the simplest configuration space integral invariant of rational homology $3$-balls, by the formula $ \Theta = \frac 14 p_1 + 6 \lambda (\hat {M})$ where $ \lambda $ is the Casson-Walker invariant. The article also includes a self-contained presentation of combings for $3$-manifolds.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{McReynolds:2015:GSC, author = "D. B. McReynolds", title = "Geometric Spectra and Commensurability", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "184--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-003-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The work of Reid, Chinburg-Hamilton-Long-Reid, Prasad-Rapinchuk, and the author with Reid have demonstrated that geodesics or totally geodesic submanifolds can sometimes be used to determine the commensurability class of an arithmetic manifold. The main results of this article show that generalizations of these results to other arithmetic manifolds will require a wide range of data. Specifically, we prove that certain incommensurable arithmetic manifolds arising from the semisimple Lie groups of the form $ (\operatorname {SL}(d, \mathbf {R}))^r \times (\operatorname {SL}(d, \mathbf {C}))^s $ have the same commensurability classes of totally geodesic submanifolds coming from a fixed field. This construction is algebraic and shows the failure of determining, in general, a central simple algebra from subalgebras over a fixed field. This, in turn, can be viewed in terms of forms of $ \operatorname {SL}_d $ and the failure of determining the form via certain classes of algebraic subgroups.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Murty:2015:TCA, author = "V. Kumar Murty and Vijay M. Patankar", title = "{Tate} Cycles on {Abelian} Varieties with Complex Multiplication", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "198--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-001-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider Tate cycles on an Abelian variety $A$ defined over a sufficiently large number field $K$ and having complex multiplication. We show that there is an effective bound $ C = C(A, K)$ so that to check whether a given cohomology class is a Tate class on $A$, it suffices to check the action of Frobenius elements at primes $v$ of norm $ \leq C$. We also show that for a set of primes $v$ of $K$ of density $1$, the space of Tate cycles on the special fibre $ A_v$ of the N{\'e}ron model of $A$ is isomorphic to the space of Tate cycles on $A$ itself.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Szpruch:2015:SGS, author = "Dani Szpruch", title = "Symmetric Genuine Spherical {Whittaker} Functions on {$ \overline {\rm GSp}_{2n}(F) $}", journal = j-CAN-J-MATH, volume = "67", number = "1", pages = "214--??", month = feb, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-033-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Feb 13 18:04:13 MST 2015", bibsource = "http://cms.math.ca/cjm/v67/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $F$ be a p-adic field of odd residual characteristic. Let $ \overline {GSp_{2n}(F)}$ and $ \overline {Sp_{2n}(F)}$ be the metaplectic double covers of the general symplectic group and the symplectic group attached to the $ 2 n$ dimensional symplectic space over $F$. Let $ \sigma $ be a genuine, possibly reducible, unramified principal series representation of $ \overline {GSp_{2n}(F)}$. In these notes we give an explicit formulas for a spanning set for the space of Spherical Whittaker functions attached to $ \sigma $. For odd $n$, and generically for even $n$, this spanning set is a basis. The significant property of this set is that each of its elements is unchanged under the action of the Weyl group of $ \overline {Sp_{2n}(F)}$. If $n$ is odd then each element in the set has an equivariant property that generalizes a uniqueness result of Gelbart, Howe and Piatetski-Shapiro. Using this symmetric set, we construct a family of reducible genuine unramified principal series representations which have more then one generic constituent. This family contains all the reducible genuine unramified principal series representations induced from a unitary data and exists only for $n$ even.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Agler:2015:GHF, author = "Jim Agler and John E. McCarthy", title = "Global Holomorphic Functions in Several Noncommuting Variables", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-024-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We define a free holomorphic function to be a function that is locally, with respect to the free topology, a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic functions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bell:2015:SML, author = "Jason P. Bell and Jeffrey C. Lagarias", title = "A {Skolem--Mahler--Lech} Theorem for Iterated Automorphisms of {$K$}-algebras", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-048-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This paper proves a commutative algebraic extension of a generalized Skolem-Mahler-Lech theorem due to the first author. Let $A$ be a finitely generated commutative $K$-algebra over a field of characteristic $0$, and let $ \sigma $ be a $K$-algebra automorphism of $A$. Given ideals $I$ and $J$ of $A$, we show that the set $S$ of integers $m$ such that $ \sigma^m(I) \supseteq J$ is a finite union of complete doubly infinite arithmetic progressions in $m$, up to the addition of a finite set. Alternatively, this result states that for an affine scheme $X$ of finite type over $K$, an automorphism $ \sigma \in \operatorname {Aut}_K(X)$, and $Y$ and $Z$ any two closed subschemes of $X$, the set of integers $m$ with $ \sigma^m(Z) \subseteq Y$ is as above. The paper presents examples showing that this result may fail to hold if the affine scheme $X$ is not of finite type, or if $X$ is of finite type but the field $K$ has positive characteristic.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bellaiche:2015:UEI, author = "Jo{\"e}l Bella{\"\i}che", title = "Unitary Eigenvarieties at Isobaric Points", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-020-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this article we study the geometry of the eigenvarieties of unitary groups at points corresponding to tempered non-stable representations with an anti-ordinary (a.k.a evil) refinement. We prove that, except in the case the Galois representation attached to the automorphic form is a sum of characters, the eigenvariety is non-smooth at such a point, and that (under some additional hypotheses) its tangent space is big enough to account for all the relevant Selmer group. We also study the local reducibility locus at those points, proving that in general, in contrast with the case of the eigencurve, it is a proper subscheme of the fiber of the eigenvariety over the weight space.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bernardes:2015:HDG, author = "Nilson C. {Bernardes, Jr.} and R{\^o}mulo M. Vermersch", title = "Hyperspace Dynamics of Generic Maps of the {Cantor} Space", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-005-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the hyperspace dynamics induced from generic continuous maps and from generic homeomorphisms of the Cantor space, with emphasis on the notions of Li-Yorke chaos, distributional chaos, topological entropy, chain continuity, shadowing and recurrence.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Colombo:2015:MOT, author = "Maria Colombo and Luigi {De Pascale} and Simone {Di Marino}", title = "Multimarginal Optimal Transport Maps for One-dimensional Repulsive Costs", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-011-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study a multimarginal optimal transportation problem in one dimension. For a symmetric, repulsive cost function, we show that given a minimizing transport plan, its symmetrization is induced by a cyclical map, and that the symmetric optimal plan is unique. The class of costs that we consider includes, in particular, the Coulomb cost, whose optimal transport problem is strictly related to the strong interaction limit of Density Functional Theory. In this last setting, our result justifies some qualitative properties of the potentials observed in numerical experiments.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Graham:2015:FPF, author = "Robert Graham and Mikael Pichot", title = "A Free Product Formula for the Sofic Dimension", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-019-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "It is proved that if $ G = G_1 *_{G_3}G_2 $ is free product of probability measure preserving $s$-regular ergodic discrete groupoids amalgamated over an amenable subgroupoid $ G_3$, then the sofic dimension $ s(G)$ satisfies the equality \[ s(G)=\mathfrak{h}(G_1^0)s(G_1)+\mathfrak{h}(G_2^0)s(G_2)-\mathfrak{h}(G_3^0)s(G_3) \] where $ \mathfrak {h}$ is the normalized Haar measure on $G$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Hua:2015:RAE, author = "Jiajie Hua and Huaxin Lin", title = "Rotation Algebras and the {Exel} Trace Formula", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-032-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We found that if $u$ and $v$ are any two unitaries in a unital $ C^*$-algebra with $ \| u v - v u \| \lt 2$ and $ u v u^*v^*$ commutes with $u$ and $ v, $ then the $ C^*$-subalgebra $ A_{u, v}$ generated by $u$ and $v$ is isomorphic to a quotient of some rotation algebra $ A_\theta $ provided that $ A_{u, v}$ has a unique tracial state. We also found that the Exel trace formula holds in any unital $ C^*$-algebra. Let $ \theta \in ( - 1 / 2, 1 / 2)$ be a real number. We prove the following: For any $ \epsilon \gt 0, $ there exists $ \delta \gt 0$ satisfying the following: if $u$ and $v$ are two unitaries in any unital simple $ C^*$-algebra $A$ with tracial rank zero such that \[ \|uv-e^{2\pi i\theta}vu\|\lt \delta \text{ and } {1\over{2\pi i}}\tau(\log(uvu^*v^*))=\theta, \] for all tracial state $ \tau $ of $ A, $ then there exists a pair of unitaries $ \tilde {u}$ and $ \tilde {v}$ in $A$ such that \[ \tilde{u}\tilde{v}=e^{2\pi i\theta} \tilde{v}\tilde{u},\,\, \|u-\tilde{u}\|\lt \epsilon \text{ and } \|v-\tilde{v}\|\lt \epsilon. \]", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Samart:2015:MML, author = "Detchat Samart", title = "{Mahler} Measures as Linear Combinations of {$L$}-values of Multiple Modular Forms", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-012-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the Mahler measures of certain families of Laurent polynomials in two and three variables. Each of the known Mahler measure formulas for these families involves $L$-values of at most one newform and/or at most one quadratic character. In this paper, we show, either rigorously or numerically, that the Mahler measures of some polynomials are related to $L$-values of multiple newforms and quadratic characters simultaneously. The results suggest that the number of modular $L$-values appearing in the formulas significantly depends on the shape of the algebraic value of the parameter chosen for each polynomial. As a consequence, we also obtain new formulas relating special values of hypergeometric series evaluated at algebraic numbers to special values of $L$-functions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Santoprete:2015:MSP, author = "Manuele Santoprete and J{\"u}rgen Scheurle and Sebastian Walcher", title = "Motion in a Symmetric Potential on the Hyperbolic Plane", journal = j-CAN-J-MATH, volume = "67", number = "2", pages = "??--??", month = apr, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2013-026-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the motion of a particle in the hyperbolic plane (embedded in Minkowski space), under the action of a potential that depends only on one variable. This problem is the analogous to the spherical pendulum in a unidirectional force field. However, for the discussion of the hyperbolic plane one has to distinguish three inequivalent cases, depending on the direction of the force field. Symmetry reduction, with respect to groups that are not necessarily compact or even reductive, is carried out by way of Poisson varieties and Hilbert maps. For each case the dynamics is discussed, with special attention to linear potentials.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{anHuef:2015:ACT, author = "Astrid an Huef and Robert John Archbold", title = "The {$ C* $}-algebras of Compact Transformation Groups", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-039-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We investigate the representation theory of the crossed-product $ C^*$-algebra associated to a compact group $G$ acting on a locally compact space $X$ when the stability subgroups vary discontinuously. Our main result applies when $G$ has a principal stability subgroup or $X$ is locally of finite $G$-orbit type. Then the upper multiplicity of the representation of the crossed product induced from an irreducible representation $V$ of a stability subgroup is obtained by restricting $V$ to a certain closed subgroup of the stability subgroup and taking the maximum of the multiplicities of the irreducible summands occurring in the restriction of $V$. As a corollary we obtain that when the trivial subgroup is a principal stability subgroup, the crossed product is a Fell algebra if and only if every stability subgroup is abelian. A second corollary is that the $ C^*$-algebra of the motion group $ \mathbb {R}^n \rtimes \operatorname {SO}(n)$ is a Fell algebra. This uses the classical branching theorem for the special orthogonal group $ \operatorname {SO}(n)$ with respect to $ \operatorname {SO}(n - 1)$. Since proper transformation groups are locally induced from the actions of compact groups, we describe how some of our results can be extended to transformation groups that are locally proper.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Borwein:2015:LPP, author = "Peter Borwein and Stephen Choi and Ron Ferguson and Jonas Jankauskas", title = "On {Littlewood} Polynomials with Prescribed Number of Zeros Inside the Unit Disk", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-007-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We investigate the numbers of complex zeros of Littlewood polynomials $ p(z) $ (polynomials with coefficients $ \{ - 1, 1 \} $) inside or on the unit circle $ |z| = 1$, denoted by $ N(p)$ and $ U(p)$, respectively. Two types of Littlewood polynomials are considered: Littlewood polynomials with one sign change in the sequence of coefficients and Littlewood polynomials with one negative coefficient. We obtain explicit formulas for $ N(p)$, $ U(p)$ for polynomials $ p(z)$ of these types. We show that, if $ n + 1$ is a prime number, then for each integer $k$, $ 0 \leq k \leq n - 1$, there exists a Littlewood polynomial $ p(z)$ of degree $n$ with $ N(p) = k$ and $ U(p) = 0$. Furthermore, we describe some cases when the ratios $ N(p) / n$ and $ U(p) / n$ have limits as $ n \to \infty $ and find the corresponding limit values.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Brugalle:2015:OAT, author = "Erwan Brugall{\'e} and Kristin Shaw", title = "Obstructions to Approximating Tropical Curves in Surfaces Via Intersection Theory", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-014-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We provide some new local obstructions to approximating tropical curves in smooth tropical surfaces. These obstructions are based on a relation between tropical and complex intersection theories which is also established here. We give two applications of the methods developed in this paper. First we classify all locally irreducible approximable 3-valent fan tropical curves in a fan tropical plane. Secondly, we prove that a generic non-singular tropical surface in tropical projective 3-space contains finitely many approximable tropical lines if it is of degree 3, and contains no approximable tropical lines if it is of degree 4 or more.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2015:TVO, author = "Fulin Chen and Yun Gao and Naihuan Jing and Shaobin Tan", title = "Twisted Vertex Operators and Unitary {Lie} Algebras", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-010-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A representation of the central extension of the unitary Lie algebra coordinated with a skew Laurent polynomial ring is constructed using vertex operators over an integral $ \mathbb Z_2$-lattice. The irreducible decomposition of the representation is explicitly computed and described. As a by-product, some fundamental representations of affine Kac--Moody Lie algebra of type $ A_n^{(2)}$ are recovered by the new method.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Drappeau:2015:SFE, author = "Sary Drappeau", title = "Sommes friables d'exponentielles et applications", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-036-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "An integer is said to be $y$-friable if its greatest prime factor is less than $y$. In this paper, we obtain estimates for exponential sums over $y$-friable numbers up to $x$ which are non-trivial when $ y \geq \exp \{ c \sqrt {\log x} \log \log x \} $. As a consequence, we obtain an asymptotic formula for the number of $y$-friable solutions to the equation $ a + b = c$ which is valid unconditionnally under the same assumption. We use a contour integration argument based on the saddle point method, as developed in the context of friable numbers by Hildebrand and Tenenbaum, and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Gonzalez:2015:PAC, author = "Jose Luis Gonzalez and Kalle Karu", title = "Projectivity in Algebraic Cobordism", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-026-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The algebraic cobordism group of a scheme is generated by cycles that are proper morphisms from smooth quasiprojective varieties. We prove that over a field of characteristic zero the quasiprojectivity assumption can be omitted to get the same theory.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Lim:2015:GSG, author = "Meng Fai Lim and V. Kumar Murty", title = "Growth of {Selmer} groups of {CM} {Abelian} varieties", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-041-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $p$ be an odd prime. We study the variation of the $p$-rank of the Selmer group of Abelian varieties with complex multiplication in certain towers of number fields.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Nishinou:2015:TDT, author = "Takeo Nishinou", title = "Toric Degenerations, Tropical Curve, and {Gromov--Witten} Invariants of {Fano} Manifolds", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-006-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we give a tropical method for computing Gromov-Witten type invariants of Fano manifolds of special type. This method applies to those Fano manifolds which admit toric degenerations to toric Fano varieties with singularities allowing small resolutions. Examples include (generalized) flag manifolds of type A, and some moduli space of rank two bundles on a genus two curve.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhang:2015:GIG, author = "Tong Zhang", title = "Geography of Irregular {Gorenstein} $3$-folds", journal = j-CAN-J-MATH, volume = "67", number = "3", pages = "??--??", month = jun, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-033-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Tue Jun 9 06:44:47 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we study the explicit geography problem of irregular Gorenstein minimal 3-folds of general type. We generalize the classical Noether-Castelnuovo type inequalities for irregular surfaces to irregular 3-folds according to the Albanese dimension.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Allen:2015:DCH, author = "Peter Allen and Julia B{\"o}ttcher and Jan Hladk{\'y} and Diana Piguet", title = "A Density {Corr{\'a}di-{Hajnal}} Theorem", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "721--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-030-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We find, for all sufficiently large $n$ and each $k$, the maximum number of edges in an $n$-vertex graph which does not contain $ k + 1$ vertex-disjoint triangles. This extends a result of Moon [Canad. J. Math. 20 (1968), 96-102] which is in turn an extension of Mantel's Theorem. Our result can also be viewed as a density version of the Corr{\'a}di-Hajnal Theorem.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Carey:2015:SFN, author = "Alan L. Carey and Victor Gayral and John Phillips and Adam Rennie and Fedor Sukochev", title = "Spectral Flow for Nonunital Spectral Triples", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "759--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-042-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove two results about nonunital index theory left open in a previous paper. The first is that the spectral triple arising from an action of the reals on a $ C^*$-algebra with invariant trace satisfies the hypotheses of the nonunital local index formula. The second result concerns the meaning of spectral flow in the nonunital case. For the special case of paths arising from the odd index pairing for smooth spectral triples in the nonunital setting we are able to connect with earlier approaches to the analytic definition of spectral flow.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Nasso:2015:SCE, author = "Mauro {Di Nasso} and Isaac Goldbring and Renling Jin and Steven Leth and Martino Lupini and Karl Mahlburg", title = "On a Sumset Conjecture of {Erd{\H{o}}s}", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "795--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-016-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "{Erd"os} conjectured that for any set $ A \subseteq \mathbb {N} $ with positive lower asymptotic density, there are infinite sets $ B, C \subseteq \mathbb {N} $ such that $ B + C \subseteq A $. We verify {Erd"os}' conjecture in the case that $A$ has Banach density exceeding $ \frac {1}{2}$. As a consequence, we prove that, for $ A \subseteq \mathbb {N}$ with positive Banach density (a much weaker assumption than positive lower density), we can find infinite $ B, C \subseteq \mathbb {N}$ such that $ B + C$ is contained in the union of $A$ and a translate of $A$. Both of the aforementioned results are generalized to arbitrary countable amenable groups. We also provide a positive solution to {Erd"os}' conjecture for subsets of the natural numbers that are pseudorandom.