Canadian Mathematical Society
Canadian Mathematical Society
  location:  Publicationsjournals
Search results

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

  Expand all        Collapse all Results 51 - 75 of 489

51. CMB 2015 (vol 58 pp. 271)

Jafari, Sayyed Heidar; Jafari Rad, Nader
On Domination of Zero-divisor Graphs of Matrix Rings
We study domination in zero-divisor graphs of matrix rings over a commutative ring with $1$.

Keywords:vector space, linear transformation, zero-divisor graph, domination, local ring

52. CMB 2015 (vol 58 pp. 285)

Karpukhin, Mikhail
Spectral Properties of a Family of Minimal Tori of Revolution in Five-dimensional Sphere
The normalized eigenvalues $\Lambda_i(M,g)$ of the Laplace-Beltrami operator can be considered as functionals on the space of all Riemannian metrics $g$ on a fixed surface $M$. In recent papers several explicit examples of extremal metrics were provided. These metrics are induced by minimal immersions of surfaces in $\mathbb{S}^3$ or $\mathbb{S}^4$. In the present paper a family of extremal metrics induced by minimal immersions in $\mathbb{S}^5$ is investigated.

Keywords:extremal metric, minimal surface

53. CMB 2015 (vol 58 pp. 415)

Willson, Benjamin
A Fixed Point Theorem and the Existence of a Haar Measure for Hypergroups Satisfying Conditions Related to Amenability
In this paper we present a fixed point property for amenable hypergroups which is analogous to Rickert's fixed point theorem for semigroups. It equates the existence of a left invariant mean on the space of weakly right uniformly continuous functions to the existence of a fixed point for any action of the hypergroup. Using this fixed point property, a certain class of hypergroups are shown to have a left Haar measure.

Keywords:invariant measure, Haar measure, hypergroup, amenability, function translations
Categories:43A62, 43A05, 43A07

54. CMB 2015 (vol 58 pp. 281)

Kalus, Matthias
On the Relation of Real and Complex Lie Supergroups
A complex Lie supergroup can be described as a real Lie supergroup with integrable almost complex structure. The necessary and sufficient conditions on an almost complex structure on a real Lie supergroup for defining a complex Lie supergroup are deduced. The classification of real Lie supergroups with such almost complex structures yields a new approach to the known classification of complex Lie supergroups by complex Harish-Chandra superpairs. A universal complexification of a real Lie supergroup is constructed.

Keywords:Lie supergroup, almost complex structure, Harish-Chandra pair, universal complexification
Categories:32C11, 58A50

55. CMB 2015 (vol 58 pp. 241)

Botelho, Fernanda
Isometries and Hermitian Operators on Zygmund Spaces
In this paper we characterize the isometries of subspaces of the little Zygmund space. We show that the isometries of these spaces are surjective and represented as integral operators. We also show that all hermitian operators on these settings are bounded.

Keywords:Zygmund spaces, the little Zygmund space, Hermitian operators, surjective linear isometries, generators of one-parameter groups of surjective isometries
Categories:46E15, 47B15, 47B38

56. CMB 2015 (vol 58 pp. 334)

Medini, Andrea
Countable Dense Homogeneity in Powers of Zero-dimensional Definable Spaces
We show that, for a coanalytic subspace $X$ of $2^\omega$, the countable dense homogeneity of $X^\omega$ is equivalent to $X$ being Polish. This strengthens a result of Hrušák and Zamora Avilés. Then, inspired by results of Hernández-Gutiérrez, Hrušák and van Mill, using a technique of Medvedev, we construct a non-Polish subspace $X$ of $2^\omega$ such that $X^\omega$ is countable dense homogeneous. This gives the first $\mathsf{ZFC}$ answer to a question of Hrušák and Zamora Avilés. Furthermore, since our example is consistently analytic, the equivalence result mentioned above is sharp. Our results also answer a question of Medini and Milovich. Finally, we show that if every countable subset of a zero-dimensional separable metrizable space $X$ is included in a Polish subspace of $X$ then $X^\omega$ is countable dense homogeneous.

