26. 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 

27. CMB Online first
 Chen, Guiyun; Li, Lili

Minimal NonSelf Dual Groups
A group $G$ is self dual if every
subgroup
of $G$ is isomorphic to a quotient of $G$ and every quotient
of $G$ is isomorphic to
a subgroup of $G$. It is minimal nonself dual if every
proper subgroup of $G$
is self dual but $G$ is not self dual. In this paper, the structure
of minimal nonself dual groups is determined.
Keywords:minimal nonself dual group, finite group, metacyclic group, metabelian group Category:20D15 

28. CMB Online first
 Kong, Qingjun; Guo, Xiuyun

On $s$semipermutable or $s$quasinormally embedded subgroups of finite groups
Suppose that $G$ is a
finite group and $H$ is a subgroup of $G$. $H$ is said to be
$s$semipermutable in $G$ if $HG_{p}=G_{p}H$ for any Sylow
$p$subgroup $G_{p}$ of $G$ with $(p,H)=1$; $H$ is said to be
$s$quasinormally embedded in $G$ if for each prime $p$ dividing the
order of $H$, a Sylow $p$subgroup of $H$ is also a Sylow
$p$subgroup of some $s$quasinormal subgroup of $G$. We fix in
every noncyclic Sylow subgroup $P$ of $G$ some subgroup $D$
satisfying $1\lt D\lt P$ and study the structure of $G$ under the
assumption that every subgroup $H$ of $P$ with $H=D$ is either
$s$semipermutable or $s$quasinormally embedded in $G$.
Some recent results are generalized and unified.
Keywords:$s$semipermutable subgroup, $s$quasinormally embedded subgroup, saturated formation. Categories:20D10, 20D20 

29. 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 FukukawaHaradaMasuda,
which was only for Lie type $A$.
Keywords:equivariant cohomology, Peterson varieties, flag varieties, Monk formula, Giambelli formula Categories:55N91, 14N15 

30. CMB Online first
 Li, Benling; Shen, Zhongmin

Ricci Curvature Tensor and NonRiemannian Quantities
There are several notions of Ricci curvature tensor
in Finsler geometry and spray geometry. One of them is defined by the
Hessian of the wellknown Ricci curvature.
In this paper we will introduce a new notion of Ricci curvature
tensor and discuss its relationship with the Ricci curvature and some
nonRiemannian quantities. By this Ricci curvature tensor, we shall
have a better understanding on these nonRiemannian quantities.
Keywords:Finsler metrics, sprays, Ricci curvature, nonRiemanian quantity Categories:53B40, 53C60 

31. CMB Online first
 Boynton, Jason Greene; Coykendall, Jim

On the Graph of Divisibility of an Integral Domain
It is well known that the factorization properties of a domain are reflected
in the structure of its group of divisibility. The main theme of this paper
is to introduce a topological/graphtheoretic point of view to the current
understanding of factorization in integral domains. We also show that
connectedness properties in the graph and topological space give rise to a
generalization of atomicity.
Keywords:atomic, factorization, divisibility Categories:13F15, 13A05 

32. CMB Online first
 MartinezMaure, Yves

Plane Lorentzian and Fuchsian Hedgehogs
Parts of the BrunnMinkowski 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 LorentzMinkowski 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 

33. CMB 2014 (vol 58 pp. 432)
 Yang, Dachun; Yang, Sibei

Secondorder Riesz Transforms and Maximal Inequalities Associated with Magnetic SchrÃ¶dinger Operators
Let $A:=(\nablai\vec{a})\cdot(\nablai\vec{a})+V$ be a
magnetic SchrÃ¶dinger 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
HÃ¶lder 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
secondorder Riesz transforms $VA^{1}$ and
$(\nablai\vec{a})^2A^{1}$ are bounded from the
MusielakOrliczHardy space $H_{\varphi,\,A}(\mathbb{R}^n)$, associated with $A$,
to the MusielakOrlicz 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:MusielakOrliczHardy space, magnetic SchrÃ¶dinger operator, atom, secondorder Riesz transform, maximal inequality Categories:42B30, 42B35, 42B25, 35J10, 42B37, 46E30 

34. CMB 2014 (vol 58 pp. 51)
 De Nitties, Giuseppe; SchulzBaldes, 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 

35. CMB 2014 (vol 58 pp. 182)
36. CMB 2014 (vol 58 pp. 196)
37. 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 

38. CMB 2014 (vol 58 pp. 134)
39. 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 

40. 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 

41. CMB 2014 (vol 58 pp. 188)
42. CMB 2014 (vol 58 pp. 158)
43. 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 

44. 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 

45. 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 

46. CMB 2014 (vol 57 pp. 697)
47. 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 

48. CMB Online first
49. 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 

50. 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 
