Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices
295
323
EN
Mehdi
Dehghan
Prof.
dehghan@aut.ac.ir
Masoud
Hajarian
Department of Mathematics
Faculty of Mathematical Sciences
Shahid Beheshti University, G.C.,
Evin, Tehran 19839
Iran
mhajarian@aut.ac.ir
A matrix $Pintextmd{C}^{ntimes n}$ is called a generalized reflection matrix if $P^{H}=P$ and $P^{2}=I$. An $ntimes n$ complex matrix $A$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $P$ if $A=PAP$ ($A=-PAP$). In this paper, we introduce two iterative methods for solving the pair of matrix equations $AXB=C$ and $DXE=F$ over reflexive and anti-reflexive matrices. The convergence of the iterative methods is also proposed. Finally, a numerical example is given to show the efficiency of the presented results.
Matrix equation,Reflexive matrix,Anti-reflexive matrix
http://bims.iranjournals.ir/article_498.html
http://bims.iranjournals.ir/article_498_e826f705a8bcdc93e8b4e86ef70af573.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Bilateral composition operators on vector-valued Hardy spaces
325
337
EN
Hamid
Rezaei
Yasouj University
rezaei@mail.yu.ac.ir
Let $T$ be a bounded operator on the Banach space $X$ and $ph$ be an analytic self-map of the unit disk $Bbb{D}$. We investigate some operator theoretic properties of bilateral composition operator $C_{ph, T}: f ri T circ f circ ph$ on the vector-valued Hardy space $H^p(X)$ for $1 leq p leq +infty$. Compactness and weak compactness of $C_{ph, T}$ on $H^p(X)$ are characterized and when $p=2$, a concrete formula for its adjoint is given.
vector-valued Hardy space,composition operator,linear fractional map,weak compactness
http://bims.iranjournals.ir/article_499.html
http://bims.iranjournals.ir/article_499_de6518007dfc715846c6f2e18e395a31.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Periodically correlated and multivariate symmetric stable processes related to periodic and cyclic flows
339
355
EN
Afshin
Parvardeh
Academic Professor
a.parvardeh@sci.ui.ac.ir
Sareh
Goliforushani
Academic Professor
sareh.goli@gmail.com
Ahmad Reza
Soltani
Academic Professor
soltani@kuc01.kuniv.edu.kw
In this work we introduce and study discrete time periodically correlated stable processes and multivariate stationary stable processes related to periodic and cyclic flows. Our study involves producing a spectral representation and a spectral identification for such processes. We show that the third component of a periodically correlated stable process has a component related to a periodic-cyclic flow.
multivariate stationary stable processes,flows,periodic and cyclic flows
http://bims.iranjournals.ir/article_500.html
http://bims.iranjournals.ir/article_500_37ead49e70ddc70e5d343101a2a9cebe.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Improvements of two preconditioned AOR iterative methods for Z-matrices
357
371
EN
Mohsen
Hasani
Islamic Azad University
hasani.mo@gmail.com
Davod
Khojasteh Salkuyeh
University of Guilan
salkuyeh@gmail.com
In this paper, we propose two preconditioned AOR iterative methods to solve systems of linear equations whose coefficient matrices are Z-matrix. These methods can be considered as improvements of two previously presented ones in the literature. Finally some numerical experiments are given to show the effectiveness of the proposed preconditioners.
System of linear equations,preconditioner,AOR iterative method,Z-matrix
http://bims.iranjournals.ir/article_501.html
http://bims.iranjournals.ir/article_501_8a1c873672368b347de367b050646428.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Ostrowski type inequalities for functions whose derivatives are preinvex
373
386
EN
Imdat
Işcan
Giresun University
imdat.iscan@giresun.edu.tr
In this paper, making use of a new identity, we establish new inequalities of Ostrowski type for the class of preinvex functions and gave some midpoint type inequalities.