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Elliott:2015:AIE, author = "George A. Elliott and Zhuang Niu", title = "All Irrational Extended Rotation Algebras are {AF} Algebras", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "810--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-022-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \theta \in [0, 1] $ be any irrational number. It is shown that the extended rotation algebra $ \mathcal B_\theta $ introduced in a previous paper is always an AF algebra.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kaniuth:2015:BSE, author = "Eberhard Kaniuth", title = "The {Bochner--Schoenberg--Eberlein} Property and Spectral Synthesis for Certain {Banach} Algebra Products", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "827--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-028-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Associated with two commutative Banach algebras $A$ and $B$ and a character $ \theta $ of $B$ is a certain Banach algebra product $ A \times_\theta B$, which is a splitting extension of $B$ by $A$. We investigate two topics for the algebra $ A \times_\theta B$ in relation to the corresponding ones of $A$ and $B$. The first one is the Bochner-Schoenberg-Eberlein property and the algebra of Bochner-Schoenberg-Eberlein functions on the spectrum, whereas the second one concerns the wide range of spectral synthesis problems for $ A \times_\theta B$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kock:2015:FAR, author = "Bernhard K{\"o}ck and Joseph Tait", title = "Faithfulness of Actions on {Riemann--Roch} Spaces", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "848--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-015-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Given a faithful action of a finite group $G$ on an algebraic curve~$X$ of genus $ g_X \geq 2$, we give explicit criteria for the induced action of~$G$ on the Riemann--Roch space~$ H^0 (X, \mathcal {O}_X(D))$ to be faithful, where $D$ is a $G$-invariant divisor on $X$ of degree at least~$ 2 g_X - 2$. This leads to a concise answer to the question when the action of~$G$ on the space~$ H^0 (X, \Omega_X^{\otimes m})$ of global holomorphic polydifferentials of order $m$ is faithful. If $X$ is hyperelliptic, we furthermore provide an explicit basis of~$ H^0 (X, \Omega_X^{\otimes m})$. Finally, we give applications in deformation theory and in coding theory and we discuss the analogous problem for the action of~$G$ on the first homology $ H_1 (X, \mathbb {Z} / m \mathbb {Z})$ if $X$ is a Riemann surface.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Lin:2015:MDS, author = "Huaxin Lin", title = "Minimal Dynamical Systems on Connected Odd Dimensional Spaces", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "870--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-035-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \beta \colon S^{2n + 1} \to S^{2n + 1} $ be a minimal homeomorphism ($ n \ge 1$). We show that the crossed product $ C(S^{2n + 1}) \rtimes_\beta \mathbb {Z}$ has rational tracial rank at most one. Let $ \Omega $ be a connected compact metric space with finite covering dimension and with $ H^1 (\Omega, \mathbb {Z}) = \{ 0 \} .$ Suppose that $ K_i(C(\Omega)) = \mathbb {Z} \oplus G_i, $ where $ G_i$ is a finite abelian group, $ i = 0, 1.$ Let $ \beta \colon \Omega \to \Omega $ be a minimal homeomorphism. We also show that $ A = C(\Omega) \rtimes_\beta \mathbb {Z}$ has rational tracial rank at most one and is classifiable. In particular, this applies to the minimal dynamical systems on odd dimensional real projective spaces. This is done by studying minimal homeomorphisms on $ X \times \Omega, $ where $X$ is the Cantor set.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Mok:2015:OFS, author = "Chung Pang Mok and Fucheng Tan", title = "Overconvergent Families of {Siegel--Hilbert} Modular Forms", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "893--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-017-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We construct one-parameter families of overconvergent Siegel-Hilbert modular forms. This result has applications to construction of Galois representations for automorphic forms of non-cohomological weights.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Pan:2015:CMJ, author = "Ivan Edgardo Pan and Aron Simis", title = "{Cremona} Maps of {de Jonqui{\`e}res} Type", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "923--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-037-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This paper is concerned with suitable generalizations of a plane de Jonqui{\`e}res map to higher dimensional space $ \mathbb {P}^n $ with $ n \geq 3 $. For each given point of $ \mathbb {P}^n $ there is a subgroup of the entire Cremona group of dimension $n$ consisting of such maps. One studies both geometric and group-theoretical properties of this notion. In the case where $ n = 3$ one describes an explicit set of generators of the group and gives a homological characterization of a basic subgroup thereof.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Roth:2015:PMP, author = "Oliver Roth", title = "{Pontryagin}'s Maximum Principle for the {Loewner} Equation in Higher Dimensions", journal = j-CAN-J-MATH, volume = "67", number = "4", pages = "942--??", month = aug, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-027-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we develop a variational method for the Loewner equation in higher dimensions. As a result we obtain a version of Pontryagin's maximum principle from optimal control theory for the Loewner equation in several complex variables. Based on recent work of Arosio, Bracci and Wold, we then apply our version of the Pontryagin maximum principle to obtain first-order necessary conditions for the extremal mappings for a wide class of extremal problems over the set of normalized biholomorphic mappings on the unit ball in $ \mathbb {C}^n $.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Abuaf:2015:OBS, author = "Roland Abuaf and Ada Boralevi", title = "Orthogonal Bundles and Skew-{Hamiltonian} Matrices", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "961--??", month = oct, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-034-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Using properties of skew-Hamiltonian matrices and classic connectedness results, we prove that the moduli space $ M_{ort}^0 (r, n) $ of stable rank $r$ orthogonal vector bundles on $ \mathbb {P}^2$, with Chern classes $ (c_1, c_2) = (0, n)$, and trivial splitting on the general line, is smooth irreducible of dimension $ (r - 2)n - \binom {r}{2}$ for $ r = n$ and $ n \ge 4$, and $ r = n - 1$ and $ n \ge 8$. We speculate that the result holds in greater generality.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Amini:2015:CBD, author = "Massoud Amini and George A. Elliott and Nasser Golestani", title = "The Category of {Bratteli} Diagrams", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "990--??", month = oct, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-001-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A category structure for Bratteli diagrams is proposed and a functor from the category of AF algebras to the category of Bratteli diagrams is constructed. Since isomorphism of Bratteli diagrams in this category coincides with Bratteli's notion of equivalence, we obtain in particular a functorial formulation of Bratteli's classification of AF algebras (and at the same time, of Glimm's classification of UHF~algebras). It is shown that the three approaches to classification of AF~algebras, namely, through Bratteli diagrams, K-theory, and abstract classifying categories, are essentially the same from a categorical point of view.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ashraf:2015:RSP, author = "Samia Ashraf and Haniya Azam and Barbu Berceanu", title = "Representation Stability of Power Sets and Square Free Polynomials", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "1024--??", month = oct, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-029-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The symmetric group $ \mathcal {S}_n $ acts on the power set $ \mathcal {P}(n) $ and also on the set of square free polynomials in $n$ variables. These two related representations are analyzed from the stability point of view. An application is given for the action of the symmetric group on the cohomology of the pure braid group.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Dubickas:2015:EFC, author = "Arturas Dubickas and Min Sha and Igor Shparlinski", title = "Explicit Form of {Cassels} $p$-adic Embedding Theorem for Number Fields", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "1046--??", month = oct, year = "2015", CODEN = "CJMAAB", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we mainly give a general explicit form of Cassels' $p$-adic embedding theorem for number fields. We also give its refined form in the case of cyclotomic fields. As a byproduct, given an irreducible polynomial $f$ over $ \mathbb {Z}$, we give a general unconditional upper bound for the smallest prime number $p$ such that $f$ has a simple root modulo $p$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ducrot:2015:FTC, author = "Arnaud Ducrot and Pierre Magal and Ousmane Seydi", title = "A Finite-time Condition for Exponential Trichotomy in Infinite Dynamical Systems", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "1065--??", month = oct, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-023-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this article we study exponential trichotomy for infinite dimensional discrete time dynamical systems. The goal of this article is to prove that finite time exponential trichotomy conditions allow to derive exponential trichotomy for any times. We present an application to the case of pseudo orbits in some neighborhood of a normally hyperbolic set.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Mine:2015:MCC, author = "Kotaro Mine and Atsushi Yamashita", title = "Metric Compactifications and Coarse Structures", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "1091--??", month = oct, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-029-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathbf {TB} $ be the category of totally bounded, locally compact metric spaces with the $ C_0 $ coarse structures. We show that if $X$ and $Y$ are in $ \mathbf {TB}$ then $X$ and $Y$ are coarsely equivalent if and only if their Higson coronas are homeomorphic. In fact, the Higson corona functor gives an equivalence of categories $ \mathbf {TB} \to \mathbf {K}$, where $ \mathbf {K}$ is the category of compact metrizable spaces. We use this fact to show that the continuously controlled coarse structure on a locally compact space $X$ induced by some metrizable compactification $ \tilde {X}$ is determined only by the topology of the remainder $ \tilde {X} \setminus X$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Nohara:2015:GSB, author = "Yuichi Nohara and Kazushi Ueda", title = "{Goldman} Systems and Bending Systems", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "1109--??", month = oct, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-004-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We show that the moduli space of parabolic bundles on the projective line and the polygon space are isomorphic, both as complex manifolds and symplectic manifolds equipped with structures of completely integrable systems, if the stability parameters are small.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Nystedt:2015:OPA, author = "Patrik Nystedt and Johan {\"O}inert", title = "Outer Partial Actions and Partial Skew Group Rings", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "1144--??", month = oct, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-043-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We extend the classicial notion of an outer action $ \alpha $ of a group $G$ on a unital ring $A$ to the case when $ \alpha $ is a partial action on ideals, all of which have local units. We show that if $ \alpha $ is an outer partial action of an abelian group $G$, then its associated partial skew group ring $ A \star_\alpha G$ is simple if and only if $A$ is $G$-simple. This result is applied to partial skew group rings associated with two different types of partial dynamical systems.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhang:2015:NTM, author = "Junqiang Zhang and Jun Cao and Renjin Jiang and Dachun Yang", title = "Non-tangential Maximal Function Characterizations of {Hardy} Spaces Associated with Degenerate Elliptic Operators", journal = j-CAN-J-MATH, volume = "67", number = "5", pages = "1161--??", month = oct, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-038-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 19 16:04:46 MDT 2015", bibsource = "http://cms.math.ca/cjm/v67/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $w$ be either in the Muckenhoupt class of $ A_2 (\mathbb {R}^n)$ weights or in the class of $ Q C(\mathbb {R}^n)$ weights, and $ L_w := - w^{-1} \mathop {\mathrm {div}}(A \nabla)$ the degenerate elliptic operator on the Euclidean space $ \mathbb {R}^n$, $ n \ge 2$. In this article, the authors establish the non-tangential maximal function characterization of the Hardy space $ H_{L_w}^p(\mathbb {R}^n)$ associated with $ L_w$ for $ p \in (0, 1]$ and, when $ p \in (\frac {n}{n + 1}, 1]$ and $ w \in A_{q_0}(\mathbb {R}^n)$ with $ q_0 \in [1, \frac {p(n + 1)}n)$, the authors prove that the associated Riesz transform $ \nabla L_w^{-1 / 2}$ is bounded from $ H_{L_w}^p(\mathbb {R}^n)$ to the weighted classical Hardy space $ H_w^p(\mathbb {R}^n)$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Aluffi:2015:CCS, author = "Paolo Aluffi and Eleonore Faber", title = "{Chern} Classes of Splayed Intersections", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1201--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-010-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We generalize the Chern class relation for the transversal intersection of two nonsingular varieties to a relation for possibly singular varieties, under a splayedness assumption. We show that the relation for the Chern-Schwartz-MacPherson classes holds for two splayed hypersurfaces in a nonsingular variety, and under a `strong splayedness' assumption for more general subschemes. Moreover, the relation is shown to hold for the Chern-Fulton classes of any two splayed subschemes. The main tool is a formula for Segre classes of splayed subschemes. We also discuss the Chern class relation under the assumption that one of the varieties is a general very ample divisor.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Balwe:2015:AMM, author = "Chetan Balwe", title = "$p$-adic and {Motivic} Measure on {Artin} $n$-stacks", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1219--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-021-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We define a notion of $p$-adic measure on Artin $n$-stacks which are of strongly finite type over the ring of $p$-adic integers. $p$-adic measure on schemes can be evaluated by counting points on the reduction of the scheme modulo $ p^n$. We show that an analogous construction works in the case of Artin stacks as well if we count the points using the counting measure defined by To{\"e}n. As a consequence, we obtain the result that the Poincar{\'e} and Serre series of such stacks are rational functions, thus extending Denef's result for varieties. Finally, using motivic integration we show that as $p$ varies, the rationality of the Serre series of an Artin stack defined over the integers is uniform with respect to $p$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Barros:2015:LSA, author = "Carlos Braga Barros and Victor Rocha and Josiney Souza", title = "{Lyapunov} Stability and Attraction Under Equivariant Maps", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1247--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-007-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $M$ and $N$ be admissible Hausdorff topological spaces endowed with admissible families of open coverings. Assume that $ \mathcal {S}$ is a semigroup acting on both $M$ and $N$. In this paper we study the behavior of limit sets, prolongations, prolongational limit sets, attracting sets, attractors and Lyapunov stable sets (all concepts defined for the action of the semigroup $ \mathcal {S}$) under equivariant maps and semiconjugations from $M$ to $N$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Carcamo:2015:SES, author = "Cristian Carcamo and Claudio Vidal", title = "Stability of Equilibrium Solutions in Planar {Hamiltonian} Difference Systems", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1270--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-040-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we study the stability in the Lyapunov sense of the equilibrium solutions of discrete or difference Hamiltonian systems in the plane. First, we perform a detailed study of linear Hamiltonian systems as a function of the parameters, in particular we analyze the regular and the degenerate cases. Next, we give a detailed study of the normal form associated with the linear Hamiltonian system. At the same time we obtain the conditions under which we can get stability (in linear approximation) of the equilibrium solution, classifying all the possible phase diagrams as a function of the parameters. After that, we study the stability of the equilibrium solutions of the first order difference system in the plane associated to mechanical Hamiltonian system and Hamiltonian system defined by cubic polynomials. Finally, important differences with the continuous case are pointed out.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Charlesworth:2015:TFF, author = "Ian Charlesworth and Brent Nelson and Paul Skoufranis", title = "On Two-faced Families of Non-commutative Random Variables", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1290--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-002-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We demonstrate that the notions of bi-free independence and combinatorial-bi-free independence of two-faced families are equivalent using a diagrammatic view of bi-non-crossing partitions. These diagrams produce an operator model on a Fock space suitable for representing any two-faced family of non-commutative random variables. Furthermore, using a Kreweras complement on bi-non-crossing partitions we establish the expected formulas for the multiplicative convolution of a bi-free pair of two-faced families.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Cojocaru:2015:DFE, author = "Alina Carmen Cojocaru and Andrew Michael Shulman", title = "The Distribution of the First Elementary Divisor of the Reductions of a Generic {Drinfeld} Module of Arbitrary Rank", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1326--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-006-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \psi $ be a generic Drinfeld module of rank $ r \geq 2 $. We study the first elementary divisor $ d_{1, \wp }(\psi) $ of the reduction of $ \psi $ modulo a prime $ \wp $, as $ \wp $ varies. In particular, we prove the existence of the density of the primes $ \wp $ for which $ d_{1, \wp } (\psi) $ is fixed. For $ r = 2 $, we also study the second elementary divisor (the exponent) of the reduction of $ \psi $ modulo $ \wp $ and prove that, on average, it has a large norm. Our work is motivated by the study of J.-P. Serre of an elliptic curve analogue of Artin's Primitive Root Conjecture, and, moreover, by refinements to Serre's study developed by the first author and M.R. Murty.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Trillos:2015:RCE, author = "Nicolas Garcia Trillos and Dejan Slepcev", title = "On the Rate of Convergence of Empirical Measures in $ \infty $-transportation Distance", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1358--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-044-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $ \infty $-transportation distance between the measure and the empirical measure of the sample. The bound is optimal in terms of scaling with the number of sample points.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Graczyk:2015:SLS, author = "Piotr Graczyk and Todd Kemp and Jean-Jacques Loeb", title = "Strong Logarithmic {Sobolev} Inequalities for Log-Subharmonic Functions", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1384--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-015-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove an intrinsic equivalence between strong hypercontractivity and a strong logarithmic Sobolev inequality for the cone of logarithmically subharmonic (LSH) functions. We introduce a new large class of measures, Euclidean regular and exponential type, in addition to all compactly-supported measures, for which this equivalence holds. We prove a Sobolev density theorem through LSH functions and use it to prove the equivalence of strong hypercontractivity and the strong logarithmic Sobolev inequality for such log-subharmonic functions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kawakami:2015:FTP, author = "Yu Kawakami", title = "Function-theoretic Properties for the {Gauss} Maps of Various Classes of Surfaces", journal = j-CAN-J-MATH, volume = "67", number = "6", pages = "1411--??", month = dec, year = "2015", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-008-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v67/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We elucidate the geometric background of function-theoretic properties for the Gauss maps of several classes of immersed surfaces in three-dimensional space forms, for example, minimal surfaces in Euclidean three-space, improper affine spheres in the affine three-space, and constant mean curvature one surfaces and flat surfaces in hyperbolic three-space. To achieve this purpose, we prove an optimal curvature bound for a specified conformal metric on an open Riemann surface and give some applications. We also provide unicity theorems for the Gauss maps of these classes of surfaces.