2011
37
0
0
On the knullity foliations in Finsler geometry
2
2
Here, a Finsler manifold $(M,F)$ is considered with corresponding curvature tensor, regarded as $2$forms on the bundle of nonzero tangent vectors. Certain subspaces of the tangent spaces of $M$ determined by the curvature are introduced and called $k$nullity foliations of the curvature operator. It is shown that if the dimension of foliation is constant, then the distribution is involutive and each maximal integral manifold is totally geodesic. Characterization of the $k$nullity foliation is given, as well as some results concerning constancy of the flag curvature, and completeness of their integral manifolds, providing completeness of $(M,F)$. The introduced $k$nullity space is a natural extension of nullity space in Riemannian geometry, introduced by Chern and Kuiper and enlarged to Finsler setting by AkbarZadeh and contains it as a special case.
1

1
18


B.
Bidabad
Iran


M.
RafieRad
Iran
Foliation
knullity
Finsler manifolds
curvature operator
Ranks of modules relative to a torsion theory
2
2
Relative to a hereditary torsion theory $tau$ we introduce a dimension for a module $M$, called {em $tau$rank of} $M$, which coincides with the reduced rank of $M$ whenever $tau$ is the Goldie torsion theory. It is shown that the $tau$rank of $M$ is measured by the length of certain decompositions of the $tau$injective hull of $M$. Moreover, some relations between the $tau$rank of $M$ and complements to $tau$torsionfree submodules of $M$ are obtained.
1

19
33


Sh.
Asgari
Iran
sh_asgari@math.iut.ac.ir


A.
Haghany
Iran
aghagh@cc.iut.ac.ir
Hereditary torsion theory
pseudo $tau$essential
pseudo $tau$uniform
$tau$rank
pLambdabounded variation
2
2
A characteriation of continuity of the $p$$Lambda$variation function is given and the Helly's selection principle for $Lambda BV^{(p)}$ functions is established. A characterization of the inclusion of WatermanShiba classes into classes of functions with given integral modulus of continuity is given. A useful estimate on modulus of variation of functions of class $Lambda BV^{(p)}$ is found.
1

35
49


M.
Hormozi
Sweden
hormozi@chalmers.se


A.
Ledari
Iran
ahmadi@hamoon.usb.ac.ir


F.
PrusWisniowski
Iran
wisniows@univ.szczecin.pl
generalized bounded variation
Helly's theorem
modulus of variation
Classical quasiprimary submodules
2
2
In this paper we introduce the notion of classical quasiprimary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasiprimary submodules. In particular, existence and uniqueness of classical quasiprimary decompositions in finitely generated modules over Noetherian rings are proved. Moreover, we show that this decomposition and the decomposition into classical primary submodules are the same when $R$ is a domain with ${rm dim}(R)leq 1$.
1

51
71


M.
Behboodi
Iran
mbehbood@cc.iut.ac.ir


R.
JahaniNezhad
Iran
jahanian@kashanu.ac.ir


M.
Naderi
Iran
mhnaderi@qom.ac.ir
Primary
classical primary
Classical quasiprimary
decomposition
Proving the efficiency of pro2groups of fixed coclasses
2
2
Among the six classes of pro2groups of finite and fixed coclasses and trivial Schur Multiplicator which studied by Abdolzadeh and Eick in 2009, there are two classes $$S_5=langle a,bmid [b,a^2]=1, a^2=[b,a]^2, (b^2)^{[b,a]}b^2=1rangle$$ and $$S_6=langle a,t,bmid a^2=b^2,[b,a]^2=1, t^a=t^{1}[b,a], b^t=abarangle$$that have been conjectured to have deficiency zero presentations. In this paper we prove these conjectures. This completes the efficiency of all six classes of pro$2$groups of fixed coclasses.
1

