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Ideals with componentwise linear powers Can. Math. Bull. (IF 0.6) Pub Date : 2024-03-12 Takayuki Hibi, Somayeh Moradi
Let $S=K[x_1,\ldots ,x_n]$ be the polynomial ring over a field K, and let A be a finitely generated standard graded S-algebra. We show that if the defining ideal of A has a quadratic initial ideal, then all the graded components of A are componentwise linear. Applying this result to the Rees ring $\mathcal {R}(I)$ of a graded ideal I gives a criterion on I to have componentwise linear powers. Moreover
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A class of Hessian quotient equations in de Sitter space Can. Math. Bull. (IF 0.6) Pub Date : 2024-03-06 Jinyu Gao, Guanghan Li, Kuicheng Ma
In this paper, we consider the closed spacelike solution to a class of Hessian quotient equations in de Sitter space. Under mild assumptions, we obtain an existence result using standard degree theory based on a priori estimates.
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Linear independence of series related to the Thue–Morse sequence along powers Can. Math. Bull. (IF 0.6) Pub Date : 2024-03-06 Michael Coons, Yohei Tachiya
The Thue–Morse sequence $\{t(n)\}_{n\geqslant 0}$ is the indicator function of the parity of the number of ones in the binary expansion of nonnegative integers n, where $t(n)=1$ (resp. $=0$) if the binary expansion of n has an odd (resp. even) number of ones. In this paper, we generalize a recent result of E. Miyanohara by showing that, for a fixed Pisot or Salem number $\beta>\sqrt {\varphi }=1.272019\ldots
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Moments of the central L-values of the Asai lifts Can. Math. Bull. (IF 0.6) Pub Date : 2024-03-04 Wenzhi Luo
We study some analytic properties of the Asai lifts associated with cuspidal Hilbert modular forms, and prove sharp bounds for the second moment of their central L-values.
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Hausdorff operators on some classical spaces of analytic functions Can. Math. Bull. (IF 0.6) Pub Date : 2024-02-29 Huayou Xie, Qingze Lin
In this note, we start on the study of the sufficient conditions for the boundedness of Hausdorff operators $$ \begin{align*}(\mathcal{H}_{K,\mu}f)(z):=\int_{\mathbb{D}}K(w)f(\sigma_w(z))d\mu(w)\end{align*} $$on three important function spaces (i.e., derivative Hardy spaces, weighted Dirichlet spaces, and Bloch type spaces), which is a continuation of the previous works of Mirotin et al. Here, $\mu
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The degree one Laguerre–Pólya class and the shuffle-word-embedding conjecture Can. Math. Bull. (IF 0.6) Pub Date : 2024-02-28 James E. Pascoe, Hugo J. Woerdeman
We discuss the class of functions, which are well approximated on compacta by the geometric mean of the eigenvalues of a unital (completely) positive map into a matrix algebra or more generally a type $II_1$ factor, using the notion of a Fuglede–Kadison determinant. In two variables, the two classes are the same, but in three or more noncommuting variables, there are generally functions arising from
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Theoretical study of a -Hilfer fractional differential system in Banach spaces Can. Math. Bull. (IF 0.6) Pub Date : 2024-02-27 Oualid Zentar, Mohamed Ziane, Mohammed Al Horani
In this work, we study the existence of solutions of nonlinear fractional coupled system of $\varphi $-Hilfer type in the frame of Banach spaces. We improve a property of a measure of noncompactness in a suitably selected Banach space. Darbo’s fixed point theorem is applied to obtain a new existence result. Finally, the validity of our result is illustrated through an example.