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Boden:2016:SCI, author = "Hans Ulysses Boden and Cynthia L. Curtis", title = "The {$ {\rm SL}(2, C) $} {Casson} Invariant for Knots and the {$ \hat {A} $}-polynomial", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "3--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-025-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we extend the definition of the $ {SL(2, {\mathbb C})} $ Casson invariant to arbitrary knots $K$ in integral homology 3-spheres and relate it to the $m$-degree of the $ \widehat {A}$-polynomial of $K$. We prove a product formula for the $ \widehat {A}$-polynomial of the connected sum $ K_1 \# K_2$ of two knots in $ S^3$ and deduce additivity of $ {SL(2, {\mathbb C})}$ Casson knot invariant under connected sum for a large class of knots in $ S^3$. We also present an example of a nontrivial knot $K$ in $ S^3$ with trivial $ \widehat {A}$-polynomial and trivial $ {SL(2, {\mathbb C})}$ Casson knot invariant, showing that neither of these invariants detect the unknot.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bonfanti:2016:ASA, author = "Matteo Alfonso Bonfanti and Bert van Geemen", title = "{Abelian} Surfaces with an Automorphism and Quaternionic Multiplication", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "24--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-045-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We construct one dimensional families of Abelian surfaces with quaternionic multiplication which also have an automorphism of order three or four. Using Barth's description of the moduli space of $ (2, 4)$-polarized Abelian surfaces, we find the Shimura curve parametrizing these Abelian surfaces in a specific case. We explicitly relate these surfaces to the Jacobians of genus two curves studied by Hashimoto and Murabayashi. We also describe a (Humbert) surface in Barth's moduli space which parametrizes Abelian surfaces with real multiplication by $ \mathbf {Z}[\sqrt {2}]$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Breton:2016:SSU, author = "David J. Fern{\'a}ndez Bret{\'o}n", title = "Strongly Summable Ultrafilters, Union Ultrafilters, and the Trivial Sums Property", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "44--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-023-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We answer two questions of Hindman, Steprans and Strauss, namely we prove that every strongly summable ultrafilter on an abelian group is sparse and has the trivial sums property. Moreover we show that in most cases the sparseness of the given ultrafilter is a consequence of its being isomorphic to a union ultrafilter. However, this does not happen in all cases: we also construct (assuming Martin's Axiom for countable partial orders, i.e. $ \operatorname {cov}(\mathcal {M}) = \mathfrak c$), on the Boolean group, a strongly summable ultrafilter that is not additively isomorphic to any union ultrafilter.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ishida:2016:LBE, author = "Hirotaka Ishida", title = "A Lower Bound on the {Euler--Poincar{\'e}} Characteristic of Certain Surfaces of General Type with a Linear Pencil of Hyperelliptic Curves", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "67--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-032-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $S$ be a surface of general type. In this article, when there exists a relatively minimal hyperelliptic fibration $ f \colon S \rightarrow \mathbb {P}^1$ whose slope is less than or equal to four, we show the lower bound on the Euler-Poincar{\'e} characteristic of $S$. Furthermore, we prove that our bound is the best possible by giving required hyperelliptic fibrations.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Jaffe:2016:PPD, author = "Ethan Y. Jaffe", title = "Pathological Phenomena in {Denjoy--Carleman} Classes", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "88--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-009-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathcal {C}^M $ denote a Denjoy-Carleman class of $ \mathcal {C}^\infty $ functions (for a given logarithmically-convex sequence $ M = (M_n)$). We construct: (1) a function in $ \mathcal {C}^M(( - 1, 1))$ which is nowhere in any smaller class; (2) a function on $ \mathbb {R}$ which is formally $ \mathcal {C}^M$ at every point, but not in $ \mathcal {C}^M(\mathbb {R})$; (3) (under the assumption of quasianalyticity) a smooth function on $ \mathbb {R}^p$ ($ p \geq 2$) which is $ \mathcal {C}^M$ on every $ \mathcal {C}^M$ curve, but not in $ \mathcal {C}^M(\mathbb {R}^p)$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kopotun:2016:CAJ, author = "Kirill Kopotun and Dany Leviatan and Igor Shevchuk", title = "Constrained Approximation with {Jacobi} Weights", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "109--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-034-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we prove that, for $ \ell = 1 $ or $2$, the rate of best $ \ell $-monotone polynomial approximation in the $ L_p$ norm ($ 1 \leq p \leq \infty $) weighted by the Jacobi weight $ w_{\alpha, \beta }(x) := (1 + x)^\alpha (1 - x)^\beta $ with $ \alpha, \beta \gt - 1 / p$ if $ p \lt \infty $, or $ \alpha, \beta \geq 0$ if $ p = \infty $, is bounded by an appropriate $ (\ell + 1)$ st modulus of smoothness with the same weight, and that this rate cannot be bounded by the $ (\ell + 2)$ nd modulus. Related results on constrained weighted spline approximation and applications of our estimates are also given.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Shiozawa:2016:LER, author = "Yuichi Shiozawa", title = "Lower Escape Rate of Symmetric Jump-diffusion Processes", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "129--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-014-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We establish an integral test on the lower escape rate of symmetric jump-diffusion processes generated by regular Dirichlet forms. Using this test, we can find the speed of particles escaping to infinity. We apply this test to symmetric jump processes of variable order. We also derive the upper and lower escape rates of time changed processes by using those of underlying processes.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Stavrova:2016:NSF, author = "Anastasia Stavrova", title = "Non-stable {$ K_1 $}-functors of Multiloop Groups", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "150--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-035-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $k$ be a field of characteristic 0. Let $G$ be a reductive group over the ring of Laurent polynomials $ R = k[x_1^{\pm 1}, ..., x_n^{\pm 1}]$. Assume that $G$ contains a maximal $R$-torus, and that every semisimple normal subgroup of $G$ contains a two-dimensional split torus $ \mathbf {G}_m^2$. We show that the natural map of non-stable $ K_1$-functors, also called Whitehead groups, $ K_1^G(R) \to K_1^G \bigl (k((x_1))...((x_n)) \bigr)$ is injective, and an isomorphism if $G$ is semisimple. As an application, we provide a way to compute the difference between the full automorphism group of a Lie torus (in the sense of Yoshii-Neher) and the subgroup generated by exponential automorphisms.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Takeda:2016:MTP, author = "Shuichiro Takeda", title = "Metaplectic Tensor Products for Automorphic Representation of {$ \widetilde {GL}(r) $}", journal = j-CAN-J-MATH, volume = "68", number = "1", pages = "179--??", month = feb, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2014-046-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Feb 8 16:27:09 MST 2016", bibsource = "http://cms.math.ca/cjm/v68/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ M = \operatorname {GL}_{r_1} \times \cdots \times \operatorname {GL}_{r_k} \subseteq \operatorname {GL}_r $ be a Levi subgroup of $ \operatorname {GL}_r $, where $ r = r_1 + \cdots + r_k $, and $ \widetilde {M} $ its metaplectic preimage in the $n$-fold metaplectic cover $ \widetilde {\operatorname {GL}}_r$ of $ \operatorname {GL}_r$. For automorphic representations $ \pi_1, \dots, \pi_k$ of $ \widetilde {\operatorname {GL}}_{r_1}(\mathbb {A}), \dots, \widetilde {\operatorname {GL}}_{r_k}(\mathbb {A})$, we construct (under a certain technical assumption, which is always satisfied when $ n = 2$) an automorphic representation $ \pi $ of $ \widetilde {M}(\mathbb {A})$ which can be considered as the ``tensor product'' of the representations $ \pi_1, \dots, \pi_k$. This is the global analogue of the metaplectic tensor product defined by P. Mezo in the sense that locally at each place $v$, $ \pi_v$ is equivalent to the local metaplectic tensor product of $ \pi_{1, v}, \dots, \pi_{k, v}$ defined by Mezo. Then we show that if all of $ \pi_i$ are cuspidal (resp. square-integrable modulo center), then the metaplectic tensor product is cuspidal (resp. square-integrable modulo center). We also show that (both locally and globally) the metaplectic tensor product behaves in the expected way under the action of a Weyl group element, and show the compatibility with parabolic inductions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Allermann:2016:RET, author = "Lars Allermann and Simon Hampe and Johannes Rau", title = "On Rational Equivalence in Tropical Geometry", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "241--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-036-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This article discusses the concept of rational equivalence in tropical geometry (and replaces an older and imperfect version). We give the basic definitions in the context of tropical varieties without boundary points and prove some basic properties. We then compute the ``bounded'' Chow groups of $ \mathbb {R}^n $ by showing that they are isomorphic to the group of fan cycles. The main step in the proof is of independent interest: We show that every tropical cycle in $ \mathbb {R}^n $ is a sum of (translated) fan cycles. This also proves that the intersection ring of tropical cycles is generated in codimension 1 (by hypersurfaces).", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Calixto:2016:EMQ, author = "Lucas Calixto and Adriano Moura and Alistair Savage", title = "Equivariant Map Queer {Lie} Superalgebras", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "258--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-033-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "An equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) $X$ to a queer Lie superalgebra $ \mathfrak {q}$ that are equivariant with respect to the action of a finite group $ \Gamma $ acting on $X$ and $ \mathfrak {q}$. In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that $ \Gamma $ is abelian and acts freely on $X$. We show that such representations are parameterized by a certain set of $ \Gamma $-equivariant finitely supported maps from $X$ to the set of isomorphism classes of irreducible finite-dimensional representations of $ \mathfrak {q}$. In the special case where $X$ is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{daSilva:2016:ADP, author = "Genival {da Silva, Jr.} and Matt Kerr and Gregory Pearlstein", title = "Arithmetic of Degenerating Principal Variations of {Hodge} Structure: Examples Arising from Mirror Symmetry and Middle Convolution", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "280--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-020-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We collect evidence in support of a conjecture of Griffiths, Green and Kerr on the arithmetic of extension classes of limiting mixed Hodge structures arising from semistable degenerations over a number field. After briefly summarizing how a result of Iritani implies this conjecture for a collection of hypergeometric Calabi--Yau threefold examples studied by Doran and Morgan, the authors investigate a sequence of (non-hypergeometric) examples in dimensions $ 1 \leq d \leq 6 $ arising from Katz's theory of the middle convolution. A crucial role is played by the Mumford-Tate group (which is $ G_2$) of the family of 6-folds, and the theory of boundary components of Mumford-Tate domains.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Daws:2016:CAQ, author = "Matthew Daws", title = "Categorical Aspects of Quantum Groups: Multipliers and Intrinsic Groups", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "309--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-022-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We show that the assignment of the (left) completely bounded multiplier algebra $ M_{cb}^l(L^1 (\mathbb G)) $ to a locally compact quantum group $ \mathbb G $, and the assignment of the intrinsic group, form functors between appropriate categories. Morphisms of locally compact quantum groups can be described by Hopf $ *$-homomorphisms between universal $ C^*$-algebras, by bicharacters, or by special sorts of coactions. We show that the whole theory of completely bounded multipliers can be lifted to the universal $ C^*$-algebra level, and that then the different pictures of both multipliers (reduced, universal, and as centralisers) and morphisms interact in extremely natural ways. The intrinsic group of a quantum group can be realised as a class of multipliers, and so our techniques immediately apply. We also show how to think of the intrinsic group using the universal $ C^*$-algebra picture, and then, again, show how the differing views on the intrinsic group interact naturally with morphisms. We show that the intrinsic group is the ``maximal classical'' quantum subgroup of a locally compact quantum group, show that it is even closed in the strong Vaes sense, and that the intrinsic group functor is an adjoint to the inclusion functor from locally compact groups to quantum groups.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Demchenko:2016:KCF, author = "Oleg Demchenko and Alexander Gurevich", title = "Kernels in the Category of Formal Group Laws", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "334--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-024-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Fontaine described the category of formal groups over the ring of Witt vectors over a finite field of characteristic $p$ with the aid of triples consisting of the module of logarithms, the Dieudonn{\'e} module and the morphism from the former to the latter. We propose an explicit construction for the kernels in this category in term of Fontaine's triples. The construction is applied to the formal norm homomorphism in the case of an unramified extension of $ \mathbb {Q}_p$ and of a totally ramified extension of degree less or equal than $p$. A similar consideration applied to a global extension allows us to establish the existence of a strict isomorphism between the formal norm torus and a formal group law coming from $L$-series.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Fite:2016:FDQ, author = "Francesc Fit{\'e} and Josep Gonz{\'a}lez and Joan Carles Lario", title = "{Frobenius} Distribution for Quotients of {Fermat} Curves of Prime Exponent", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "361--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-028-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathcal {C} $ denote the Fermat curve over $ \mathbb {Q} $ of prime exponent $ \ell $. The Jacobian $ \operatorname {Jac}(\mathcal {C}) $ of~$ \mathcal {C} $ splits over $ \mathbb {Q} $ as the product of Jacobians $ \operatorname {Jac}(\mathcal {C}_k) $, $ 1 \leq k \leq \ell - 2 $, where $ \mathcal {C}_k $ are curves obtained as quotients of $ \mathcal {C} $ by certain subgroups of automorphisms of $ \mathcal {C} $. It is well known that $ \operatorname {Jac}(\mathcal {C}_k) $ is the power of an absolutely simple abelian variety $ B_k $ with complex multiplication. We call degenerate those pairs $ (\ell, k) $ for which $ B_k $ has degenerate CM type. For a non-degenerate pair $ (\ell, k) $, we compute the Sato--Tate group of $ \operatorname {Jac}(\mathcal {C}_k) $, prove the generalized Sato--Tate Conjecture for it, and give an explicit method to compute the moments and measures of the involved distributions. Regardless of $ (\ell, k) $ being degenerate or not, we also obtain Frobenius equidistribution results for primes of certain residue degrees in the $ \ell $-th cyclotomic field. Key to our results is a detailed study of the rank of certain generalized Demjanenko matrices.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Garibaldi:2016:BQF, author = "Skip Garibaldi and Daniel K. Nakano", title = "Bilinear and Quadratic Forms on Rational Modules of Split Reductive Groups", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "395--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-042-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The representation theory of semisimple algebraic groups over the complex numbers (equivalently, semisimple complex Lie algebras or Lie groups, or real compact Lie groups) and the question of whether a given complex representation is symplectic or orthogonal has been solved since at least the 1950s. Similar results for Weyl modules of split reductive groups over fields of characteristic different from 2 hold by using similar proofs. This paper considers analogues of these results for simple, induced and tilting modules of split reductive groups over fields of prime characteristic as well as a complete answer for Weyl modules over fields of characteristic 2.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kohen:2016:HPC, author = "Daniel Kohen and Ariel Pacetti", title = "{Heegner} Points on {Cartan} Non-split Curves", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "422--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-047-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ E / \mathbb {Q} $ be an elliptic curve of conductor $N$, and let $K$ be an imaginary quadratic field such that the root number of $ E / K$ is $ - 1$. Let $ \mathscr {O}$ be an order in $K$ and assume that there exists an odd prime $p$, such that $ p^2 \mid \mid N$, and $p$ is inert in $ \mathscr {O}$. Although there are no Heegner points on $ X_0 (N)$ attached to $ \mathscr {O}$, in this article we construct such points on Cartan non-split curves. In order to do that we give a method to compute Fourier expansions for forms on Cartan non-split curves, and prove that the constructed points form a Heegner system as in the classical case.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Martins:2016:GIC, author = "Luciana de F{\'a}tima Martins and Kentaro Saji", title = "Geometric Invariants of Cuspidal Edges", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "445--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-011-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We give a normal form of the cuspidal edge which uses only diffeomorphisms on the source and isometries on the target. Using this normal form, we study differential geometric invariants of cuspidal edges which determine them up to order three. We also clarify relations between these invariants.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Sadykov:2016:WPM, author = "Rustam Sadykov", title = "The Weak $b$-principle: {Mumford} Conjecture", journal = j-CAN-J-MATH, volume = "68", number = "2", pages = "463--??", month = apr, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-003-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this note we introduce and study a new class of maps called oriented colored broken submersions. This is the simplest class of maps that satisfies a version of the b-principle and in dimension $2$ approximates the class of oriented submersions well in the sense that every oriented colored broken submersion of dimension $2$ to a closed simply connected manifold is bordant to a submersion. We show that the Madsen-Weiss theorem (the standard Mumford Conjecture) fits a general setting of the b-principle. Namely, a version of the b-principle for oriented colored broken submersions together with the Harer stability theorem and Miller-Morita theorem implies the Madsen-Weiss theorem.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bacher:2016:NRI, author = "Roland Bacher and Christophe Reutenauer", title = "Number of Right Ideals and a $q$-analogue of Indecomposable Permutations", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "481--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-004-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove that the number of right ideals of codimension $n$ in the algebra of noncommutative Laurent polynomials in two variables over the finite field $ \mathbb F_q$ is equal to $ (q - 1)^{n + 1} q^{\frac {(n + 1)(n - 2)}{2}} \sum_\theta q^{inv(\theta)}$, where the sum is over all indecomposable permutations in $ S_{n + 1}$ and where $ i n v(\theta)$ stands for the number of inversions of $ \theta $.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Biswas:2016:IST, author = "Indranil Biswas and Tom{\'a}s L. G{\'o}mez and Marina Logares", title = "Integrable Systems and {Torelli} Theorems for the Moduli Spaces of Parabolic Bundles and Parabolic {Higgs} Bundles", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "504--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-039-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove a Torelli theorem for the moduli space of semistable parabolic Higgs bundles over a smooth complex projective algebraic curve under the assumption that the parabolic weight system is generic. When the genus is at least two, using this result we also prove a Torelli theorem for the moduli space of semistable parabolic bundles of rank at least two with generic parabolic weights. The key input in the proofs is a method of J.C. Hurtubise.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Emamizadeh:2016:ORS, author = "Behrouz Emamizadeh and Amin Farjudian and Mohsen Zivari-Rezapour", title = "Optimization Related to Some Nonlocal Problems of {Kirchhoff} Type", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "521--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-040-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we introduce two rearrangement optimization problems, one being a maximization and the other a minimization problem, related to a nonlocal boundary value problem of Kirchhoff type. Using the theory of rearrangements as developed by G. R. Burton we are able to show that both problems are solvable, and derive the corresponding optimality conditions. These conditions in turn provide information concerning the locations of the optimal solutions. The strict convexity of the energy functional plays a crucial role in both problems. The popular case in which the rearrangement class (i.e., the admissible set) is generated by a characteristic function is also considered. We show that in this case, the maximization problem gives rise to a free boundary problem of obstacle type, which turns out to be unstable. On the other hand, the minimization problem leads to another free boundary problem of obstacle type, which is stable. Some numerical results are included to confirm the theory.