2011
37
0
304
A characterization of shellable and sequentially CohenMacaulay
2
2
We consider a class of hypergraphs called
hypercycles and we show that a hypercycle $C_n^{d,alpha}$ is
shellable or sequentially the CohenMacaulay if and only if
$nin{3,5}$. Also, we characterize CohenMacaulay hypercycles.
These results are hypergraph versions of results proved for cycles
in graphs.
3

1
9


S.
Moradi
Amirkabir University of Technology
Amirkabir University of Technology
Iran
smoradi@araku.ac.ir


D.
Kiani
Amirkabir University of Technology
Amirkabir University of Technology
Iran
dkiani@aut.ac.ir
Edge ideals
shellable complex
sequentially CohenMacaulay ring
Nonlinear ergodic theorems in complete nonpositive curvature metric spaces
2
2
Hadamard (or complete $CAT(0)$) spaces are complete, nonpositive curvature, metric spaces. Here,
we prove a nonlinear ergodic theorem for continuous nonexpansive semigroup in these spaces as well as a strong convergence theorem for
the commutative case. Our results extend the standard nonlinear
ergodic theorems for nonexpansive maps on real Hilbert spaces,
to nonexpansive maps on Hadamard spaces, which include for example (possibly infinitedimensional) complete simply
connected Riemannian manifolds with nonpositive sectional
curvature.
3

11
20


B.
Ahmadi Kakavandi
Tarbiat Modares University
Tarbiat Modares University
Iran


M.
Amini
Tarbiat Modares University
Tarbiat Modares University
Iran
mamini48@yahoo.com
Hadamard Space
continuous nonexpansive semigroup
invariant mean
asymptotic center
nonlinear ergodic theorem
A characterization of Ldual frames and Ldual Riesz bases
2
2
This paper is an investigation of $L$dual frames with respect
to a functionvalued inner product, the so called $L$bracket
product on $L^{2}(G)$, where G is a locally compact abelian group
with a uniform lattice $L$. We show that several well known theorems
for dual frames and dual Riesz bases in a Hilbert space
remain valid for $L$dual frames and $L$dual Riesz bases in $L^{2}(G)$.
3

21
32


A.
Ahmadi
Iran


A.
Askari Hemmat
Iran
HyersUlamRassias stability
generalized derivation
bounded central approximate identity
faithful Banach algebra
On rainbow 4term arithmetic progressions
2
2
{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow
AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose
elements have different colors. Conlon, Jungi'{c} and
Radoiv{c}i'{c} cite{conlon} prove that there exists an
equinumerous 4coloring of $[4n]$ which is rainbow AP(4) free,
when $n$ is even. Based on their construction, we show that such
a coloring of $[4n]$
also exists for odd $n>1$.
We conclude that for nonnegative integers $kgeq 3$
and $n > 1$, every equinumerous $k$coloring of $[kn]$ contains a
rainbow AP$(k)$ if and only if $k=3$.}
3

33
37


M. H.
Shirdareh Haghighi
Iran


P.
Salehi Nowbandegani
Iran
Rainbow arithmetic progression
4term arithmetic progression
AP(4)
AP($k$)
Second symmetric powers of chain complexes
2
2
We investigate Buchbaum and Eisenbud's construction of the second
symmetric power $s_R(X)$ of a chain complex $X$ of modules over
a commutative ring $R$. We state and prove a number of results
from the folklore of the subject for which we know of no good
direct references. We also provide several explicit computations
and examples. We use this construction to prove the following
version of a result of Avramov, Buchweitz, and c{S}ega: let
$Rto S$ be a modulefinite ring homomorphism such that $R$ is
noetherian and local, and such that 2 is a unit in $R$. Let $X$
be a complex of finite rank free $S$modules such that $X_n=0$
for each $n<0$. If
$cup_nass_R(HH_n(Xotimes_SX))subseteqass(R)$ and if
$X_{p}simeq S_{p}$ for each $pinass(R)$, then $Xsimeq S$.
3

39
75


A.
Frankild
United States of America


S.
SatherWagstaff
United States of America


A.
Taylor
United States of America
Chain complex
symmetric power
symmetric square
General HardyType Inequalities with Nonconjugate Exponents
2
2
We derive whole series of new integral
inequalities of the Hardytype, with nonconjugate exponents.
First, we prove and discuss two equivalent general
inequalities of such type, as well as their corresponding
reverse inequalities. General results are then applied to special
Hardytype kernel and power weights. Also, some estimates of
weight functions and constant factors are obtained. In
particular, we obtain generalizations and improvements of some
recent results, in the literature.
3