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Integral equivariant cohomology of affine Grassmannians Can. Math. Bull. (IF 0.6) Pub Date : 2024-02-08 David Anderson
We give explicit presentations of the integral equivariant cohomology of the affine Grassmannians and flag varieties in type A, arising from their natural embeddings in the corresponding infinite (Sato) Grassmannian and flag variety. These presentations are compared with results obtained by Lam and Shimozono, for rational equivariant cohomology of the affine Grassmannian, and by Larson, for the integral
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Some examples of noncommutative projective Calabi–Yau schemes Can. Math. Bull. (IF 0.6) Pub Date : 2024-02-08 Yuki Mizuno
In this article, we construct some examples of noncommutative projective Calabi–Yau schemes by using noncommutative Segre products and quantum weighted hypersurfaces. We also compare our constructions with commutative Calabi–Yau varieties and examples constructed in Kanazawa (2015, Journal of Pure and Applied Algebra 219, 2771–2780). In particular, we show that some of our constructions are essentially
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Nowhere constant families of maps and resolvability Can. Math. Bull. (IF 0.6) Pub Date : 2024-02-06 István Juhász, Jan van Mill
If X is a topological space and Y is any set, then we call a family $\mathcal {F}$ of maps from X to Y nowhere constant if for every non-empty open set U in X there is $f \in \mathcal {F}$ with $|f[U]|> 1$, i.e., f is not constant on U. We prove the following result that improves several earlier results in the literature. If X is a topological space for which $C(X)$, the family of all continuous maps
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Relations for quadratic Hodge integrals via stable maps Can. Math. Bull. (IF 0.6) Pub Date : 2024-01-17 Georgios Politopoulos
Following Faber–Pandharipande, we use the virtual localization formula for the moduli space of stable maps to $\mathbb {P}^{1}$ to compute relations between Hodge integrals. We prove that certain generating series of these integrals are polynomials.
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Borel reducibility of equivalence relations on Can. Math. Bull. (IF 0.6) Pub Date : 2024-01-17 Riccardo Camerlo
The structure of Borel reducibility for equivalence relations on $\omega _1$ is determined.
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A characterization of random analytic functions satisfying Blaschke-type conditions Can. Math. Bull. (IF 0.6) Pub Date : 2024-01-17 Yongjiang Duan, Xiang Fang, Na Zhan
Let $f(z)=\sum _{n=0}^{\infty }a_n z^n \in H(\mathbb {D})$ be an analytic function over the unit disk in the complex plane, and let $\mathcal {R} f$ be its randomization: $$ \begin{align*}(\mathcal{R} f)(z)= \sum_{n=0}^{\infty} a_n X_n z^n \in H(\mathbb{D}),\end{align*} $$ where $(X_n)_{n\ge 0}$ is a standard sequence of independent Bernoulli, Steinhaus, or Gaussian random variables. In this note,
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Integral mean estimates for univalent and locally univalent harmonic mappings Can. Math. Bull. (IF 0.6) Pub Date : 2024-01-15 Suman Das, Anbareeswaran Sairam Kaliraj
We verify a long-standing conjecture on the membership of univalent harmonic mappings in the Hardy space, whenever the functions have a “nice” analytic part. We also produce a coefficient estimate for these functions, which is in a sense best possible. The problem is then explored in a new direction, without the additional hypothesis. Interestingly, our ideas extend to certain classes of locally univalent
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A rigid analytic proof that the Abel–Jacobi map extends to compact-type models Can. Math. Bull. (IF 0.6) Pub Date : 2024-01-09 Taylor Dupuy, Joseph Rabinoff
Let K be a non-Archimedean valued field with valuation ring R. Let $C_\eta $ be a K-curve with compact-type reduction, so its Jacobian $J_\eta $ extends to an abelian R-scheme J. We prove that an Abel–Jacobi map $\iota \colon C_\eta \to J_\eta $ extends to a morphism $C\to J$, where C is a compact-type R-model of J, and we show this is a closed immersion when the special fiber of C has no rational
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How to determine a curve singularity Can. Math. Bull. (IF 0.6) Pub Date : 2024-01-09 J. Elias
We characterize the finite codimension sub-${\mathbf {k}}$-algebras of ${\mathbf {k}}[\![t]\!]$ as the solutions of a computable finite family of higher differential operators. For this end, we establish a duality between such a sub-algebras and the finite codimension ${\mathbf {k}}$-vector spaces of ${\mathbf {k}}[u]$, this ring acts on ${\mathbf {k}}[\![t]\!]$ by differentiation.
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On the Extension of Bounded Holomorphic Maps from Gleason Parts of the Maximal Ideal Space of Can. Math. Bull. (IF 0.6) Pub Date : 2024-01-08 Alexander Brudnyi
Let $H^\infty $ be the algebra of bounded holomorphic functions on the open unit disk, and let $\mathfrak M$ be its maximal ideal space. Let $\mathfrak M_a$ be the union of nontrivial Gleason parts (analytic disks) of $\mathfrak M$. In this paper, we study the problem of extensions of bounded Banach-valued holomorphic functions and holomorphic maps with values in Oka manifolds from Gleason parts of
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On the root of unity ambiguity in a formula for the Brumer–Stark units Can. Math. Bull. (IF 0.6) Pub Date : 2023-12-27 Matthew H. Honnor
We prove a conjectural formula for the Brumer–Stark units. Dasgupta and Kakde have shown the formula is correct up to a bounded root of unity. In this paper, we resolve the ambiguity in their result. We also remove an assumption from Dasgupta–Kakde’s result on the formula.