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Garcia-Armas:2016:SIC, author = "Mario Garcia-Armas", title = "Strongly Incompressible Curves", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "541--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-012-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $G$ be a finite group. A faithful $G$-variety $X$ is called strongly incompressible if every dominant $G$-equivariant rational map of $X$ onto another faithful $G$-variety $Y$ is birational. We settle the problem of existence of strongly incompressible $G$-curves for any finite group $G$ and any base field $k$ of characteristic zero.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Gras:2016:RLN, author = "Georges Gras", title = "Les $ \theta $-r{\'e}gulateurs locaux d'un nombre alg{\'e}brique : Conjectures $p$-adiques. ({French}) [{The} local $ \theta $ regulators of an algebraic number: $p$-adic conjectures]", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "571--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-026-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ K / \mathbb {Q} $ be Galois and let $ \eta \in K^\times $ be such that $ \operatorname {Reg}_\infty (\eta) \ne 0 $. We define the local $ \theta $-regulators $ \Delta_p^\theta (\eta) \in \mathbb {F}_p$ for the $ \mathbb {Q}_p \, $-irreducible characters $ \theta $ of $ G = \operatorname {Gal}(K / \mathbb {Q})$. A linear representation $ {\mathcal L}^\theta \simeq \delta \, V_\theta $ is associated with $ \Delta_p^\theta (\eta)$ whose nullity is equivalent to $ \delta \geq 1$. Each $ \Delta_p^\theta (\eta)$ yields $ \operatorname {Reg}_p^\theta (\eta)$ modulo $p$ in the factorization $ \prod_{\theta }(\operatorname {Reg}_p^\theta (\eta))^{\varphi (1)}$ of $ \operatorname {Reg}_p^G (\eta) := \frac { \operatorname {Reg}_p(\eta)}{p^{[K : \mathbb {Q} \,]} }$ (normalized $p$-adic regulator). From $ \operatorname {Prob} \big (\Delta_p^\theta (\eta) = 0 \ \{ \& } \ {\mathcal L}^\theta \simeq \delta \, V_\theta \big) \leq p^{- f \delta^2}$ ($ f \geq 1$ is a residue degree) and the Borel-Cantelli heuristic, we conjecture that, for $p$ large enough, $ \operatorname {Reg}_p^G (\eta)$ is a $p$-adic unit or that $ p^{\varphi (1)} \parallel \operatorname {Reg}_p^G (\eta)$ (a single $ \theta $ with $ f = \delta = 1$); this obstruction may be lifted assuming the existence of a binomial probability law confirmed through numerical studies (groups $ C_3$, $ C_5$, $ D_6$). This conjecture would imply that, for all $p$ large enough, Fermat quotients, normalized $p$-adic regulators are $p$-adic units and that number fields are $p$-rational. We recall some deep cohomological results that may strengthen such conjectures.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Ingram:2016:RHB, author = "Patrick Ingram", title = "Rigidity and Height Bounds for Certain Post-critically Finite Endomorphisms of {$ \mathbb P^N $}", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "625--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-045-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The morphism $ f : \mathbb {P}^N \to \mathbb {P}^N $ is called post-critically finite (PCF) if the forward image of the critical locus, under iteration of $f$, has algebraic support. In the case $ N = 1$, a result of Thurston implies that there are no algebraic families of PCF morphisms, other than a well-understood exceptional class known as the flexible Latt{\`e}s maps. A related arithmetic result states that the set of PCF morphisms corresponds to a set of bounded height in the moduli space of univariate rational functions. We prove corresponding results for a certain subclass of the regular polynomial endomorphisms of $ \mathbb {P}^N$, for any $N$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Klartag:2016:DCA, author = "Bo'az Klartag and Gady Kozma and Peter Ralli and Prasad Tetali", title = "Discrete Curvature and {Abelian} Groups", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "655--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-046-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study a natural discrete Bochner-type inequality on graphs, and explore its merit as a notion of ``curvature'' in discrete spaces. An appealing feature of this discrete version of the so-called $ \Gamma_2$-calculus (of Bakry-{\'E}mery) seems to be that it is fairly straightforward to compute this notion of curvature parameter for several specific graphs of interest -- particularly, abelian groups, slices of the hypercube, and the symmetric group under various sets of generators. We further develop this notion by deriving Buser-type inequalities ({\`a} la Ledoux), relating functional and isoperimetric constants associated with a graph. Our derivations provide a tight bound on the Cheeger constant (i.e., the edge-isoperimetric constant) in terms of the spectral gap, for graphs with nonnegative curvature, particularly, the class of abelian Cayley graphs -- a result of independent interest.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Martinez-de-la-Vega:2016:MCD, author = "Veronica Mart{\'\i}nez-de-la-Vega and Christopher Mouron", title = "Monotone Classes of Dendrites", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "675--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-027-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Continua $X$ and $Y$ are monotone equivalent if there exist monotone onto maps $ f : X \longrightarrow Y$ and $ g : Y \longrightarrow X$. A continuum $X$ is isolated with respect to monotone maps if every continuum that is monotone equivalent to $X$ must also be homeomorphic to $X$. In this paper we show that a dendrite $X$ is isolated with respect to monotone maps if and only if the set of ramification points of $X$ is finite. In this way we fully characterize the classes of dendrites that are monotone isolated.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Skalski:2016:QFI, author = "Adam Skalski and Piotr Soltan", title = "Quantum Families of Invertible Maps and Related Problems", journal = j-CAN-J-MATH, volume = "68", number = "3", pages = "698--??", month = jun, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-037-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Thu Jun 9 14:54:55 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The notion of families of quantum invertible maps (C$^*$-algebra homomorphisms satisfying Podle's' condition) is employed to strengthen and reinterpret several results concerning universal quantum groups acting on finite quantum spaces. In particular Wang's quantum automorphism groups are shown to be universal with respect to quantum families of invertible maps. Further the construction of the Hopf image of Banica and Bichon is phrased in the purely analytic language and employed to define the quantum subgroup generated by a family of quantum subgroups or more generally a family of quantum invertible maps.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Chandee:2016:FEC, author = "Vorrapan Chandee and Chantal David and Dimitris Koukoulopoulos and Ethan Smith", title = "The Frequency of Elliptic Curve Groups Over Prime Finite Fields", journal = j-CAN-J-MATH, volume = "68", number = "4", pages = "721--??", month = aug, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-013-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Letting $p$ vary over all primes and $E$ vary over all elliptic curves over the finite field $ \mathbb {F}_p$, we study the frequency to which a given group $G$ arises as a group of points $ E(\mathbb {F}_p)$. It is well-known that the only permissible groups are of the form $ G_{m, k} := \mathbb {Z} / m \mathbb {Z} \times \mathbb {Z} / m k \mathbb {Z}$. Given such a candidate group, we let $ M(G_{m, k})$ be the frequency to which the group $ G_{m, k}$ arises in this way. Previously, the second and fourth named authors determined an asymptotic formula for $ M(G_{m, k})$ assuming a conjecture about primes in short arithmetic progressions. In this paper, we prove several unconditional bounds for $ M(G_{m, k})$, pointwise and on average. In particular, we show that $ M(G_{m, k})$ is bounded above by a constant multiple of the expected quantity when $ m \le k^A$ and that the conjectured asymptotic for $ M(G_{m, k})$ holds for almost all groups $ G_{m, k}$ when $ m \le k^{1 / 4 - \epsilon }$. We also apply our methods to study the frequency to which a given integer $N$ arises as the group order $ \# E(\mathbb {F}_p)$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Colesanti:2016:LRP, author = "Andrea Colesanti and Eugenia Saor{\'\i}n G{\'o}mez and Jesus Yepes Nicol{\'a}s", title = "On a Linear Refinement of the {Pr{\'e}kopa--Leindler} Inequality", journal = j-CAN-J-MATH, volume = "68", number = "4", pages = "762--??", month = aug, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-016-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "If $ f, g : \mathbb {R}^n \longrightarrow \mathbb {R}_{\geq 0} $ are non-negative measurable functions, then the Pr{\'e}kopa-Leindler inequality asserts that the integral of the Asplund sum (provided that it is measurable) is greater or equal than the $0$-mean of the integrals of $f$ and $g$. In this paper we prove that under the sole assumption that $f$ and $g$ have a common projection onto a hyperplane, the Pr{\'e}kopa-Leindler inequality admits a linear refinement. Moreover, the same inequality can be obtained when assuming that both projections (not necessarily equal as functions) have the same integral. An analogous approach may be also carried out for the so-called Borell-Brascamp-Lieb inequality.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Doran:2016:TDL, author = "Charles F. Doran and Andrew Harder", title = "Toric Degenerations and {Laurent} Polynomials Related to {Givental}'s {Landau--Ginzburg} Models", journal = j-CAN-J-MATH, volume = "68", number = "4", pages = "784--??", month = aug, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-049-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For an appropriate class of Fano complete intersections in toric varieties, we prove that there is a concrete relationship between degenerations to specific toric subvarieties and expressions for Givental's Landau--Ginzburg models as Laurent polynomials. As a result, we show that Fano varieties presented as complete intersections in partial flag manifolds admit degenerations to Gorenstein toric weak Fano varieties, and their Givental Landau--Ginzburg models can be expressed as corresponding Laurent polynomials. We also use this to show that all of the Laurent polynomials obtained by Coates, Kasprzyk and Prince by the so called Przyjalkowski method correspond to toric degenerations of the corresponding Fano variety. We discuss applications to geometric transitions of Calabi--Yau varieties.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Guo:2016:CSI, author = "Xiaoli Guo and Guoen Hu", title = "On the Commutators of Singular Integral Operators with Rough Convolution Kernels", journal = j-CAN-J-MATH, volume = "68", number = "4", pages = "816--??", month = aug, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-044-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ T_{\Omega } $ be the singular integral operator with kernel $ \frac {\Omega (x)}{|x|^n} $, where $ \Omega $ is homogeneous of degree zero, has mean value zero and belongs to $ L^q(S^{n - 1}) $ for some $ q \in (1, \, \infty] $. In this paper, the authors establish the compactness on weighted $ L^p $ spaces, and the Morrey spaces, for the commutator generated by $ \operatorname {CMO}(\mathbb {R}^n) $ function and $ T_{\Omega } $. The associated maximal operator and the discrete maximal operator are also considered.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Gupta:2016:CAC, author = "Sanjiv Kumar Gupta and Kathryn Hare", title = "Characterizing the Absolute Continuity of the Convolution of Orbital Measures in a Classical {Lie} Algebra", journal = j-CAN-J-MATH, volume = "68", number = "4", pages = "841--??", month = aug, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-018-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathfrak {g} $ be a compact, simple Lie algebra of dimension $d$. It is a classical result that the convolution of any $d$ non-trivial, $G$-invariant, orbital measures is absolutely continuous with respect to Lebesgue measure on $ \mathfrak {g}$ and the sum of any $d$ non-trivial orbits has non-empty interior. The number $d$ was later reduced to the rank of the Lie algebra (or rank $ + 1$ in the case of type $ A_n$). More recently, the minimal integer $ k = k(X)$ such that the $k$-fold convolution of the orbital measure supported on the orbit generated by $X$ is an absolutely continuous measure was calculated for each $ X \in \mathfrak {g}$. In this paper $ \mathfrak {g}$ is any of the classical, compact, simple Lie algebras. We characterize the tuples $ (X_1, \dots, X_L)$, with $ X_i \in \mathfrak {g}, $ which have the property that the convolution of the $L$-orbital measures supported on the orbits generated by the $ X_i$ is absolutely continuous and, equivalently, the sum of their orbits has non-empty interior. The characterization depends on the Lie type of $ \mathfrak {g}$ and the structure of the annihilating roots of the $ X_i$. Such a characterization was previously known only for type $ A_n$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ostrovskii:2016:MSA, author = "Mikhail Ostrovskii and Beata Randrianantoanina", title = "Metric Spaces Admitting Low-distortion Embeddings into All $n$-dimensional {Banach} Spaces", journal = j-CAN-J-MATH, volume = "68", number = "4", pages = "876--??", month = aug, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-041-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For a fixed $ K \gg 1 $ and $ n \in \mathbb {N} $, $ n \gg 1 $, we study metric spaces which admit embeddings with distortion $ \le K $ into each $n$-dimensional Banach space. Classical examples include spaces embeddable into $ \log n$-dimensional Euclidean spaces, and equilateral spaces. We prove that good embeddability properties are preserved under the operation of metric composition of metric spaces. In particular, we prove that $n$-point ultrametrics can be embedded with uniformly bounded distortions into arbitrary Banach spaces of dimension $ \log n$. The main result of the paper is a new example of a family of finite metric spaces which are not metric compositions of classical examples and which do embed with uniformly bounded distortion into any Banach space of dimension $n$. This partially answers a question of G. Schechtman.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Sugiyama:2016:EHC, author = "Shingo Sugiyama and Masao Tsuzuki", title = "Existence of {Hilbert} Cusp Forms with Non-vanishing {$L$}-values", journal = j-CAN-J-MATH, volume = "68", number = "4", pages = "908--??", month = aug, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-048-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We develop a derivative version of the relative trace formula on $ \operatorname {PGL}(2) $ studied in our previous work, and derive an asymptotic formula of an average of central values (derivatives) of automorphic $L$-functions for Hilbert cusp forms. As an application, we prove the existence of Hilbert cusp forms with non-vanishing central values (derivatives) such that the absolute degrees of their Hecke fields are arbitrarily large.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Greenberg:2016:AFC, author = "Matthew Greenberg and Marco Seveso", title = "$p$-adic Families of Cohomological Modular Forms for Indefinite Quaternion Algebras and the {Jacquet--Langlands} Correspondence", journal = j-CAN-J-MATH, volume = "68", number = "5", pages = "961--??", month = oct, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-062-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We use the method of Ash and Stevens to prove the existence of small slope $p$-adic families of cohomological modular forms for an indefinite quaternion algebra $B$. We prove that the Jacquet-Langlands correspondence relating modular forms on $ \textbf {GL}_2 / \mathbb {Q}$ and cohomomological modular forms for $B$ is compatible with the formation of $p$-adic families. This result is an analogue of a theorem of Chenevier concerning definite quaternion algebras.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Izumi:2016:Q, author = "Masaki Izumi and Scott Morrison and David Penneys", title = "Quotients of {$ A_2 * T_2 $}", journal = j-CAN-J-MATH, volume = "68", number = "5", pages = "999--??", month = oct, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-017-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study unitary quotients of the free product unitary pivotal category $ A_2 *T_2 $. We show that such quotients are parametrized by an integer $ n \geq 1 $ and an $ 2 n$-th root of unity $ \omega $. We show that for $ n = 1, 2, 3$, there is exactly one quotient and $ \omega = 1$. For $ 4 \leq n \leq 10$, we show that there are no such quotients. Our methods also apply to quotients of $ T_2 *T_2$, where we have a similar result. The essence of our method is a consistency check on jellyfish relations. While we only treat the specific cases of $ A_2 * T_2$ and $ T_2 * T_2$, we anticipate that our technique can be extended to a general method for proving nonexistence of planar algebras with a specified principal graph. During the preparation of this manuscript, we learnt of Liu's independent result on composites of $ A_3$ and $ A_4$ subfactor planar algebras (arxiv:1308.5691). In 1994, Bisch-Haagerup showed that the principal graph of a composite of $ A_3$ and $ A_4$ must fit into a certain family, and Liu has classified all such subfactor planar algebras. We explain the connection between the quotient categories and the corresponding composite subfactor planar algebras. As a corollary of Liu's result, there are no such quotient categories for $ n \geq 4$. This is an abridged version of arxiv:1308.5723.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Phillips:2016:CVI, author = "John Phillips and Iain Raeburn", title = "Centre-valued Index for {Toeplitz} Operators with Noncommuting Symbols", journal = j-CAN-J-MATH, volume = "68", number = "5", pages = "1023--??", month = oct, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-038-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We formulate and prove a ``winding number'' index theorem for certain ``Toeplitz'' operators in the same spirit as Gohberg-Krein, Lesch and others. The ``number'' is replaced by a self-adjoint operator in a subalgebra $ Z \subseteq Z(A) $ of a unital $ C^*$-algebra, $A$. We assume a faithful $Z$-valued trace $ \tau $ on $A$ left invariant under an action $ \alpha : {\mathbf R} \to A u t(A)$ leaving $Z$ pointwise fixed.If $ \delta $ is the infinitesimal generator of $ \alpha $ and $u$ is invertible in $ \operatorname {dom}(\delta)$ then the ``winding operator'' of $u$ is $ \frac {1}{2 \pi i} \tau (\delta (u)u^{-1}) \in Z_{sa}.$ By a careful choice of representations we extend $ (A, Z, \tau, \alpha)$ to a von Neumann setting $ (\mathfrak {A}, \mathfrak {Z}, \bar \tau, \bar \alpha)$ where $ \mathfrak {A} = A^{\prime \prime }$ and $ \mathfrak {Z} = Z^{\prime \prime }.$ Then $ A \subset \mathfrak {A} \subset \mathfrak {A} \rtimes {\bf R}$, the von Neumann crossed product, and there is a faithful, dual $ \mathfrak {Z}$-trace on $ \mathfrak {A} \rtimes {\bf R}$. If $P$ is the projection in $ \mathfrak {A} \rtimes {\bf R}$ corresponding to the non-negative spectrum of the generator of $ \mathbf R$ inside $ \mathfrak {A} \rtimes {\mathbf R}$ and $ \tilde \pi : A \to \mathfrak {A} \rtimes {\mathbf R}$ is the embedding then we define for $ u \in A^{-1}$, $ T_u = P \tilde \pi (u) P$ and show it is Fredholm in an appropriate sense and the $ \mathfrak {Z}$-valued index of $ T_u$ is the negative of the winding operator. In outline the proof follows the proof of the scalar case done previously by the authors. The main difficulty is making sense of the constructions with the scalars replaced by $ \mathfrak {Z}$ in the von Neumann setting. The construction of the dual $ \mathfrak {Z}$-trace on $ \mathfrak {A} \rtimes {\mathbf R}$ required the nontrivial development of a $ \mathfrak {Z}$-Hilbert Algebra theory. We show that certain of these Fredholm operators fiber as a ``section'' of Fredholm operators with scalar-valued index and the centre-valued index fibers as a section of the scalar-valued indices.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Runde:2016:PDL, author = "Volker Runde and Ami Viselter", title = "On Positive Definiteness over Locally Compact Quantum Groups", journal = j-CAN-J-MATH, volume = "68", number = "5", pages = "1067--??", month = oct, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-019-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The notion of positive-definite functions over locally compact quantum groups was recently introduced and studied by Daws and Salmi. Based on this work, we generalize various well-known results about positive-definite functions over groups to the quantum framework. Among these are theorems on {"square} {roots"} of positive-definite functions, comparison of various topologies, positive-definite measures and characterizations of amenability, and the separation property with respect to compact quantum subgroups.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Smith:2016:SM, author = "Benjamin H. Smith", title = "Singular {$G$}-Monopoles on {$ S^1 \times \Sigma $}", journal = j-CAN-J-MATH, volume = "68", number = "5", pages = "1096--??", month = oct, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-010-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This article provides an account of the functorial correspondence between irreducible singular $G$-monopoles on $ S^1 \times \Sigma $ and $ \vec {t}$-stable meromorphic pairs on $ \Sigma $. A theorem of B. Charbonneau and J. Hurtubise is thus generalized here from unitary to arbitrary compact, connected gauge groups. The required distinctions and similarities for unitary versus arbitrary gauge are clearly outlined and many parallels are drawn for easy transition. Once the correspondence theorem is complete, the spectral decomposition is addressed.