Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
A lower estimate of harmonic functions
1
7
EN
Guoshuang
Pan
Beijing National Day School
gsp1979@163.com
Lei
Qiao
Department of Mathematics and Information Science, Henan University of Economics and Law, Zhengzhou, People's Republic of China
qiaocqu@163.com
Guantie
Deng
School of Mathematical
Science, Beijing Normal University, Beijing, People's Republic of China.
denggt@bnu.edu.cn
We shall give a lower estimate of harmonic functions of order greater than one in a half space, which generalize the result obtained by B. Ya. Levin in a half plane.
Lower estimate,Harmonic function,Half space
http://bims.iranjournals.ir/article_479.html
http://bims.iranjournals.ir/article_479_2cdf12321f02f3726af6042859a49ca3.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Investigation on the Hermitian matrix expression subject to some consistent equations
9
28
EN
Xiang
Zhang
Department of Mathematics, Zunyi Normal College Shanghai Road, Zunyi
563000, P.R. China
zxjnsc@163.com
In this paper, we study the extremal ranks and inertias of the Hermitian matrix expression $$ f(X,Y)=C_{4}-B_{4}Y-(B_{4}Y)^{*}-A_{4}XA_{4}^{*},$$ where $C_{4}$ is Hermitian, $*$ denotes the conjugate transpose, $X$ and $Y$ satisfy the following consistent system of matrix equations $A_{3}Y=C_{3}, A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2},X=X^{*}.$ As consequences, we get the necessary and sufficient conditions for the above expression $f(X,Y)$ to be (semi) positive, (semi) negative. The relations between the Hermitian part of the solution to the matrix equation $A_{3}Y=C_{3}$ and the Hermitian solution to the system of matrix equations $A_{1}X=C_{1},XB_{1}=D_{1},A_{2}XA_{2}^{*}=C_{2}$ are also characterized. Moreover, we give the necessary and sufficient conditions for the solvability to the following system of matrix equations $A_{3}Y=C_{3},A_{1}X=C_{1},XB_{1}=D_{1}, A_{2}XA_{2}^{*}=C_{2},X=X^{*}, B_{4}Y+(B_{4}Y)^{*}+A_{4}XA_{4}^{*}=C_{4} $ and provide an expression of the general solution to this system when it is solvable.
Linear matrix equation,Moore-Penrose inverse,Rank,Inertia
http://bims.iranjournals.ir/article_480.html
http://bims.iranjournals.ir/article_480_368a4a67459524d7aa8a44355b07f8d1.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Coupled fixed point results for weakly related mappings in partially ordered metric spaces
29
40
EN
Naval
Singh
govt. benazir college, bhopal
drsinghnaval@gmail.com
Reena
Jain
Technocrats Institute of technology
reenakhatod@gmail.com
In the present paper, we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function $phi$. We also define the concept of weakly related mappings on an ordered space. Moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space.
Coupled fixed point,common coupled fixed point,partially ordered space,weakly related mappings
http://bims.iranjournals.ir/article_481.html
http://bims.iranjournals.ir/article_481_4e6a03a572aeff155f37a395d5757e77.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
A matrix LSQR algorithm for solving constrained linear operator equations
41
53
EN
Masoud
Hajarian
Department of Mathematics
Faculty of Mathematical Sciences
Shahid Beheshti University, G.C.,
Evin, Tehran 19839
Iran
mhajarian@aut.ac.ir
In this work, an iterative method based on a matrix form of LSQR algorithm is constructed for solving the linear operator equation $mathcal{A}(X)=B$ and the minimum Frobenius norm residual problem $||mathcal{A}(X)-B||_F$ where $Xin mathcal{S}:={Xin textsf{R}^{ntimes n}~|~X=mathcal{G}(X)}$, $mathcal{F}$ is the linear operator from $textsf{R}^{ntimes n}$ onto $textsf{R}^{rtimes s}$, $mathcal{G}$ is a linear self-conjugate involution operator and $Bin textsf{R}^{rtimes s}$. Numerical examples are given to verify the efficiency of the constructed method.