Keywords:countable dense homogeneous, infinite power, coanalytic, Polish, $\lambda'$-set
Categories:54H05, 54G20, 54E52

57. CMB 2015 (vol 58 pp. 225)

Aghigh, Kamal; Nikseresht, Azadeh
Characterizing Distinguished Pairs by Using Liftings of Irreducible Polynomials
Let $v$ be a henselian valuation of any rank of a field $K$ and $\overline{v}$ be the unique extension of $v$ to a fixed algebraic closure $\overline{K}$ of $K$. In 2005, it was studied properties of those pairs $(\theta,\alpha)$ of elements of $\overline{K}$ with $[K(\theta): K]\gt [K(\alpha): K]$ where $\alpha$ is an element of smallest degree over $K$ such that $$ \overline{v}(\theta-\alpha)=\sup\{\overline{v}(\theta-\beta) |\ \beta\in \overline{K}, \ [K(\beta): K]\lt [K(\theta): K]\}. $$ Such pairs are referred to as distinguished pairs. We use the concept of liftings of irreducible polynomials to give a different characterization of distinguished pairs.

Keywords:valued fields, non-Archimedean valued fields, irreducible polynomials
Categories:12J10, 12J25, 12E05

58. CMB Online first

Deng, Shaoqiang; Hu, Zhiguang; Li, Jifu
Cohomogeneity one Randers metrics
An action of a Lie group $G$ on a smooth manifold $M$ is called cohomogeneity one if the orbit space $M/G$ is of dimension $1$. A Finsler metric $F$ on $M$ is called invariant if $F$ is invariant under the action of $G$. In this paper, we study invariant Randers metrics on cohomogeneity one manifolds. We first give a sufficient and necessary condition for the existence of invariant Randers metrics on cohomogeneity one manifolds. Then we obtain some results on invariant Killing vector fields on the cohomogeneity one manifolds and use that to deduce some sufficient and necessary condition for a cohomogeneity one Randers metric to be Einstein.

Keywords:cohomogeneity one actions, normal geodesics, invariant vector fields, Randers metrics
Categories:53C30, 53C60

59. CMB 2014 (vol 58 pp. 80)

Harada, Megumi; Horiguchi, Tatsuya; Masuda, Mikiya
The Equivariant Cohomology Rings of Peterson Varieties in All Lie Types
Let $G$ be a complex semisimple linear algebraic group and let $Pet$ be the associated Peterson variety in the flag variety $G/B$. The main theorem of this note gives an efficient presentation of the equivariant cohomology ring $H^*_S(Pet)$ of the Peterson variety as a quotient of a polynomial ring by an ideal $J$ generated by quadratic polynomials, in the spirit of the Borel presentation of the cohomology of the flag variety. Here the group $S \cong \mathbb{C}^*$ is a certain subgroup of a maximal torus $T$ of $G$. Our description of the ideal $J$ uses the Cartan matrix and is uniform across Lie types. In our arguments we use the Monk formula and Giambelli formula for the equivariant cohomology rings of Peterson varieties for all Lie types, as obtained in the work of Drellich. Our result generalizes a previous theorem of Fukukawa-Harada-Masuda, which was only for Lie type $A$.

Keywords:equivariant cohomology, Peterson varieties, flag varieties, Monk formula, Giambelli formula
Categories:55N91, 14N15

60. CMB 2014 (vol 58 pp. 561)

Martinez-Maure, Yves
Plane Lorentzian and Fuchsian Hedgehogs
Parts of the Brunn-Minkowski theory can be extended to hedgehogs, which are envelopes of families of affine hyperplanes parametrized by their Gauss map. F. Fillastre introduced Fuchsian convex bodies, which are the closed convex sets of Lorentz-Minkowski space that are globally invariant under the action of a Fuchsian group. In this paper, we undertake a study of plane Lorentzian and Fuchsian hedgehogs. In particular, we prove the Fuchsian analogues of classical geometrical inequalities (analogues which are reversed as compared to classical ones).