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Tree structure of spectra of spectral Moran measures with consecutive digits Can. Math. Bull. (IF 0.6) Pub Date : 2023-12-22 Cong Wang, Feng-Li Yin
Let $\{b_n\}_{n=1}^{\infty }$ be a sequence of integers larger than 1. We will study the harmonic analysis of the equal-weighted Moran measures $\mu _{\{b_n\},\{{\mathcal D}_n\}}$ with ${\mathcal D}_n=\{0,1,2,\ldots ,q_n-1\}$, where $q_n$ divides $b_n$ for all $n\geq 1.$ In this paper, we first characterize all the maximal orthogonal sets of $L^2(\mu _{\{b_n\},\{{\mathcal D}_n\}})$ via a tree mapping
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A rigidity result for the product of spheres Can. Math. Bull. (IF 0.6) Pub Date : 2023-12-13 Pak Tung Ho
In this paper, we prove a rigidity result for the product metric on the product of spheres $S^1\times S^{n-1}$.
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Irreducible modules of modular Lie superalgebras and super version of the first Kac–Weisfeiler conjecture Can. Math. Bull. (IF 0.6) Pub Date : 2023-12-11 Bin Shu
Suppose $\mathfrak {g}=\mathfrak {g}_{\bar 0}+\mathfrak {g}_{\bar 1}$ is a finite-dimensional restricted Lie superalgebra over an algebraically closed field $\mathbf {k}$ of characteristic $p>2$. In this article, we propose a conjecture for maximal dimensions of irreducible modules over the universal enveloping algebra $U(\mathfrak {g})$ of $\mathfrak {g}$, as a super generalization of the celebrated
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On the Pontrjagin classes of spray manifolds Can. Math. Bull. (IF 0.6) Pub Date : 2023-12-11 Zhongmin Shen, Runzhong Zhao
The characterization of projectively flat Finsler metrics on an open subset in $R^n$ is the Hilbert’s fourth problem in the regular case. Locally projectively flat Finsler manifolds form an important class of Finsler manifolds. Every Finsler metric induces a spray on the manifold via geodesics. Therefore, it is a natural problem to investigate the geometric and topological properties of manifolds equipped
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Moore’s conjecture for connected sums Can. Math. Bull. (IF 0.6) Pub Date : 2023-12-04 Stephen Theriault
We show that under mild conditions, the connected sum $M\# N$ of simply connected, closed, orientable n-dimensional Poincaré Duality complexes M and N is hyperbolic and has no homotopy exponent at all but finitely many primes, verifying a weak version of Moore’s conjecture. This is derived from an elementary framework involving $CW$-complexes satisfying certain conditions.