iterative method,Bidiagonalization procedure,Linear operator equation
http://bims.iranjournals.ir/article_482.html
http://bims.iranjournals.ir/article_482_84ccde0152b76da6ba408ddf2be03cef.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Maximal prehomogeneous subspaces on classical groups
55
81
EN
Xiaoxiang
Yu
Xuzhou Normal University,
P.R.China
carston123@126.com
Dengyin
Wang
China University of Mining and technology
wdengyin@126.com
Suppose $G$ is a split connected reductive orthogonal or symplectic group over an infinite field $F,$ $P=MN$ is a maximal parabolic subgroup of $G,$ $frak{n}$ is the Lie algebra of the unipotent radical $N.$ Under the adjoint action of its stabilizer in $M,$ every maximal prehomogeneous subspaces of $frak{n}$ is determined.
prehomogeneous space,adjoint action,orthogonal,symplectic,orbit
http://bims.iranjournals.ir/article_483.html
http://bims.iranjournals.ir/article_483_e3bd93459034ea5c23b49e16867e543d.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Sequential second derivative general linear methods for stiff systems
83
100
EN
Ali
Karam
Ezzeddine
University of Tabriz
aliezz@tabrizu.ac.ir
Gholamreza
Hojjati
University of Tabriz
ghojjati@yahoo.com
Ali
Abdi
University of Tabriz
a_abdi@tabrizu.ac.ir
Second derivative general linear methods (SGLMs) as an extension of general linear methods (GLMs) have been introduced to improve the stability and accuracy properties of GLMs. The coefficients of SGLMs are given by six matrices, instead of four matrices for GLMs, which are obtained by solving nonlinear systems of order and usually Runge--Kutta stability conditions. In this paper, we introduce a technique for construction of an special case of SGLMs which decreases the complexity of finding coefficients matrices.
General linear methods,Two--derivative methods,ordinary differential equation,Order conditions,A- and
L-stability
http://bims.iranjournals.ir/article_484.html
http://bims.iranjournals.ir/article_484_e8bcd98926dd7174a8892e92e75c9438.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
On the numerical solution of generalized Sylvester matrix equations
101
113
EN
Amer
Kaabi
iran
kaabi_amer@kmsu.ac.ir
The global FOM and GMRES algorithms are among the effective methods to solve Sylvester matrix equations. In this paper, we study these algorithms in the case that the coefficient matrices are real symmetric (real symmetric positive definite) and extract two CG-type algorithms for solving generalized Sylvester matrix equations. The proposed methods are iterative projection methods onto matrix Krylov subspaces. Numerical examples are presented.
Generalized Sylvester matrix equations,Matrix Krylove subspace,Global gmres algorithm
http://bims.iranjournals.ir/article_485.html
http://bims.iranjournals.ir/article_485_1ba2c57bb65ad0afe866e7641b82604c.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
An extension theorem for finite positive measures on surfaces of finite dimensional unit balls in Hilbert spaces
115
124
EN
Ahmad Reza
Soltani
Kuwait University and Shiraz University
soltani@kuc01.kuniv.edu.kw
Safieh
Mahmoodi
Isfahan University of Technology
mahmoodi@cc.iut.ac.ir
A consistency criteria is given for a certain class of finite positive measures on the surfaces of the finite dimensional unit balls in a real separable Hilbert space. It is proved, through a Kolmogorov type existence theorem, that the class induces a unique positive measure on the surface of the unit ball in the Hilbert space. As an application, this will naturally accomplish the work of Kanter (1973) on the existence and uniqueness of the spectral measures of finite dimensional stable random vectors to the infinite dimensional ones. The approach presented here is direct and different from the functional analysis approach in Kuelbs (1973), Linde (1983) and the indirect approach of Tortrat (1976) and Dettweiler (1976).