Keywords:Fuchsian and Lorentzian hedgehogs, evolute, duality, convolution, reversed isoperimetric inequality, reversed Bonnesen inequality
Categories:52A40, 52A55, 53A04, 53B30

61. CMB 2014 (vol 58 pp. 432)

Yang, Dachun; Yang, Sibei
Second-order Riesz Transforms and Maximal Inequalities Associated with Magnetic Schrödinger Operators
Let $A:=-(\nabla-i\vec{a})\cdot(\nabla-i\vec{a})+V$ be a magnetic Schrödinger operator on $\mathbb{R}^n$, where $\vec{a}:=(a_1,\dots, a_n)\in L^2_{\mathrm{loc}}(\mathbb{R}^n,\mathbb{R}^n)$ and $0\le V\in L^1_{\mathrm{loc}}(\mathbb{R}^n)$ satisfy some reverse Hölder conditions. Let $\varphi\colon \mathbb{R}^n\times[0,\infty)\to[0,\infty)$ be such that $\varphi(x,\cdot)$ for any given $x\in\mathbb{R}^n$ is an Orlicz function, $\varphi(\cdot,t)\in {\mathbb A}_{\infty}(\mathbb{R}^n)$ for all $t\in (0,\infty)$ (the class of uniformly Muckenhoupt weights) and its uniformly critical upper type index $I(\varphi)\in(0,1]$. In this article, the authors prove that second-order Riesz transforms $VA^{-1}$ and $(\nabla-i\vec{a})^2A^{-1}$ are bounded from the Musielak-Orlicz-Hardy space $H_{\varphi,\,A}(\mathbb{R}^n)$, associated with $A$, to the Musielak-Orlicz space $L^{\varphi}(\mathbb{R}^n)$. Moreover, the authors establish the boundedness of $VA^{-1}$ on $H_{\varphi, A}(\mathbb{R}^n)$. As applications, some maximal inequalities associated with $A$ in the scale of $H_{\varphi, A}(\mathbb{R}^n)$ are obtained.

Keywords:Musielak-Orlicz-Hardy space, magnetic Schrödinger operator, atom, second-order Riesz transform, maximal inequality
Categories:42B30, 42B35, 42B25, 35J10, 42B37, 46E30

62. CMB 2014 (vol 58 pp. 51)

De Nitties, Giuseppe; Schulz-Baldes, Hermann
Spectral Flows of Dilations of Fredholm Operators
Given an essentially unitary contraction and an arbitrary unitary dilation of it, there is a naturally associated spectral flow which is shown to be equal to the index of the operator. This result is interpreted in terms of the $K$-theory of an associated mapping cone. It is then extended to connect $\mathbb{Z}_2$ indices of odd symmetric Fredholm operators to a $\mathbb{Z}_2$-valued spectral flow.

Keywords:spectral flow, Fredholm operators, Z2 indices
Categories:19K56, 46L80

63. CMB 2014 (vol 58 pp. 182)

Tărnăuceanu, Marius
On Finite Groups with Dismantlable Subgroup Lattices
In this note we study the finite groups whose subgroup lattices are dismantlable.

Keywords:finite groups, subgroup lattices, dismantlable lattices, planar lattices, crowns
Categories:20D30, 20D60, 20E15

64. CMB 2014 (vol 58 pp. 196)

Yang, Qingjie; Zhong, Weiting
Dihedral Groups of order $2p$ of Automorphisms of Compact Riemann Surfaces of Genus $p-1$
In this paper we prove that there is only one conjugacy class of dihedral group of order $2p$ in the $2(p-1)\times 2(p-1)$ integral symplectic group can be realized by an analytic automorphism group of compact connected Riemann surfaces of genus $p-1$. A pair of representative generators of the realizable class is also given.

