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  • Some local maximum principles along Ricci flows
    Can. J. Math. (IF 0.881) Pub Date : 2020-11-04
    Man-Chun Lee; Luen-Fai Tam

    In this work, we obtain a local maximum principle along the Ricci flow $g(t)$ under the condition that $\mathrm {Ric}(g(t))\le {\alpha } t^{-1}$ for $t>0$ for some constant ${\alpha }>0$ . As an application, we will prove that under this condition, various kinds of curvatures will still be nonnegative for $t>0$ , provided they are non-negative initially. These extend the corresponding known results

    更新日期:2020-11-25
  • Tropical geometry and Newton–Okounkov cones for Grassmannian of planes from compactifications
    Can. J. Math. (IF 0.881) Pub Date : 2020-10-12
    Christopher Manon; Jihyeon Jessie Yang

    We construct a family of compactifications of the affine cone of the Grassmannian variety of $2$ -planes. We show that both the tropical variety of the Plücker ideal and familiar valuations associated to the construction of Newton–Okounkov bodies for the Grassmannian variety can be recovered from these compactifications. In this way, we unite various perspectives for constructing toric degenerations

    更新日期:2020-11-21
  • Divisibility of torsion subgroups of abelian surfaces over number fields
    Can. J. Math. (IF 0.881) Pub Date : 2020-10-28
    John Cullinan; Jeffrey Yelton

    Let A be a two-dimensional abelian variety defined over a number field K. Fix a prime number $\ell $ and suppose $\#A({\mathbf {F}_{\mathfrak {p}}}) \equiv 0 \pmod {\ell ^2}$ for a set of primes ${\mathfrak {p}} \subset {\mathcal {O}_{K}}$ of density 1. When $\ell =2$ Serre has shown that there does not necessarily exist a K-isogenous $A'$ such that $\#A'(K)_{{tor}} \equiv 0 \pmod {4}$ . We extend

    更新日期:2020-11-17
  • Action convergence of operators and graphs
    Can. J. Math. (IF 0.881) Pub Date : 2020-09-17
    Ágnes Backhausz; Balázs Szegedy

    We present a new approach to graph limit theory that unifies and generalizes the two most well-developed directions, namely dense graph limits (even the more general $L^p$ limits) and Benjamini–Schramm limits (even in the stronger local-global setting). We illustrate by examples that this new framework provides a rich limit theory with natural limit objects for graphs of intermediate density. Moreover

    更新日期:2020-11-16
  • Densities in certain three-way prime number races
    Can. J. Math. (IF 0.881) Pub Date : 2020-10-12
    Jiawei Lin; Greg Martin

    Let $a_1$ , $a_2$ , and $a_3$ be distinct reduced residues modulo q satisfying the congruences $a_1^2 \equiv a_2^2 \equiv a_3^2 \ (\mathrm{mod}\ q)$ . We conditionally derive an asymptotic formula, with an error term that has a power savings in q, for the logarithmic density of the set of real numbers x for which $\pi (x;q,a_1)> \pi (x;q,a_2) > \pi (x;q,a_3)$ . The relationship among the $a_i$ allows

    更新日期:2020-11-13
  • Möbius automorphisms of surfaces with many circles
    Can. J. Math. (IF 0.881) Pub Date : 2020-09-02
    Niels Lubbes

    We classify real two-dimensional orbits of conformal subgroups such that the orbits contain two circular arcs through a point. Such surfaces must be toric and admit a Möbius automorphism group of dimension at least two. Our theorem generalizes the classical classification of Dupin cyclides.

    更新日期:2020-09-02
  • On a family of torsional creep problems in Finsler metrics
    Can. J. Math. (IF 0.881) Pub Date : 2020-09-02
    Maria Fărcăşeanu; Mihai Mihăilescu; Denisa Stancu-Dumitru

    The asymptotic behavior of solutions to a family of Dirichlet boundary value problems, involving differential operators in divergence form, on a domain equipped with a Finsler metric is investigated. Solutions are shown to converge uniformly to the distance function to the boundary of the domain, which takes into account the Finsler norm involved in the equation. This implies that a well-known result

    更新日期:2020-09-02
  • Spaces of knotted circles and exotic smooth structures
    Can. J. Math. (IF 0.881) Pub Date : 2020-08-24
    Gregory Arone; Markus Szymik