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Stange:2016:IPE, author = "Katherine E. Stange", title = "Integral Points on Elliptic Curves and Explicit Valuations of Division Polynomials", journal = j-CAN-J-MATH, volume = "68", number = "5", pages = "1120--??", month = oct, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-005-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Assuming Lang's conjectured lower bound on the heights of non-torsion points on an elliptic curve, we show that there exists an absolute constant $C$ such that for any elliptic curve $ E / \mathbb {Q}$ and non-torsion point $ P \in E(\mathbb {Q})$, there is at most one integral multiple $ [n]P$ such that $ n \gt C$. The proof is a modification of a proof of Ingram giving an unconditional but not uniform bound. The new ingredient is a collection of explicit formulae for the sequence $ v(\Psi_n)$ of valuations of the division polynomials. For $P$ of non-singular reduction, such sequences are already well described in most cases, but for $P$ of singular reduction, we are led to define a new class of sequences called \emph{elliptic troublemaker sequences}, which measure the failure of the N{\'e}ron local height to be quadratic. As a corollary in the spirit of a conjecture of Lang and Hall, we obtain a uniform upper bound on $ \widehat {h}(P) / h(E)$ for integer points having two large integral multiples.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Yattselev:2016:SAH, author = "Maxim L. Yattselev", title = "Strong Asymptotics of {Hermite--Pad{\'e}} Approximants for {Angelesco} Systems", journal = j-CAN-J-MATH, volume = "68", number = "5", pages = "1159--??", month = oct, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-043-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 23 14:35:22 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this work type II Hermite-Pad{\'e} approximants for a vector of Cauchy transforms of smooth Jacobi-type densities are considered. It is assumed that densities are supported on mutually disjoint intervals (an Angelesco system with complex weights). The formulae of strong asymptotics are derived for any ray sequence of multi-indices.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Banks:2016:MAU, author = "Jessica Banks and Matt Rathbun", title = "Monodromy Action on Unknotting Tunnels in Fiber Surfaces", journal = j-CAN-J-MATH, volume = "68", number = "6", pages = "1201--??", month = dec, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-002-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Nov 5 12:40:14 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In \cite{RatTOFL}, the second author showed that a tunnel of a tunnel number one, fibered link in $ S^3 $ can be isotoped to lie as a properly embedded arc in the fiber surface of the link. In this paper, we observe that this is true for fibered links in any 3-manifold, we analyze how the arc behaves under the monodromy action, and we show that the tunnel arc is nearly clean, with the possible exception of twisting around the boundary of the fiber.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Brasca:2016:ECP, author = "Riccardo Brasca", title = "Eigenvarieties for Cuspforms over {PEL} Type {Shimura} Varieties with Dense Ordinary locus", journal = j-CAN-J-MATH, volume = "68", number = "6", pages = "1227--??", month = dec, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-052-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Nov 5 12:40:14 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ p \gt 2 $ be a prime and let $X$ be a compactified PEL Shimura variety of type (A) or (C) such that $p$ is an unramified prime for the PEL datum and such that the ordinary locus is dense in the reduction of $X$. Using the geometric approach of Andreatta, Iovita, Pilloni, and Stevens we define the notion of families of overconvergent locally analytic $p$-adic modular forms of Iwahoric level for $X$. We show that the system of eigenvalues of any finite slope cuspidal eigenform of Iwahoric level can be deformed to a family of systems of eigenvalues living over an open subset of the weight space. To prove these results, we actually construct eigenvarieties of the expected dimension that parameterize finite slope systems of eigenvalues appearing in the space of families of cuspidal forms.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Cascante:2016:SNE, author = "Carme Cascante and Joan F{\`a}brega and Joaqu{\'\i}n M. Ortega", title = "Sharp Norm Estimates for the {Bergman} Operator from Weighted Mixed-norm Spaces to Weighted {Hardy} Spaces", journal = j-CAN-J-MATH, volume = "68", number = "6", pages = "1257--??", month = dec, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-005-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Nov 5 12:40:14 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we give sharp norm estimates for the Bergman operator acting from weighted mixed-norm spaces to weighted Hardy spaces in the ball, endowed with natural norms.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ehrig:2016:RSF, author = "Michael Ehrig and Catharina Stroppel", title = "$2$-row {Springer} Fibres and {Khovanov} Diagram Algebras for Type {D}", journal = j-CAN-J-MATH, volume = "68", number = "6", pages = "1285--??", month = dec, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-051-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Nov 5 12:40:14 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study in detail two row Springer fibres of even orthogonal type from an algebraic as well as topological point of view. We show that the irreducible components and their pairwise intersections are iterated $ \mathbb {P}^1$-bundles. Using results of Kumar and Procesi we compute the cohomology ring with its action of the Weyl group. The main tool is a type $ \operatorname D$ diagram calculus labelling the irreducible components in a convenient way which relates to a diagrammatical algebra describing the category of perverse sheaves on isotropic Grassmannians based on work of Braden. The diagram calculus generalizes Khovanov's arc algebra to the type $ \operatorname D$ setting and should be seen as setting the framework for generalizing well-known connections of these algebras in type $ \operatorname A$ to other types.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Jiang:2016:NPM, author = "Feida Jiang and Neil S. Trudinger and Ni Xiang", title = "On the {Neumann} Problem for {Monge--Amp{\`e}re} Type Equations", journal = j-CAN-J-MATH, volume = "68", number = "6", pages = "1334--??", month = dec, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-001-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Nov 5 12:40:14 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we study the global regularity for regular Monge-Amp{\`e}re type equations associated with semilinear Neumann boundary conditions. By establishing a priori estimates for second order derivatives, the classical solvability of the Neumann boundary value problem is proved under natural conditions. The techniques build upon the delicate and intricate treatment of the standard Monge-Amp{\`e}re case by Lions, Trudinger and Urbas in 1986 and the recent barrier constructions and second derivative bounds by Jiang, Trudinger and Yang for the Dirichlet problem. We also consider more general oblique boundary value problems in the strictly regular case.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Papikian:2016:OQJ, author = "Mihran Papikian and Joseph Rabinoff", title = "Optimal Quotients of {Jacobians} with Toric Reduction and Component Groups", journal = j-CAN-J-MATH, volume = "68", number = "6", pages = "1362--??", month = dec, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-009-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Nov 5 12:40:14 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $J$ be a Jacobian variety with toric reduction over a local field $K$. Let $ J \to E$ be an optimal quotient defined over $K$, where $E$ is an elliptic curve. We give examples in which the functorially induced map $ \Phi_J \to \Phi_E$ on component groups of the N{\'e}ron models is not surjective. This answers a question of Ribet and Takahashi. We also give various criteria under which $ \Phi_J \to \Phi_E$ is surjective, and discuss when these criteria hold for the Jacobians of modular curves.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Zydor:2016:VIF, author = "Michal Zydor", title = "La variante infinit{\'e}simale de la formule des traces de {Jacquet--Rallis} pour les groupes unitaires", journal = j-CAN-J-MATH, volume = "68", number = "6", pages = "1382--??", month = dec, year = "2016", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-054-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Nov 5 12:40:14 MDT 2016", bibsource = "http://cms.math.ca/cjm/v68/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We establish an infinitesimal version of the Jacquet-Rallis trace formula for unitary groups. Our formula is obtained by integrating a truncated kernel {\`a} la Arthur. It has a geometric side which is a sum of distributions $ J_{\mathfrak {o}} $ indexed by classes of elements of the Lie algebra of $ U(n + 1) $ stable by $ U(n)$-conjugation as well as the {"spectral} {side"} consisting of the Fourier transforms of the aforementioned distributions. We prove that the distributions $ J_{\mathfrak {o}}$ are invariant and depend only on the choice of the Haar measure on $ U(n)(\mathbb {A})$. For regular semi-simple classes $ \mathfrak {o}$, $ J_{\mathfrak {o}}$ is a relative orbital integral of Jacquet-Rallis. For classes $ \mathfrak {o}$ called relatively regular semi-simple, we express $ J_{\mathfrak {o}}$ in terms of relative orbital integrals regularised by means of z{\^e}ta functions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", language = "French", } @Article{Ghahramani:2017:BIB, author = "F. Ghahramani and S. Zadeh", title = "Bipositive Isomorphisms Between {Beurling} Algebras and Between their Second Dual Algebras", journal = j-CAN-J-MATH, volume = "69", number = "1", pages = "3--??", month = feb, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-028-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Jan 16 14:20:52 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $G$ be a locally compact group and let $ \omega $ be a continuous weight on $G$. We show that for each of the Banach algebras $ L^1 (G, \omega)$, $ M(G, \omega)$, $ L U C(G, \omega^{-1})^*$ and $ L^1 (G, \omega)^{**}$, the order structure combined with the algebra structure determines the weighted group.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Grinberg:2017:DCO, author = "Darij Grinberg", title = "Dual Creation Operators and a Dendriform Algebra Structure on the Quasisymmetric Functions", journal = j-CAN-J-MATH, volume = "69", number = "1", pages = "21--??", month = feb, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-018-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Jan 16 14:20:52 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The dual immaculate functions are a basis of the ring $ \operatorname *{QSym} $ of quasisymmetric functions, and form one of the most natural analogues of the Schur functions. The dual immaculate function corresponding to a composition is a weighted generating function for immaculate tableaux in the same way as a Schur function is for semistandard Young tableaux; an ``immaculate tableau'' is defined similarly to be a semistandard Young tableau, but the shape is a composition rather than a partition, and only the first column is required to strictly increase (whereas the other columns can be arbitrary; but each row has to weakly increase). Dual immaculate functions have been introduced by Berg, Bergeron, Saliola, Serrano and Zabrocki in arXiv:1208.5191, and have since been found to possess numerous nontrivial properties. In this note, we prove a conjecture of Mike Zabrocki which provides an alternative construction for the dual immaculate functions in terms of certain ``vertex operators''. The proof uses a dendriform structure on the ring $ \operatorname *{QSym} $; we discuss the relation of this structure to known dendriform structures on the combinatorial Hopf algebras $ \operatorname *{FQSym} $ and $ \operatorname *{WQSym} $.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Hartz:2017:IPM, author = "Michael Hartz", title = "On the Isomorphism Problem for Multiplier Algebras of {Nevanlinna--Pick} Spaces", journal = j-CAN-J-MATH, volume = "69", number = "1", pages = "54--??", month = feb, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-050-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Jan 16 14:20:52 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna--Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with restrictions of a universal space, namely the Drury-Arveson space. Instead, we work directly with the Hilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna--Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of complete Nevanlinna--Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic. This generalizes results of Davidson, Ramsey, Shalit, and the author.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kamgarpour:2017:NCL, author = "Masoud Kamgarpour", title = "On the Notion of Conductor in the Local Geometric {Langlands} Correspondence", journal = j-CAN-J-MATH, volume = "69", number = "1", pages = "107--??", month = feb, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-016-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Jan 16 14:20:52 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Under the local Langlands correspondence, the conductor of an irreducible representation of $ \operatorname {Gl}_n(F) $ is greater than the Swan conductor of the corresponding Galois representation. In this paper, we establish the geometric analogue of this statement by showing that the conductor of a categorical representation of the loop group is greater than the irregularity of the corresponding meromorphic connection.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Levin:2017:NAC, author = "Aaron Levin and Julie Tzu-Yueh Wang", title = "On Non-{Archimedean} Curves Omitting Few Components and their Arithmetic Analogues", journal = j-CAN-J-MATH, volume = "69", number = "1", pages = "130--??", month = feb, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-030-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Jan 16 14:20:52 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathbf {k} $ be an algebraically closed field complete with respect to a non-Archimedean absolute value of arbitrary characteristic. Let $ D_1, \dots, D_n $ be effective nef divisors intersecting transversally in an $n$-dimensional nonsingular projective variety $X$. We study the degeneracy of non-Archimedean analytic maps from $ \mathbf {k}$ into $ X \setminus \cup_{i = 1}^n D_i$ under various geometric conditions. When $X$ is a rational ruled surface and $ D_1$ and $ D_2$ are ample, we obtain a necessary and sufficient condition such that there is no non-Archimedean analytic map from $ \mathbf {k}$ into $ X \setminus D_1 \cup D_2$. Using the dictionary between non-Archimedean Nevanlinna theory and Diophantine approximation that originated in earlier work with T. T. H. An, we also study arithmetic analogues of these problems, establishing results on integral points on these varieties over $ \mathbb {Z}$ or the ring of integers of an imaginary quadratic field.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Levinson:2017:ODS, author = "Jake Levinson", title = "One-dimensional {Schubert} Problems with Respect to Osculating Flags", journal = j-CAN-J-MATH, volume = "69", number = "1", pages = "143--??", month = feb, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-061-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Jan 16 14:20:52 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider Schubert problems with respect to flags osculating the rational normal curve. These problems are of special interest when the osculation points are all real -- in this case, for zero-dimensional Schubert problems, the solutions are ``as real as possible''. Recent work by Speyer has extended the theory to the moduli space $ \overline {\mathcal {M}_{0, r}} $, allowing the points to collide. These give rise to smooth covers of $ \overline {\mathcal {M}_{0, r}} (\mathbb {R}) $, with structure and monodromy described by Young tableaux and jeu de taquin. In this paper, we give analogous results on one-dimensional Schubert problems over $ \overline {\mathcal {M}_{0, r}} $. Their (real) geometry turns out to be described by orbits of Sch{\"u}tzenberger promotion and a related operation involving tableau evacuation. Over $ \mathcal {M}_{0, r} $, our results show that the real points of the solution curves are smooth. We also find a new identity involving ``first-order'' K-theoretic Littlewood--Richardson coefficients, for which there does not appear to be a known combinatorial proof.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Pan:2017:FLT, author = "Shu-Yen Pan", title = "{$L$}-Functoriality for Local Theta Correspondence of Supercuspidal Representations with Unipotent Reduction", journal = j-CAN-J-MATH, volume = "69", number = "1", pages = "186--??", month = feb, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-033-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Jan 16 14:20:52 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The preservation principle of local theta correspondences of reductive dual pairs over a $p$-adic field predicts the existence of a sequence of irreducible supercuspidal representations of classical groups. Adams/Harris-Kudla-Sweet have a conjecture about the Langlands parameters for the sequence of supercuspidal representations. In this paper we prove modified versions of their conjectures for the case of supercuspidal representations with unipotent reduction.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Zheng:2017:CRF, author = "Tao Zheng", title = "The {Chern--Ricci} Flow on {Oeljeklaus--Toma} Manifolds", journal = j-CAN-J-MATH, volume = "69", number = "1", pages = "220--??", month = feb, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-053-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Jan 16 14:20:52 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the Chern-Ricci flow, an evolution equation of Hermitian metrics, on a family of Oeljeklaus-Toma (OT-) manifolds which are non-K{\"a}hler compact complex manifolds with negative Kodaira dimension. We prove that, after an initial conformal change, the flow converges, in the Gromov-Hausdorff sense, to a torus with a flat Riemannian metric determined by the OT-manifolds themselves.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Adamus:2017:FDS, author = "Janusz Adamus and Hadi Seyedinejad", title = "Finite Determinacy and Stability of Flatness of Analytic Mappings", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "241--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-008-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "It is proved that flatness of an analytic mapping germ from a complete intersection is determined by its sufficiently high jet. As a consequence, one obtains finite determinacy of complete intersections. It is also shown that flatness and openness are stable under deformations.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Brandes:2017:SAE, author = "Julia Brandes and Scott T. Parsell", title = "Simultaneous Additive Equations: Repeated and Differing Degrees", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "258--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-006-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We obtain bounds for the number of variables required to establish Hasse principles, both for existence of solutions and for asymptotic formul{\ae}, for systems of additive equations containing forms of differing degree but also multiple forms of like degree. Apart from the very general estimates of Schmidt and Browning--Heath-Brown, which give weak results when specialized to the diagonal situation, this is the first result on such {"hybrid"} systems. We also obtain specialised results for systems of quadratic and cubic forms, where we are able to take advantage of some of the stronger methods available in that setting. In particular, we achieve essentially square root cancellation for systems consisting of one cubic and $r$ quadratic equations.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2017:CPS, author = "Xianghong Chen and Andreas Seeger", title = "Convolution Powers of {Salem} Measures with Applications", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "284--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-019-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the regularity of convolution powers for measures supported on Salem sets, and prove related results on Fourier restriction and Fourier multipliers. In particular we show that for $ \alpha $ of the form $ {d} / {n} $, $ n = 2, 3, \dots $ there exist $ \alpha $-Salem measures for which the $ L^2$ Fourier restriction theorem holds in the range $ p \le \frac {2d}{2d - \alpha }$. The results rely on ideas of K{\"o}rner. We extend some of his constructions to obtain upper regular $ \alpha $-Salem measures, with sharp regularity results for $n$-fold convolutions for all $ n \in \mathbb {N}$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{DeBernardi:2017:TNS, author = "Carlo Alberto {De Bernardi} and Libor Vesel{\'y}", title = "Tilings of Normed Spaces", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "321--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-057-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "By a tiling of a topological linear space $X$ we mean a covering of $X$ by at least two closed convex sets, called tiles, whose nonempty interiors are pairwise disjoint. Study of tilings of infinite-dimensional spaces initiated in the 1980's with pioneer papers by V. Klee. We prove some general properties of tilings of locally convex spaces, and then apply these results to study existence of tilings of normed and Banach spaces by tiles possessing certain smoothness or rotundity properties. For a Banach space $X$, our main results are the following. 1. $X$ admits no tiling by Fr{\'e}chet smooth bounded tiles. 2. If $X$ is locally uniformly rotund (LUR), it does not admit any tiling by balls. 3. On the other hand, some $ \ell_1 (\Gamma)$ spaces, $ \Gamma $ uncountable, do admit a tiling by pairwise disjoint LUR bounded tiles.