51. CMB 2014 (vol 58 pp. 134)
52. CMB 2014 (vol 58 pp. 115)
 MantillaSoler, 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
nontotally real number fields, the integral trace form is invariant
under arithmetic equivalence.
Keywords:arithmeticaly equivalent number fields, root numbers Categories:11R04, 11R42 

53. CMB 2014 (vol 58 pp. 150)
 Ostrovskii, Mikhail I.

Connections Between Metric Characterizations of Superreflexivity and the RadonNikodÃ½ Property for Dual Banach Spaces
Johnson and Schechtman (2009)
characterized superreflexivity in terms of finite diamond graphs.
The present author characterized the RadonNikodÃ½m 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, RadonNikodÃ½m property, superreflexivity Categories: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 quasicomplementary, 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)
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 motives Categories:14E05, 14R10 

57. CMB 2014 (vol 58 pp. 158)
58. CMB 2014 (vol 58 pp. 174)
 Raffoul, Youssef N.

Periodic Solutions of Almost Linear Volterra Integrodynamic Equation on Periodic Time Scales
Using Krasnoselskii's fixed point theorem, we deduce
the existence of periodic solutions of nonlinear system of integrodynamic
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 integrodynamic equation, time scales, Krasnoselsii's fixed point theorem, periodic solution Categories: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 sumofdivisors function, and let $\lambda$ be Carmichael's lambdafunction. 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 ErdÅs in 1946 to prove the $10$normality of $0.235711131719\ldots$.
Keywords:normal number, Euler function, sumofdivisors function, Carmichael lambdafunction, Champernowne's number Categories:11K16, 11A63, 11N25, 11N37 

60. CMB 2014 (vol 57 pp. 697)
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. 283288. 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 quasinilpotent for each $a$ since it immediately
follows that $K$
is quasinilpotent. 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 

62. CMB Online first
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 $n1$.
Keywords:global dimension, tree type finite dimensional $k$algebra, quiver Categories: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 sumofdivisors function, and let $\lambda$ be Carmichael's lambdafunction. 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 ErdÅs in 1946 to prove the $10$normality of $0.235711131719\ldots$.
Keywords:normal number, Euler function, sumofdivisors function, Carmichael lambdafunction, Champernowne's number Categories: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
$G_{i1}\leq K \lt H\leq G_i$, 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 subgroup Categories: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 formula Category:14N35 

67. CMB 2014 (vol 57 pp. 673)
 Ahmadi, S. Ruhallah; Gilligan, Bruce

Complexifying Lie Group Actions on Homogeneous Manifolds of Noncompact 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, noncompact dimension two, complexification Category: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, realvalued continuous functions Categories: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
noncommutative polynomial in the normalized standard generators of
$O_N^+$ converges as $N \to \infty$ to the operator norm of the
corresponding noncommutative 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 matrixcoefficient version of our strong
convergence theorem, and we recover a well known $L^2$$L^\infty$ norm
equivalence for noncommutative polynomials in free semicircular
systems.
Keywords:quantum groups, free probability, asymptotic free independence, strong convergence, property of rapid decay Categories: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 space Categories: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 $L^pL^r$ 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 operators Categories: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
nonFrattini $G$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, formation Categories: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 longstanding problem to find
out the cases giving equality. Thanks to the formal grade we give
conditions in which the above inequalities become
equalities.
Keywords:settheoretically and cohomologically complete intersection ideals, analytic spread, monomials, formal grade, depth of powers of ideals Categories: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
preimage 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 tightness Categories:46A03, 54D50, 54A25 