    Suppose that $N_1$ and $N_2$ are closed smooth manifolds of dimension n that are homeomorphic. We prove that the spaces of smooth knots, $ \operatorname {\mathrm {Emb}}(\mathrm {S}^1, N_1)$ and $ \operatorname {\mathrm {Emb}}(\mathrm {S}^1, N_2),$ have the same homotopy $(2n-7)$ -type. In the four-dimensional case, this means that the spaces of smooth knots in homeomorphic $4$ -manifolds have sets

    更新日期:2020-08-24
  • Kuperberg invariants for balanced sutured 3-manifolds
    Can. J. Math. (IF 0.881) Pub Date : 2020-08-20
    Daniel López Neumann

    We construct quantum invariants of balanced sutured 3-manifolds with a ${\text {Spin}^c}$ structure out of an involutive (possibly nonunimodular) Hopf superalgebra H. If H is the Borel subalgebra of ${U_q(\mathfrak {gl}(1|1))}$ , we show that our invariant is computed via Fox calculus, and it is a normalization of Reidemeister torsion. The invariant is defined via a modification of a construction of

    更新日期:2020-08-20
  • A splicing formula for the LMO invariant
    Can. J. Math. (IF 0.881) Pub Date : 2020-08-20
    Gwénaël Massuyeau; Delphine Moussard

    We prove a “splicing formula” for the LMO invariant, which is the universal finite-type invariant of rational homology three-spheres. Specifically, if a rational homology three-sphere M is obtained by gluing the exteriors of two framed knots $K_1 \subset M_1$ and $K_2\subset M_2$ in rational homology three-spheres, our formula expresses the LMO invariant of M in terms of the Kontsevich–LMO invariants

    更新日期:2020-08-20
  • A revisit on the compactness of commutators
    Can. J. Math. (IF 0.881) Pub Date : 2020-08-20
    Weichao Guo; Huoxiong Wu; Dongyong Yang

    A new characterization of $\text {CMO}(\mathbb R^n)$ is established replying upon local mean oscillations. Some characterizations of iterated compact commutators on weighted Lebesgue spaces are given, which are new even in the unweighted setting for the first order commutators.

    更新日期:2020-08-20
  • A new approach to weak convergence of random cones and polytopes
    Can. J. Math. (IF 0.881) Pub Date : 2020-08-11
    Zakhar Kabluchko; Daniel Temesvari; Christoph Thäle

    A new approach to prove weak convergence of random polytopes on the space of compact convex sets is presented. This is used to show that the profile of the rescaled Schläfli random cone of a random conical tessellation, generated by n independent and uniformly distributed random linear hyperplanes in $\mathbb {R}^{d+1}$ , weakly converges to the typical cell of a stationary and isotropic Poisson hyperplane

    更新日期:2020-08-11
  • Extremal problems for convex geometric hypergraphs and ordered hypergraphs
    Can. J. Math. (IF 0.881) Pub Date : 2020-08-10
    Zoltán Füredi; Tao Jiang; Alexandr Kostochka; Dhruv Mubayi; Jacques Verstraëte

    An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal problems for ordered and convex geometric graphs have a rich history with applications to a variety of problems in combinatorial geometry. In this paper, we consider analogous extremal problems for uniform hypergraphs, and determine

    更新日期:2020-08-10
  • Étale groupoid algebras with coefficients in a sheaf and skew inverse semigroup rings
    Can. J. Math. (IF 0.881) Pub Date : 2020-08-07
    Daniel Gonçalves; Benjamin Steinberg

    Given an action ${\varphi }$ of inverse semigroup S on a ring A (with domain of ${\varphi }(s)$ denoted by $D_{s^*}$ ), we show that if the ideals $D_e$ , with e an idempotent, are unital, then the skew inverse semigroup ring $A\rtimes S$ can be realized as the convolution algebra of an ample groupoid with coefficients in a sheaf of (unital) rings. Conversely, we show that the convolution algebra of

    更新日期:2020-08-07
  • On the number of linearly independent admissible solutions to linear differential and linear difference equations
    Can. J. Math. (IF 0.881) Pub Date : 2020-07-30
    Janne Heittokangas; Hui Yu; Mohamed Amine Zemirni

