September 2013

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69 Reads

Published by Springer Nature

Online ISSN: 1735-8515

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Print ISSN: 1017-060X

September 2013

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69 Reads

In this notes we construct and count all ordinary irreducible characters of
Sylow $p$-subgroups of the Steinberg triality groups ${}^3D_4(p^{3m})$.

December 2010

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87 Reads

In this paper, we will study the topological centers of $n-th$ dual of Banach $A-module$ and we extend some propositions from Lau and \"{U}lger into $n-th$ dual of Banach $A-modules$ where $n\geq 0$ is even number. Let $B$ be a Banach $A-bimodule$. By using some new conditions, we show that ${{Z}^\ell}_{A^{(n)}}(B^{(n)})=B^{(n)}$ and ${{Z}^\ell}_{B^{(n)}}(A^{(n)})=A^{(n)}$. We also have some conclusions in group algebras.

June 2009

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57 Reads

The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter's conditions for such an action are discussed. Several applications to some specific actions related to certain representations and corepresentaions are presented. Comment: 13 pages, To appear in Bull. Iranian Math. Soc

April 2015

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109 Reads

Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^{*}$-algebras such that
$\mathcal{B}$ is prime. In this paper, we investigate the additivity of map
$\Phi$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective unital and
satisfies $$\Phi(AP+\eta PA^{*})=\Phi(A)\Phi(P)+\eta \Phi(P)\Phi(A)^{*},$$ for
all $A\in\mathcal{A}$ and $P\in\{P_{1},I_{\mathcal{A}}-P_{1}\}$ where $P_{1}$
is a nontrivial projection in $\mathcal{A}$. Let $\eta$ be a non-zero complex
number such that $|\eta|\neq1$, then $\Phi$ is additive. Moreover, if $\eta$ is
rational then $\Phi$ is $\ast$-additive.

April 2014

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27 Reads

Hyperplanes and hyperplane complements in the Segre product of partial linear
spaces are investigated . The parallelism of such a complement is characterized
in terms of the point-line incidence. Assumptions, under which the
automorphisms of the complement are the restrictions of the automorphisms of
the ambient space, are given. An affine covering for the Segre product of
Veblenian gamma spaces is established. A general construction that produces
non-degenerate hyperplanes in the Segre product of partial linear spaces
embeddable into projective space is introduced.

July 2016

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52 Reads

In this paper we study curvature properties of semi-symmetric type of totally
umbilical radical transversal lightlike hypersurfaces $(M,g)$ and
$(M,\widetilde g)$ of a K\"ahler-Norden manifold $(\overline M,\overline
J,\overline g,\overline { \widetilde g})$ of constant totally real sectional
curvatures $\overline \nu$ and $\overline {\widetilde \nu}$ ($g$ and
$\widetilde g$ are the induced metrics on $M$ by the Norden metrics $\overline
g$ and $\overline {\widetilde g}$, respectively). We obtain a condition for
$\overline {\widetilde \nu}$ (resp. $\overline \nu$) which is equivalent to
each of the following conditions: $(M,g)$ $(resp.\, (M,\widetilde g))$ is
locally symmetric, semi-symmetric, Ricci semi-symmetric and almost Einstein. We
construct an example of a totally umbilical radical transversal lightlike
hypersurface, which is locally symmetric, semi-symmetric, Ricci semi-symmetric
and almost Einstein.

January 2013

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346 Reads

Let $f: A\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of
$B$. In this paper, we investigate the transfert of the property of coherence
to the amalgamation $A\bowtie^{f}J$. We provide necessary and sufficient
conditions for $A\bowtie^{f}J$ to be a coherent ring.

February 2007

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133 Reads

In this paper, we provide a simple proof for the fact that two simplicial complexes are isomorphic if and only if their associated Stanley-Reisner rings, or their associated facet rings are isomorphic as $K$-algebras. As a consequence, we show that two graphs are isomorphic if and only if their associated edge rings are isomorphic as $K$-algebras. Based on an explicit $K$-algebra isomorphism of two Stanley-Reisner rings, or facet rings or edge rings, we present a fast algorithm to find explicitly the isomorphism of the associated simplicial complexes, or graphs.

March 2012

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71 Reads

June 2005

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266 Reads

Introducing the notions of (inner) $\sigma$-derivation, (inner) $\sigma$-endomorphism and one-parameter group of $\sigma$-endomorphisms ($\sigma$-dynamics) on a Banach algebra, we correspond to each $\sigma$-dynamics a $\sigma$-derivation named as its $\sigma$-infinitesimal generator. We show that the $\sigma$-infinitesimal generator of a $\sigma$-dynamics of inner $\sigma$-endomorphisms is an inner $\sigma$-derivation and deal with the converse. We also establish a nice generalized Leibniz formula and extend the Kleinenckr--Sirokov theorem for $\sigma$-derivations under certain conditions.

