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51. 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 ringsCategories:13D07, 16E30, 16E65

52. 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 numbersCategories:11R04, 11R42

53. CMB 2014 (vol 58 pp. 150)

Ostrovskii, Mikhail I.
 Connections Between Metric Characterizations of Superreflexivity and the Radon-NikodÃ½ Property for Dual Banach Spaces Johnson and Schechtman (2009) characterized superreflexivity in terms of finite diamond graphs. The present author characterized the Radon-NikodÃ½m 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-NikodÃ½m property, superreflexivityCategories:46B85, 46B07, 46B22

54. 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

55. 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 formulaCategories:26D15, 40A25, 97I30

56. 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 motivesCategories:14E05, 14R10

57. CMB 2014 (vol 58 pp. 158)

 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. ÃzgÃ¼r, "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 curvatureCategories:53C40, 53B05, 53B15

58. 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 solutionCategories:45J05, 45D05

59. 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 ErdÅs 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 numberCategories:11K16, 11A63, 11N25, 11N37

60. 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 systemsCategories:32S22, 32S55, 32S25, 32S40

61. 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 groupsCategories:58B25, 17B65, 81R10, 57P99

62. CMB Online first

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 ringsCategories:13D07, 16E30, 16E65

63. CMB 2014 (vol 57 pp. 814)

Hou, Ruchen
 On Global Dimensions of Tree Type Finite Dimensional Algebras A formula is provided to explicitly describe global dimensions of all kinds of tree type finite dimensional $k-$algebras for $k$ an algebraic closed field. In particular, it is pointed out that if the underlying tree type quiver has $n$ vertices, then the maximum of possible global dimensions is $n-1$. Keywords:global dimension, tree type finite dimensional $k-$algebra, quiverCategories:16D40, 16E10, , 16G20

64. CMB Online first

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 ErdÅs 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 numberCategories:11K16, 11A63, 11N25, 11N37

65. CMB 2014 (vol 57 pp. 884)

Xu, Yong; Zhang, Xinjian
 $m$-embedded Subgroups and $p$-nilpotency of Finite Groups Let $A$ be a subgroup of a finite group $G$ and $\Sigma : G_0\leq G_1\leq\cdots \leq G_n$ some subgroup series of $G$. Suppose that for each pair $(K,H)$ such that $K$ is a maximal subgroup of $H$ and $G_{i-1}\leq K \lt H\leq G_i$, for some $i$, either $A\cap H = A\cap K$ or $AH = AK$. Then $A$ is said to be $\Sigma$-embedded in $G$; $A$ is said to be $m$-embedded in $G$ if $G$ has a subnormal subgroup $T$ and a $\{1\leq G\}$-embedded subgroup $C$ in $G$ such that $G = AT$ and $T\cap A\leq C\leq A$. In this article, some sufficient conditions for a finite group $G$ to be $p$-nilpotent are given whenever all subgroups with order $p^{k}$ of a Sylow $p$-subgroup of $G$ are $m$-embedded for a given positive integer $k$. Keywords:finite group, $p$-nilpotent group, $m$-embedded subgroupCategories:20D10, 20D15

66. CMB 2014 (vol 57 pp. 749)

Cavalieri, Renzo; Marcus, Steffen
 Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers We describe double Hurwitz numbers as intersection numbers on the moduli space of curves $\overline{\mathcal{M}}_{g,n}$. Using a result on the polynomiality of intersection numbers of psi classes with the Double Ramification Cycle, our formula explains the polynomiality in chambers of double Hurwitz numbers, and the wall crossing phenomenon in terms of a variation of correction terms to the $\psi$ classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle (which is only known in genera $0$ and $1$). Keywords:double Hurwitz numbers, wall crossings, moduli spaces, ELSV formulaCategory:14N35

67. CMB 2014 (vol 57 pp. 673)

 Complexifying Lie Group Actions on Homogeneous Manifolds of Non-compact Dimension Two If $X$ is a connected complex manifold with $d_X = 2$ that admits a (connected) Lie group $G$ acting transitively as a group of holomorphic transformations, then the action extends to an action of the complexification $\widehat{G}$ of $G$ on $X$ except when either the unit disk in the complex plane or a strictly pseudoconcave homogeneous complex manifold is the base or fiber of some homogeneous fibration of $X$. Keywords:homogeneous complex manifold, non-compact dimension two, complexificationCategory:32M10

68. CMB 2014 (vol 58 pp. 7)

Boulabiar, Karim
 Characters on $C(X)$ The precise condition on a completely regular space $X$ for every character on $C(X)$ to be an evaluation at some point in $X$ is that $X$ be realcompact. Usually, this classical result is obtained relying heavily on involved (and even nonconstructive) extension arguments. This note provides a direct proof that is accessible to a large audience. Keywords:characters, realcompact, evaluation, real-valued continuous functionsCategories:54C30, 46E25

69. CMB 2014 (vol 57 pp. 708)

Brannan, Michael
 Strong Asymptotic Freeness for Free Orthogonal Quantum Groups It is known that the normalized standard generators of the free orthogonal quantum group $O_N^+$ converge in distribution to a free semicircular system as $N \to \infty$. In this note, we substantially improve this convergence result by proving that, in addition to distributional convergence, the operator norm of any non-commutative polynomial in the normalized standard generators of $O_N^+$ converges as $N \to \infty$ to the operator norm of the corresponding non-commutative polynomial in a standard free semicircular system. Analogous strong convergence results are obtained for the generators of free unitary quantum groups. As applications of these results, we obtain a matrix-coefficient version of our strong convergence theorem, and we recover a well known $L^2$-$L^\infty$ norm equivalence for non-commutative polynomials in free semicircular systems. Keywords:quantum groups, free probability, asymptotic free independence, strong convergence, property of rapid decayCategories:46L54, 20G42, 46L65

