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3  A Short Proof of Paouris' Inequality Adamczak, Radosław; Latała, Rafał; Litvak, Alexander E.; Oleszkiewicz, Krzysztof; Pajor, Alain; TomczakJaegermann, Nicole
We give a short proof of a result of G.~Paouris on
the tail behaviour of the Euclidean norm $X$ of an isotropic
logconcave random vector $X\in\mathbb{R}^n,$
stating that for every $t\geq 1$,
\[\mathbb{P} \big( X\geq ct\sqrt n\big)\leq \exp(t\sqrt n).\]
More precisely we show that for any logconcave random vector $X$
and any $p\geq 1$,
\[(\mathbb{E}X^p)^{1/p}\sim \mathbb{E} X+\sup_{z\in
S^{n1}}(\mathbb{E} \langle
z,X\rangle^p)^{1/p}.\]


9  Integral Sets and the Center of a Finite Group Alperin, Roger C.; Peterson, Brian L.
We give a description of the atoms in the Boolean algebra generated by the integral subsets of a finite group.


12  On the Continuity of the Eigenvalues of a Sublaplacian Aribi, Amine; Dragomir, Sorin; El Soufi, Ahmad
We study the behavior of the eigenvalues of a sublaplacian $\Delta_b$ on a compact strictly pseudoconvex CR manifold $M$, as functions on the set
${\mathcal P}_+$ of positively oriented contact forms on $M$ by endowing ${\mathcal P}_+$ with a natural metric topology.


25  Subadditivity Inequalities for Compact Operators Bourin, JeanChristophe; Harada, Tetsuo; Lee, EunYoung
Some subadditivity inequalities for matrices and concave functions also hold for Hilbert space operators, but (unfortunately!) with an additional $\varepsilon$ term. It seems not possible to erase this residual term. However, in case of compact operators we show that the $\varepsilon$ term is unnecessary. Further, these inequalities are strict in a certain sense when some natural assumptions are satisfied. The discussion also stresses on matrices and their compressions and several open questions or conjectures are considered, both in the matrix and operator settings.


37  Character Amenability of Lipschitz Algebras Dashti, Mahshid; NasrIsfahani, Rasoul; Renani, Sima Soltani
Let ${\mathcal X}$ be a locally compact metric space and let
${\mathcal A}$ be any of the Lipschitz algebras
${\operatorname{Lip}_{\alpha}{\mathcal X}}$, ${\operatorname{lip}_{\alpha}{\mathcal X}}$ or
${\operatorname{lip}_{\alpha}^0{\mathcal X}}$. In this paper, we show, as a
consequence of rather more general results on Banach algebras,
that ${\mathcal A}$ is $C$character amenable if and only if
${\mathcal X}$ is uniformly discrete.


42  Covering the Unit Sphere of Certain Banach Spaces by Sequences of Slices and Balls Fonf, Vladimir P.; Zanco, Clemente
e prove that, given any covering of any infinitedimensional Hilbert space $H$ by countably many closed balls, some point exists in $H$ which belongs to infinitely many balls. We do that by characterizing isomorphically polyhedral separable Banach spaces as those whose unit sphere admits a pointfinite covering by the union of countably many slices of the unit ball.


51  Jordan $*$Derivations of FiniteDimensional Semiprime Algebras Fošner, Ajda; Lee, TsiuKwen
In the paper, we characterize Jordan $*$derivations of a $2$torsion
free, finitedimensional semiprime algebra $R$ with involution $*$. To
be precise, we prove the theorem: Let $deltacolon R o R$ be a Jordan
$*$derivation. Then there exists a $*$algebra decomposition
$R=Uoplus V$ such that both $U$ and $V$ are invariant under
$delta$. Moreover, $*$ is the identity map of $U$ and $delta,_U$ is a
derivation, and the Jordan $*$derivation $delta,_V$ is inner.
We also prove the theorem: Let $R$ be a noncommutative, centrally
closed prime algebra with involution $*$, $operatorname{char},R
e 2$,
and let $delta$ be a nonzero Jordan $*$derivation of $R$. If $delta$ is
an elementary operator of $R$, then $operatorname{dim}_CRlt infty$ and
$delta$ is inner.


61  2dimensional Convexity Numbers and $P_4$free Graphs Geschke, Stefan
For $S\subseteq\mathbb R^n$ a set
$C\subseteq S$ is an $m$clique if the convex hull of no $m$element subset of
$C$ is contained in $S$.
We show that there is essentially just one way to construct
a closed set $S\subseteq\mathbb R^2$ without an uncountable
$3$clique that is not the union of countably many convex sets.
In particular, all such sets have the same convexity number;
that is, they
require the same number of convex subsets to cover them.
The main result follows from an analysis of the convex structure of closed
sets in $\mathbb R^2$ without uncountable 3cliques in terms of
clopen, $P_4$free graphs on Polish spaces.


