CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  Publicationsjournals
Publications        
Search results

Search: All articles in the CMB digital archive with keyword f

  Expand all        Collapse all Results 26 - 50 of 547

26. CMB Online first

Gauthier, Paul M; Sharifi, Fatemeh
Luzin-type holomorphic approximation on closed subsets of open Riemann surfaces
It is known that if $E$ is a closed subset of an open Riemann surface $R$ and $f$ is a holomorphic function on a neighbourhood of $E,$ then it is ``usually" not possible to approximate $f$ uniformly by functions holomorphic on all of $R.$ We show, however, that for every open Riemann surface $R$ and every closed subset $E\subset R,$ there is closed subset $F\subset E,$ which approximates $E$ extremely well, such that every function holomorphic on $F$ can be approximated much better than uniformly by functions holomorphic on $R$.

Keywords:Carleman approximation, tangential approximation, Myrberg surface
Categories:30E15, 30F99

27. CMB Online first

Werner, Elisabeth; Ye, Deping
Mixed $f$-divergence for multiple pairs of measures
In this paper, the concept of the classical $f$-divergence for a pair of measures is extended to the mixed $f$-divergence for multiple pairs of measures. The mixed $f$-divergence provides a way to measure the difference between multiple pairs of (probability) measures. Properties for the mixed $f$-divergence are established, such as permutation invariance and symmetry in distributions. An Alexandrov-Fenchel type inequality and an isoperimetric inequality for the mixed $f$-divergence are proved.

Keywords:Alexandrov-Fenchel inequality, $f$-dissimilarity, $f$-divergence, isoperimetric inequality
Categories:28-XX, 52-XX, 60-XX

28. CMB Online first

Liu, Feng; Wu, Huoxiong
Endpoint Regularity of Multisublinear Fractional Maximal Functions
In this paper we investigate the endpoint regularity properties of the multisublinear fractional maximal operators, which include the multisublinear Hardy-Littlewood maximal operator. We obtain some new bounds for the derivative of the one-dimensional multisublinear fractional maximal operators acting on vector-valued function $\vec{f}=(f_1,\dots,f_m)$ with all $f_j$ being $BV$-functions.

Keywords:multisublinear fractional maximal operators, Sobolev spaces, bounded variation
Categories:42B25, 46E35

29. CMB 2016 (vol 59 pp. 813)

Kaimakamis, George; Panagiotidou, Konstantina; Pérez, Juan de Dios
A Classification of Three-dimensional Real Hypersurfaces in Non-flat Complex Space Forms in Terms of Their generalized Tanaka-Webster Lie Derivative
On a real hypersurface $M$ in a non-flat complex space form there exist the Levi-Civita and the k-th generalized Tanaka-Webster connections. The aim of the present paper is to study three dimensional real hypersurfaces in non-flat complex space forms, whose Lie derivative of the structure Jacobi operator with respect to the Levi-Civita connections coincides with the Lie derivative of it with respect to the k-th generalized Tanaka-Webster connection. The Lie derivatives are considered in direction of the structure vector field and in directions of any vecro field orthogonal to the structure vector field.

Keywords:$k$-th generalized Tanaka-Webster connection, non-flat complex space form, real hypersurface, Lie derivative, structure Jacobi operator
Categories:53C15, 53B25

30. CMB Online first

Liu, Ye
On chromatic functors and stable partitions of graphs
The chromatic functor of a simple graph is a functorization of the chromatic polynomial. M. Yoshinaga showed that two finite graphs have isomorphic chromatic functors if and only if they have the same chromatic polynomial. The key ingredient in the proof is the use of stable partitions of graphs. The latter is shown to be closely related to chromatic functors. In this note, we further investigate some interesting properties of chromatic functors associated to simple graphs using stable partitions. Our first result is the determination of the group of natural automorphisms of the chromatic functor, which is in general a larger group than the automorphism group of the graph. The second result is that the composition of the chromatic functor associated to a finite graph restricted to the category $\mathrm{FI}$ of finite sets and injections with the free functor into the category of complex vector spaces yields a consistent sequence of representations of symmetric groups which is representation stable in the sense of Church-Farb.