    A classical theorem of Frei states that if $A_p$ is the last transcendental function in the sequence $A_0,\ldots ,A_{n-1}$ of entire functions, then each solution base of the differential equation $f^{(n)}+A_{n-1}f^{(n-1)}+\cdots +A_{1}f'+A_{0}f=0$ contains at least $n-p$ entire functions of infinite order. Here, the transcendental coefficient $A_p$ dominates the growth of the polynomial coefficients

    更新日期:2020-07-30
  • Bounding Selmer Groups for the Rankin–Selberg Convolution of Coleman Families
    Can. J. Math. (IF 0.881) Pub Date : 2020-07-17
    Andrew Graham; Daniel R. Gulotta; Yujie Xu

    Let f and g be two cuspidal modular forms and let ${\mathcal {F}}$ be a Coleman family passing through f, defined over an open affinoid subdomain V of weight space $\mathcal {W}$ . Using ideas of Pottharst, under certain hypotheses on f and g, we construct a coherent sheaf over $V \times \mathcal {W}$ that interpolates the Bloch–Kato Selmer group of the Rankin–Selberg convolution of two modular forms

    更新日期:2020-07-27
  • Mallows permutations as stable matchings
    Can. J. Math. (IF 0.881) Pub Date : 2020-07-27
    Omer Angel; Alexander E. Holroyd; Tom Hutchcroft; Avi Levy

    We show that the Mallows measure on permutations of $1,\dots ,n$ arises as the law of the unique Gale–Shapley stable matching of the random bipartite graph with vertex set conditioned to be perfect, where preferences arise from the natural total ordering of the vertices of each gender but are restricted to the (random) edges of the graph. We extend this correspondence to infinite intervals, for which

    更新日期:2020-07-27
  • On the compositum of orthogonal cyclic fields of the same odd prime degree
    Can. J. Math. (IF 0.881) Pub Date : 2020-07-14
    Cornelius Greither; Radan Kučera

    The aim of this paper is to study circular units in the compositum K of t cyclic extensions of ${\mathbb {Q}}$ ( $t\ge 2$ ) of the same odd prime degree $\ell $ . If these fields are pairwise arithmetically orthogonal and the number s of primes ramifying in $K/{\mathbb {Q}}$ is larger than $t,$ then a nontrivial root $\varepsilon $ of the top generator $\eta $ of the group of circular units of K is

    更新日期:2020-07-14
  • Large values of Dirichlet L-functions at zeros of a class of L-functions
    Can. J. Math. (IF 0.881) Pub Date : 2020-07-01
    Junxian Li

    In this paper, we are interested in obtaining large values of Dirichlet L-functions evaluated at zeros of a class of L-functions, that is, $$ \begin{align*}\max_{\substack{F(\rho)=0\\ T\leq \Im \rho \leq 2T}}L(\rho,\chi), \end{align*} $$ where $\chi $ is a primitive Dirichlet character and F belongs to a class of L-functions. The class we consider includes L-functions associated with automorphic representations

    更新日期:2020-07-01
  • Variation of constants formula and exponential dichotomy for nonautonomous non-densely defined Cauchy problems
    Can. J. Math. (IF 0.881) Pub Date : 2020-06-29
    Pierre Magal; Ousmane Seydi

    In this paper, we extend to the non-Hille–Yosida case a variation of constants formula for a nonautonomous and nonhomogeneous Cauchy problems first obtained by Gühring and Räbiger. By using this variation of constants formula, we derive a necessary and sufficient condition for the existence of an exponential dichotomy for the evolution family generated by the associated nonautonomous homogeneous problem

    更新日期:2020-06-29
  • Ring-theoretic (In)finiteness in reduced products of Banach algebras
    Can. J. Math. (IF 0.881) Pub Date : 2020-06-29
    Matthew Daws; Bence Horváth

    We study ring-theoretic (in)finiteness properties—such as Dedekind-finiteness and proper infiniteness—of ultraproducts (and more generally, reduced products) of Banach algebras. While we characterise when an ultraproduct has these ring-theoretic properties in terms of its underlying sequence of algebras, we find that, contrary to the $C^*$ -algebraic setting, it is not true in general that an ultraproduct

    更新日期:2020-06-29
  • Bounding the Iwasawa invariants of Selmer groups
    Can. J. Math. (IF 0.881) Pub Date : 2020-06-29
    Sören Kleine

