Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
10
15
A characterization of shellable and sequentially Cohen-Macaulay
1
9
EN
S.
Moradi
Amirkabir University of Technology
s-moradi@araku.ac.ir
D.
Kiani
Amirkabir University of Technology
dkiani@aut.ac.ir
We 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.
Edge ideals,shellable complex,sequentially Cohen-Macaulay ring
http://bims.iranjournals.ir/article_347.html
http://bims.iranjournals.ir/article_347_7a249698165516accceec04e5a5ba578.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Non-linear ergodic theorems in complete non-positive curvature metric spaces
11
20
EN
B.
Ahmadi Kakavandi
Tarbiat Modares University
M.
Amini
Tarbiat Modares University
mamini48@yahoo.com
Hadamard (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.
Hadamard Space,continuous non-expansive semigroup,invariant mean,asymptotic center,non-linear ergodic theorem
http://bims.iranjournals.ir/article_348.html
http://bims.iranjournals.ir/article_348_bd937fd396e4bfd643f273cb0f5b9aed.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
A characterization of L-dual frames and L-dual Riesz bases
21
32
EN
A.
Ahmadi
A.
Askari Hemmat
This 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 $L^{2}(G)$.
Hyers-Ulam-Rassias stability,generalized
derivation,bounded central approximate identity,faithful Banach
algebra
http://bims.iranjournals.ir/article_349.html
http://bims.iranjournals.ir/article_349_e505bfd0f796940777bc05b6fd51c8f5.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2012
09
15
On rainbow 4-term arithmetic progressions
33
37
EN
M. H.
Shirdareh Haghighi
P.
Salehi Nowbandegani
{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 $k=3$.}
Rainbow arithmetic progression,4-term arithmetic progression,AP(4),AP($k$)
http://bims.iranjournals.ir/article_350.html
http://bims.iranjournals.ir/article_350_89e63dba5b5df3fefe16dd3a01425b8e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Second symmetric powers of chain complexes
39
75
EN
A.
J.
Frankild
S.
Sather-Wagstaff
A.
Taylor
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 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
Chain complex,symmetric power,symmetric square
http://bims.iranjournals.ir/article_352.html
http://bims.iranjournals.ir/article_352_3993b9c37fc0e81314ac0cd20be606cf.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2012
09
15
General Hardy-Type Inequalities with Non-conjugate Exponents
77
108
EN
A.
Cizmesija
M.
Krnic
J.
Pecaric
We 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.
Hardy inequality,Hilbert inequality,Hardy-type kernel,Hardy-type inequality,Hilbert-type inequality
http://bims.iranjournals.ir/article_351.html
http://bims.iranjournals.ir/article_351_52e9e19972fed6970fe01efd0a82b904.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Some Optimal Codes From Designs
109
115
EN
M.
Emami
Ch.
Maysoori
The 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.
Optimal code,t-design
http://bims.iranjournals.ir/article_353.html
http://bims.iranjournals.ir/article_353_1c31d56b10fe384966174ee83e0eb049.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Extension functors of local cohomology modules
117
134
EN
M.
Aghapournahr
A.
Taherizadeh
A.
Vahidi
Let $R$ 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.
Local cohomology modules,Serre subcategories,cofinite
modules
http://bims.iranjournals.ir/article_354.html
http://bims.iranjournals.ir/article_354_a36964c381b38b75e5e066579630220a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Convergence of product integration method applied for numerical
solution of linear weakly singular Volterra
systems
135
148
EN
B.
Babayar-Razlighi
Babayar@tabrizu.ac.ir
K.
Ivaz
M.
R.
Mokhtarzadeh
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.
Product integration technique,system of singular Volterra integral equations,heat equation
http://bims.iranjournals.ir/article_355.html
http://bims.iranjournals.ir/article_355_4c05419e0679e03a7d612b134a6c9404.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
On Semi-artinian Weakly Co-semisimple Modules
149
157
EN
E.
Momtahan
We 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.