Keywords:chromatic functor, stable partition, representation stability
Categories:05C15, 20C30

31. CMB Online first

Chang, Gyu Whan
Power series rings over Prufer $v$-multiplication domains, II
Let $D$ be an integral domain, $X^1(D)$ be the set of height-one prime ideals of $D$, $\{X_{\beta}\}$ and $\{X_{\alpha}\}$ be two disjoint nonempty sets of indeterminates over $D$, $D[\{X_{\beta}\}]$ be the polynomial ring over $D$, and $D[\{X_{\beta}\}][\![\{X_{\alpha}\}]\!]_1$ be the first type power series ring over $D[\{X_{\beta}\}]$. Assume that $D$ is a Prüfer $v$-multiplication domain (P$v$MD) in which each proper integral $t$-ideal has only finitely many minimal prime ideals (e.g., $t$-SFT P$v$MDs, valuation domains, rings of Krull type). Among other things, we show that if $X^1(D) = \emptyset$ or $D_P$ is a DVR for all $P \in X^1(D)$, then ${D[\{X_{\beta}\}][\![\{X_{\alpha}\}]\!]_1}_{D - \{0\}}$ is a Krull domain. We also prove that if $D$ is a $t$-SFT P$v$MD, then the complete integral closure of $D$ is a Krull domain and ht$(M[\{X_{\beta}\}][\![\{X_{\alpha}\}]\!]_1)$ = $1$ for every height-one maximal $t$-ideal $M$ of $D$.

Keywords:Krull domain, P$v$MD, multiplicatively closed set of ideals, power series ring
Categories:13A15, 13F05, 13F25

32. CMB Online first

Chen, Jianlong; Patricio, Pedro; Zhang, Yulin; Zhu, Huihui
Characterizations and representations of core and dual core inverses
In this paper, double commutativity and the reverse order law for the core inverse are considered. Then, new characterizations of the Moore-Penrose inverse of a regular element are given by one-sided invertibilities in a ring. Furthermore, the characterizations and representations of the core and dual core inverses of a regular element are considered.

Keywords:regularities, group inverses, Moore-Penrose inverses, core inverses, dual core inverses, Dedekind-finite rings
Categories:15A09, 15A23

33. CMB Online first

Karzhemanov, Ilya
On polarized K3 surfaces of genus 33
We prove that the moduli space of smooth primitively polarized $\mathrm{K3}$ surfaces of genus $33$ is unirational.

Keywords:K3 surface, moduli space, unirationality
Categories:14J28, 14J15, 14M20

34. CMB 2016 (vol 59 pp. 834)

Liao, Fanghui; Liu, Zongguang
Some Properties of Triebel-Lizorkin and Besov Spaces Associated with Zygmund Dilations
In this paper, using Calderón's reproducing formula and almost orthogonality estimates, we prove the lifting property and the embedding theorem of the Triebel-Lizorkin and Besov spaces associated with Zygmund dilations.

Keywords:Triebel-Lizorkin and Besov spaces, Riesz potential, Calderón's reproducing formula, almost orthogonality estimate, Zygmund dilation, embedding theorem
Categories:42B20, 42B35

35. CMB Online first

Ghaani Farashahi, Arash
Abstract Plancherel (Trace) Formulas over Homogeneous Spaces of Compact Groups
This paper introduces a unified operator theory approach to the abstract Plancherel (trace) formulas over homogeneous spaces of compact groups. Let $G$ be a compact group and $H$ be a closed subgroup of $G$. Let $G/H$ be the left coset space of $H$ in $G$ and $\mu$ be the normalized $G$-invariant measure on $G/H$ associated to the Weil's formula. Then, we present a generalized abstract notion of Plancherel (trace) formula for the Hilbert space $L^2(G/H,\mu)$.