    We study the growth of p-primary Selmer groups of abelian varieties with good ordinary reduction at p in ${{Z}}_p$ -extensions of a fixed number field K. Proving that in many situations the knowledge of the Selmer groups in a sufficiently large number of finite layers of a ${{Z}}_p$ -extension over K suffices for bounding the over-all growth, we relate the Iwasawa invariants of Selmer groups in different

    更新日期:2020-06-29
  • Threefolds fibred by mirror sextic double planes
    Can. J. Math. (IF 0.881) Pub Date : 2020-06-24
    Remkes Kooistra; Alan Thompson

    We present a systematic study of threefolds fibred by K3 surfaces that are mirror to sextic double planes. There are many parallels between this theory and the theory of elliptic surfaces. We show that the geometry of such threefolds is controlled by a pair of invariants, called the generalized functional and generalized homological invariants, and we derive an explicit birational model for them, which

    更新日期:2020-06-24
  • Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space
    Can. J. Math. (IF 0.881) Pub Date : 2020-06-16
    Hong-Quan Li; Peter Sjögren

    Let $v \ne 0$ be a vector in ${\mathbb {R}}^n$ . Consider the Laplacian on ${\mathbb {R}}^n$ with drift $\Delta _{v} = \Delta + 2v\cdot \nabla $ and the measure $d\mu (x) = e^{2 \langle v, x \rangle } dx$ , with respect to which $\Delta _{v}$ is self-adjoint. This measure has exponential growth with respect to the Euclidean distance. We study weak type $(1, 1)$ and other sharp endpoint estimates for

    更新日期:2020-06-16
  • Erratum: The Jiang–Su Absorption for Inclusions of Unital C*-algebras
    Can. J. Math. (IF 0.881) Pub Date : 2020-06-11
    Hiroyuki Osaka; Tamotsu Teruya

    We correct an error in the statement in a proposition and a theorem in Jiang–Su absorption for inclusions of unital C*-algebras. Canad. J. Math. 70(2018), 400–425. This error was found by Dr. M. Ali Asadi-Vasfi and communicated to the authors by N. Christopher Phillips of the University of Oregon, who also suggested the outline for the following correct proofs.

    更新日期:2020-06-11
  • Khovanov–Rozansky homology for infinite multicolored braids
    Can. J. Math. (IF 0.881) Pub Date : 2020-06-08
    Michael Willis

    We define a limiting ${\mathfrak {sl}_N}$ Khovanov–Rozansky homology for semi-infinite positive multicolored braids. For a large class of such braids, we show that this limiting homology categorifies a highest-weight projector in the tensor product of fundamental representations determined by the coloring of the braid. This effectively completes the extension of Cautis’ similar result for infinite

    更新日期:2020-06-08
  • Sigma-Prikry forcing I: The Axioms
    Can. J. Math. (IF 0.881) Pub Date : 2020-05-26
    Alejandro Poveda; Assaf Rinot; Dima Sinapova

    We introduce a class of notions of forcing which we call $\Sigma $ -Prikry, and show that many of the known Prikry-type notions of forcing that centers around singular cardinals of countable cofinality are $\Sigma $ -Prikry. We show that given a $\Sigma $ -Prikry poset $\mathbb P$ and a name for a non-reflecting stationary set T, there exists a corresponding $\Sigma $ -Prikry poset that projects to

    更新日期:2020-05-26
  • A certain structure of Artin groups and the isomorphism conjecture
    Can. J. Math. (IF 0.881) Pub Date : 2020-05-21
    S.K. Roushon

    We observe an inductive structure in a large class of Artin groups of finite real, complex and affine types and exploit this information to deduce the Farrell–Jones isomorphism conjecture for these groups.

    更新日期:2020-05-21
  • Stability of rotation relations in $C^*$ -algebras
    Can. J. Math. (IF 0.881) Pub Date : 2020-05-21
    Jiajie Hua; Qingyun Wang

    Let $\Theta =(\theta _{j,k})_{3\times 3}$ be a nondegenerate real skew-symmetric $3\times 3$ matrix, where $\theta _{j,k}\in [0,1).$ For any $\varepsilon>0$ , we prove that there exists $\delta>0$ satisfying the following: if $v_1,v_2,v_3$ are three unitaries in any unital simple separable $C^*$ -algebra A with tracial rank at most one, such that $\begin{align*}\|v_kv_j-e^{2\pi i \theta_{j,k}}v_jv_k\|<\delta