Ostrowski type inequalities,preinvex function,condition C
http://bims.iranjournals.ir/article_502.html
http://bims.iranjournals.ir/article_502_aa3a54cac93833e16043e4a243cffb1f.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
On the decomposable numerical range of operators
387
398
EN
Yousef
Zamani
Sahand University of Technology
zamani@sut.ac.ir
Sima
Ahsani
Sahand University of Technology
s-ahsani@sut.ac.ir
Let $V$ be an $n$-dimensional complex inner product space. Suppose $H$ is a subgroup of the symmetric group of degree $m$, and $chi :Hrightarrow mathbb{C} $ is an irreducible character (not necessarily linear). Denote by $V_{chi}(H)$ the symmetry class of tensors associated with $H$ and $chi$. Let $K(T)in
(V_{chi}(H))$ be the operator induced by $Tin
text{End}(V)$. The decomposable numerical range $W_{chi}(T)$ of
$T$ is a subset of the classical numerical range $W(K(T))$ of $K(T)$ defined as:$$
W_{chi}(T)={(K(T)x^{ast }, x^{ast}):x^{ast } is a decomposable unit tensor}.$$
In this paper, we study the interplay between the geometric properties of $W_{chi}(T)$ and the algebraic properties of $T$. In fact, we extend some of the results of [C. K. Li and A. Zaharia, Decomposable numerical range on orthonormal decomposable tensors, Linear Algebra Appl. 308 (2000), no, 1-3, 139--152] and [C. K. Li and A. Zaharia, Induced operators on symmetry classes of tensors, Trans. Amer. Math. Soc. 354 (2002), no. 2, 807--836], to non-linear irreducible characters.
symmetry class of tensors,decomposable
numerical range,induced operator
http://bims.iranjournals.ir/article_503.html
http://bims.iranjournals.ir/article_503_b7e2e3cc8e6d67d8124fdf498d842b65.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
WZ factorization via Abay-Broyden-Spedicato algorithms
399
411
EN
Effat
Golpar-Raboky
null
University of Qom
g_raboky@yahoo.com
N.
Mahdavi-Amiri
null
Sharif University of Technology
nezamm@sharif.edu
Classes of Abaffy-Broyden-Spedicato (ABS) methods have been introduced for solving linear systems of equations. The algorithms are powerful methods for developing matrix factorizations and many fundamental numerical linear algebra processes. Here, we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW factorizations of a nonsingular matrix as well as the $W^TW$ and $Z^TZ$ factorizations of a symmetric positives definite matrix. We also describe the QZ and the QW factorizations, with Q orthogonal, and show how to appropriate the parameters of the ABS algorithms to compute these factorizations.
ABS algorithms,WZ factorization,ZW factorizatio,WTW factorization,ZTZ factorization,QZ factoriation,QW factorization
http://bims.iranjournals.ir/article_504.html
http://bims.iranjournals.ir/article_504_cc2f035a33cf3308b3f1d82d42cd6624.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
A graphical difference between the inverse and regular semigroups
413
421
EN
Ayoub
Gharibkhajeh
Islamic Azad university North-Tehran Branch
a_gharib@iau-tnb.ac.ir
Hossein
Doostie
Science and Research, Islamic Azad University Tehran- Iran
doostih@tmu.ac.ir
In this paper we investigate the Green graphs for the regular and inverse semigroups by considering the Green classes of them. And by using the properties of these semigroups, we prove that all of the five Green graphs for the inverse semigroups are isomorphic complete graphs, while this doesn't hold for the regular semigroups. In other words, we prove that in a regular semigroup $S$ two Green graph $Gamma_{mathcal{L}}(S)$ and $Gamma_{mathcal{H}}(S)$ are isomorphic, however, the other three Green graphs are non-isomorphic to them.
Regular and inverse semigroup,Green relations,Green graphs
http://bims.iranjournals.ir/article_505.html
http://bims.iranjournals.ir/article_505_8d4a7f029daec49b029448a7f5252b20.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Gorenstein global dimensions for Hopf algebra actions
423
431
EN
Qunxing
Pan
Department of Mathematics, Nanjing Agricultural University
pqxjs98@njau.edu.cn
Faqun
Cai
Department of Economic Management, Nanjing College of Chemical Technology
cfq1217@163.com
Let $H$ be a Hopf algebra and $A$ an $H$-bimodule algebra. In this paper, we investigate Gorenstein global dimensions for Hopf algebras and twisted smash product algebras $Astar H$. Results from the literature are generalized.