77
108


A.
Cizmesija
Croatia


M.
Krnic
Croatia


J.
Pecaric
Croatia
Hardy inequality
Hilbert inequality
Hardytype kernel
Hardytype inequality
Hilberttype inequality
Some Optimal Codes From Designs
2
2
The binary and ternary codes spanned by the rows of the point by
block incidence matrices of some 2designs and their
complementary
and orthogonal designs are studied. A new method is also introduced to study optimal codes.
3

109
115


M.
Emami
Iran


Ch.
Maysoori
Iran
Optimal code
tdesign
Extension functors of local cohomology modules
2
2
Let $R$ be a commutative Noetherian ring with nonzero identity,
$fa$ an ideal of $R$, and $X$ an $R$module. Here, for fixed
integers $s, t$ and a finite $fa$torsion $R$module $N$, we
first study the membership of $Ext^{s+t}_{R}(N, X)$ and
$Ext^{s}_{R}(N, H^{t}_{fa}(X))$ in the Serre subcategories of
the category of $R$modules. Then, we present some conditions
which ensure the existence of an isomorphism between them.
Finally, we introduce the concept of the Serre cofiniteness as a
generalization of cofiniteness and study this property for
certain local cohomology modules.
3

117
134


M.
Aghapournahr
Iran


A.
Taherizadeh
Iran


A.
Vahidi
Iran
Local cohomology modules
Serre subcategories
cofinite modules
Convergence of product integration method applied for numerical
solution of linear weakly singular Volterra
systems
2
2
We develop and apply the product integration method to a large class of linear weakly singular Volterra
systems. We show that under certain sufficient conditions this
method converges. Numerical implementation of the method is
illustrated by a benchmark problem originated from heat
conduction.
3

135
148


B.
BabayarRazlighi
Iran
Babayar@tabrizu.ac.ir


K.
Ivaz
Iran


M.
Mokhtarzadeh
Iran
Product integration technique
system of singular Volterra integral equations
heat equation
On Semiartinian Weakly Cosemisimple Modules
2
2
We show that every semiartinian module which is contained in a
direct sum of
finitely presented modules in $si[M]$, is weakly cosemisimple if and only if it is regular in $si[M]$.
As a consequence, we observe that every
semiartinian ring is regular in the sense of von Neumann if
and only if its simple modules are $FP$injective.
3

149
157


E.
Momtahan
Iran
Semiartinian module
weakly cosemisimple module
Various topological forms of Von Neumann regularity in Banach algebras
2
2
We study topological von Neumann regularity
and principal von Neumann regularity of Banach algebras. Our
main objective is comparing these two types of Banach algebras and
some other known Banach algebras with one another. In particular,
we show that the class of topologically von Neumann regular Banach
algebras contains all $C^*$algebras, group algebras of compact
abelian groups and certain weakly amenable Banach algebras while
it excludes measure algebras, of certain locally compact Abelian
groups. Moreover, we show that in a unital amenable Banach
algebra, principal regularity implies topological regularity.
Finally, we use topological regularity to obtain some information
about hereditary $C^*$subalgebras of a given $C^*$algebra.
3

159
170


G.
Esslamzadeh
Iran


M.
Shadab
Iran
Topologically von Neumann regular
principally von Neumann regular
Insertion of a gammacontinuous function
2
2
A necessary and sufficient condition in terms of lower cut sets
are given for the insertion of a $gamma$continuous function
between two comparable realvalued functions.
3

171
181


M.
Mirmiran
Iran
Insertion
strong binary relation
preopen set
semiopen set
$gamma$open set
lower cut set
Monomial Irreducible slnModules
2
2
In this article, we introduce monomial irreducible representations of the special linear Lie
algebra $sln$. We will show that this kind of representations have bases for
which the action of the Chevalley generators of the Lie algebra on the basis elements
can be given by a simple formula.
3

183
195


M.
Shahryari
Iran
symmetric group
character theory
representations of Lie algebras
symmetry classes of tensors
Permanence and global asymptotic stability of a delayed
predatorprey model with HassellVarley type functional response
2
2
Here, a predatorprey model with HassellVarley type functional
responses is studied. Some sufficient conditions are obtained
for the permanence and global asymptotic stability of the
system by using comparison theorem and constructing a suitable
Lyapunov functional. Moreover, an example is illustrated to
verify the results by simulation.
3