    更新日期:2020-05-21
  • On the structure of Kac–Moody algebras
    Can. J. Math. (IF 0.881) Pub Date : 2020-05-20
    Timothée Marquis

    Let A be a symmetrisable generalised Cartan matrix, and let $\mathfrak {g}(A)$ be the corresponding Kac–Moody algebra. In this paper, we address the following fundamental question on the structure of $\mathfrak {g}(A)$ : given two homogeneous elements $x,y\in \mathfrak {g}(A)$ , when is their bracket $[x,y]$ a nonzero element? As an application of our results, we give a description of the solvable

    更新日期:2020-05-20
  • Categorification via blocks of modular representations for $\mathfrak {sl}_n$
    Can. J. Math. (IF 0.881) Pub Date : 2020-05-19
    Vinoth Nandakumar; Gufang Zhao

    Bernstein, Frenkel, and Khovanov have constructed a categorification of tensor products of the standard representation of $\mathfrak {sl}_2$ , where they use singular blocks of category $\mathcal {O}$ for $\mathfrak {sl}_n$ and translation functors. Here we construct a positive characteristic analogue using blocks of representations of $\mathfrak {s}\mathfrak {l}_n$ over a field $\mathbf {k}$ of characteristic

    更新日期:2020-05-19
  • Données endoscopiques d’un groupe réductif connexe : applications d’une construction de Langlands
    Can. J. Math. (IF 0.881) Pub Date : 2020-05-15
    Bertrand Lemaire; Jean-Loup Waldspurger

    Soient $F$ un corps global, et $G$ un groupe réductif connexe défini sur $F$ . On prouve que si deux données endoscopiques de $G$ sont équivalentes en presque toute place de $F$ , alors elles sont équivalentes. Le résultat est encore vrai pour l’endoscopie (ordinaire) avec caractère. On donne aussi, pour $F$ global ou local et $G$ quasi-simple simplement connexe, une description des données endoscopiques

    更新日期:2020-05-15
  • Free abelian group actions on normal projective varieties: submaximal dynamical rank case
    Can. J. Math. (IF 0.881) Pub Date : 2020-05-14
    Fei Hu; Sichen Li

    Let X be a normal projective variety of dimension n and G an abelian group of automorphisms such that all elements of $G\setminus \{\operatorname {id}\}$ are of positive entropy. Dinh and Sibony showed that G is actually free abelian of rank $\le n - 1$ . The maximal rank case has been well understood by De-Qi Zhang. We aim to characterize the pair $(X, G)$ such that $\operatorname {rank} G = n - 2$

    更新日期:2020-05-14
  • Bundles on $\textbf{P}^n$ with vanishing lower cohomologies
    Can. J. Math. (IF 0.881) Pub Date : 2020-04-24
    Mengyuan Zhang

    We study bundles on projective spaces that have vanishing lower cohomologies using their short minimal free resolutions. We partition the moduli $\mathcal{M}$ according to the Hilbert function H and classify all possible Hilbert functions H of such bundles. For each H, we describe a stratification of $\mathcal{M}_H$ by quotients of rational varieties. We show that the closed strata form a graded lattice

    更新日期:2020-04-24
  • Isospectrality for Orbifold Lens Spaces
    Can. J. Math. (IF 0.881) Pub Date : 2019-08-27
    Naveed S. Bari; Eugenie Hunsicker

    We answer Mark Kac’s famous question, “Can one hear the shape of a drum?” in the positive for orbifolds that are 3-dimensional and 4-dimensional lens spaces; we thus complete the answer to this question for orbifold lens spaces in all dimensions. We also show that the coefficients of the asymptotic expansion of the trace of the heat kernel are not sufficient to determine the above results.