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Truncations of generalized shift-invariant systems Can. Math. Bull. (IF 0.6) Pub Date : 2023-11-29 Ole Christensen, Pablo Garcia Alvarez, Rae Young Kim
We provide conditions under which a generalized shift-invariant (GSI) system can be approximated by a GSI system for which the generators have compact support in the Fourier domain. The approximation quality will be measured in terms of the Bessel bound (upper frame bound) for the difference between the two GSI systems. In particular, this leads to easily verifiable conditions for a perturbation of
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Nonlinear Beltrami equation: lower estimates of Schwarz lemma’s type Can. Math. Bull. (IF 0.6) Pub Date : 2023-11-29 Igor Petkov, Ruslan Salimov, Mariia Stefanchuk
We study a nonlinear Beltrami equation $f_\theta =\sigma \,|f_r|^m f_r$ in polar coordinates $(r,\theta ),$ which becomes the classical Cauchy–Riemann system under $m=0$ and $\sigma =ir.$ Using the isoperimetric technique, various lower estimates for $|f(z)|/|z|, f(0)=0,$ as $z\to 0,$ are derived under appropriate integral conditions on complex/directional dilatations. The sharpness of the above bounds
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Topological stability for homeomorphisms with global attractor Can. Math. Bull. (IF 0.6) Pub Date : 2023-11-29 Carlos Arnoldo Morales, Nguyen Thanh Nguyen
We prove that every topologically stable homeomorphism with global attractor of $\mathbb {R}^n$ is topologically stable on its global attractor. The converse is not true. On the other hand, if a homeomorphism with global attractor of a locally compact metric space is expansive and has the shadowing property, then it is topologically stable. This extends the Walters stability theorem (Walters, On the
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Remarks on Naimark dilation theorem Can. Math. Bull. (IF 0.6) Pub Date : 2023-11-28 Sergiusz Kużel
Although Naimark dilation theorem was originally stated in 1940, it still finds many important applications in various areas. The objective of this paper is to introduce a method for explicitly constructing the vectors of complementary frames in the Naimark dilation theorem, specifically in cases where the initial Parseval frame contains a Riesz basis as a subset. These findings serve as a foundation
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Selection principles and proofs from the Book Can. Math. Bull. (IF 0.6) Pub Date : 2023-11-23 Boaz Tsaban
I provide simplified proofs for each of the following fundamental theorems regarding selection principles: (1) The Quasinormal Convergence Theorem, due to the author and Zdomskyy, asserting that a certain, important property of the space of continuous functions on a space is actually preserved by Borel images of that space. (2) The Scheepers Diagram Last Theorem, due to Peng, completing all provable
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Linear fractional self-maps of the unit ball Can. Math. Bull. (IF 0.6) Pub Date : 2023-11-15 Michael R. Pilla
Determining the range of complex maps plays a fundamental role in the study of several complex variables and operator theory. In particular, one is often interested in determining when a given holomorphic function is a self-map of the unit ball. In this paper, we discuss a class of maps in $\mathbb {C}^N$ that generalize linear fractional maps. We then proceed to determine precisely when such a map
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Eisenstein congruences among Euler systems Can. Math. Bull. (IF 0.6) Pub Date : 2023-11-06 Ó. Rivero, V. Rotger
We investigate Eisenstein congruences between the so-called Euler systems of Garrett–Rankin–Selberg type. This includes the cohomology classes of Beilinson–Kato, Beilinson–Flach, and diagonal cycles. The proofs crucially rely on different known versions of the Bloch–Kato conjecture, and are based on the study of the Perrin-Riou formalism and the comparison between the different p-adic L-functions.
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Norms on complex matrices induced by random vectors II: extension of weakly unitarily invariant norms Can. Math. Bull. (IF 0.6) Pub Date : 2023-11-06 Ángel Chávez, Stephan Ramon Garcia, Jackson Hurley
We improve and expand in two directions the theory of norms on complex matrices induced by random vectors. We first provide a simple proof of the classification of weakly unitarily invariant norms on the Hermitian matrices. We use this to extend the main theorem in Chávez, Garcia, and Hurley (2023, Canadian Mathematical Bulletin 66, 808–826) from exponent $d\geq 2$ to $d \geq 1$. Our proofs are much
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Bregman distance regularization for nonsmooth and nonconvex optimization Can. Math. Bull. (IF 0.6) Pub Date : 2023-10-26 Zeinab Mashreghi, Mostafa Nasri
Solving a nonsmooth and nonconvex minimization problem can be approached as finding a zero of a set-valued operator. With this perspective, we propose a novel Majorizer–Minimizer technique to find a local minimizer of a nonsmooth and nonconvex function and establish its convergence. Our approach leverages Bregman distances to generalize the classical quadratic regularization. By doing so, we generate
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Some results on various types of compactness of weak* Dunford–Pettis operators on Banach lattices Can. Math. Bull. (IF 0.6) Pub Date : 2023-10-23 Redouane Nouira, Belmesnaoui Aqzzouz
We study the relationship between weak* Dunford–Pettis and weakly (resp. M-weakly, order weakly, almost M-weakly, and almost L-weakly) operators on Banach lattices. The following is one of the major results dealing with this matter: If E and F are Banach lattices such that F is Dedekind $\sigma $-complete, then each positive weak* Dunford–Pettis operator $T:E\rightarrow F$ is weakly compact if and
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Bounded cohomology is not a profinite invariant Can. Math. Bull. (IF 0.6) Pub Date : 2023-10-20 Daniel Echtler, Holger Kammeyer
We construct pairs of residually finite groups with isomorphic profinite completions such that one has non-vanishing and the other has vanishing real second bounded cohomology. The examples are lattices in different higher-rank simple Lie groups. Using Galois cohomology, we actually show that $\operatorname {SO}^0(n,2)$ for $n \ge 6$ and the exceptional groups $E_{6(-14)}$ and $E_{7(-25)}$ constitute
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Universal spaces for asymptotic dimension via factorization Can. Math. Bull. (IF 0.6) Pub Date : 2023-10-20 Jerzy Dydak, Michael Levin, Jeremy Siegert
The main goal of this paper is to construct universal spaces for asymptotic dimension by generalizing to the coarse context an approach to constructing universal spaces for covering dimension using a factorization result due to Mardesic.