Keywords:compact group, homogeneous space, dual space, Plancherel (trace) formula
Categories:20G05, 43A85, 43A32, 43A40

36. CMB 2016 (vol 59 pp. 760)

Fichou, Goulwen; Quarez, Ronan; Shiota, Masahiro
Artin Approximation Compatible with a Change of Variables
We propose a version of the classical Artin approximation which allows to perturb the variables of the approximated solution. Namely, it is possible to approximate a formal solution of a Nash equation by a Nash solution in a compatible way with a given Nash change of variables. This result is closely related to the so-called nested Artin approximation and becomes false in the analytic setting. We provide local and global versions of this approximation in real and complex geometry together with an application to the Right-Left equivalence of Nash maps.

Keywords:Artin approximation, global case, Nash functions
Categories:14P20, 58A07

37. CMB 2016 (vol 59 pp. 673)

Bačák, Miroslav; Kovalev, Leonid V.
Lipschitz Retractions in Hadamard Spaces Via Gradient Flow Semigroups
Let $X(n),$ for $n\in\mathbb{N},$ be the set of all subsets of a metric space $(X,d)$ of cardinality at most $n.$ The set $X(n)$ equipped with the Hausdorff metric is called a finite subset space. In this paper we are concerned with the existence of Lipschitz retractions $r\colon X(n)\to X(n-1)$ for $n\ge2.$ It is known that such retractions do not exist if $X$ is the one-dimensional sphere. On the other hand L. Kovalev has recently established their existence in case $X$ is a Hilbert space and he also posed a question as to whether or not such Lipschitz retractions exist for $X$ being a Hadamard space. In the present paper we answer this question in the positive.

Keywords:finite subset space, gradient flow, Hadamard space, Lie-Trotter-Kato formula, Lipschitz retraction
Categories:53C23, 47H20, 54E40, 58D07

38. CMB 2016 (vol 59 pp. 721)

Pérez, Juan de Dios; Lee, Hyunjin; Suh, Young Jin; Woo, Changhwa
Real Hypersurfaces in Complex Two-plane Grassmannians with Reeb Parallel Ricci Tensor in the GTW Connection
There are several kinds of classification problems for real hypersurfaces in complex two-plane Grassmannians $G_2({\mathbb C}^{m+2})$. Among them, Suh classified Hopf hypersurfaces $M$ in $G_2({\mathbb C}^{m+2})$ with Reeb parallel Ricci tensor in Levi-Civita connection. In this paper, we introduce the notion of generalized Tanaka-Webster (in shortly, GTW) Reeb parallel Ricci tensor for Hopf hypersurface $M$ in $G_2({\mathbb C}^{m+2})$. Next, we give a complete classification of Hopf hypersurfaces in $G_2({\mathbb C}^{m+2})$ with GTW Reeb parallel Ricci tensor.

Keywords:Complex two-plane Grassmannian, real hypersurface, Hopf hypersurface, generalized Tanaka-Webster connection, parallelism, Reeb parallelism, Ricci tensor
Categories:53C40, 53C15

39. CMB 2016 (vol 59 pp. 472)

Clay, Adam; Desmarais, Colin; Naylor, Patrick
Testing Bi-orderability of Knot Groups
We investigate the bi-orderability of two-bridge knot groups and the groups of knots with 12 or fewer crossings by applying recent theorems of Chiswell, Glass and Wilson. Amongst all knots with 12 or fewer crossings (of which there are 2977), previous theorems were only able to determine bi-orderability of 499 of the corresponding knot groups. With our methods we are able to deal with 191 more.