Extension Theorem,Separable Hilbert space,Finite Measures on
Surfaces of the Unit Balls,Stable distribution,Spectral measure
http://bims.iranjournals.ir/article_486.html
http://bims.iranjournals.ir/article_486_e2f1c822857f6f622874900911e812f6.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Embedding measure spaces
125
155
EN
M.R.
Koushesh
Isfahan University of Technology
koushesh@cc.iut.ac.ir
For a given measure space $(X,{mathscr B},mu)$ we construct all measure spaces $(Y,{mathscr C},lambda)$ in which $(X,{mathscr B},mu)$ is embeddable. The construction is modeled on the ultrafilter construction of the Stone--v{C}ech compactification of a completely regular topological space. Under certain conditions the construction simplifies. Examples are given when this simplification occurs.
Ultrafilter,thick subset,set of full outer measure,topological measure space,Baire measure,Stone--v{C}ech compactification,realcompactification
http://bims.iranjournals.ir/article_487.html
http://bims.iranjournals.ir/article_487_5d8ac1365f2e598525cbe53890ad515d.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
A class of Artinian local rings of homogeneous type
157
181
EN
Leila
Sharifan
Hakim Sabzevari University, Sabzevar, Iran
leilasharifan@gmail.com
Let $I$ be an ideal in a regular local ring $(R,n)$, we will find bounds on the first and the last Betti numbers of $(A,m)=(R/I,n/I)$. if $A$ is an Artinian ring of the embedding codimension $h$, $I$ has the initial degree $t$ and $mu(m^t)=1$, we call $A$ a {it $t-$extended stretched local ring}. This class of local rings is a natural generalization of the class of stretched local rings studied by Sally, Elias and Valla. For a $t-$extended stretched local ring, we show that ${h+t-2choose t-1}-h+1leq tau(A)leq {h+t-2choose t-1}$ and $ {h+t-1choose t}-1 leq mu(I) leq {h+t-1choose t}$. Moreover $tau(A)$ reaches the upper bound if and only if $mu(I)$ is the maximum value. Using these results, we show when $beta_i(A)=beta_i(gr_m(A))$ for each $igeq 0$. Beside, we will investigate the rigid behavior of the Betti numbers of $A$ in the case that $I$ has initial degree $t$ and $mu(m^t)=2$. This class is a natural generalization of {it almost stretched local rings} again studied by Elias and Valla. Our research extends several results of two papers by Rossi, Elias and Valla.
artinian rings,Hilbert function,number of
generators,Cohen-Macaulay type
http://bims.iranjournals.ir/article_488.html
http://bims.iranjournals.ir/article_488_46a770dbf68f66aa47bf6509eded267f.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Stochastic bounds for a single server queue with general retrial times
183
198
EN
Mohamed
Boualem
University of Bejaia
robertt15dz@yahoo.fr
Natalia
Djellab
University of Annaba
djellab@yahoo.fr
Djamil
Aïssani
University of béjaia
lamos_bejaia@hotmail.com
We propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indice bounds. The main goal of this paper is to investigate various monotonicity properties of a single server retrial queue with first-come-first-served (FCFS) orbit and general retrial times using the stochastic ordering techniques.
Retrial queues,Markov chain,stochastic bounds,Monotonicity,ageing distributions
http://bims.iranjournals.ir/article_489.html
http://bims.iranjournals.ir/article_489_d8f721e663cfe851a582b1a8bde9e06e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Existence and uniqueness of common coupled fixed point results via auxiliary functions
199
215
EN
Sumit
Chandok
Khalsa College of Engineering & Technology (Punjab Technical University)
chandhok.sumit@gmail.com
Erdal
Karapinar
ATILIM UNIVERSITY
erdalkarapinar@yahoo.com
Mohammad Saeed
Khan
Sultan Qaboos University
mohammad@squ.edu.om
The purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.