73
80


A.
Arjomandfar
Iran
ab.arj44@gmail.com


H.
Doostie
Iran
doostih@saba.tmu.ac.ir
Pro2groups
modified ToddCoxeter algorithm
Generalized sigmaderivation on Banach algebras
2
2
Let $mathcal{A}$ be a Banach algebra and $mathcal{M}$ be a Banach $mathcal{A}$bimodule. We say that a linear mapping $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$derivation whenever there exists a $sigma$derivation $d:mathcal{A} rightarrow mathcal{M}$ such that $delta(ab) = delta(a)sigma(b) + sigma(a)d(b)$, for all $a,b in mathcal{A}$. Giving some facts concerning generalized $sigma$derivations, we prove that if $mathcal{A}$ is unital and if $delta:mathcal{A} rightarrow mathcal{A}$ is a generalized $sigma$derivation and there exists an element $a in mathcal{A}$ such that emph{d(a)} is invertible, then $delta$ is continuous if and only if emph{d} is continuous. We also show that if $mathcal{M}$ is unital, has no zero divisor and $delta:mathcal{A} rightarrow mathcal{M}$ is a generalized $sigma$derivation such that $d(textbf{1}) neq 0$, then $ker(delta)$ is a biideal of $mathcal{A}$ and $ker(delta) = ker(sigma) = ker(d)$, where textbf{1} denotes the unit element of $mathcal{A}$.
1

81
94


A.
Hosseini
Iran
A.hosseini@mshdiau.ac.ir


M.
Hassani
Iran
hassani@mshdiau.ac.ir


A.
Niknam
Iran
niknam@math.um.ac.ir
derivation
$sigma$derivation
$(sigma
d)$derivation
$sigma$algebraic map
Upper bounds on the solutions to n = p+m^2
2
2
ardy and Littlewood conjectured that every large integer $n$ that is not a square is the sum of a prime and a square. They believed that the number $mathcal{R}(n)$ of such representations for $n = p+m^2$ is asymptotically given by begin{equation*} mathcal{R}(n) sim frac{sqrt{n}}{log n}prod_{p=3}^{infty}left(1frac{1}{p1}left(frac{n}{p}right)right), end{equation*} where $p$ is a prime, $m$ is an integer, and $left(frac{n}{p}right)$ denotes the Legendre symbol. Unfortunately, as we will later point out, this conjecture is difficult to prove and not emph{all} integers that are nonsquares can be represented as the sum of a prime and a square. Instead in this paper we prove two upper bounds for $mathcal{R}(n)$ for $n le N$. The first upper bound applies to emph{all} $n le N$. The second upper bound depends on the possible existence of the Siegel zero, and assumes its existence, and applies to all $N/2 < n le N$ but at most $ll N^{1delta_1}$ of these integers, where $N$ is a sufficiently large positive integer and $0
1

95
108


A.
Nayebi
United States of America
aran.nayebi@gmail.com
Additive
Conjecture H
circle method
Connections between C(X) and C(Y), where Y is a subspace of X
2
2
In this paper, we introduce a method by which we can find a close connection between the set of prime $z$ideals of $C(X)$ and the same of $C(Y)$, for some special subset $Y$ of $X$. For instance, if $Y=Coz(f)$ for some $fin C(X)$, then there exists a onetoone correspondence between the set of prime $z$ideals of $C(Y)$ and the set of prime $z$ideals of $C(X)$ not containing $f$. Moreover, considering these relations, we obtain some new characterizations of classical concepts in the context of $C(X)$. For example, $X$ is an $F$space if and only if the extension $Phi : beta Yrightarrowbeta X$ of the identity map $imath: Yrightarrow X$ is onetoone, for each $z$embedded subspace $Y$ of $X$. Supposing $p$ is a nonisolated $G_delta$point in $X$ and $Y=Xsetminus{p}$, we prove that $M^p(X)$ contains no nontrivial maximal $z$ideal if and only if $pinbe X$ is a quasi $P$point if and only if each point of $beta Y setminus Y$ is a $P$point with respect to $Y$.
1