72  Un Anneau Commutatif associé à un design symétrique Grari, A.
Dans les articles \cite{1}, \cite{2} et \cite{3}; l'auteur développe une représentation
d'un plan projectif fini par un
anneau commutatif unitaire dont les propriétés algébriques dépendent
de la structure géométrique du plan. Dans l'article \cite{4}; il étend cette représentation aux designs symétriques. Cependant l'auteur de l'article \cite{7} fait remarquer que la multiplication définie dans ce cas ne peut être associative que si le design est un plan projectif.
Dans ce papier on mènera
une étude de cette représentation dans le cas des designs
symétriques. On y montrera comment on peut faire associer un
anneau commutatif unitaire à
tout design symétrique , on y précisera certaines de ses propriétés, en
particulier, celles qui relèvent de son invariance. On caractérisera aussi les géométries projectives finies de dimension supérieure moyennant cette représentation.


80  Semicrossed Products of the Disk Algebra and the Jacobson Radical Khemphet, Anchalee; Peters, Justin R.
We consider semicrossed products of the disk algebra with respect to
endomorphisms defined by finite Blaschke products. We characterize the Jacobson radical
of these operator algebras. Furthermore, in the case the finite Blaschke product is elliptic,
we show that the semicrossed product contains no nonzero quasinilpotent
elements. However, if the finite Blaschke product is hyperbolic or parabolic with positive hyperbolic step,
the Jacobson radical is nonzero and a proper subset of the set of quasinilpotent elements.


90  Compact Subsets of the Glimm Space of a $C^*$algebra Lazar, Aldo J.
If $A$ is a $\sigma$unital $C^*$algebra and $a$ is a strictly positive element of $A$ then for every compact subset $K$ of the complete
regularization $\mathrm{Glimm}(A)$ of $\mathrm{Prim}(A)$ there exists
$\alpha \gt 0$ such that $K\subset \{G\in \mathrm{Glimm}(A) \mid \Vert a + G\Vert \geq
\alpha\}$. This extends
a result of J. Dauns
to all $\sigma$unital $C^*$algebras. However, there are a $C^*$algebra $A$
and a compact subset of $\mathrm{Glimm}(A)$ that is not contained in any set of the form $\{G\in \mathrm{Glimm}(A) \mid \Vert a + G\Vert \geq
\alpha\}$, $a\in A$ and $\alpha \gt 0$.


97  Rationality and the JordanGattiViniberghi decomposition Levy, Jason
We verify
our earlier conjecture
and use it to prove that the
semisimple parts of the rational JordanKacVinberg decompositions of
a rational vector all lie in a single rational orbit.


105  On the Counting Function of Elliptic Carmichael Numbers Luca, Florian; Shparlinski, Igor E.
We give an upper bound for the number elliptic Carmichael numbers $n \le x$
that have recently been introduced by J. H. Silverman in the case of an elliptic curve without complex multiplication (non CM). We also discuss
several possible ways for further improvements.


113  A Lower Bound for the EndtoEnd Distance of SelfAvoiding Walk Madras, Neal
For an $N$step selfavoiding walk on the hypercubic lattice ${\bf Z}^d$,
we prove that the meansquare endtoend distance is at least
$N^{4/(3d)}$ times a constant.
This implies that the associated critical exponent $\nu$ is
at least $2/(3d)$, assuming that $\nu$ exists.


119  Splitting Families and Complete Separability Mildenberger, Heike; Raghavan, Dilip; Steprans, Juris
We answer a question from Raghavan and Steprāns
by showing that $\mathfrak{s} = {\mathfrak{s}}_{\omega, \omega}$. Then we use this to construct a completely separable maximal almost disjoint family under $\mathfrak{s} \leq \mathfrak{a}$, partially answering a question of Shelah.


125  Camina Triples Mlaiki, Nabil M.
In this paper, we study Camina triples. Camina triples are a
generalization of Camina pairs. Camina pairs were first introduced
in 1978 by A .R. Camina.
Camina's work
was inspired by the study of Frobenius groups. We
show that if $(G,N,M)$ is a Camina triple, then either $G/N$ is a
$p$group, or $M$ is abelian, or $M$ has a nontrivial nilpotent or
Frobenius quotient.