Coupled coincidence
point,ordered sets,Coupled fixed point,mixed monotone property
http://bims.iranjournals.ir/article_490.html
http://bims.iranjournals.ir/article_490_ff5cc3dca3e0121e2ecee853eea3a1ed.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Relative volume comparison theorems in Finsler geometry and their applications
217
234
EN
Bing Ye
Wu
Department of Mathematics
Minjiang University
569405943@qq.com
We establish some relative volume comparison theorems for extremal volume forms of Finsler manifolds under suitable curvature bounds. As their applications, we obtain some results on curvature and topology of Finsler manifolds. Our results remove the usual assumption on S-curvature that is needed in the literature.
extreme volume form,Finsler manifold,Gromov pre-compactness,first Betti number,fundamental group
http://bims.iranjournals.ir/article_491.html
http://bims.iranjournals.ir/article_491_a6a751d01b68cc3adc7d1c13f8010dc7.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
An eigenvalue study on the sufficient descent property of a modified Polak-Ribière-Polyak conjugate gradient method
235
242
EN
Saman
Babaie-Kafaki
Semnan University
sbk@semnan.ac.ir
Based on an eigenvalue analysis, a new proof for the sufficient descent property of the modified Polak-Ribière-Polyak conjugate gradient method proposed by Yu et al. is presented.
unconstrained optimization,Conjugate gradient algorithm,Sufficient descent condition,Eigenvalue
http://bims.iranjournals.ir/article_492.html
http://bims.iranjournals.ir/article_492_329f84fb9fa3da162a1ea3377a2c650e.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Various kinds of regular injectivity for $S$-posets
243
261
EN
Leila
Shahbaz
University of Maragheh
leilashahbaz@yahoo.com
Mojgan
Mahmoudi
Shahid Beheshti University
mojganmahmoudi@yahoo.com
In this paper some properties of weak regular injectivity for $S$-posets, where $S$ is a pomonoid, are studied. The behaviour of different kinds of weak regular injectivity with products, coproducts and direct sums is considered. Also, some characterizations of pomonoids over which all $S$-posets are of some kind of weakly regular injective are obtained. Further, we give some Baer conditions which state the relation among some kinds of weak regular injectivity.
$S$-poset,regular injective,weakly regular injective
http://bims.iranjournals.ir/article_493.html
http://bims.iranjournals.ir/article_493_ffd4d4411686956bba1a760f8c5969b5.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
Implicit iteration approximation for a finite family of asymptotically quasi-pseudocontractive type mappings
263
279
EN
Shuyi
Zhang
Department of Mathematics, BoHai University
jzzhangshuyi@126.com
In this paper, strong convergence theorems of Ishikawa type implicit iteration process with errors for a finite family of asymptotically nonexpansive in the intermediate sense and asymptotically quasi-pseudocontractive type mappings in normed linear spaces are established by using a new analytical method, which essentially improve and extend some recent results obtained by Yang [Convergence theorems of implicit iteration process for asymptotically pseudocontractive mappings, Bulletin of the Iranian Mathematical Society, Available Online from 12 April 2011] and others.
Normed linear spaces,implicit iteration process,asymptotically quasi-pseudocontractive type mappings,nonexpansive mappings
http://bims.iranjournals.ir/article_494.html
http://bims.iranjournals.ir/article_494_3783b5bd681d2f9f26ad8b170b0d7dba.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
1
2014
02
01
On the norm of the derived subgroups of all subgroups of a finite group
281
291
EN
Zhencai
Shen
LMAM and School of Mathematical Sciences, Peking
University,
Beijing, 100871, China.
zhencai688@sina.com
Shirong
Li
Guangxi University
shirong@sina.com
Wujie
Shi
Chongqing University of Arts and Sciences
shiwujie@gmail.com
In this paper, we give a complete proof of Theorem 4.1(ii) and a new elementary proof of Theorem 4.1(i) in [Li and Shen, On the intersection of the normalizers of the derived subgroups of all subgroups of a finite group, J. Algebra, 323 (2010) 1349--1357]. In addition, we also give a generalization of Baer's Theorem.
Derived subgroup,solvable group,nilpotency class,Fitting length
http://bims.iranjournals.ir/article_495.html
http://bims.iranjournals.ir/article_495_6dc0df68eafac1db15b433778ac7a5c1.pdf