70. CMB 2014 (vol 58 pp. 297)

Khamsi, M. A.
 Approximate Fixed Point Sequences of Nonlinear Semigroup in Metric Spaces In this paper, we investigate the common approximate fixed point sequences of nonexpansive semigroups of nonlinear mappings $\{T_t\}_{t \geq 0}$, i.e., a family such that $T_0(x)=x$, $T_{s+t}=T_s(T_t(x))$, where the domain is a metric space $(M,d)$. In particular we prove that under suitable conditions, the common approximate fixed point sequences set is the same as the common approximate fixed point sequences set of two mappings from the family. Then we use the Ishikawa iteration to construct a common approximate fixed point sequence of nonexpansive semigroups of nonlinear mappings. Keywords:approximate fixed point, fixed point, hyperbolic metric space, Ishikawa iterations, nonexpansive mapping, semigroup of mappings, uniformly convex hyperbolic spaceCategories:47H09, 46B20, 47H10, 47E10

71. CMB 2014 (vol 57 pp. 834)

Koh, Doowon
 Restriction Operators Acting on Radial Functions on Vector Spaces Over Finite Fields We study $L^p-L^r$ restriction estimates for algebraic varieties $V$ in the case when restriction operators act on radial functions in the finite field setting. We show that if the varieties $V$ lie in odd dimensional vector spaces over finite fields, then the conjectured restriction estimates are possible for all radial test functions. In addition, assuming that the varieties $V$ are defined in even dimensional spaces and have few intersection points with the sphere of zero radius, we also obtain the conjectured exponents for all radial test functions. Keywords:finite fields, radial functions, restriction operatorsCategories:42B05, 43A32, 43A15

72. CMB 2014 (vol 57 pp. 648)

Tang, Juping; Miao, Long
 On the ${\mathcal F}{\Phi}$-Hypercentre of Finite Groups Let $G$ be a finite group, $\mathcal F$ a class of groups. Then $Z_{{\mathcal F}{\Phi}}(G)$ is the ${\mathcal F}{\Phi}$-hypercentre of $G$ which is the product of all normal subgroups of $G$ whose non-Frattini $G$-chief factors are $\mathcal F$-central in $G$. A subgroup $H$ is called $\mathcal M$-supplemented in a finite group $G$, if there exists a subgroup $B$ of $G$ such that $G=HB$ and $H_1B$ is a proper subgroup of $G$ for any maximal subgroup $H_1$ of $H$. The main purpose of this paper is to prove: Let $E$ be a normal subgroup of a group $G$. Suppose that every noncyclic Sylow subgroup $P$ of $F^{*}(E)$ has a subgroup $D$ such that $1\lt |D|\lt |P|$ and every subgroup $H$ of $P$ with order $|H|=|D|$ is $\mathcal M$-supplemented in $G$, then $E\leq Z_{{\mathcal U}{\Phi}}(G)$. Keywords:${\mathcal F}{\Phi}$-hypercentre, Sylow subgroups, $\mathcal M$-supplemented subgroups, formationCategories:20D10, 20D20

73. CMB 2014 (vol 57 pp. 477)

Eghbali, Majid
 On Set Theoretically and Cohomologically Complete Intersection Ideals Let $(R,\mathfrak m)$ be a local ring and $\mathfrak a$ be an ideal of $R$. The inequalities $\operatorname{ht}(\mathfrak a) \leq \operatorname{cd}(\mathfrak a,R) \leq \operatorname{ara}(\mathfrak a) \leq l(\mathfrak a) \leq \mu(\mathfrak a)$ are known. It is an interesting and long-standing problem to find out the cases giving equality. Thanks to the formal grade we give conditions in which the above inequalities become equalities. Keywords:set-theoretically and cohomologically complete intersection ideals, analytic spread, monomials, formal grade, depth of powers of idealsCategories:13D45, 13C14

74. CMB 2014 (vol 57 pp. 579)

Larson, Paul; Tall, Franklin D.
 On the Hereditary Paracompactness of Locally Compact, Hereditarily Normal Spaces We establish that if it is consistent that there is a supercompact cardinal, then it is consistent that every locally compact, hereditarily normal space which does not include a perfect pre-image of $\omega_1$ is hereditarily paracompact. Keywords:locally compact, hereditarily normal, paracompact, Axiom R, PFA$^{++}$Categories:54D35, 54D15, 54D20, 54D45, 03E65, 03E35

75. CMB 2014 (vol 57 pp. 803)

Gabriyelyan, S. S.
 Free Locally Convex Spaces and the $k$-space Property Let $L(X)$ be the free locally convex space over a Tychonoff space $X$. Then $L(X)$ is a $k$-space if and only if $X$ is a countable discrete space. We prove also that $L(D)$ has uncountable tightness for every uncountable discrete space $D$. Keywords:free locally convex space, $k$-space, countable tightnessCategories:46A03, 54D50, 54A25
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