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A new lower bound in the conjecture Can. Math. Bull. (IF 0.6) Pub Date : 2023-10-09 Curtis Bright
We prove that there exist infinitely many coprime numbers a, b, c with $a+b=c$ and $c>\operatorname {\mathrm {rad}}(abc)\exp (6.563\sqrt {\log c}/\log \log c)$. These are the most extremal examples currently known in the $abc$ conjecture, thereby providing a new lower bound on the tightest possible form of the conjecture. Our work builds on that of van Frankenhuysen (J. Number Theory 82(2000), 91–95)
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Ramanujan-type series for , revisited Can. Math. Bull. (IF 0.6) Pub Date : 2023-10-05 Dongxi Ye
In this note, we revisit Ramanujan-type series for $\frac {1}{\pi }$ and show how they arise from genus zero subgroups of $\mathrm {SL}_{2}(\mathbb {R})$ that are commensurable with $\mathrm {SL}_{2}(\mathbb {Z})$. As illustrations, we reproduce a striking formula of Ramanujan for $\frac {1}{\pi }$ and a recent result of Cooper et al., as well as derive a new rational Ramanujan-type series for $\frac
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A new upper bound for the asymptotic dimension of RACGs Can. Math. Bull. (IF 0.6) Pub Date : 2023-10-04 Panagiotis Tselekidis
Let $W_{\Gamma} $ be the right-angled Coxeter group with defining graph $\Gamma $. We show that the asymptotic dimension of $W_{\Gamma} $ is smaller than or equal to $\mathrm{dim}_{CC}(\Gamma )$, the clique-connected dimension of the graph. We generalize this result to graph products of finite groups.
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On the metric dimension of circulant graphs Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-28 Rui Gao, Yingqing Xiao, Zhanqi Zhang
In this note, we bound the metric dimension of the circulant graphs $C_n(1,2,\ldots ,t)$. We shall prove that if $n=2tk+t$ and if t is odd, then $\dim (C_n(1,2,\ldots ,t))=t+1$, which confirms Conjecture 4.1.1 in Chau and Gosselin (2017, Opuscula Mathematica 37, 509–534). In Vetrík (2017, Canadian Mathematical Bulletin 60, 206–216; 2020, Discussiones Mathematicae. Graph Theory 40, 67–76), the author
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Piecewise contracting maps on the interval: Hausdorff dimension, entropy, and attractors Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-21 Alfredo E. Calderón, Edgardo Villar-Sepúlveda
We consider the attractor $\Lambda $ of a piecewise contracting map f defined on a compact interval. If f is injective, we show that it is possible to estimate the topological entropy of f (according to Bowen’s formula) and the Hausdorff dimension of $\Lambda $ via the complexity associated with the orbits of the system. Specifically, we prove that both numbers are zero.
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A universal inequality for Neumann eigenvalues of the Laplacian on a convex domain in Euclidean space Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-19 Kei Funano
We obtain a new upper bound for Neumann eigenvalues of the Laplacian on a bounded convex domain in Euclidean space. As an application of the upper bound, we derive universal inequalities for Neumann eigenvalues of the Laplacian.