197
215


K.
Wang
China, R. O. C.


Y.
Zhu
China, R. O. C.
Permanence
asymptotic stability
comparison theorem
Lyapunov functional
Semistar dimension of polynomial rings and Pruferlike
domains
2
2
Let $D$ be an integral domain and $star$ a semistar operation stable and of finite type on
it. We define the semistar dimension (inequality) formula and
discover their relations with $star$universally catenarian
domains and $star$stably strong Sdomains. As an application, we
give new characterizations of $star$quasiPr"{u}fer domains
and UM$t$ domains in terms of dimension inequality formula (and
the notions of universally catenarian domain, stably strong
Sdomain, strong Sdomain, and Jaffard domain). We also extend
Arnold's formula to the setting of semistar operations.
3

217
233


P.
Sahandi
Iran
Semistar operation
Krull dimension
strong Sdomain
Jaffard domain
quasiPr"{u}fer domain
UM$t$ domain
A Sharp Maximal Function Estimate for VectorValued Multilinear
Singular Integral Operator
2
2
We establish a sharp maximal function estimate for some vectorvalued multilinear singular integral operators.
As an application, we obtain the $(L^p, L^q)$norm inequality for vectorvalued multilinear operators.
3

235
248


Zhou
Xiaosha
China, R. O. C.


Liu
Lanzhe
China, R. O. C.
lanzheliu@163.com
Vectorvalued multilinear operator
singular integral operator
sharp maximal function estimate
BMO
Symmetric curvature tensor
2
2
Recently, we have used the symmetric bracket of vector fields,
and developed the notion of the symmetric derivation. Using this
machinery, we have defined the concept of symmetric curvature.
This concept is natural and is related to the notions divergence
and Laplacian of vector fields. This concept is also related to
the derivations on the algebra of symmetric forms which has been
discussed by the authors. We introduce a new class of geometric
vector fields and prove some basic facts about them. We call
these vector fields affinewise. By contraction of the symmetric
curvature, we define two new curvatures which have direct
relations to the notions of divergence, Laplacian, and the Ricci
tensor.
3

249
267


A.
Heydari
Iran


N.
Boroojerdian
Iran


E.
Peyghan
Iran
Curvature tensor
derivation
Fr"{o}licherNijenhuis bracket
Lie derivative
symmetric differential
symmetric curvature
The (R,S)symmetric and (R,S)skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
2
2
Let $Rin textbf{C}^{mtimes m}$ and $Sin textbf{C}^{ntimes n}$ be nontrivial involution matrices; i.e., $R=R^{1}neq pm~I$ and $S=S^{1}neq pm~I$.
An $mtimes n$ complex matrix $A$ is said to be an $(R, S)$symmetric ($(R, S)$skew symmetric) matrix if $RAS =A$ ($ RAS =A$).
The $(R, S)$symmetric and $(R, S)$skew symmetric matrices have
a number of special properties and widely used in engineering and
scientific computating. Here, we introduce the necessary and
sufficient conditions for the solvability of the pair of matrix
equations $A_{1}XB_{1}=C_{1}$ and $A_{2}XB_{2}=C_{2}$, over $(R,
S)$symmetric and $(R, S)$skew symmetric matrices, and give the
general expressions of the solutions for the solvable cases.
Finally, we give necessary and sufficient conditions for the
existence of $(R, S)$symmetric and $(R, S)$skew symmetric
solutions and representations of these solutions to the pair of
matrix equations in some special cases.
3

269
279


M.
Dehghan
Iran


M.
Hajarian
Iran
Matrix equation
(R
S)symmetric matrix
S)skew symmetric matrix
On the nilpotency class of the automorphism group of some finite
pgroups
2
2
Let $G$ be a $p$group of order $p^n$ and $Phi$=$Phi(G)$ be the
Frattini subgroup of $G$. It is shown that the nilpotency class of
$Autf(G)$, the group of all automorphisms of $G$ centralizing $G/
Fr(G)$, takes the maximum value $n2$ if and only if $G$ is of
maximal class. We also determine the nilpotency class of
$Autf(G)$ when $G$ is a finite abelian $p$group.
3

281
289


S.
Fouladi
Iran


R.
Orfi
Iran
Finite pgroup
automorphism group
nilpotency class
Linear Sphericity Testing of 3Connected Single Source Digraphs
2
2
It has been proved that sphericity testing for digraphs is an
NPcomplete problem. Here, we
investigate sphericity of 3connected single source digraphs. We
provide a new combinatorial characterization of sphericity and give
a linear time algorithm for sphericity testing. Our algorithm tests
whether a 3connected single source digraph with $n$ vertices is
spherical in $O(n)$ time.
3

291
304


A.
Dolati
Iran
Embedding
upward embedding
sphericity
single source digraph