Hopf algebras,Gorenstein global
dimensions,Morita equivalence,twisted smash products
http://bims.iranjournals.ir/article_506.html
http://bims.iranjournals.ir/article_506_9440f67571725993f34bcd0d32f3296c.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
$(m,n)$-algebraically compactness and $(m,n)$-pure injectivity
433
445
EN
Mahmood
Behboodi
Isfahan University of Technology
mbehbood@cc.iut.ac.ir
Atefeh
Ghorbani
Isfahan University of Technology
a_ghorbani@cc.iut.ac.ir
Seyed Hossein
Shojaee
Isfahan university of technology
hshojaee@math.iut.ac.ir
In this paper, we introduce the notion of $(m,n)$-algebraically compact modules as an analogue of algebraically compact modules and then we show that $(m,n)$-algebraically compactness and $(m,n)$-pure injectivity for modules coincide. Moreover, further characterizations of a $(m,n)$-pure injective module over a commutative ring are given.
(n,m)-pure exact,m)-pure injective,m)-algebraically compact,pure injective,algebraically compact
http://bims.iranjournals.ir/article_507.html
http://bims.iranjournals.ir/article_507_09d25bec7f5a7b3bdf5caa983c9d38ba.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
A Stochastic algorithm to solve multiple dimensional Fredholm integral equations of the second kind
447
458
EN
Rahman
Farnoosh
School of Mathematics, Iran University of Science and Technology.
rfarnoosh@iust.ac.ir
Mahboubeh
Aalaei
School of Mathematics, Iran University of Science and Technology.
aalaei@iust.ac.ir
In the present work, a new stochastic algorithm is proposed to solve multiple dimensional Fredholm integral equations of the second kind. The solution of the integral equation is described by the Neumann series expansion. Each term of this expansion can be considered as an expectation which is approximated by a continuous Markov chain Monte Carlo method. An algorithm is proposed to simulate a continuous Markov chain with probability density function arisen from an importance sampling technique. Theoretical results are established in a normed space to justify the convergence of the proposed method. The method has a simple structure and it is a good candidate for parallelization because of the fact that many independent sample paths are used to estimate the solution. Numerical results are performed in order to confirm the efficiency and accuracy of the present work.
Fredholm integral equations,Monte Carlo method,Continuous Markov chain,Neumann series expansion,Importance sampling
http://bims.iranjournals.ir/article_508.html
http://bims.iranjournals.ir/article_508_c94cabec98592f562c8a3e4567221f96.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
On $I$-statistical and $I$-lacunary statistical convergence of order $alpha$
459
472
EN
Pratulananda
Das
Jadavpour University
pratulananda@yahoo.co.in
Ekrem
Savas
Istanbul Commerce University
ekremsavas@yahoo.com
In this paper, following a very recent and new approach, we further generalize recently introduced summability methods, namely, $I$-statistical convergence and $I$-lacunary statistical convergence (which extend the important summability methods, statistical convergence and lacunary statistical convergence using ideals of $mathbb{N}$) and introduce the notions of $I$-statistical convergence of order $alpha$ and $I$-lacunary statistical convergence of order $alpha$, where $0<alpha< 1$. We mainly investigate their relationship and also make some observations about these classes and in the way try to give an answer to an open problem posed By Das, Savas and Ghosal in 2011. The study leaves a lot of interesting open problems.
I-statistical convergence,I-lacunary statistical convergence,statistical convergence of order $alpha$
http://bims.iranjournals.ir/article_509.html
http://bims.iranjournals.ir/article_509_fe820582c3d031263737aa3b6e5a7007.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
A characterization of the symmetric group of prime degree
473
480
EN
Qingliang
Zhang
School of Sciences, Nantong University, 226007, Nantong, P. R. China
qingliangstudent@163.com
Jinhua
Wang
School of Sciences, Nantong University, 226007, Nantong, P. R. China
jhwang@ntu.edu.cn
Weijun
Liu
School of Sciences, Nantong University, 226007, Nantong, P. R. China
wjliu6210@126.com
Let $G$ be a finite group and $Gamma(G)$ the prime graph of $G$. Recently people have been using prime graphs to study simple groups. Naturally we pose a question: can we use prime graphs to study almost simple groups or non-simple groups? In this paper some results in this respect are obtained and as follows: $Gcong S_p$ if and only if $|G|=|S_p|$ and $Gamma(G)=Gamma(S_p)$, where $p$ is a prime.