    更新日期:2020-04-20
  • Newforms of Half-integral Weight: The Minus Space Counterpart
    Can. J. Math. (IF 0.881) Pub Date : 2019-10-31
    Ehud Moshe Baruch; Soma Purkait

    We study genuine local Hecke algebras of the Iwahori type of the double cover of $\operatorname{SL}_{2}(\mathbb{Q}_{p})$ and translate the generators and relations to classical operators on the space $S_{k+1/2}(\unicode[STIX]{x1D6E4}_{0}(4M))$ , $M$ odd and square-free. In [9] Manickam, Ramakrishnan, and Vasudevan defined the new space of $S_{k+1/2}(\unicode[STIX]{x1D6E4}_{0}(4M))$ that maps Hecke

    更新日期:2020-04-20
  • Marginals with Finite Repulsive Cost
    Can. J. Math. (IF 0.881) Pub Date : 2019-05-07
    Ugo Bindini

    We consider a multimarginal transport problem with repulsive cost, where the marginals are all equal to a fixed probability $\unicode[STIX]{x1D70C}\in {\mathcal{P}}(\mathbb{R}^{d})$ . We prove that, if the concentration of $\unicode[STIX]{x1D70C}$ is less than $1/N$ , then the problem has a solution of finite cost. The result is sharp, in the sense that there exists $\unicode[STIX]{x1D70C}$ with concentration

    更新日期:2020-04-20
  • Automatic Sequences and Generalised Polynomials
    Can. J. Math. (IF 0.881) Pub Date : 2019-06-13
    Jakub Byszewski; Jakub Konieczny

    We conjecture that bounded generalised polynomial functions cannot be generated by finite automata, except for the trivial case when they are ultimately periodic.

    更新日期:2020-04-20
  • One-Level Density of Low-lying Zeros of Quadratic and Quartic Hecke $L$ -functions
    Can. J. Math. (IF 0.881) Pub Date : 2019-08-30
    Peng Gao; Liangyi Zhao

    In this paper we prove some one-level density results for the low-lying zeros of families of quadratic and quartic Hecke $L$ -functions of the Gaussian field. As corollaries, we deduce that at least 94.27% and 5%, respectively, of the members of the quadratic family and the quartic family do not vanish at the central point.

    更新日期:2020-04-20
  • Orlicz Addition for Measures and an Optimization Problem for the $f$ -divergence
    Can. J. Math. (IF 0.881) Pub Date : 2019-07-16
    Shaoxiong Hou; Deping Ye

    This paper provides a functional analogue of the recently initiated dual Orlicz–Brunn–Minkowski theory for star bodies. We first propose the Orlicz addition of measures, and establish the dual functional Orlicz–Brunn–Minkowski inequality. Based on a family of linear Orlicz additions of two measures, we provide an interpretation for the famous $f$ -divergence. Jensen’s inequality for integrals is also

    更新日期:2020-04-20
  • Primes Dividing Invariants of CM Picard Curves
    Can. J. Math. (IF 0.881) Pub Date : 2019-05-07
    Pınar Kılıçer; Elisa Lorenzo García; Marco Streng

    We give a bound on the primes dividing the denominators of invariants of Picard curves of genus 3 with complex multiplication. Unlike earlier bounds in genus 2 and 3, our bound is based, not on bad reduction of curves, but on a very explicit type of good reduction. This approach simultaneously yields a simplification of the proof and much sharper bounds. In fact, unlike all previous bounds for genus

    更新日期:2020-04-20
  • On the Chow Ring of Cynk–Hulek Calabi–Yau Varieties and Schreieder Varieties
    Can. J. Math. (IF 0.881) Pub Date : 2019-09-03
    Robert Laterveer; Charles Vial

    This note is about certain locally complete families of Calabi–Yau varieties constructed by Cynk and Hulek, and certain varieties constructed by Schreieder. We prove that the cycle class map on the Chow ring of powers of these varieties admits a section, and that these varieties admit a multiplicative self-dual Chow–Künneth decomposition. As a consequence of both results, we prove that the subring

    更新日期:2020-04-20
  • Almost Simplicial Polytopes: The Lower and Upper Bound Theorems
    Can. J. Math. (IF 0.881) Pub Date : 2019-05-21
    Eran Nevo; Guillermo Pineda-Villavicencio; Julien Ugon; David Yost

    We study $n$ -vertex $d$ -dimensional polytopes with at most one nonsimplex facet with, say, $d+s$ vertices, called almost simplicial polytopes. We provide tight lower and upper bound theorems for these polytopes as functions of $d,n$ , and $s$ , thus generalizing the classical Lower Bound Theorem by Barnette and the Upper Bound Theorem by McMullen, which treat the case where $s=0$ . We characterize

    更新日期:2020-04-20
  • CJM volume 72 Issue 2 Cover and Front matter
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-31