Keywords:knots, fundamental groups, orderable groups
Categories:57M25, 57M27, 06F15

40. CMB 2016 (vol 59 pp. 483)

Crooks, Peter; Holden, Tyler
Generalized Equivariant Cohomology and Stratifications
For $T$ a compact torus and $E_T^*$ a generalized $T$-equivariant cohomology theory, we provide a systematic framework for computing $E_T^*$ in the context of equivariantly stratified smooth complex projective varieties. This allows us to explicitly compute $E_T^*(X)$ as an $E_T^*(\text{pt})$-module when $X$ is a direct limit of smooth complex projective $T_{\mathbb{C}}$-varieties with finitely many $T$-fixed points and $E_T^*$ is one of $H_T^*(\cdot;\mathbb{Z})$, $K_T^*$, and $MU_T^*$. We perform this computation on the affine Grassmannian of a complex semisimple group.

Keywords:equivariant cohomology theory, stratification, affine Grassmannian
Categories:55N91, 19L47

41. CMB 2016 (vol 59 pp. 769)

García-Pacheco, Francisco Javier; Hill, Justin R.
Geometric Characterizations of Hilbert Spaces
We study some geometric properties related to the set $\Pi_X:= \{ (x,x^* )\in\mathsf{S}_X\times \mathsf{S}_{X^*}:x^* (x )=1 \}$ obtaining two characterizations of Hilbert spaces in the category of Banach spaces. We also compute the distance of a generic element $ (h,k )\in H\oplus_2 H$ to $\Pi_H$ for $H$ a Hilbert space.

Keywords:Hilbert space, extreme point, smooth, $\mathsf{L}^2$-summands
Categories:46B20, 46C05

42. CMB 2016 (vol 59 pp. 652)

Su, Huadong
On the Diameter of Unitary Cayley Graphs of Rings
The unitary Cayley graph of a ring $R$, denoted $\Gamma(R)$, is the simple graph defined on all elements of $R$, and where two vertices $x$ and $y$ are adjacent if and only if $x-y$ is a unit in $R$. The largest distance between all pairs of vertices of a graph $G$ is called the diameter of $G$, and is denoted by ${\rm diam}(G)$. It is proved that for each integer $n\geq1$, there exists a ring $R$ such that ${\rm diam}(\Gamma(R))=n$. We also show that ${\rm diam}(\Gamma(R))\in \{1,2,3,\infty\}$ for a ring $R$ with $R/J(R)$ self-injective and classify all those rings with ${\rm diam}(\Gamma(R))=1$, 2, 3 and $\infty$, respectively.

Keywords:unitary Cayley graph, diameter, $k$-good, unit sum number, self-injective ring
Categories:05C25, 16U60, 05C12

43. CMB 2016 (vol 59 pp. 606)

Mihăilescu, Mihai; Moroşanu, Gheorghe
Eigenvalues of $ -\Delta_p -\Delta_q $ Under Neumann Boundary Condition
The eigenvalue problem $-\Delta_p u-\Delta_q u=\lambda|u|^{q-2}u$ with $p\in(1,\infty)$, $q\in(2,\infty)$, $p\neq q$ subject to the corresponding homogeneous Neumann boundary condition is investigated on a bounded open set with smooth boundary from $\mathbb{R}^N$ with $N\geq 2$. A careful analysis of this problem leads us to a complete description of the set of eigenvalues as being a precise interval $(\lambda_1, +\infty )$ plus an isolated point $\lambda =0$. This comprehensive result is strongly related to our framework which is complementary to the well-known case $p=q\neq 2$ for which a full description of the set of eigenvalues is still unavailable.

Keywords:eigenvalue problem, Sobolev space, Nehari manifold, variational methods
Categories:35J60, 35J92, 46E30, 49R05

44. CMB 2016 (vol 59 pp. 617)

Nakashima, Norihiro; Terao, Hiroaki; Tsujie, Shuhei
Canonical Systems of Basic Invariants for Unitary Reflection Groups
It has been known that there exists a canonical system for every finite real reflection group. The first and the third authors obtained an explicit formula for a canonical system in the previous paper. In this article, we first define canonical systems for the finite unitary reflection groups, and then prove their existence. Our proof does not depend on the classification of unitary reflection groups. Furthermore, we give an explicit formula for a canonical system for every unitary reflection group.