Semi-artinian module,weakly co-semisimple module
http://bims.iranjournals.ir/article_356.html
http://bims.iranjournals.ir/article_356_cf010bff12b9e95965d9ffb69052de01.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Various topological forms of Von Neumann regularity in Banach algebras
159
170
EN
G.
Esslamzadeh
M.
Shadab
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.
Topologically von Neumann regular,principally von Neumann regular
http://bims.iranjournals.ir/article_357.html
http://bims.iranjournals.ir/article_357_bceaa5c7dfeb6e2303668f1f6eee51b4.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Insertion of a gamma-continuous function
171
181
EN
M.
Mirmiran
A 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.
Insertion,strong binary relation,preopen set,semi-open set,$gamma-$open set,lower cut set
http://bims.iranjournals.ir/article_358.html
http://bims.iranjournals.ir/article_358_585a7ccdab5fde974ec45e285e1cc82f.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Monomial Irreducible sln-Modules
183
195
EN
M.
Shahryari
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.
symmetric group,character theory,representations of Lie algebras,symmetry classes of tensors
http://bims.iranjournals.ir/article_359.html
http://bims.iranjournals.ir/article_359_c314a69d352fa6f7d05794e57d93f5e2.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Permanence and global asymptotic stability of a delayed
predator-prey model with Hassell-Varley type functional response
197
215
EN
K.
Wang
Y.
L.
Zhu
Here, 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.
Permanence,asymptotic stability,comparison theorem,Lyapunov functional
http://bims.iranjournals.ir/article_360.html
http://bims.iranjournals.ir/article_360_e5991d60269c657b39ab2541a80032d9.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Semistar dimension of polynomial rings and Prufer-like
domains
217
233
EN
P.
Sahandi
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 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.
Semistar operation,Krull dimension,strong S-domain,Jaffard domain,quasi-Pr"{u}fer domain,UM$t$ domain
http://bims.iranjournals.ir/article_361.html
http://bims.iranjournals.ir/article_361_6dbe9e5fa7817562fab715a62353d061.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
A Sharp Maximal Function Estimate for Vector-Valued Multilinear
Singular Integral Operator
235
248
EN
Zhou
Xiaosha
Liu
Lanzhe
lanzheliu@163.com
We 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.
Vector-valued multilinear operator,singular integral operator,sharp maximal function estimate,BMO
http://bims.iranjournals.ir/article_362.html
http://bims.iranjournals.ir/article_362_3e71d982083b4f407804702f349a53e1.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
Symmetric curvature tensor
249
267
EN
A.
Heydari
N.
Boroojerdian
E.
Peyghan
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.
Curvature tensor,derivation,Fr"{o}licher-Nijenhuis bracket,Lie derivative,symmetric
differential,symmetric curvature
http://bims.iranjournals.ir/article_363.html
http://bims.iranjournals.ir/article_363_e4d5cfe09b33d8f0691b0f0663d7edef.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
The (R,S)-symmetric and (R,S)-skew symmetric solutions of the pair of matrix equations A1XB1 = C1 and A2XB2 = C2
269
279
EN
M.
Dehghan
M.
Hajarian
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.
Matrix equation,(R,S)-symmetric matrix,S)-skew symmetric matrix
http://bims.iranjournals.ir/article_364.html
http://bims.iranjournals.ir/article_364_7532efcddc42e213d1eae59596ad5a4a.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
09
15
On the nilpotency class of the automorphism group of some finite
p-groups
281
289
EN
S.
Fouladi
R.
Orfi
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 $n-2$ 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.
Finite p-group,automorphism group,nilpotency class
http://bims.iranjournals.ir/article_365.html
http://bims.iranjournals.ir/article_365_cf69e5755ef787ecc4678fb8887eef0b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
37
No. 3
2011
03
15
Linear Sphericity Testing of 3-Connected Single Source Digraphs
291
304
EN
A.
Dolati
It 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.
Embedding,upward embedding,sphericity,single
source digraph
http://bims.iranjournals.ir/article_366.html
http://bims.iranjournals.ir/article_366_32f7b095391488c7c2d848a209f52492.pdf