Keywords:dihedral group, automorphism group, Riemann surface, integral symplectic matrix, fundamental domain
Categories:20H25, 57M60

65. CMB 2014 (vol 58 pp. 276)

Johnson, William; Nasseri, Amir Bahman; Schechtman, Gideon; Tkocz, Tomasz
Injective Tauberian Operators on $L_1$ and Operators with Dense Range on $\ell_\infty$
There exist injective Tauberian operators on $L_1(0,1)$ that have dense, nonclosed range. This gives injective, nonsurjective operators on $\ell_\infty$ that have dense range. Consequently, there are two quasi-complementary, noncomplementary subspaces of $\ell_\infty$ that are isometric to $\ell_\infty$.

Keywords:$L_1$, Tauberian operator, $\ell_\infty$
Categories:46E30, 46B08, 47A53

66. CMB 2014 (vol 58 pp. 134)

Nasseh, Saeed
On the Generalized Auslander-Reiten Conjecture under Certain Ring Extensions
We show under some conditions that a Gorenstein ring $R$ satisfies the Generalized Auslander-Reiten Conjecture if and only if so does $R[x]$. When $R$ is a local ring we prove the same result for some localizations of $R[x]$.

Keywords:Auslander-Reiten conjecture, finitistic extension degree, Gorenstein rings
Categories:13D07, 16E30, 16E65

67. CMB 2014 (vol 58 pp. 150)

Ostrovskii, Mikhail I.
Connections Between Metric Characterizations of Superreflexivity and the Radon-Nikodý Property for Dual Banach Spaces
Johnson and Schechtman (2009) characterized superreflexivity in terms of finite diamond graphs. The present author characterized the Radon-Nikodým property (RNP) for dual spaces in terms of the infinite diamond. This paper is devoted to further study of relations between metric characterizations of superreflexivity and the RNP for dual spaces. The main result is that finite subsets of any set $M$ whose embeddability characterizes the RNP for dual spaces, characterize superreflexivity. It is also observed that the converse statement does not hold, and that $M=\ell_2$ is a counterexample.

Keywords:Banach space, diamond graph, finite representability, metric characterization, Radon-Nikodým property, superreflexivity
Categories:46B85, 46B07, 46B22

68. CMB 2014 (vol 58 pp. 115)

Mantilla-Soler, Guillermo
Weak Arithmetic Equivalence
Inspired by the invariant of a number field given by its zeta function, we define the notion of weak arithmetic equivalence and show that under certain ramification hypotheses, this equivalence determines the local root numbers of the number field. This is analogous to a result of Rohrlich on the local root numbers of a rational elliptic curve. Additionally, we prove that for tame non-totally real number fields, the integral trace form is invariant under arithmetic equivalence.

Keywords:arithmeticaly equivalent number fields, root numbers
Categories:11R04, 11R42

69. CMB 2014 (vol 58 pp. 188)

Wirths, Karl Joachim
Telescoping Estimates for Smooth Series
We derive telescoping majorants and minorants for some classes of series and give applications of these results.

Keywords:telescoping series, Stietjes constant, Hardy's formula, Stirling's formula
Categories:26D15, 40A25, 97I30

70. CMB 2014 (vol 58 pp. 158)

Özgür, Cihan; Mihai, Adela
Corrigendum to "Chen Inequalities for Submanifolds of Real Space Forms with a Semi-symmetric Non-metric Connection"
We fix the coefficients in the inequality (4.1) in the Theorem 4.1(i) from A. Mihai and C. Özgür, "Chen inequalities for submanifolds of real space forms with a semi-symmetric non-metric connection" Canad. Math. Bull. 55 (2012), no. 3, 611-622.