    None

    更新日期:2020-04-20
  • CJM volume 72 Issue 2 Cover and Back matter
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-31

    None

    更新日期:2020-04-20
  • Steiner symmetry in the minimization of the first eigenvalue of a fractional eigenvalue problem with indefinite weight
    Can. J. Math. (IF 0.881) Pub Date : 2020-04-14
    Claudia Anedda; Fabrizio Cuccu; Silvia Frassu

    Let $\Omega \subset \mathbb {R}^N$ , $N\geq 2$ , be an open bounded connected set. We consider the fractional weighted eigenvalue problem $(-\Delta )^s u =\lambda \rho u$ in $\Omega $ with homogeneous Dirichlet boundary condition, where $(-\Delta )^s$ , $s\in (0,1)$ , is the fractional Laplacian operator, $\lambda \in \mathbb {R}$ and $ \rho \in L^\infty (\Omega )$ . We study weak* continuity, convexity

    更新日期:2020-04-14
  • The Trace Form Over Cyclic Number Fields
    Can. J. Math. (IF 0.881) Pub Date : 2020-04-14
    Wilmar Bolaños; Guillermo Mantilla-Soler

    In the mid 80’s Conner and Perlis showed that for cyclic number fields of prime degree p the isometry class of integral trace is completely determined by the discriminant. Here we generalize their result to tame cyclic number fields of arbitrary degree. Furthermore, for such fields, we give an explicit description of a Gram matrix of the integral trace in terms of the discriminant of the field.

    更新日期:2020-04-14
  • Dimension groups for self-similar maps and matrix representations of the cores of the associated C*-algebras
    Can. J. Math. (IF 0.881) Pub Date : 2020-04-12
    Tsuyoshi Kajiwara; Yasuo Watatani

    We introduce a dimension group for a self-similar map as the $\mathrm {K}_0$ -group of the core of the C*-algebra associated with the self-similar map together with the canonical endomorphism. The key step for the computation is an explicit description of the core as the inductive limit using their matrix representations over the coefficient algebra, which can be described explicitly by the singularity

    更新日期:2020-04-12
  • Factorization problems in complex reflection groups
    Can. J. Math. (IF 0.881) Pub Date : 2020-04-02
    Joel Brewster Lewis; Alejandro H. Morales

    We enumerate factorizations of a Coxeter element in a well-generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our approach is fully combinatorial. It gives results analogous to those of Jackson in the symmetric group and can be refined to encode a notion of cycle type. As one application

    更新日期:2020-04-02
  • Albert algebras over rings and related torsors
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-30
    Seidon Alsaody

    We study exceptional Jordan algebras and related exceptional group schemes over commutative rings from a geometric point of view, using appropriate torsors to parametrize and explain classical and new constructions, and proving that over rings, they give rise to nonisomorphic structures. We begin by showing that isotopes of Albert algebras are obtained as twists by a certain $\mathrm F_4$ -torsor with

    更新日期:2020-03-30
  • Classifying spaces for étale algebras with generators
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-30
    Abhishek Kumar Shukla; Ben Williams

    We construct a scheme $B(r; {\mathbb {A}}^n)$ such that a map $X \to B(r; {\mathbb {A}}^n)$ corresponds to a degree-n étale algebra on X equipped with r generating global sections. We then show that when $n=2$ , i.e., in the quadratic étale case, the singular cohomology of $B(r; {\mathbb {A}}^n)({\mathbb {R}})$ can be used to reconstruct a famous example of S. Chase and to extend its application to

    更新日期:2020-03-30
  • Reflection of Willmore Surfaces with Free Boundaries
    Can. J. Math. (IF 0.881) Pub Date : 2020-03-11
    Ernst Kuwert; Tobias Lamm

    We study immersed surfaces in $${\mathbb R}^3$$ that are critical points of the Willmore functional under boundary constraints. The two cases considered are when the surface meets a plane orthogonally along the boundary and when the boundary is contained in a line. In both cases we derive weak forms of the resulting free boundary conditions and prove regularity by reflection.

    更新日期:2020-03-11
  • On Restriction Estimates for the Zero Radius Sphere over Finite Fields
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-27
    Alex Iosevich; Doowon Koh; Sujin Lee; Thang Pham; Chun-Yen Shen

    In this paper, we completely solve the $L^{2}\to L^{r}$ extension conjecture for the zero radius sphere over finite fields. We also obtain the sharp $L^{p}\to L^{4}$ extension estimate for non-zero radii spheres over finite fields, which improves the previous result of the first and second authors significantly.