109
126


A.
Aliabad
Iran
aliabady r@scu.ac.ir


M.
Badie
Iran
badie@jsu.ac.ir
$z$filter
prime $z$ideal
prime $z^circ$ideal
$P$space
quasi $P$space
$F$space
$CC$space
$G_delta$point
Banach module valued separating maps and automatic continuity
2
2
For two algebras $A$ and $B$, a linear map $T:A longrightarrow B$ is called separating, if $xcdot y=0$ implies $Txcdot Ty=0$ for all $x,yin A$. The general form and the automatic continuity of separating maps between various Banach algebras have been studied extensively. In this paper, we first extend the notion of separating map for module case and then we give a description of a linear separating map $T:B longrightarrow X$, where $B$ is a unital commutative semisimple regular Banach algebra satisfying the Ditkin's condition and $X$ is a left Banach module over a unital commutative Banach algebra. We also show that if $X$ is hyper semisimple and $T$ is bijective, then $T$ is automatically continuous and $T^{1}$ is separating as well.
1

127
139


L.
Mousavi
Iran
l.mousavi@srbiau.ac.ir


F.
Sady
Iran
sady@modares.ac.ir
Banach algebras
Banach modules
separating maps
cozero set
point multiplier
Automatic continuity
Gframes and HilbertSchmidt operators
2
2
In this paper we introduce and study Besselian $g$frames. We show that the kernel of associated synthesis operator for a Besselian $g$frame is finite dimensional. We also introduce $alpha$dual of a $g$frame and we get some results when we use the HilbertSchmidt norm for the members of a $g$frame in a finite dimensional Hilbert space.
1

141
155


M.
Abdollahpour
Iran
mrabdollahpour@yahoo.com


A.
Najati
Iran
a.nejati@yahoo.com
frame
gframe
Besselian gframe
alphadual
HilbertSchmidt operator
Module cohomology group of inverse semigroup algebras
2
2
Let $S$ be an inverse semigroup and let $E$ be its subsemigroup of idempotents. In this paper we define the $n$th module cohomology group of Banach algebras and show that the first module cohomology group $HH^1_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is zero, for every odd $ninmathbb{N}$. Next, for a Clifford semigroup $S$ we show that $HH^2_{ell^1(E)}(ell^1(S),ell^1(S)^{(n)})$ is a Banach space, for every odd $ninmathbb{N}$.
1

157
169


E.
Nasrabadi
Iran
enasrabadi@birjand.ac.ir


A.
Pourabbas
Iran
arpabbas@aut.ac.ir
Module amenability
inverse semigroup algebra
module cohomology group
On module extension Banach algebras
2
2
Let $A$ be a Banach algebra and $X$ be a Banach $A$bimodule. Then ${mathcal{S}}=A oplus X$, the $l^1$direct sum of $A$ and $X$ becomes a module extension Banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ In this paper, we investigate biflatness and biprojectivity for these Banach algebras. We also discuss on automatic continuity of derivations on ${mathcal{S}}=Aoplus A$.
1

171
183


A.
Medghalchi
Iran
a_medghalchi@saba.tmu.ac.ir


H.
PourmahmoodAghababa
Iran
h_p_aghababa@tabrizu.ac.ir
Module extension Banach algebras
Biflatness
biprojectivity
Weak amenability
Automatic continuity
On the Ishikawa iteration process in CAT(0) spaces
2
2
In this paper, several $Delta$ and strong convergence theorems are established for the Ishikawa iterations for nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and improve the corresponding results
1