January 2013

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55 Reads

In the present paper, the concepts of module (uniform) approximate
amenability and contractibility of Banach algebras that are modules over
another Banach algebra, are introduced. The general theory is developed and
some hereditary properties are given. In analogy with the Banach algebraic
approximate amenability, it is shown that module approximate amenability and
contractibility are the same properties. It is also shown that module uniform
approximate (contractibility) amenability and module (contractibility,
respectively) amenability for commutative Banach modules are equivalent.
Applying these results to $\ell^1(S)$ as an $\ell^1(E)$-module, for an inverse
semigroup $S$ with the set of idempotents $E$, it is shown that $\ell^1(S)$ is
module approximately amenable (contractible) if and only if it is module
uniformly approximately amenable if and only if $S$ is amenable. Moreover,
$\ell^1(S)^{**}$ is module (uniformly) approximately amenable if and only if a
maximal group homomorphic image of $S$ is finite.

July 2013

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26 Reads

We study some properties of \(Z^{*}\) algebras, those \(C^{*}\) algebras whose all positive elements are zero divisors. Using an example, we show that an extension of a \(Z^{*}\) algebra by a \(Z^{*}\) algebra is not necessarily a \(Z^{*}\) algebra. However, we prove that the extension of a non-\(Z^{*}\) algebra by a non-\(Z^{*}\) algebra is a non-\(Z^{*}\) algebra. We also prove that the tensor product of a \(Z^{*}\) algebra by a \(C^{*}\) algebra is a \(Z^{*}\) algebra. As an indirect consequence of our methods, we prove the following inequality type results: (i) Let \(a_{n}\) be a sequence of positive elements of a \(C^{*}\) algebra A which converges to zero. Then, there are positive sequences \(b_{n}\) of real numbers and \(c_{n}\) of elements of A which converge to zero such that \(a_{n+k}\le b_{n}c_{k}.\) (ii) Every compact subset of the positive cones of a \(C^{*}\) algebra has an upper bound in the algebra.

November 2006

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69 Reads

We introduce two notions of amenability for a Banach algebra $\cal A$. Let $n\in \Bbb N$ and let $I$ be a closed two-sided ideal in $\cal A$, $\cal A$ is $n-I-$weakly amenable if the first cohomology group of $\cal A$ with coefficients in the n-th dual space $I^{(n)}$ is zero; i.e., $H^1({\cal A},I^{(n)})=\{0\}$. Further, $\cal A$ is n-ideally amenable if $\cal A$ is $n-I-$weakly amenable for every closed two-sided ideal $I$ in $\cal A$. We find some relationships of $n-I-$ weak amenability and $m-J-$ weak amenability for some different m and n or for different closed ideals $I$ and $J$ of $\cal A$.

April 2009

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145 Reads

In this work, we investigate the transfer of some homological properties from a ring $R$ to his amalgamated duplication along some ideal $I$ of $R$, and then generate new and original families of rings with these properties.

May 2013

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50 Reads

In this paper we discuss on the fixed points of asymptotic contractions and
Boyd-Wong type contractions in uniform spaces equipped with an E-distance. A
new version of Kirk's fixed point theorem is given for asymptotic contractions
and Boyd-Wong type contractions is investigated in uniform spaces.

February 2010

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21 Reads

We consider the semigroup S of highest weights appearing in tensor powers V^k
of a finite dimensional representation V of a connected reductive group. We
describe the cone generated by S as the cone over the weight polytope of V
intersected with the positive Weyl chamber. From this we get a description for
the asymptotic of the number of highest weights appearing in V^k in terms of
the volume of this polytope.

June 2012

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213 Reads

To demonstrate more visibly the close relation between the continuity and integrability, a new proof for the Banach-Zarecki theorem is presented on the basis of the Radon-Nikodym theorem which emphasizes on measure-type properties of the Lebesgue integral. The Banach-Zarecki theorem says that a real-valued function F is absolutely continuous on a finite closed interval if and only if it is continuous and of bounded variation when it satisfies Lusin's condition. In the present proof indeed a more general result is obtained for the Jordan decomposition of F.

September 2010

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247 Reads

In this paper we show that a simplicial complex can be determined uniquely up to isomorphism by its barycentric subdivision or comparability graph. At the end, it is summarized several algebraic, combinatorial and topological invariants of simplicial complexes.