132  Twisted Conjugacy Classes in Abelian Extensions of Certain Linear Groups Mubeena, T.; Sankaran, P.
Given a group automorphism $\phi:\Gamma\longrightarrow \Gamma$, one has
an action of $\Gamma$ on itself by $\phi$twisted conjugacy, namely, $g.x=gx\phi(g^{1})$.
The orbits of this action are called $\phi$twisted conjugacy classes. One says
that $\Gamma$ has the $R_\infty$property if there are infinitely many $\phi$twisted conjugacy
classes for every automorphism $\phi$ of $\Gamma$. In this paper we
show that $\operatorname{SL}(n,\mathbb{Z})$ and its
congruence subgroups have the $R_\infty$property. Further we show that
any (countable) abelian extension of $\Gamma$ has the $R_\infty$property where $\Gamma$ is a torsion
free nonelementary hyperbolic group, or $\operatorname{SL}(n,\mathbb{Z}),
\operatorname{Sp}(2n,\mathbb{Z})$ or a principal congruence
subgroup of $\operatorname{SL}(n,\mathbb{Z})$ or the fundamental group of a complete Riemannian
manifold of constant negative curvature.


141  Size, Order, and Connected Domination Mukwembi, Simon
We give a sharp upper bound on the size of a
trianglefree graph of a given order and connected domination. Our
bound, apart from
strengthening an old classical theorem of Mantel and of
Turán , improves on a theorem of Sanchis.
Further, as corollaries, we settle a long standing
conjecture of Graffiti on the leaf number and local independence for
trianglefree graphs and answer a question of Griggs, Kleitman and
Shastri on a lower bound of the leaf number in
trianglefree graphs.


145  The Essential Spectrum of the Essentially Isometric Operator Mustafayev, H. S.
Let $T$ be a contraction on a complex, separable, infinite dimensional
Hilbert space and let $\sigma \left( T\right) $ (resp. $\sigma _{e}\left(
T\right) )$ be its spectrum (resp. essential spectrum). We assume that $T$
is an essentially isometric operator, that is $I_{H}T^{\ast }T$ is compact.
We show that if $D\diagdown \sigma \left( T\right) \neq \emptyset ,$ then
for every $f$ from the discalgebra,
\begin{equation*}
\sigma _{e}\left( f\left( T\right) \right) =f\left( \sigma _{e}\left(
T\right) \right) ,
\end{equation*}
where $D$ is the open unit disc. In addition, if $T$ lies in the class
$ C_{0\cdot }\cup C_{\cdot 0},$ then
\begin{equation*}
\sigma _{e}\left( f\left( T\right) \right) =f\left( \sigma \left( T\right)
\cap \Gamma \right) ,
\end{equation*}
where $\Gamma $ is the unit circle. Some related problems are also discussed.


159  Strongly $0$dimensional Modules Oral, Kürşat Hakan; Özkirişci, Neslihan Ayşen; Tekir, Ünsal
In a multiplication module, prime submodules have the property, if a prime
submodule contains a finite intersection of submodules then one of the
submodules is contained in the prime submodule. In this paper, we generalize
this property to infinite intersection of submodules and call such prime
submodules strongly prime submodule. A multiplication module in which every
prime submodule is strongly prime will be called strongly 0dimensional
module. It is also an extension of strongly 0dimensional rings. After
this we investigate properties of strongly 0dimensional modules and give
relations of von Neumann regular modules, Qmodules and strongly
0dimensional modules.


166  On Minimal and Maximal $p$operator Space Structures Öztop, Serap; Spronk, Nico
We show that for $p$operator spaces, there are natural notions of minimal and maximal
structures. These are useful for dealing with tensor products.


178  Quasiconvexity and Density Topology Rabier, Patrick J.
We prove that if $f:\mathbb{R}^{N}\rightarrow \overline{\mathbb{R}}$ is
quasiconvex and $U\subset \mathbb{R}^{N}$ is open in the density topology, then
$\sup_{U}f=\operatorname{ess\,sup}_{U}f,$ while
$\inf_{U}f=\operatorname{ess\,inf}_{U}f$
if and only if the equality holds when $U=\mathbb{R}^{N}.$ The first (second)
property is typical of lsc (usc) functions and, even when $U$ is an ordinary
open subset, there seems to be no record that they both hold for all
quasiconvex functions.


188  A Characterization of Bipartite Zerodivisor Graphs Rad, Nader Jafari; Jafari, Sayyed Heidar
In this paper we obtain a characterization for all bipartite
zerodivisor graphs of commutative rings $R$ with $1$, such that
$R$ is finite or $Nil(R)\neq2$.


194  A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold Zhao, Wei
In this paper, we obtain a lower bound for the length of closed geodesics on an arbitrary closed Finsler manifold.


209  Erratum to the Paper "A Lower Bound for the Length of Closed Geodesics on a Finsler Manifold" Zhao, Wei
We correct two clerical errors made in the paper "A Lower Bound for
the Length of Closed Geodesics on a Finsler Manifold".


210  An Explicit Formula for the Generalized Cyclic Shuffle Map Zhang, Jiao; Wang, QingWen
We provide an explicit formula for the generalized cyclic shuffle map for cylindrical modules.
Using this formula we give a combinatorial proof of the generalized
cyclic EilenbergZilber theorem.