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Equal-Sum-Product problem II Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-13 Maciej Zakarczemny
In this paper, we present the results related to a problem posed by Andrzej Schinzel. Does the number $N_1(n)$ of integer solutions of the equation $$ \begin{align*}x_1+x_2+\cdots+x_n=x_1x_2\cdot\ldots\cdot x_n,\,\,x_1\ge x_2\ge\cdots\ge x_n\ge 1\end{align*} $$tend to infinity with n? Let a be a positive integer. We give a lower bound on the number of integer solutions, $N_a(n)$, to the equation $$
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Ideals with approximate unit in semicrossed products Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-12 Charalampos Magiatis
We characterize the ideals of the semicrossed product $C_0(X)\times _\phi {\mathbb Z}_+$, associated with suitable sequences of closed subsets of X, with left (resp. right) approximate unit. As a consequence, we obtain a complete characterization of ideals with left (resp. right) approximate unit under the assumptions that X is metrizable and the dynamical system $(X,\phi )$ contains no periodic points
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On theorems of Fermat, Wilson, and Gegenbauer Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-12 Heng Huat Chan, Song Heng Chan, Teoh Guan Chua, Cheng Yeaw Ku
In this article, we give generalizations of the well-known Fermat’s Little Theorem, Wilson’s theorem, and the little-known Gegenbauer’s theorem.
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Entry and leaving arcs of turnpikes: their exact computation in the calculus of variations Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-12 Luis Bayón, Pedro Fortuny Ayuso, José María Grau, Maria del Mar Ruiz
We settle the question of how to compute the entry and leaving arcs for turnpikes in autonomous variational problems, in the one-dimensional case using the phase space of the vector field associated with the Euler equation, and the initial/final and/or the transversality condition. The results hinge on the realization that extremals are the contours of a well-known function and that the transversality
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Problems for generalized Monge–Ampère equations Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-11 Cristian Enache, Giovanni Porru
This paper deals with some Monge–Ampère type equations involving the gradient that are elliptic in the framework of convex functions. First, we show that such equations may be obtained by minimizing a suitable functional. Moreover, we investigate a P-function associated with the solution to a boundary value problem of our generalized Monge–Ampère equation in a bounded convex domain. It will be shown
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Every symmetric Kubo–Ando connection has the order-determining property Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-11 Emmanuel Chetcuti, Curt Healey
In this article, the question of whether the Löwner partial order on the positive cone of an operator algebra is determined by the norm of any arbitrary Kubo–Ando mean is studied. The question was affirmatively answered for certain classes of Kubo–Ando means, yet the general case was left as an open problem. We here give a complete answer to this question, by showing that the norm of every symmetric
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A tracial characterization of Furstenberg’s conjecture Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-06 Chris Bruce, Eduardo Scarparo
We investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers p and q, we show that Furstenberg’s $\times p,\times q$ conjecture holds if and only if the canonical trace is the only faithful extreme tracial state on the $C^*$-algebra of the group $\mathbb {Z}[\frac {1}{pq}]\rtimes \mathbb {Z}^2$. We also compute the
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Convexity of the radial sum of a star body and a ball Can. Math. Bull. (IF 0.6) Pub Date : 2023-09-04 Shigehiro Sakata
We investigate the convexity of the radial sum of two convex bodies containing the origin. Generally, the radial sum of two convex bodies containing the origin is not convex. We show that the radial sum of a star body (with respect to the origin) and any large centered ball is convex, which produces a pair of convex bodies containing the origin whose radial sum is convex. We also investigate the convexity
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A minimax inequality for inscribed cones revisited Can. Math. Bull. (IF 0.6) Pub Date : 2023-08-31 Zokhrab Mustafaev
In 1993, E. Lutwak established a minimax inequality for inscribed cones of origin symmetric convex bodies. In this work, we re-prove Lutwak’s result using a maxmin inequality for circumscribed cylinders. Furthermore, we explore connections between the maximum volume of inscribed double cones of a centered convex body and the minimum volume of circumscribed cylinders of its polar body.
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Block perturbation of symplectic matrices in Williamson’s theorem Can. Math. Bull. (IF 0.6) Pub Date : 2023-08-15 Gajendra Babu, Hemant K. Mishra
Williamson’s theorem states that for any $2n \times 2n$ real positive definite matrix A, there exists a $2n \times 2n$ real symplectic matrix S such that $S^TAS=D \oplus D$, where D is an $n\times n$ diagonal matrix with positive diagonal entries known as the symplectic eigenvalues of A. Let H be any $2n \times 2n$ real symmetric matrix such that the perturbed matrix $A+H$ is also positive definite
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Nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in Can. Math. Bull. (IF 0.6) Pub Date : 2023-08-14 Qianshun Cui, Zejun Hu
In this paper, we solved an open problem raised by Cecil and Ryan (2015, Geometry of Hypersurfaces, Springer Monographs in Mathematics, Springer, New York, p. 531) by proving the nonexistence of non-Hopf Ricci-semisymmetric real hypersurfaces in $\mathbb {C}P^{2}$ and $\mathbb {C}H^{2}$.