Keywords:basic invariant, invariant theory, finite unitary reflection group
Categories:13A50, 20F55

45. CMB 2016 (vol 59 pp. 449)

Abdallah, Nancy
On Hodge Theory of Singular Plane Curves
The dimensions of the graded quotients of the cohomology of a plane curve complement $U=\mathbb P^2 \setminus C$ with respect to the Hodge filtration are described in terms of simple geometrical invariants. The case of curves with ordinary singularities is discussed in detail. We also give a precise numerical estimate for the difference between the Hodge filtration and the pole order filtration on $H^2(U,\mathbb C)$.

Keywords:plane curves, Hodge and pole order filtrations
Categories:32S35, 32S22, 14H50

46. CMB 2016 (vol 59 pp. 528)

Jahan, Qaiser
Characterization of Low-pass Filters on Local Fields of Positive Characteristic
In this article, we give necessary and sufficient conditions on a function to be a low-pass filter on a local field $K$ of positive characteristic associated to the scaling function for multiresolution analysis of $L^2(K)$. We use probability and martingale methods to provide such a characterization.

Keywords:multiresolution analysis, local field, low-pass filter, scaling function, probability, conditional probability and martingales
Categories:42C40, 42C15, 43A70, 11S85

47. CMB 2016 (vol 59 pp. 734)

Dimassi, Mouez
Semi-classical Asymptotics for Schrödinger Operator with Oscillating Decaying Potential
We study the distribution of the discrete spectrum of the Schrödinger operator perturbed by a fast oscillating decaying potential depending on a small parameter $h$.

Keywords:periodic Schrödinger operator, semi-classical asymptotics, effective Hamiltonian, asymptotic expansion, spectral shift function
Categories:81Q10, 35P20, 47A55, 47N50, 81Q15

48. CMB 2016 (vol 59 pp. 497)

De Carli, Laura; Samad, Gohin Shaikh
One-parameter Groups of Operators and Discrete Hilbert Transforms
We show that the discrete Hilbert transform and the discrete Kak-Hilbert transform are infinitesimal generator of one-parameter groups of operators in $\ell^2$.

Keywords:discrete Hilbert transform, groups of operators, isometries
Categories:42A45, 42A50, 41A44

49. CMB 2016 (vol 59 pp. 461)

Ara, Pere; O'Meara, Kevin C.
The Nilpotent Regular Element Problem
We use George Bergman's recent normal form for universally adjoining an inner inverse to show that, for general rings, a nilpotent regular element $x$ need not be unit-regular. This contrasts sharply with the situation for nilpotent regular elements in exchange rings (a large class of rings), and for general rings when all powers of the nilpotent element $x$ are regular.

Keywords:nilpotent element, von Neumann regular element, unit-regular, Bergman's normal form
Categories:16E50, 16U99, 16S10, 16S15

50. CMB Online first

Khavinson, Dmitry; Lundberg, Erik; Render, Hermann
The Dirichlet problem for the slab with entire data and a difference equation for harmonic functions
It is shown that the Dirichlet problem for the slab $(a,b) \times \mathbb{R}^{d}$ with entire boundary data has an entire solution. The proof is based on a generalized Schwarz reflection principle. Moreover, it is shown that for a given entire harmonic function $g$ the inhomogeneous difference equation $h ( t+1,y) -h (t,y) =g ( t,y)$ has an entire harmonic solution $h$.

Keywords:reflection principle, entire harmonic function, analytic continuation
Categories:31B20, 31B05
Page
   1 2 3 4 ... 22    

© Canadian Mathematical Society, 2016 : https://cms.math.ca/