Keywords:real space form, semi-symmetric non-metric connection, Ricci curvature
Categories:53C40, 53B05, 53B15

71. CMB 2014 (vol 58 pp. 356)

Sebag, Julien
Homological Planes in the Grothendieck Ring of Varieties
In this note, we identify, in the Grothendieck group of complex varieties $K_0(\mathrm Var_\mathbf{C})$, the classes of $\mathbf{Q}$-homological planes. Precisely, we prove that a connected smooth affine complex algebraic surface $X$ is a $\mathbf{Q}$-homological plane if and only if $[X]=[\mathbf{A}^2_\mathbf{C}]$ in the ring $K_0(\mathrm Var_\mathbf{C})$ and $\mathrm{Pic}(X)_\mathbf{Q}:=\mathrm{Pic}(X)\otimes_\mathbf{Z}\mathbf{Q}=0$.

Keywords:motivic nearby cycles, motivic Milnor fiber, nearby motives
Categories:14E05, 14R10

72. CMB 2014 (vol 58 pp. 174)

Raffoul, Youssef N.
Periodic Solutions of Almost Linear Volterra Integro-dynamic Equation on Periodic Time Scales
Using Krasnoselskii's fixed point theorem, we deduce the existence of periodic solutions of nonlinear system of integro-dynamic equations on periodic time scales. These equations are studied under a set of assumptions on the functions involved in the equations. The equations will be called almost linear when these assumptions hold. The results of this papers are new for the continuous and discrete time scales.

Keywords:Volterra integro-dynamic equation, time scales, Krasnoselsii's fixed point theorem, periodic solution
Categories:45J05, 45D05

73. CMB 2014 (vol 58 pp. 160)

Pollack, Paul; Vandehey, Joseph
Some Normal Numbers Generated by Arithmetic Functions
Let $g \geq 2$. A real number is said to be $g$-normal if its base $g$ expansion contains every finite sequence of digits with the expected limiting frequency. Let $\phi$ denote Euler's totient function, let $\sigma$ be the sum-of-divisors function, and let $\lambda$ be Carmichael's lambda-function. We show that if $f$ is any function formed by composing $\phi$, $\sigma$, or $\lambda$, then the number \[ 0. f(1) f(2) f(3) \dots \] obtained by concatenating the base $g$ digits of successive $f$-values is $g$-normal. We also prove the same result if the inputs $1, 2, 3, \dots$ are replaced with the primes $2, 3, 5, \dots$. The proof is an adaptation of a method introduced by Copeland and Erdős in 1946 to prove the $10$-normality of $0.235711131719\ldots$.

Keywords:normal number, Euler function, sum-of-divisors function, Carmichael lambda-function, Champernowne's number
Categories:11K16, 11A63, 11N25, 11N37

74. CMB 2014 (vol 57 pp. 697)

Bailet, Pauline
On the Monodromy of Milnor Fibers of Hyperplane Arrangements
We describe a general setting where the monodromy action on the first cohomology group of the Milnor fiber of a hyperplane arrangement is the identity.

Keywords:hyperplane arrangements, Milnor fiber, monodromy, local systems
Categories:32S22, 32S55, 32S25, 32S40

75. CMB 2014 (vol 58 pp. 69)

Fulp, Ronald Owen
Correction to "Infinite Dimensional DeWitt Supergroups and Their Bodies"
The Theorem below is a correction to Theorem 3.5 in the article entitled " Infinite Dimensional DeWitt Supergroups and Their Bodies" published in Canad. Math. Bull. Vol. 57 (2) 2014 pp. 283-288. Only part (iii) of that Theorem requires correction. The proof of Theorem 3.5 in the original article failed to separate the proof of (ii) from the proof of (iii). The proof of (ii) is complete once it is established that $ad_a$ is quasi-nilpotent for each $a$ since it immediately follows that $K$ is quasi-nilpotent. The proof of (iii) is not complete in the original article. The revision appears as the proof of (iii) of the revised Theorem below.

Keywords:super groups, body of super groups, Banach Lie groups
Categories:58B25, 17B65, 81R10, 57P99
   1 2 3 4 ... 20    

© Canadian Mathematical Society, 2015 :