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Erdős–Ko–Rado theorem in Peisert-type graphs Can. Math. Bull. (IF 0.6) Pub Date : 2023-08-04 Chi Hoi Yip
The celebrated Erdős–Ko–Rado (EKR) theorem for Paley graphs of square order states that all maximum cliques are canonical in the sense that each maximum clique arises from the subfield construction. Recently, Asgarli and Yip extended this result to Peisert graphs and other Cayley graphs which are Peisert-type graphs with nice algebraic properties on the connection set. On the other hand, there are
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Weak random periodic solutions of random dynamical systems Can. Math. Bull. (IF 0.6) Pub Date : 2023-07-12 Wei Sun, Zuo-Huan Zheng
We first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their relationship with weak random periodic solutions. In particular, we establish the existence of invariant measures of random dynamical systems by virtue of their weak
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Uncertainty principles in holomorphic function spaces on the unit ball Can. Math. Bull. (IF 0.6) Pub Date : 2023-07-10 H. Turgay Kaptanoğlu
On all Bergman–Besov Hilbert spaces on the unit disk, we find self-adjoint weighted shift operators that are differential operators of half-order whose commutators are the identity, thereby obtaining uncertainty relations in these spaces. We also obtain joint average uncertainty relations for pairs of commuting tuples of operators on the same spaces defined on the unit ball. We further identify functions
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Landau-type theorems for certain bounded bi-analytic functions and biharmonic mappings Can. Math. Bull. (IF 0.6) Pub Date : 2023-07-05 Ming-Sheng Liu, Saminathan Ponnusamy
In this article, we establish three new versions of Landau-type theorems for bounded bi-analytic functions of the form $F(z)=\bar {z}G(z)+H(z)$, where G and H are analytic in the unit disk with $G(0)=H(0)=0$ and $H'(0)=1$. In particular, two of them are sharp, while the other one either generalizes or improves the corresponding result of Abdulhadi and Hajj. As consequences, several new sharp versions
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An optimal autoconvolution inequality Can. Math. Bull. (IF 0.6) Pub Date : 2023-07-05 Ethan Patrick White
Let $\mathcal {F}$ denote the set of functions $f \colon [-1/2,1/2] \to \mathbb {R}_{\geq 0}$ such that $\int f = 1$. We determine the value of $\inf _{f \in \mathcal {F}} \| f \ast f \|_2^2$ up to a $4 \cdot 10^{-6}$ error, thereby making progress on a problem asked by Ben Green. Furthermore, we prove that a unique minimizer exists. As a corollary, we obtain improvements on the maximum size of $B_h[g]$
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A logarithmic lower bound for the second Bohr radius Can. Math. Bull. (IF 0.6) Pub Date : 2023-06-27 Nilanjan Das
The purpose of this note is to obtain an improved lower bound for the multidimensional Bohr radius introduced by L. Aizenberg (2000, Proceedings of the American Mathematical Society 128, 1147–1155), by means of a rather simple argument.
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The Łojasiewicz exponent of nondegenerate surface singularities Can. Math. Bull. (IF 0.6) Pub Date : 2023-06-26 Szymon Brzostowski, Tadeusz Krasiński, Grzegorz Oleksik
Let f be an isolated singularity at the origin of $\mathbb {C}^n$. One of many invariants that can be associated with f is its Łojasiewicz exponent $\mathcal {L}_0 (f)$, which measures, to some extent, the topology of f. We give, for generic surface singularities f, an effective formula for $\mathcal {L}_0 (f)$ in terms of the Newton polyhedron of f. This is a realization of one of Arnold’s postulates
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Maximal operators on BMO and slices Can. Math. Bull. (IF 0.6) Pub Date : 2023-06-26 Shahaboddin Shaabani
We prove that the uncentered Hardy–Littlewood maximal operator is discontinuous on ${BMO}(\mathbb {R}^n)$ and maps ${VMO}(\mathbb {R}^n)$ to itself. A counterexample to the boundedness of the strong and directional maximal operators on ${BMO}(\mathbb {R}^n)$ is given, and properties of slices of ${BMO}(\mathbb {R}^n)$ functions are discussed.