185
197


B.
Panyanak
Thailand
banchap@chiangmai.ac.th


T.
Laokul
Thailand
thanom kul@hotmail.com
nonexpansive mappings
Fixed points
$Delta$convergence
strong convergence
CAT(0) spaces
Onepoint extensions of locally compact paracompact spaces
2
2
A space $Y$ is called an {em extension} of a space $X$, if $Y$ contains $X$ as a dense subspace. Two extensions of $X$ are said to be {em equivalent}, if there is a homeomorphism between them which fixes $X$ pointwise. For two (equivalence classes of) extensions $Y$ and $Y'$ of $X$ let $Yleq Y'$, if there is a continuous function of $Y'$ into $Y$ which fixes $X$ pointwise. An extension $Y$ of $X$ is called a {em onepoint extension}, if $Yackslash X$ is a singleton. An extension $Y$ of $X$ is called {em firstcountable}, if $Y$ is firstcountable at points of $Yackslash X$. Let ${mathcal P}$ be a topological property. An extension $Y$ of $X$ is called a {em ${mathcal P}$extension}, if it has ${mathcal P}$. In this article, for a given locally compact paracompact space $X$, we consider the two classes of onepoint v{C}echcomplete; ${mathcal P}$extensions of $X$ and onepoint firstcountable locally${mathcal P}$ extensions of $X$, and we study their orderstructures, by relating them to the topology of a certain subspace of the outgrowth $eta Xackslash X$. Here ${mathcal P}$ is subject to some requirements and include $sigma$compactness and the Lindel"{o}f property as special cases.
1

199
228


M.
Koushesh
Iran
koushesh@cc.iut.ac.ir
Stonev{C}ech compactification, onepoint extension, onepoint compactification, locally compact, paracompact, v{C}ech complete
firstcountable
Best proximity pair and coincidence point theorems for nonexpansive setvalued maps in Hilbert spaces
2
2
This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the setvalued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: xy=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$
1

229
234


A.
AminiHarandi
Iran
aminih_a@yahoo.com
Best proximity pair
coincidence point
nonexpansive map
Hilbert space
On a conjecture of a bound for the exponent of the Schur multiplier of a finite $p$group
2
2
Let $G$ be a $p$group of nilpotency class $k$ with finite exponent $exp(G)$ and let $m=lfloorlog_pk floor$. We show that $exp(M^{(c)}(G))$ divides $exp(G)p^{m(k1)}$, for all $cgeq1$, where $M^{(c)}(G)$ denotes the cnilpotent multiplier of $G$. This implies that $exp( M(G))$ divides $exp(G)$, for all finite $p$groups of class at most $p1$. 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.
1

235
242


B.
Mashayekhy
Iran
bmashayekhyf@yahoo.com


A.
Hokmabadi
Iran
hokmabadiah@yahoo.com


F.
Mohammadzadeh
Iran
fa36407@yahoo.com
Schur multiplier
nilpotent multiplier
exponent
finite $p$groups
The unit sum number of discrete modules
2
2
In this paper, we show that every element of a discrete module is a sum of two units if and only if its endomorphism ring has no factor ring isomorphic to $Z_{2}$. We also characterize unit sum number equal to two for the endomorphism ring of quasidiscrete modules with finite exchange property.
1

243
249


N
Ashrafi
Iran
nashrafi@semnan.ac.ir


N.
Pouyan
Iran
neda.pouyan@gmail.com
unit sum number
discrete Module
hollow module
lifting property
On ncoherent rings, nhereditary rings and nregular rings
2
2
We observe some new characterizations of $n$presented modules. Using the concepts of $(n,0)$injectivity and $(n,0)$flatness of modules, we also present some characterizations of right $n$coherent rings, right $n$hereditary rings, and right $n$regular rings.
1

251
267


Z.
Zhu
China, R. O. C.
zhuzhanminzjxu@hotmail.com
(n
0)injective modules
0)flat modules
ncoherent rings
nhereditary rings nregular rings
Using KullbackLeibler distance for performance evaluation of search designs
2
2
This paper considers the search problem, introduced by Srivastava cite{Sr}. This is a model discrimination problem. In the context of search linear models, discrimination ability of search designs has been studied by several researchers. Some criteria have been developed to measure this capability, however, they are restricted in a sense of being able to work for searching only one possible nonzero effect. In this paper, two criteria are proposed, based on KullbackLeibler distance. These criteria are able to evaluate the search ability of designs, without any restriction on the number of nonzero effects.
1

269
279


H.
Talebi
Iran
htalebi@sci.ui.ac.ir


N.
Esmailzadeh
Iran
n.esmailzadeh@uok.ac.ir
Search designs
search linear model
KullbackLeibler distance
model discrimination