Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320111015A characterization of shellable and sequentially Cohen-Macaulay19347ENS. MoradiAmirkabir University of TechnologyD. KianiAmirkabir University of TechnologyJournal Article20090825We consider a class of hypergraphs called
hypercycles and we show that a hypercycle $C_n^{d,alpha}$ is
shellable or sequentially the Cohen--Macaulay if and only if
$nin{3,5}$. Also, we characterize Cohen--Macaulay hypercycles.
These results are hypergraph versions of results proved for cycles
in graphs.http://bims.iranjournals.ir/article_347_7a249698165516accceec04e5a5ba578.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Non-linear ergodic theorems in complete non-positive curvature metric spaces1120348ENB. Ahmadi KakavandiTarbiat Modares UniversityM. AminiTarbiat Modares UniversityJournal Article20091108Hadamard (or complete $CAT(0)$) spaces are complete, non-positive curvature, metric spaces. Here,
we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for
the commutative case. Our results extend the standard non-linear
ergodic theorems for non-expansive maps on real Hilbert spaces,
to non-expansive maps on Hadamard spaces, which include for example (possibly infinite-dimensional) complete simply
connected Riemannian manifolds with non-positive sectional
curvature.http://bims.iranjournals.ir/article_348_bd937fd396e4bfd643f273cb0f5b9aed.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915A characterization of L-dual frames and L-dual Riesz bases2132349ENA. AhmadiA. Askari HemmatJournal Article20091106This paper is an investigation of $L$-dual frames with respect
to a function-valued 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 $L^{2}(G)$.http://bims.iranjournals.ir/article_349_e505bfd0f796940777bc05b6fd51c8f5.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320120915On rainbow 4-term arithmetic progressions3337350ENM. H. Shirdareh HaghighiP. Salehi NowbandeganiJournal Article20090826{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 4-coloring 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 $k=3$.}http://bims.iranjournals.ir/article_350_89e63dba5b5df3fefe16dd3a01425b8e.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Second symmetric powers of chain complexes3975352ENA. J.FrankildS. Sather-WagstaffA. TaylorJournal Article20090330We 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 module-finite 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 $Xsimeq S$.http://bims.iranjournals.ir/article_352_3993b9c37fc0e81314ac0cd20be606cf.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320120915General Hardy-Type Inequalities with Non-conjugate Exponents77108351ENA. CizmesijaM. KrnicJ. PecaricJournal Article20091209We derive whole series of new integral
inequalities of the Hardy-type, with non-conjugate exponents.
First, we prove and discuss two equivalent general
inequa-li-ties of such type, as well as their corresponding
reverse inequalities. General results are then applied to special
Hardy-type 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.http://bims.iranjournals.ir/article_351_52e9e19972fed6970fe01efd0a82b904.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Some Optimal Codes From Designs109115353ENM. EmamiCh. MaysooriJournal Article20090518The binary and ternary codes spanned by the rows of the point by
block incidence matrices of some 2-designs and their
complementary
and orthogonal designs are studied. A new method is also introduced to study optimal codes.http://bims.iranjournals.ir/article_353_1c31d56b10fe384966174ee83e0eb049.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Extension functors of local cohomology modules117134354ENM. AghapournahrA. TaherizadehA. VahidiJournal Article20091007Let $R$ be a commutative Noetherian ring with non-zero 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.http://bims.iranjournals.ir/article_354_a36964c381b38b75e5e066579630220a.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Convergence of product integration method applied for numerical
solution of linear weakly singular Volterra
systems135148355ENB. Babayar-RazlighiK. IvazM. R.MokhtarzadehJournal Article20090628We 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.http://bims.iranjournals.ir/article_355_4c05419e0679e03a7d612b134a6c9404.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915On Semi-artinian Weakly Co-semisimple Modules149157356ENE. MomtahanJournal Article20091128We show that every semi-artinian module which is contained in a
direct sum of
finitely presented modules in $si[M]$, is weakly co-semisimple if and only if it is regular in $si[M]$.
As a consequence, we observe that every
semi-artinian ring is regular in the sense of von Neumann if
and only if its simple modules are $FP$-injective.http://bims.iranjournals.ir/article_356_cf010bff12b9e95965d9ffb69052de01.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Various topological forms of Von Neumann regularity in Banach algebras159170357ENG. EsslamzadehM. ShadabJournal Article20090917We 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.http://bims.iranjournals.ir/article_357_bceaa5c7dfeb6e2303668f1f6eee51b4.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Insertion of a gamma-continuous function171181358ENM. MirmiranJournal Article20091129A necessary and sufficient condition in terms of lower cut sets
are given for the insertion of a $gamma-$continuous function
between two comparable real-valued functions.http://bims.iranjournals.ir/article_358_585a7ccdab5fde974ec45e285e1cc82f.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Monomial Irreducible sln-Modules183195359ENM. ShahryariJournal Article20090902In 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.http://bims.iranjournals.ir/article_359_c314a69d352fa6f7d05794e57d93f5e2.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Permanence and global asymptotic stability of a delayed
predator-prey model with Hassell-Varley type functional response197215360ENK. WangY. L.ZhuJournal Article20090721Here, a predator-prey model with Hassell-Varley 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.http://bims.iranjournals.ir/article_360_e5991d60269c657b39ab2541a80032d9.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Semistar dimension of polynomial rings and Prufer-like
domains217233361ENP. SahandiJournal Article20091129Let $D$ 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 S-domains. As an application, we
give new characterizations of $star$-quasi-Pr"{u}fer domains
and UM$t$ domains in terms of dimension inequality formula (and
the notions of universally catenarian domain, stably strong
S-domain, strong S-domain, and Jaffard domain). We also extend
Arnold's formula to the setting of semistar operations.http://bims.iranjournals.ir/article_361_6dbe9e5fa7817562fab715a62353d061.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915A Sharp Maximal Function Estimate for Vector-Valued Multilinear
Singular Integral Operator235248362ENZhou XiaoshaLiu LanzheJournal Article20090810We establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators.
As an application, we obtain the $(L^p, L^q)$-norm inequality for vector-valued multilinear operators.http://bims.iranjournals.ir/article_362_3e71d982083b4f407804702f349a53e1.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915Symmetric curvature tensor249267363ENA. HeydariN. BoroojerdianE. PeyghanJournal Article20090822Recently, 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.http://bims.iranjournals.ir/article_363_e4d5cfe09b33d8f0691b0f0663d7edef.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2269279364ENM. DehghanM. HajarianJournal Article20090203Let $Rin textbf{C}^{mtimes m}$ 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.http://bims.iranjournals.ir/article_364_7532efcddc42e213d1eae59596ad5a4a.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110915On the nilpotency class of the automorphism group of some finite
p-groups281289365ENS. FouladiR. OrfiJournal Article20100118Let $G$ 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 $n-2$ 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.http://bims.iranjournals.ir/article_365_cf69e5755ef787ecc4678fb8887eef0b.pdfIranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X37No. 320110315Linear Sphericity Testing of 3-Connected Single Source Digraphs291304366ENA. DolatiJournal Article20090531It has been proved that sphericity testing for digraphs is an
NP-complete problem. Here, we
investigate sphericity of 3-connected 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 3-connected single source digraph with $n$ vertices is
spherical in $O(n)$ time.http://bims.iranjournals.ir/article_366_32f7b095391488c7c2d848a209f52492.pdf