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Garbagnati:2017:KSQ, author = "Alice Garbagnati", title = "On {K3} Surface Quotients of {K3} or {Abelian} Surfaces", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "338--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-058-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The aim of this paper is to prove that a K3 surface is the minimal model of the quotient of an Abelian surface by a group $G$ (respectively of a K3 surface by an Abelian group $G$) if and only if a certain lattice is primitively embedded in its N{\'e}ron-Severi group. This allows one to describe the coarse moduli space of the K3 surfaces which are (rationally) $G$-covered by Abelian or K3 surfaces (in the latter case $G$ is an Abelian group). If either $G$ has order 2 or $G$ is cyclic and acts on an Abelian surface, this result was already known, so we extend it to the other cases. Moreover, we prove that a K3 surface $ X_G$ is the minimal model of the quotient of an Abelian surface by a group $G$ if and only if a certain configuration of rational curves is present on $ X_G$. Again this result was known only in some special cases, in particular if $G$ has order 2 or 3.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kaftal:2017:SCP, author = "Victor Kaftal and Ping Wong Ng and Shuang Zhang", title = "Strict Comparison of Positive Elements in Multiplier Algebras", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "373--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-015-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Main result: If a C*-algebra $ \mathcal {A} $ is simple, $ \sigma $-unital, has finitely many extremal traces, and has strict comparison of positive elements by traces, then its multiplier algebra $ \operatorname {\mathcal {M}}(\mathcal {A})$ also has strict comparison of positive elements by traces. The same results holds if ``finitely many extremal {traces"} is replaced by ``quasicontinuous {scale"}. A key ingredient in the proof is that every positive element in the multiplier algebra of an arbitrary $ \sigma $-unital C*-algebra can be approximated by a bi-diagonal series. An application of strict comparison: If $ \mathcal {A}$ is a simple separable stable C*-algebra with real rank zero, stable rank one, and strict comparison of positive elements by traces, then whether a positive element is a positive linear combination of projections is determined by the trace values of its range projection.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Klep:2017:FFT, author = "Igor Klep and Spela Spenko", title = "Free Function Theory Through Matrix Invariants", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "408--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-055-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This paper concerns free function theory. Free maps are free analogs of analytic functions in several complex variables, and are defined in terms of freely noncommuting variables. A function of $g$ noncommuting variables is a function on $g$-tuples of square matrices of all sizes that respects direct sums and simultaneous conjugation. Examples of such maps include noncommutative polynomials, noncommutative rational functions and convergent noncommutative power series. In sharp contrast to the existing literature in free analysis, this article investigates free maps \emph{with involution} -- free analogs of real analytic functions. To get a grip on these, techniques and tools from invariant theory are developed and applied to free analysis. Here is a sample of the results obtained. A characterization of polynomial free maps via properties of their finite-dimensional slices is presented and then used to establish power series expansions for analytic free maps about scalar and non-scalar points; the latter are series of generalized polynomials for which an invariant-theoretic characterization is given. Furthermore, an inverse and implicit function theorem for free maps with involution is obtained. Finally, with a selection of carefully chosen examples it is shown that free maps with involution do not exhibit strong rigidity properties enjoyed by their involution-free counterparts.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Lee:2017:NDC, author = "Hun Hee Lee and Sang-gyun Youn", title = "New Deformations of Convolution Algebras and {Fourier} Algebras on Locally Compact Groups", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "434--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-027-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we introduce a new way of deforming convolution algebras and Fourier algebras on locally compact groups. We demonstrate that this new deformation allows us to reveal some information of the underlying groups by examining Banach algebra properties of deformed algebras. More precisely, we focus on representability as an operator algebra of deformed convolution algebras on compact connected Lie groups with connection to the real dimension of the underlying group. Similarly, we investigate complete representability as an operator algebra of deformed Fourier algebras on some finitely generated discrete groups with connection to the growth rate of the group.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Marquis:2017:ITH, author = "Timoth{\'e}e Marquis and Karl-Hermann Neeb", title = "Isomorphisms of Twisted {Hilbert} Loop Algebras", journal = j-CAN-J-MATH, volume = "69", number = "2", pages = "453--??", month = apr, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-003-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Mar 11 12:59:41 MST 2017", bibsource = "http://cms.math.ca/cjm/v69/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The closest infinite dimensional relatives of compact Lie algebras are Hilbert-Lie algebras, i.e. real Hilbert spaces with a Lie algebra structure for which the scalar product is invariant. Locally affine Lie algebras (LALAs) correspond to double extensions of (twisted) loop algebras over simple Hilbert-Lie algebras $ \mathfrak {k} $, also called affinisations of $ \mathfrak {k} $. They possess a root space decomposition whose corresponding root system is a locally affine root system of one of the $7$ families $ A_J^{(1)}$, $ B_J^{(1)}$, $ C_J^{(1)}$, $ D_J^{(1)}$, $ B_J^{(2)}$, $ C_J^{(2)}$ and $ B C_J^{(2)}$ for some infinite set $J$. To each of these types corresponds a ``{minimal"} affinisation of some simple Hilbert-Lie algebra $ \mathfrak {k}$, which we call standard. In this paper, we give for each affinisation $ \mathfrak {g}$ of a simple Hilbert-Lie algebra $ \mathfrak {k}$ an explicit isomorphism from $ \mathfrak {g}$ to one of the standard affinisations of $ \mathfrak {k}$. The existence of such an isomorphism could also be derived from the classification of locally affine root systems, but for representation theoretic purposes it is crucial to obtain it explicitly as a deformation between two twists which is compatible with the root decompositions. We illustrate this by applying our isomorphism theorem to the study of positive energy highest weight representations of $ \mathfrak {g}$. In subsequent work, the present paper will be used to obtain a complete classification of the positive energy highest weight representations of affinisations of $ \mathfrak {k}$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Cordero-Erausquin:2017:TIL, author = "Dario Cordero-Erausquin", title = "Transport Inequalities for Log-concave Measures, Quantitative Forms and Applications", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "481--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-046-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We review some simple techniques based on monotone mass transport that allow us to obtain transport-type inequalities for any log-concave probability measure, and for more general measures as well. We discuss quantitative forms of these inequalities, with application to the Brascamp-Lieb variance inequality.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Fischer:2017:SBA, author = "Vera Fischer and Diego Alejandro Mejia", title = "Splitting, Bounding, and Almost Disjointness Can Be Quite Different", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "502--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-021-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove the consistency of \operatorname{add}(\mathcal{N})\lt \operatorname{cov}(\mathcal{N}) \lt \mathfrak{p}=\mathfrak{s} =\mathfrak{g}\lt \operatorname{add}(\mathcal{M}) = \operatorname{cof}(\mathcal{M}) \lt \mathfrak{a} =\mathfrak{r}=\operatorname{non}(\mathcal{N})=\mathfrak{c} with $ \mathrm {ZFC} $, where each of these cardinal invariants assume arbitrary uncountable regular values.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ganguly:2017:DTF, author = "Arijit Ganguly and Anish Ghosh", title = "{Dirichlet}'s Theorem in Function Fields", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "532--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-024-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study metric Diophantine approximation for function fields specifically the problem of improving Dirichlet's theorem in Diophantine approximation.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Hartglass:2017:FPC, author = "Michael Hartglass", title = "Free Product {$ C^* $}-algebras Associated with Graphs, Free Differentials, and Laws of Loops", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "548--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-022-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study a canonical C$^*$-algebra, $ \mathcal {S}(\Gamma, \mu)$, that arises from a weighted graph $ (\Gamma, \mu)$, specific cases of which were previously studied in the context of planar algebras. We discuss necessary and sufficient conditions of the weighting which ensure simplicity and uniqueness of trace of $ \mathcal {S}(\Gamma, \mu)$, and study the structure of its positive cone. We then study the $ *$-algebra, $ \mathcal {A}$, generated by the generators of $ \mathcal {S}(\Gamma, \mu)$, and use a free differential calculus and techniques of Charlesworth and Shlyakhtenko, as well as Mai, Speicher, and Weber to show that certain ``{loop"} elements have no atoms in their spectral measure. After modifying techniques of Shlyakhtenko and Skoufranis to show that self adjoint elements $ x \in M_n(\mathcal {A})$ have algebraic Cauchy transform, we explore some applications to eigenvalues of polynomials in Wishart matrices and to diagrammatic elements in von Neumann algebras initially considered by Guionnet, Jones, and Shlyakhtenko.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Lee:2017:RIF, author = "Jungyun Lee and Yoonjin Lee", title = "Regulators of an Infinite Family of the Simplest Quartic Function Fields", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "579--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-038-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We explicitly find regulators of an infinite family $ \{ L_m \} $ of the simplest quartic function fields with a parameter $m$ in a polynomial ring $ \mathbb {F}_q [t]$, where $ \mathbb {F}_q$ is the finite field of order $q$ with odd characteristic. In fact, this infinite family of the simplest quartic function fields are subfields of maximal real subfields of cyclotomic function fields, where they have the same conductors. We obtain a lower bound on the class numbers of the family $ \{ L_m \} $ and some result on the divisibility of the divisor class numbers of cyclotomic function fields which contain $ \{ L_m \} $ as their subfields. Furthermore, we find an explicit criterion for the characterization of splitting types of all the primes of the rational function field $ \mathbb {F}_q (t)$ in $ \{ L_m \} $.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Mauduit:2017:DS, author = "Christian Mauduit and Jo{\"e}l Rivat and Andr{\'a}s S{\'a}rk{\"o}zy", title = "On the Digits of Sumsets", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "595--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-007-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathcal A $, $ \mathcal B $ be large subsets of $ \{ 1, \ldots, N \} $. We study the number of pairs $ (a, b) \in \mathcal A \times \mathcal B $ such that the sum of binary digits of $ a + b $ is fixed.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Moon:2017:MPS, author = "Han-Bom Moon", title = "{Mori}'s Program for {$ \overline {M}_{0, 7} $} with Symmetric Divisors", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "613--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-059-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We complete Mori's program with symmetric divisors for the moduli space of stable seven-pointed rational curves. We describe all birational models in terms of explicit blow-ups and blow-downs. We also give a moduli theoretic description of the first flip, which has not appeared in the literature.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Oikhberg:2017:ADP, author = "Timur Oikhberg and Pedro Tradacete", title = "Almost Disjointness Preservers", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "650--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-020-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the stability of disjointness preservers on Banach lattices. In many cases, we prove that an {"almost} disjointness {preserving"} operator is well approximable by a disjointness preserving one. However, this approximation is not always possible, as our examples show.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ovchinnikov:2017:TCS, author = "Alexey Ovchinnikov and Michael Wibmer", title = "{Tannakian} Categories with Semigroup Actions", journal = j-CAN-J-MATH, volume = "69", number = "3", pages = "687--??", month = jun, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-011-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Ostrowski's theorem implies that $ \log (x), \log (x + 1), \dots $ are algebraically independent over $ \mathbb {C}(x) $. More generally, for a linear differential or difference equation, it is an important problem to find all algebraic dependencies among a non-zero solution $y$ and particular transformations of $y$, such as derivatives of $y$ with respect to parameters, shifts of the arguments, rescaling, etc. In the present paper, we develop a theory of Tannakian categories with semigroup actions, which will be used to attack such questions in full generality, as each linear differential equation gives rise to a Tannakian category. Deligne studied actions of braid groups on categories and obtained a finite collection of axioms that characterizes such actions to apply it to various geometric constructions. In this paper, we find a finite set of axioms that characterizes actions of semigroups that are finite free products of semigroups of the form $ \mathbb {N}^n \times \mathbb {Z} / {n_1} \mathbb {Z} \times \cdots \times \mathbb {Z} / {n_r} \mathbb {Z}$ on Tannakian categories. This is the class of semigroups that appear in many applications.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Allison:2017:WIK, author = "Bruce Allison and John Faulkner and Oleg Smirnov", title = "{Weyl} Images of {Kantor} Pairs", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "721--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-047-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Kantor pairs arise naturally in the study of $5$-graded Lie algebras. In this article, we introduce and study Kantor pairs with short Peirce gradings and relate them to Lie algebras graded by the root system of type $ \mathrm {BC}_2$. This relationship allows us to define so called Weyl images of short Peirce graded Kantor pairs. We use Weyl images to construct new examples of Kantor pairs, including a class of infinite dimensional central simple Kantor pairs over a field of characteristic $ \ne 2$ or $3$, as well as a family of forms of a split Kantor pair of type $ \mathrm {E}_6$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Choi:2017:WOT, author = "Suyoung Choi and Hanchul Park", title = "Wedge Operations and Torus Symmetries {II}", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "767--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-037-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A fundamental idea in toric topology is that classes of manifolds with well-behaved torus actions (simply, toric spaces) are classified by pairs of simplicial complexes and (non-singular) characteristic maps. The authors in their previous paper provided a new way to find all characteristic maps on a simplicial complex $ K(J) $ obtainable by a sequence of wedgings from $K$. The main idea was that characteristic maps on $K$ theoretically determine all possible characteristic maps on a wedge of $K$. In this work, we further develop our previous work for classification of toric spaces. For a star-shaped simplicial sphere $K$ of dimension $ n - 1$ with $m$ vertices, the Picard number $ \operatorname {Pic}(K)$ of $K$ is $ m - n$. We refer to $K$ as a seed if $K$ cannot be obtained by wedgings. First, we show that, for a fixed positive integer $ \ell $, there are at most finitely many seeds of Picard number $ \ell $ supporting characteristic maps. As a corollary, the conjecture proposed by V.V. Batyrev in 1991 is solved affirmatively. Second, we investigate a systematic method to find all characteristic maps on $ K(J)$ using combinatorial objects called (realizable) puzzles that only depend on a seed $K$. These two facts lead to a practical way to classify the toric spaces of fixed Picard number.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Diacu:2017:CBP, author = "Florin Diacu", title = "The Classical {$N$}-body Problem in the Context of Curved Space", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "790--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-041-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We provide the differential equations that generalize the Newtonian $N$-body problem of celestial mechanics to spaces of constant Gaussian curvature, $ \kappa $, for all $ \kappa \in \mathbb R$. In previous studies, the equations of motion made sense only for $ \kappa \ne 0$. The system derived here does more than just include the Euclidean case in the limit $ \kappa \to 0$: it recovers the classical equations for $ \kappa = 0$. This new expression of the laws of motion allows the study of the $N$-body problem in the context of constant curvature spaces and thus offers a natural generalization of the Newtonian equations that includes the classical case. We end the paper with remarks about the bifurcations of the first integrals.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Gunther:2017:NFR, author = "Christian G{\"u}nther and Kai-Uwe Schmidt", title = "{$ L^q $} Norms of {Fekete} and Related Polynomials", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "807--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-023-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A Littlewood polynomial is a polynomial in $ \mathbb {C}[z] $ having all of its coefficients in $ \{ - 1, 1 \} $. There are various old unsolved problems, mostly due to Littlewood and {Erd"os}, that ask for Littlewood polynomials that provide a good approximation to a function that is constant on the complex unit circle, and in particular have small $ L^q $ norm on the complex unit circle. We consider the Fekete polynomials \[ f_p(z)=\sum_{j=1}^{p-1}(j\,|\,p)\,z^j, \] where $p$ is an odd prime and $ (\, \cdot \, | \, p)$ is the Legendre symbol (so that $ z^{-1}f_p(z)$ is a Littlewood polynomial). We give explicit and recursive formulas for the limit of the ratio of $ L^q$ and $ L^2$ norm of $ f_p$ when $q$ is an even positive integer and $ p \to \infty $. To our knowledge, these are the first results that give these limiting values for specific sequences of nontrivial Littlewood polynomials and infinitely many $q$. Similar results are given for polynomials obtained by cyclically permuting the coefficients of Fekete polynomials and for Littlewood polynomials whose coefficients are obtained from additive characters of finite fields. These results vastly generalise earlier results on the $ L^4$ norm of these polynomials.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Lei:2017:AGB, author = "Antonio Lei and David Loeffler and Sarah Livia Zerbes", title = "On the Asymptotic Growth of {Bloch--Kato--Shafarevich--Tate} Groups of Modular Forms over Cyclotomic Extensions", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "826--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-034-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the asymptotic behaviour of the Bloch--Kato--Shafarevich--Tate group of a modular form $f$ over the cyclotomic $ \mathbb {Z}_p$-extension of $ \mathbb {Q}$ under the assumption that $f$ is non-ordinary at $p$. In particular, we give upper bounds of these groups in terms of Iwasawa invariants of Selmer groups defined using $p$-adic Hodge Theory. These bounds have the same form as the formulae of Kobayashi, Kurihara and Sprung for supersingular elliptic curves.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Pronk:2017:ETG, author = "Dorette Pronk and Laura Scull", title = "Erratum: {Translation Groupoids and Orbifold Cohomology}", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "851--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-004-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", note = "See \cite{Pronk:2010:TGO}.", abstract = "We correct an error in the proof of a lemma in {"Translation} Groupoids and Orbifold {Cohomology"}, Canadian J. Math Vol 62 (3), pp 614-645 (2010). This error was pointed out to the authors by Li Du of the Georg-August-Universit{\"a}t at Gottingen, who also suggested the outline for the corrected proof.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Saanouni:2017:GNG, author = "Tarek Saanouni", title = "Global and non Global Solutions for Some Fractional Heat Equations with Pure Power Nonlinearity", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "854--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-012-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The initial value problem for a semi-linear fractional heat equation is investigated. In the focusing case, global well-posedness and exponential decay are obtained. In the focusing sign, global and non global existence of solutions are discussed via the potential well method.