    更新日期:2020-02-27
  • Coisotropic Submanifolds in b-symplectic Geometry
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-24
    Stephane Geudens; Marco Zambon

    We study coisotropic submanifolds of b-symplectic manifolds. We prove that b-coisotropic submanifolds (those transverse to the degeneracy locus) determine the b-symplectic structure in a neighborhood, and provide a normal form theorem. This extends Gotay’s theorem in symplectic geometry. Further, we introduce strong b-coisotropic submanifolds and show that their coisotropic quotient, which locally

    更新日期:2020-02-24
  • Coxeter Diagrams and the Köthe’s Problem
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-24
    Ziba Fazelpour; Alireza Nasr-Isfahani

    A ring $\unicode[STIX]{x1D6EC}$ is called right Köthe if every right $\unicode[STIX]{x1D6EC}$ -module is a direct sum of cyclic modules. In this paper, we give a characterization of basic hereditary right Köthe rings in terms of their Coxeter valued quivers. We also give a characterization of basic right Köthe rings with radical square zero. Therefore, we give a solution to Köthe’s problem in these

    更新日期:2020-02-24
  • Extension Property and Universal Sets
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-24
    Łukasz Kosiński; Włodzimierz Zwonek

    Motivated by works on extension sets in standard domains, we introduce a notion of the Carathéodory set that seems better suited for the methods used in proofs of results on characterization of extension sets. A special stress is put on a class of two-dimensional submanifolds in the tridisc that not only turns out to be Carathéodory but also provides examples of two-dimensional domains for which the

    更新日期:2020-02-24
  • An Application of Spherical Geometry to Hyperkähler Slices
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-24
    Peter Crooks; Maarten van Pruijssen

    This work is concerned with Bielawski’s hyperkähler slices in the cotangent bundles of homogeneous affine varieties. One can associate such a slice with the data of a complex semisimple Lie group  $G$ , a reductive subgroup $H\subseteq G$ , and a Slodowy slice $S\subseteq \mathfrak{g}:=\text{Lie}(G)$ , defining it to be the hyperkähler quotient of $T^{\ast }(G/H)\times (G\times S)$ by a maximal compact

    更新日期:2020-02-24
  • Universal Alternating Semiregular Polytopes
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-12
    B. Monson; Egon Schulte

    In the classical setting, a convex polytope is said to be semiregular if its facets are regular and its symmetry group is transitive on vertices. This paper continues our study of alternating semiregular abstract polytopes, which have abstract regular facets, still with combinatorial automorphism group transitive on vertices and with two kinds of regular facets occurring in an alternating fashion.

    更新日期:2020-02-12
  • Boundedness of Differential Transforms for Heat Semigroups Generated by Schrödinger Operators
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-12
    Zhang Chao; José L. Torrea

    In this paper we analyze the convergence of the following type of series $$\begin{eqnarray}T_{N}^{{\mathcal{L}}}f(x)=\mathop{\sum }_{j=N_{1}}^{N_{2}}v_{j}\big(e^{-a_{j+1}{\mathcal{L}}}f(x)-e^{-a_{j}{\mathcal{L}}}f(x)\big),\quad x\in \mathbb{R}^{n},\end{eqnarray}$$ where ${\{e^{-t{\mathcal{L}}}\}}_{t>0}$ is the heat semigroup of the operator ${\mathcal{L}}=-\unicode[STIX]{x1D6E5}+V$ with $\unicode[STIX]{x1D6E5}$

    更新日期:2020-02-12
  • Generalized Beilinson Elements and Generalized Soulé Characters
    Can. J. Math. (IF 0.881) Pub Date : 2020-02-06
    Kenji Sakugawa

    The generalized Soulé character was introduced by H. Nakamura and Z. Wojtkowiak and is a generalization of Soulé’s cyclotomic character. In this paper, we prove that certain linear sums of generalized Soulé characters essentially coincide with the image of generalized Beilinson elements in K-groups under Soulé’s higher regulator maps. This result generalizes Huber–Wildeshaus’ theorem, which is a cyclotomic

    更新日期:2020-02-06
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