June 2014

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43 Reads

In 2009 Lipman published his polished LNM book, the product of a decade's
work, giving the definitive, state-of-the-art treatment of Grothendieck
duality. In this article we achieve some sharp improvements: we begin by giving
a short, sweet, new proof of the base change theorem. As it happens our proof
delivers a stronger result than any of the old arguments, it allows us to
handle unbounded complexes. This means that our base-change theorem must be
subtle and delicate, it is right at the boundary of known counterexamples,
counterexamples that had led the experts to believe that major parts of the
theory could only be developed in the bounded-below derived category.
Having proved our new base-change theorem, we then use it to define the
functor $f^!$ on the unbounded derived category and establish its functoriality
properties. In Section 1 we will use this to clarify the relation among all the
various constructions of Grothendieck duality. One illustration of the power of
the new methods is that we can improve Lipman's Theorem 4.9.4 to handle
complexes that are not necessarily bounded. We also present applications to the
theory developed by Avramov, Iyengar, Lipman and Nayak on the connection
between Grothendieck duality and Hochschild homology and cohomology.

March 2009

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82 Reads

Recently the present authors introduced a general class of Finsler connections which leads to a smart representation of connection theory in Finsler geometry and yields to a classification of Finsler connections into the three classes. Here the properties of one of these classes namely the Berwald-type connections which contains Berwald and Chern(Rund) connections as a special case is studied. It is proved among the other that the hv-curvature of these connections vanishes if and only if the Finsler space is a Berwald one. Some applications of this connection is discussed.

October 2015

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123 Reads

Let $X$ be the Hankel matrix of size $2\times n$ and let $G$ be a closed
graph on the vertex set $[n].$ We study the binomial ideal $I_G\subset
K[x_1,\ldots,x_{n+1}]$ which is generated by all the $2$-minors of $X$ which
correspond to the edges of $G.$ We show that $I_G$ is Cohen-Macaulay. We find
the minimal primes of $I_G$ and show that $I_G$ is a set theoretical complete
intersection. Moreover, a sharp upper bound for the regularity of $I_G$ is
given.

February 2009

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182 Reads

In this paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, investigate some of their properties and show that a pairwise weakly Lindelof property is not a hereditary property.

October 2014

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25 Reads

For any $n$-by-$n$ matrix $A$ of the form \[[\begin{array}{cccc} 0 & A_1 & &
\\ & 0 & \ddots & \\ & & \ddots & A_{k-1} \\ & & & 0\end{array}],\] we consider
two $k$-by-$k$ matrices \[A'=[\begin{array}{cccc} 0 & \|A_1\| & & \\ & 0 &
\ddots & \\ & & \ddots & \|A_{k-1}\| \\ & & & 0\end{array}] \ {and} \
A''=[\begin{array}{cccc} 0 & m(A_1) & & \\ & 0 & \ddots & \\ & & \ddots &
m(A_{k-1}) \\ & & & 0\end{array}],\] where $\|\cdot\|$ and $m(\cdot)$ denote
the operator norm and minimum modulus of a matrix, respectively. It is shown
that the numerical radii $w(\cdot)$ of $A$, $A'$ and $A''$ are related by the
inequalities $w(A'')\le w(A)\le w(A')$. We also determine exactly when either
of the inequalities becomes an equality.

November 2010

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28 Reads

Let $G$ be a $p$-group of nilpotency class $k$ with finite exponent $\exp(G)$ and let $m=\lfloor\log_pk\rfloor$. We show that $\exp(M^{(c)}(G))$ divides $\exp(G)p^{m(k-1)}$, for all $c\geq1$, where $M^{(c)}(G)$ denotes the c-nilpotent multiplier of $G$. This implies that $\exp(M(G))$ divides $\exp(G)$ for all finite $p$-groups of class at most $p-1$. Moreover, we show that our result is an improvement of some previous bounds for the exponent of $M^{(c)}(G)$ given by M. R. Jones, G. Ellis and P. Moravec in some cases. Comment: 8 pages, to appear in Bulletin of the Iranian Mathematical Society

February 2011

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42 Reads

A proper vertex coloring of a simple graph is $k$-forested if the graph
induced by the vertices of any two color classes is a forest with maximum
degree less than $k$. A graph is $k$-forested $q$-choosable if for a given list
of $q$ colors associated with each vertex $v$, there exists a $k$-forested
coloring of $G$ such that each vertex receives a color from its own list. In
this paper, we prove that the $k$-forested choosability of a graph with maximum
degree $\Delta\geq k\geq 4$ is at most $\lceil\frac{\Delta}{k-1}\rceil+1$,
$\lceil\frac{\Delta}{k-1}\rceil+2$ or $\lceil\frac{\Delta}{k-1}\rceil+3$ if its
maximum average degree is less than 12/5, $8/3 or 3, respectively.