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Xiao:2017:ASC, author = "Jie Xiao and Deping Ye", title = "Anisotropic {Sobolev} Capacity with Fractional Order", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "873--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2015-060-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we introduce the anisotropic Sobolev capacity with fractional order and develop some basic properties for this new object. Applications to the theory of anisotropic fractional Sobolev spaces are provided. In particular, we give geometric characterizations for a nonnegative Radon measure $ \mu $ that naturally induces an embedding of the anisotropic fractional Sobolev class $ \dot {\Lambda }_{\alpha, K}^{1, 1} $ into the $ \mu $-based-Lebesgue-space $ L^{n / \beta }_\mu $ with $ 0 \lt \beta \le n$. Also, we investigate the anisotropic fractional $ \alpha $-perimeter. Such a geometric quantity can be used to approximate the anisotropic Sobolev capacity with fractional order. Estimation on the constant in the related Minkowski inequality, which is asymptotically optimal as $ \alpha \rightarrow 0^+$, will be provided.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Xu:2017:MPA, author = "Bin Xu", title = "On {Moeglin}'s Parametrization of {Arthur} Packets for $p$-adic Quasisplit {$ {\rm Sp}(N)$} and {$ {\rm SO}(N)$}", journal = j-CAN-J-MATH, volume = "69", number = "4", pages = "890--??", month = aug, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-029-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:12 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n4; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We give a survey on Moeglin's construction of representations in the Arthur packets for $p$-adic quasisplit symplectic and orthogonal groups. The emphasis is on comparing Moeglin's parametrization of elements in the Arthur packets with that of Arthur.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Andrade:2017:DRK, author = "Jaime Andrade and Nestor D{\'a}vila and Ernesto P{\'e}rez-Chavela and Claudio Vidal", title = "Dynamics and Regularization of the {Kepler} Problem on Surfaces of Constant Curvature", journal = j-CAN-J-MATH, volume = "69", number = "5", pages = "961--??", month = oct, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-014-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:13 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We classify and analyze the orbits of the Kepler problem on surfaces of constant curvature (both positive and negative, $ \mathbb S^2 $ and $ \mathbb H^2 $, respectively) as function of the angular momentum and the energy. Hill's region are characterized and the problem of time-collision is studied. We also regularize the problem in Cartesian and intrinsic coordinates, depending on the constant angular momentum and we describe the orbits of the regularized vector field. The phase portrait both for $ \mathbb S^2 $ and $ \mathbb H^2 $ are pointed out.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bremner:2017:CRP, author = "Murray Bremner and Vladimir Dotsenko", title = "Classification of Regular Parametrized One-relation Operads", journal = j-CAN-J-MATH, volume = "69", number = "5", pages = "992--??", month = oct, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-018-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:13 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Jean-Louis Loday introduced a class of symmetric operads generated by one bilinear operation subject to one relation making each left-normed product of three elements equal to a linear combination of right-normed products: \[ (a_1a_2)a_3=\sum_{\sigma\in S_3}x_\sigma\, a_{\sigma(1)}(a_{\sigma(2)}a_{\sigma(3)})\ ; \] such an operad is called a parametrized one-relation operad. For a particular choice of parameters $ \{ x_\sigma \} $, this operad is said to be regular if each of its components is the regular representation of the symmetric group; equivalently, the corresponding free algebra on a vector space $V$ is, as a graded vector space, isomorphic to the tensor algebra of $V$. We classify, over an algebraically closed field of characteristic zero, all regular parametrized one-relation operads. In fact, we prove that each such operad is isomorphic to one of the following five operads: the left-nilpotent operad defined by the relation $ ((a_1 a_2)a_3) = 0$, the associative operad, the Leibniz operad, the dual Leibniz (Zinbiel) operad, and the Poisson operad. Our computational methods combine linear algebra over polynomial rings, representation theory of the symmetric group, and Gr{\"o}bner bases for determinantal ideals and their radicals.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Carlen:2017:SBM, author = "Eric Carlen and Francesco Maggi", title = "Stability for the {Brunn--Minkowski} and {Riesz} Rearrangement Inequalities, with Applications to {Gaussian} Concentration and Finite Range Non-local Isoperimetry", journal = j-CAN-J-MATH, volume = "69", number = "5", pages = "1036--??", month = oct, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-026-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:13 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We provide a simple, general argument to obtain improvements of concentration-type inequalities starting from improvements of their corresponding isoperimetric-type inequalities. We apply this argument to obtain robust improvements of the Brunn-Minkowski inequality (for Minkowski sums between generic sets and convex sets) and of the Gaussian concentration inequality. The former inequality is then used to obtain a robust improvement of the Riesz rearrangement inequality under certain natural conditions. These conditions are compatible with the applications to a finite-range nonlocal isoperimetric problem arising in statistical mechanics.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Crann:2017:ACI, author = "Jason Crann", title = "Amenability and Covariant Injectivity of Locally Compact Quantum Groups {II}", journal = j-CAN-J-MATH, volume = "69", number = "5", pages = "1064--??", month = oct, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-031-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:13 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Building on our previous work, we study the non-relative homology of quantum group convolution algebras. Our main result establishes the equivalence of amenability of a locally compact quantum group $ \mathbb {G} $ and 1-injectivity of $ L^{\infty }(\widehat {\mathbb {G}}) $ as an operator $ L^1 (\widehat {\mathbb {G}})$-module. In particular, a locally compact group $G$ is amenable if and only if its group von Neumann algebra $ V N(G)$ is 1-injective as an operator module over the Fourier algebra $ A(G)$. As an application, we provide a decomposability result for completely bounded $ L^1 (\widehat {\mathbb {G}})$-module maps on $ L^{\infty }(\widehat {\mathbb {G}})$, and give a simplified proof that amenable discrete quantum groups have co-amenable compact duals which avoids the use of modular theory and the Powers--St{\o}rmer inequality, suggesting that our homological techniques may yield a new approach to the open problem of duality between amenability and co-amenability.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Jiang:2017:ACW, author = "Yin Jiang", title = "Absolute Continuity of {Wasserstein} Barycenters Over {Alexandrov} Spaces", journal = j-CAN-J-MATH, volume = "69", number = "5", pages = "1087--??", month = oct, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-035-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:13 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we prove that, on a compact, $n$-dimensional Alexandrov space with curvature $ \geqslant - 1$, the Wasserstein barycenter of Borel probability measures $ \mu_1, ..., \mu_m$ is absolutely continuous with respect to the $n$-dimensional Hausdorff measure if one of them is.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ng:2017:CCH, author = "P. W. Ng and P. Skoufranis", title = "Closed Convex Hulls of Unitary Orbits in Certain Simple Real Rank Zero {$ C^* $}-algebras", journal = j-CAN-J-MATH, volume = "69", number = "5", pages = "1109--??", month = oct, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-045-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:13 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper, we characterize the closures of convex hulls of unitary orbits of self-adjoint operators in unital, separable, simple C$^*$-algebras with non-trivial tracial simplex, real rank zero, stable rank one, and strict comparison of projections with respect to tracial states. In addition, an upper bound for the number of unitary conjugates in a convex combination needed to approximate a self-adjoint are obtained.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Sikiric:2017:SDP, author = "Mathieu Dutour Sikiri{\'c}", title = "The seven Dimensional Perfect {Delaunay} Polytopes and {Delaunay} Simplices", journal = j-CAN-J-MATH, volume = "69", number = "5", pages = "1143--??", month = oct, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-013-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:13 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For a lattice $L$ of $ \mathbb {RR}^n$, a sphere $ S(c, r)$ of center $c$ and radius $r$ is called empty if for any $ v \in L$ we have $ \Vert v - c \Vert \geq r$. Then the set $ S(c, r) \cap L$ is the vertex set of a {\em Delaunay polytope} $ P = \operatorname {conv}(S(c, r) \cap L)$. A Delaunay polytope is called {\em perfect} if any affine transformation $ \phi $ such that $ \phi (P)$ is a Delaunay polytope is necessarily an isometry of the space composed with an homothety. Perfect Delaunay polytopes are remarkable structure that exist only if $ n = 1$ or $ n \geq 6$ and they have shown up recently in covering maxima studies. Here we give a general algorithm for their enumeration that relies on the Erdahl cone. We apply this algorithm in dimension $7$ which allow us to find that there are only two perfect Delaunay polytopes: $ 3_{21}$ which is a Delaunay polytope in the root lattice $ \mathsf {E}_7$ and the Erdahl Rybnikov polytope. We then use this classification in order to get the list of all types Delaunay simplices in dimension $7$ and found $ 11$ types.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Varma:2017:RIO, author = "Sandeep Varma", title = "On Residues of Intertwining Operators in Cases with Prehomogeneous Nilradical", journal = j-CAN-J-MATH, volume = "69", number = "5", pages = "1169--??", month = oct, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-032-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Mon Oct 2 13:47:13 MDT 2017", bibsource = "http://cms.math.ca/cjm/v69/n5; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \operatorname {P} = \operatorname {M} \operatorname {N} $ be a Levi decomposition of a maximal parabolic subgroup of a connected reductive group $ \operatorname {G} $ over a $p$-adic field $F$. Assume that there exists $ w_0 \in \operatorname {G}(F)$ that normalizes $ \operatorname {M}$ and conjugates $ \operatorname {P}$ to an opposite parabolic subgroup. When $ \operatorname {N}$ has a Zariski dense $ \operatorname {Int} \operatorname {M}$-orbit, F. Shahidi and X. Yu describe a certain distribution $D$ on $ \operatorname {M}(F)$ such that, for irreducible unitary supercuspidal representations $ \pi $ of $ \operatorname {M}(F)$ with $ \pi \cong \pi \circ \operatorname {Int} w_0$, $ \operatorname {Ind}_{\operatorname {P}(F)}^{\operatorname {G}(F)} \pi $ is irreducible if and only if $ D(f) \neq 0$ for some pseudocoefficient $f$ of $ \pi $. Since this irreducibility is conjecturally related to $ \pi $ arising via transfer from certain twisted endoscopic groups of $ \operatorname {M}$, it is of interest to realize $D$ as endoscopic transfer from a simpler distribution on a twisted endoscopic group $ \operatorname {H}$ of $ \operatorname {M}$. This has been done in many situations where $ \operatorname {N}$ is abelian. Here, we handle the `standard examples' in cases where $ \operatorname {N}$ is nonabelian but admits a Zariski dense $ \operatorname {Int} \operatorname {M}$-orbit.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Abe:2017:CPL, author = "Tetsuya Abe and Keiji Tagami", title = "Characterization of Positive Links and the $s$-invariant for Links", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1201--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-030-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We characterize positive links in terms of strong quasipositivity, homogeneity and the value of Rasmussen and Beliakova-Wehrli's $s$-invariant. We also study almost positive links, in particular, determine the $s$-invariants of almost positive links. This result suggests that all almost positive links might be strongly quasipositive. On the other hand, it implies that almost positive links are never homogeneous links.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Almeida:2017:AHL, author = "V{\'\i}ctor Almeida and Jorge J. Betancor and Lourdes Rodr{\'\i}guez-Mesa", title = "Anisotropic {Hardy--Lorentz} Spaces with Variable Exponents", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1219--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-053-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this paper we introduce Hardy-Lorentz spaces with variable exponents associated to dilations in $ {\mathbb R}^n $. We establish maximal characterizations and atomic decompositions for our variable exponent anisotropic Hardy-Lorentz spaces.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Favacchio:2017:MFR, author = "Giuseppe Favacchio and Elena Guardo", title = "The Minimal Free Resolution of Fat Almost Complete Intersections in {$ \mathbb {P}^1 \times \mathbb {P}^1 $}", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1274--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-040-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "A current research theme is to compare symbolic powers of an ideal $I$ with the regular powers of $I$. In this paper, we focus on the case that $ I = I_X$ is an ideal defining an almost complete intersection (ACI) set of points $X$ in $ \mathbb {P}^1 \times \mathbb {P}^1$. In particular, we describe a minimal free bigraded resolution of a non arithmetically Cohen-Macaulay (also non homogeneous) set $ \mathcal Z$ of fat points whose support is an ACI, generalizing a result of S. Cooper et al. for homogeneous sets of triple points. We call $ \mathcal Z$ a fat ACI. We also show that its symbolic and ordinary powers are equal, i.e, $ I_{\mathcal Z}^{(m)} = I_{\mathcal Z}^m$ for any $ m \geq 1.$", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Folha:2017:WTS, author = "Abigail Folha and Carlos Pe{\~n}afiel", title = "{Weingarten} Type Surfaces in {$ \mathbb {H}^2 \times \mathbb {R} $} and {$ \mathbb {S}^2 \times \mathbb {R} $}", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1292--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-054-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "In this article, we study complete surfaces $ \Sigma $, isometrically immersed in the product space $ \mathbb {H}^2 \times \mathbb {R} $ or $ \mathbb {S}^2 \times \mathbb {R} $ having positive extrinsic curvature $ K_e $. Let $ K_i $ denote the intrinsic curvature of $ \Sigma $. Assume that the equation $ a K_i + b K_e = c $ holds for some real constants $ a \neq 0 $, $ b \gt 0 $ and $c$. The main result of this article state that when such a surface is a topological sphere it is rotational.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Fricain:2017:AOS, author = "Emmanuel Fricain and Rishika Rupam", title = "On Asymptotically Orthonormal Sequences", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1312--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-001-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "An asymptotically orthonormal sequence is a sequence which is {"nearly"} orthonormal in the sense that it satisfies the Parseval equality up to two constants close to one. In this paper, we explore such sequences formed by normalized reproducing kernels for model spaces and de Branges-Rovnyak spaces.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Harrison-Trainor:2017:CFE, author = "Matthew Harrison-Trainor and Alexander Melnikov and Russell Miller", title = "On Computable Field Embeddings and Difference Closed Fields", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1338--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-044-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of computable difference fields into computable difference closed fields.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Nikolidakis:2017:ESB, author = "Eleftherios Nikolaos Nikolidakis", title = "Extremal Sequences for the {Bellman} Function of the Dyadic Maximal Operator and Applications to the {Hardy} Operator", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1364--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-025-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove that the extremal sequences for the Bellman function of the dyadic maximal operator behave approximately as eigenfunctions of this operator for a specific eigenvalue. We use this result to prove the analogous one with respect to the Hardy operator.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Pasnicu:2017:WIP, author = "Cornel Pasnicu and N. Christopher Phillips", title = "The Weak Ideal Property and Topological Dimension Zero", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1385--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-012-4", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Following up on previous work, we prove a number of results for C*-algebras with the weak ideal property or topological dimension zero, and some results for C*-algebras with related properties. Some of the more important results include: $ \bullet $ The weak ideal property implies topological dimension zero. $ \bullet $ For a separable C*-algebra~$A$, topological dimension zero is equivalent to $ {\operatorname {RR}} ({\mathcal {O}}_2 \otimes A) = 0$, to $ D \otimes A$ having the ideal property for some (or any) Kirchberg algebra~$D$, and to $A$ being residually hereditarily in the class of all C*-algebras $B$ such that $ {\mathcal {O}}_{\infty } \otimes B$ contains a nonzero projection. $ \bullet $ Extending the known result for $ {\mathbb {Z}}_2$, the classes of C*-algebras with residual (SP), which are residually hereditarily (properly) infinite, or which are purely infinite and have the ideal property, are closed under crossed products by arbitrary actions of abelian $2$-groups. $ \bullet $ If $A$ and $B$ are separable, one of them is exact, $A$ has the ideal property, and $B$ has the weak ideal property, then $ A \otimes_{\mathrm {min}} B$ has the weak ideal property. $ \bullet $ If $X$ is a totally disconnected locally compact Hausdorff space and $A$ is a $ C_0 (X)$-algebra all of whose fibers have one of the weak ideal property, topological dimension zero, residual (SP), or the combination of pure infiniteness and the ideal property, then $A$ also has the corresponding property (for topological dimension zero, provided $A$ is separable). $ \bullet $ Topological dimension zero, the weak ideal property, and the ideal property are all equivalent for a substantial class of separable C*-algebras including all separable locally AH~algebras. $ \bullet $ The weak ideal property does not imply the ideal property for separable $Z$-stable C*-algebras. We give other related results, as well as counterexamples to several other statements one might hope for.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Semrl:2017:OSP, author = "Peter Semrl", title = "Order and Spectrum Preserving Maps on Positive Operators", journal = j-CAN-J-MATH, volume = "69", number = "6", pages = "1422--??", month = dec, year = "2017", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-039-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v69/n6; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We describe the general form of surjective maps on the cone of all positive operators which preserve order and spectrum. The result is optimal as shown by counterexamples. As an easy consequence we characterize surjective order and spectrum preserving maps on the set of all self-adjoint operators.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Benaych-Georges:2018:FME, author = "Florent Benaych-Georges and Guillaume C{\'e}bron and Jean Rochet", title = "Fluctuation of matrix entries and application to outliers of elliptic matrices", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "3--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-024-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For any family of $ N \times N $ random matrices $ (\mathbf {A}_k)_{k \in K} $ which is invariant, in law, under unitary conjugation, we give general sufficient conditions for central limit theorems for random variables of the type $ \operatorname {Tr}(\mathbf {A}_k \mathbf {M}) $, where the matrix $ \mathbf {M} $ is deterministic (such random variables include for example the normalized matrix entries of the $ \mathbf {A}_k $'s). A consequence is the asymptotic independence of the projection of the matrices $ \mathbf {A}_k $ onto the subspace of null trace matrices from their projections onto the orthogonal of this subspace. These results are used to study the asymptotic behavior of the outliers of a spiked elliptic random matrix. More precisely, we show that the fluctuations of these outliers around their limits can have various rates of convergence, depending on the Jordan Canonical Form of the additive perturbation. Also, some correlations can arise between outliers at a macroscopic distance from each other. These phenomena have already been observed with random matrices from the Single Ring Theorem.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bosa:2018:CPC, author = "Joan Bosa and Henning Petzka", title = "Comparison Properties of the {Cuntz} semigroup and applications to {$ C* $}-algebras", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "26--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-049-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study comparison properties in the category $ \mathrm {Cu} $ aiming to lift results to the C*-algebraic setting. We introduce a new comparison property and relate it to both the CFP and $ \omega $-comparison. We show differences of all properties by providing examples, which suggest that the corona factorization for C*-algebras might allow for both finite and infinite projections. In addition, we show that R{\o}rdam's simple, nuclear C*-algebra with a finite and an infinite projection does not have the CFP.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Dantas:2018:BPB, author = "Sheldon Dantas and Domingo Garc{\'\i}a and Manuel Maestre and Miguel Mart{\'\i}n", title = "The {Bishop--Phelps--Bollob{\'a}s} property for compact operators", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "53--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-036-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study the Bishop-Phelps-Bollob{\'a}s property (BPBp for short) for compact operators. We present some abstract techniques which allows to carry the BPBp for compact operators from sequence spaces to function spaces. As main applications, we prove the following results. Let $X$, $Y$ be Banach spaces. If $ (c_0, Y)$ has the BPBp for compact operators, then so do $ (C_0 (L), Y)$ for every locally compact Hausdorff topological space $L$ and $ (X, Y)$ whenever $ X^*$ is isometrically isomorphic to $ \ell_1$. If $ X^*$ has the Radon-Nikod{\'y}m property and $ (\ell_1 (X), Y)$ has the BPBp for compact operators, then so does $ (L_1 (\mu, X), Y)$ for every positive measure $ \mu $; as a consequence, $ (L_1 (\mu, X), Y)$ has the the BPBp for compact operators when $X$ and $Y$ are finite-dimensional or $Y$ is a Hilbert space and $ X = c_0$ or $ X = L_p(\nu)$ for any positive measure $ \nu $ and $ 1 \lt p \lt \infty $. For $ 1 \leq p \lt \infty $, if $ (X, \ell_p(Y))$ has the BPBp for compact operators, then so does $ (X, L_p(\mu, Y))$ for every positive measure $ \mu $ such that $ L_1 (\mu)$ is infinite-dimensional. If $ (X, Y)$ has the BPBp for compact operators, then so do $ (X, L_\infty (\mu, Y))$ for every $ \sigma $-finite positive measure $ \mu $ and $ (X, C(K, Y))$ for every compact Hausdorff topological space $K$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Dow:2018:NVP, author = "Alan Dow and Franklin D. Tall", title = "Normality versus paracompactness in locally compact spaces", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "74--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-006-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This note provides a correct proof of the result claimed by the second author that locally compact normal spaces are collectionwise Hausdorff in certain models obtained by forcing with a coherent Souslin tree. A novel feature of the proof is the use of saturation of the non-stationary ideal on $ \omega_1 $, as well as of a strong form of Chang's Conjecture. Together with other improvements, this enables the consistent characterization of locally compact hereditarily paracompact spaces as those locally compact, hereditarily normal spaces that do not include a copy of $ \omega_1 $.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Farashahi:2018:CAL, author = "Arash Ghaani Farashahi", title = "A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "97--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-043-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "This paper introduces a class of abstract linear representations on Banach convolution function algebras over homogeneous spaces of compact groups. Let $G$ be a compact group and $H$ be a closed subgroup of $G$. Let $ \mu $ be the normalized $G$-invariant measure over the compact homogeneous space $ G / H$ associated to the Weil's formula and $ 1 \le p \lt \infty $. We then present a structured class of abstract linear representations of the Banach convolution function algebras $ L^p(G / H, \mu)$.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ha:2018:SPS, author = "Junsoo Ha", title = "Smooth Polynomial Solutions to a Ternary Additive Equation", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "117--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-023-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \mathbf {F}_q[T] $ be the ring of polynomials over the finite field of $q$ elements, and $Y$ be a large integer. We say a polynomial in $ \mathbf {F}_q[T]$ is $Y$-smooth if all of its irreducible factors are of degree at most $Y$. We show that a ternary additive equation $ a + b = c$ over $Y$-smooth polynomials has many solutions. As an application, if $S$ is the set of first $s$ primes in $ \mathbf {F}_q[T]$ and $s$ is large, we prove that the $S$-unit equation $ u + v = 1$ has at least $ \exp (s^{1 / 6 - \epsilon } \log q)$ solutions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Hajir:2018:IFC, author = "Farshid Hajir and Christian Maire", title = "On the invariant factors of class groups in towers of number fields", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "142--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-032-9", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For a finite abelian $p$-group $A$ of rank $ d = \dim A / p A$, let $ \mathbb {M}_A := \log_p |A|^{1 / d}$ be its \emph{(logarithmic) mean exponent}. We study the behavior of the mean exponent of $p$-class groups in pro-$p$ towers $ \mathrm {L} / K$ of number fields. Via a combination of results from analytic and algebraic number theory, we construct infinite tamely ramified pro-$p$ towers in which the mean exponent of $p$-class groups remains bounded. Several explicit examples are given with $ p = 2$. Turning to group theory, we introduce an invariant $ \underline {\mathbb {M}}(G)$ attached to a finitely generated pro-$p$ group $G$; when $ G = \operatorname {Gal}(\mathrm {L} / \mathrm {K})$, where $ \mathrm {L}$ is the Hilbert $p$-class field tower of a number field $K$, $ \underline {\mathbb {M}}(G)$ measures the asymptotic behavior of the mean exponent of $p$-class groups inside $ \mathrm {L} / \mathrm {K}$. We compare and contrast the behavior of this invariant in analytic versus non-analytic groups. We exploit the interplay of group-theoretical and number-theoretical perspectives on this invariant and explore some open questions that arise as a result, which may be of independent interest in group theory.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Hakl:2018:PSI, author = "Robert Hakl and Manuel Zamora", title = "Periodic solutions of an indefinite singular equation arising from the {Kepler} problem on the sphere", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "173--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-050-1", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We study a second-order ordinary differential equation coming from the Kepler problem on $ \mathbb {S}^2 $. The forcing term under consideration is a piecewise constant with singular nonlinearity which changes sign. We establish necessary and sufficient conditions to the existence and multiplicity of $T$-periodic solutions.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Kitchloo:2018:C, author = "Nitu Kitchloo and Vitaly Lorman and W. Stephen Wilson", title = "The {$ E R(2) $}-cohomology of {$ B \mathbb {Z} / (2^q) $} and {$ \mathbb {C} \mathbb {P}^n $}", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "191--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-003-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The $ E R(2)$-cohomology of $ B \mathbb {Z} / (2^q)$ and $ \mathbb {C} \mathbb {P}^n$ are computed along with the Atiyah-Hirzebruch spectral sequence for $ E R(2)^*(\mathbb {C} \mathbb {P}^\infty)$. This, along with other papers in this series, gives us the $ E R(2)$-cohomology of all Eilenberg-MacLane spaces.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Speissegger:2018:QIA, author = "Patrick Speissegger", title = "Quasianalytic {Ilyashenko} algebras", journal = j-CAN-J-MATH, volume = "70", number = "1", pages = "218--??", month = feb, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-048-x", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Sat Jan 13 15:40:45 MST 2018", bibsource = "http://cms.math.ca/cjm/v70/n1; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "I construct a quasianalytic field $ \mathcal {F} $ of germs at $ + \infty $ of real functions with logarithmic generalized power series as asymptotic expansions, such that $ \mathcal {F} $ is closed under differentiation and $ \log $-composition; in particular, $ \mathcal {F}$ is a Hardy field. Moreover, the field $ \mathcal {F} \circ ( - \log)$ of germs at $ 0^+$ contains all transition maps of hyperbolic saddles of planar real analytic vector fields.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bocherer:2018:WMK, author = "Siegfried B{\"o}cherer and Toshiyuki Kikuta and Sho Takemori", title = "Weights of the mod $p$ kernel of the theta operators", journal = j-CAN-J-MATH, volume = "70", number = "2", pages = "241--??", month = apr, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-014-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $ \Theta^{[j]} $ be an analogue of the Ramanujan theta operator for Siegel modular forms. For a given prime $p$, we give the weights of elements of mod $p$ kernel of $ \Theta^{[j]}$, where the mod $p$ kernel of $ \Theta^{[j]}$ is the set of all Siegel modular forms $F$ such that $ \Theta^{[j]}(F)$ is congruent to zero modulo $p$. In order to construct examples of the mod $p$ kernel of $ \Theta^{[j]}$ from any Siegel modular form, we introduce new operators $ A^{(j)}(M)$ and show the modularity of $ F|A^{(j)}(M)$ when $F$ is a Siegel modular form. Finally, we give some examples of the mod $p$ kernel of $ \Theta^{[j]}$ and the filtrations of some of them.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Bulens:2018:RMC, author = "Hector Cordova Bulens and Pascal Lambrechts and Don Stanley", title = "Rational models of the complement of a subpolyhedron in a manifold with boundary", journal = j-CAN-J-MATH, volume = "70", number = "2", pages = "265--??", month = apr, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-021-3", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Let $W$ be a compact simply connected triangulated manifold with boundary and $ K \subset W$ be a subpolyhedron. We construct an algebraic model of the rational homotopy type of $ W \backslash K$ out of a model of the map of pairs $ (K, K \cap \partial W) \hookrightarrow (W, \partial W)$ under some high codimension hypothesis. We deduce the rational homotopy invariance of the configuration space of two points in a compact manifold with boundary under 2-connectedness hypotheses. Also, we exhibit nice explicit models of these configuration spaces for a large class of compact manifolds.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Eilers:2018:GCG, author = "S{\o}ren Eilers and Gunnar Restorff and Efren Ruiz and Adam P. W. S{\o}rensen", title = "Geometric classification of graph {$ C* $}-algebras over finite graphs", journal = j-CAN-J-MATH, volume = "70", number = "2", pages = "294--??", month = apr, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-016-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We address the classification problem for graph $ C^*$-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that the graphs satisfy the standard condition (K), so that the graph $ C^*$-algebras may come with uncountably many ideals. We find that in this generality, stable isomorphism of graph $ C^*$-algebras does not coincide with the geometric notion of Cuntz move equivalence. However, adding a modest condition on the graphs, the two notions are proved to be mutually equivalent and equivalent to the $ C^*$-algebras having isomorphic $K$-theories. This proves in turn that under this condition, the graph $ C^*$-algebras are in fact classifiable by $K$-theory, providing in particular complete classification when the $ C^*$-algebras in question are either of real rank zero or type I/postliminal. The key ingredient in obtaining these results is a characterization of Cuntz move equivalence using the adjacency matrices of the graphs. Our results are applied to discuss the classification problem for the quantum lens spaces defined by Hong and Szyma{\'n}ski, and to complete the classification of graph $ C^*$-algebras associated to all simple graphs with four vertices or less.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Manon:2018:TGF, author = "Christopher Manon", title = "Toric geometry of {$ S L_2 (\mathbb {C}) $} free group character varieties from outer space", journal = j-CAN-J-MATH, volume = "70", number = "2", pages = "354--??", month = apr, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-042-0", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "Culler and Vogtmann defined a simplicial space $ O(g) $ called outer space to study the outer automorphism group of the free group $ F_g $. Using representation theoretic methods, we give an embedding of $ O(g) $ into the analytification of $ \mathcal {X}(F_g, S L_2 (\mathbb {C})), $ the $ S L_2 (\mathbb {C}) $ character variety of $ F_g, $ reproving a result of Morgan and Shalen. Then we show that every point $v$ contained in a maximal cell of $ O(g)$ defines a flat degeneration of $ \mathcal {X}(F_g, S L_2 (\mathbb {C}))$ to a toric variety $ X(P_{\Gamma })$. We relate $ \mathcal {X}(F_g, S L_2 (\mathbb {C}))$ and $ X(v)$ topologically by showing that there is a surjective, continuous, proper map $ \Xi_v : \mathcal {X}(F_g, S L_2 (\mathbb {C})) \to X(v)$. We then show that this map is a symplectomorphism on a dense, open subset of $ \mathcal {X}(F_g, S L_2 (\mathbb {C}))$ with respect to natural symplectic structures on $ \mathcal {X}(F_g, S L_2 (\mathbb {C}))$ and $ X(v)$. In this way, we construct an integrable Hamiltonian system in $ \mathcal {X}(F_g, S L_2 (\mathbb {C}))$ for each point in a maximal cell of $ O(g)$, and we show that each $v$ defines a topological decomposition of $ \mathcal {X}(F_g, S L_2 (\mathbb {C}))$ derived from the decomposition of $ X(P_{\Gamma })$ by its torus orbits. Finally, we show that the valuations coming from the closure of a maximal cell in $ O(g)$ all arise as divisorial valuations built from an associated projective compactification of $ \mathcal {X}(F_g, S L_2 (\mathbb {C})).$", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Osaka:2018:JSA, author = "Hiroyuki Osaka and Tamotsu Teruya", title = "The {Jiang--Su} absorption for inclusions of unital {$ C* $}-algebras", journal = j-CAN-J-MATH, volume = "70", number = "2", pages = "400--??", month = apr, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-033-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib; https://www.math.utah.edu/pub/tex/bib/canjmath2020.bib", note = "See erratum \cite{Osaka:2021:EJA}.", abstract = "We introduce the tracial Rokhlin property for a conditional expectation for an inclusion of unital C*-algebras $ P \subset A $ with index finite, and show that an action $ \alpha $ from a finite group $G$ on a simple unital C*-algebra $A$ has the tracial Rokhlin property in the sense of N. C. Phillips if and only if the canonical conditional expectation $ E \colon A \rightarrow A^G$ has the tracial Rokhlin property. Let $ \mathcal {C}$ be a class of infinite dimensional stably finite separable unital C*-algebras which is closed under the following conditions: (1) If $ A \in {\mathcal C}$ and $ B \cong A$, then $ B \in \mathcal {C}$. (2) If $ A \in \mathcal {C}$ and $ n \in \mathbb {N}$, then $ M_n(A) \in \mathcal {C}$. (3) If $ A \in \mathcal {C}$ and $ p \in A$ is a nonzero projection, then $ p A p \in \mathcal {C}$. Suppose that any C*-algebra in $ \mathcal {C}$ is weakly semiprojective. We prove that if $A$ is a local tracial $ \mathcal {C}$-algebra in the sense of Fan and Fang and a conditional expectation $ E \colon A \rightarrow P$ is of index-finite type with the tracial Rokhlin property, then $P$ is a unital local tracial $ \mathcal {C}$-algebra. The main result is that if $A$ is simple, separable, unital nuclear, Jiang-Su absorbing and $ E \colon A \rightarrow P$ has the tracial Rokhlin property, then $P$ is Jiang-Su absorbing. As an application, when an action $ \alpha $ from a finite group $G$ on a simple unital C*-algebra $A$ has the tracial Rokhlin property, then for any subgroup $H$ of $G$ the fixed point algebra $ A^H$ and the crossed product algebra $ A \rtimes_{\alpha_{|H}} H$ is Jiang-Su absorbing. We also show that the strict comparison property for a Cuntz semigroup $ W(A)$ is hereditary to $ W(P)$ if $A$ is simple, separable, exact, unital, and $ E \colon A \rightarrow P$ has the tracial Rokhlin property.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Perez-Chavela:2018:ETR, author = "Ernesto P{\'e}rez-Chavela and Juan Manuel S{\'a}nchez-Cerritos", title = "{Euler}-type relative equilibria in spaces of constant curvature and their stability", journal = j-CAN-J-MATH, volume = "70", number = "2", pages = "426--??", month = apr, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-002-7", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We consider three point positive masses moving on $ S^2 $ and $ H^2 $. An Eulerian-relative equilibrium, is a relative equilibrium where the three masses are on the same geodesic, in this paper we analyze the spectral stability of these kind of orbits where the mass at the middle is arbitrary and the masses at the ends are equal and located at the same distance from the central mass. For the case of $ S^2 $, we found a positive measure set in the set of parameters where the relative equilibria are spectrally stable, and we give a complete classification of the spectral stability of these solutions, in the sense that, except on an algebraic curve in the space of parameters, we can determine if the corresponding relative equilibria is spectrally stable or unstable. On $ H^2 $, in the elliptic case, we prove that generically all Eulerian-relative equilibria are unstable; in the particular degenerate case when the two equal masses are negligible we get that the corresponding solutions are spectrally stable. For the hyperbolic case we consider the system where the mass in the middle is negligible, in this case the Eulerian-relative equilibria are unstable.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Zhang:2018:EOS, author = "Chao Zhang", title = "{Ekedahl--Oort} strata for good reductions of {Shimura} varieties of {Hodge} type", journal = j-CAN-J-MATH, volume = "70", number = "2", pages = "451--??", month = apr, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-020-5", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n2; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "For a Shimura variety of Hodge type with hyperspecial level structure at a prime~$p$, Vasiu and Kisin constructed a smooth integral model (namely the integral canonical model) uniquely determined by a certain extension property. We define and study the Ekedahl-Oort stratifications on the special fibers of those integral canonical models when $ p \gt 2$. This generalizes Ekedahl-Oort stratifications defined and studied by Oort on moduli spaces of principally polarized abelian varieties and those defined and studied by Moonen, Wedhorn and Viehmann on good reductions of Shimura varieties of PEL type. We show that the Ekedahl-Oort strata are parameterized by certain elements $w$ in the Weyl group of the reductive group in the Shimura datum. We prove that the stratum corresponding to $w$ is smooth of dimension $ l(w)$ (i.e. the length of $w$) if it is non-empty. We also determine the closure of each stratum.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Asakura:2018:CPC, author = "Masanori Asakura and Noriyuki Otsubo", title = "{CM} Periods, {CM} Regulators and Hypergeometric Functions, {I}", journal = j-CAN-J-MATH, volume = "70", number = "3", pages = "481--??", month = jun, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-008-6", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "We prove the Gross-Deligne conjecture on CM periods for motives associated with $ H^2 $ of certain surfaces fibered over the projective line. Then we prove for the same motives a formula which expresses the $ K_1$-regulators in terms of hypergeometric functions ${}_3 F_2$, and obtain a new example of non-trivial regulators.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Chen:2018:BTG, author = "Yanni Chen and Don Hadwin and Zhe Liu and Eric Nordgren", title = "A {Beurling} Theorem for Generalized {Hardy} Spaces on a Multiply Connected Domain", journal = j-CAN-J-MATH, volume = "70", number = "3", pages = "515--??", month = jun, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2017-007-8", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The object of this paper is to prove a version of the Beurling-Helson-Lowdenslager invariant subspace theorem for operators on certain Banach spaces of functions on a multiply connected domain in $ \mathbb {C} $. The norms for these spaces are either the usual Lebesgue and Hardy space norms or certain continuous gauge norms. In the Hardy space case the expected corollaries include the characterization of the cyclic vectors as the outer functions in this context, a demonstration that the set of analytic multiplication operators is maximal abelian and reflexive, and a determination of the closed operators that commute with all analytic multiplication operators.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Ciesielski:2018:FPT, author = "Krzysztof Chris Ciesielski and Jakub Jasinski", title = "Fixed Point Theorems for Maps with Local and Pointwise Contraction Properties", journal = j-CAN-J-MATH, volume = "70", number = "3", pages = "538--??", month = jun, year = "2018", CODEN = "CJMAAB", DOI = "https://doi.org/10.4153/CJM-2016-055-2", ISSN = "0008-414X (print), 1496-4279 (electronic)", ISSN-L = "0008-414X", bibdate = "Fri Sep 28 09:16:56 MDT 2018", bibsource = "http://cms.math.ca/cjm/v70/n3; https://www.math.utah.edu/pub/tex/bib/canjmath2010.bib", abstract = "The paper constitutes a comprehensive study of ten classes of self-maps on metric spaces $ \langle X, d \rangle $ with the local and pointwise (a.k.a. local radial) contraction properties. Each of those classes appeared previously in the literature in the context of fixed point theorems. We begin with presenting an overview of these fixed point results, including concise self contained sketches of their proofs. Then, we proceed with a discussion of the relations among the ten classes of self-maps with domains $ \langle X, d \rangle $ having various topological properties which often appear in the theory of fixed point theorems: completeness, compactness, (path) connectedness, rectifiable path connectedness, and $d$-convexity. The bulk of the results presented in this part consists of examples of maps that show non-reversibility of the previously established inclusions between theses classes. Among these examples, the most striking is a differentiable auto-homeomorphism $f$ of a compact perfect subset $X$ of $ \mathbb R$ with $ f' \equiv 0$, which constitutes also a minimal dynamical system. We finish with discussing a few remaining open problems on weather the maps with specific pointwise contraction properties must have the fixed points.", acknowledgement = ack-nhfb, journal-URL = "http://cms.math.ca/cjm/", } @Article{Cohen:2018:TRO, author = "Jonathan Cohen", title = "Transfer of Representations and Orbital Integrals for Inner Forms of {$ G