characterization,symmetric group,Prime graph
http://bims.iranjournals.ir/article_510.html
http://bims.iranjournals.ir/article_510_dee5dd7e5a3f35385b5ddbc71bf0cc1b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Approximating fixed points of nonexpansive mappings and solving systems of variational inequalities
481
504
EN
Hossein
Piri
Department of Mathematics,
University of Bonab, Bonab 5551761167, Iran
hossein_piri1979@yahoo.com
A new approximation method for the set of common fixed points of nonexpansive mappings and the set of solutions of systems of variational inequalities is introduced and studied. Moreover, we apply our main result to obtain strong convergence theorem to a common fixed point of a nonexpannsive mapping and solutions of a system of variational inequalities of an inverse strongly monotone mapping and strictly pseudo-contractive mapping of Browder-Petryshyn type.
fixed point,$delta$- strongly monotone,$lambda$- strictly pseudo-contractive
http://bims.iranjournals.ir/article_511.html
http://bims.iranjournals.ir/article_511_d0c5befcc72c8fd3470d89ccbd4d2ba3.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Arens regularity of bilinear forms and unital Banach module spaces
505
520
EN
kazem
Haghnejad Azar
Faculty member of Mohghegh Ardabili Universsity
haghnejadmath@yahoo.com
Assume that $A$, $B$ are Banach algebras and that $m:Atimes Brightarrow B$, $m^prime:Atimes Arightarrow B$ are bounded bilinear mappings. We study the relationships between Arens regularity of $m$, $m^prime$ and the Banach algebras $A$, $B$. For a Banach $A$-bimodule $B$, we show that $B$ factors with respect to $A$ if and only if $B^{**}$ is unital as an $A^{**}$-module. Let $Z_{e^{primeprime}}(B^{**})=B^{**}$ where $e^{primeprime}$ is a mixed unit of $A^{**}$. Then $B^*$ factors on both sides with respect to $A$ if and only if $B^{**}$ has a unit as $A^{**}$-module.
Arens regularity,bilinear mappings,Topological center,Unital A-module,Module action
http://bims.iranjournals.ir/article_512.html
http://bims.iranjournals.ir/article_512_7cc3f3725b7b3c1fe554083605917069.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
Weak Banach-Saks property in the space of compact operators
521
530
EN
B. Khadijeh
Moosavi
Islamic Azad University, Bafgh Branch
khmosavi@gmail.com
S. Mohammad
Moshtaghioun
Yazd University
moshtagh90@gmail.com
For suitable Banach spaces $X$ and $Y$ with Schauder decompositions and a suitable closed subspace $mathcal{M}$ of some compact operator space from $X$ to $Y$, it is shown that the strong Banach-Saks-ness of all evaluation operators on ${mathcal M}$ is a sufficient condition for the weak Banach-Saks property of ${mathcal M}$, where for each $xin X$ and $y^*in Y^*$, the evaluation operators on $mathcal{M}$ are defined by $phi_x(T)= Tx$ and $psi_{y^*}(T)= T^*y^*.$
weak Banach-Saks property,P- property,Schauder decomposition,compact operator,completely continuous operator
http://bims.iranjournals.ir/article_513.html
http://bims.iranjournals.ir/article_513_d1178361f94ff0d658d4159f2e3bc59b.pdf
Iranian Mathematical Society (IMS)
Bulletin of the Iranian Mathematical Society
1017-060X
1735-8515
40
2
2014
04
01
On generalisations of almost prime and weakly prime ideals
531
540
EN
Mahdieh
Ebrahimpour
University of Vali-e-Asr
mahdieh_ebrahimpour@yahoo.com
Let $R$ be a commutative ring with identity. A proper ideal $P$ of $R$ is a<n> $(n-1,n)$-$Phi_m$-prime ($(n-1,n)$-weakly prime) ideal if $a_1,ldots,a_nin R$, $a_1cdots a_nin Pbackslash P^m$ ($a_1cdots a_nin Pbackslash {0}$) implies $a_1cdots a_{i-1}a_{i+1}cdots a_nin P$, for some $iin{1,ldots,n}$; ($m,ngeq 2$). In this paper several results concerning $(n-1,n)$-$Phi_m$-prime and $(n-1,n)$-weakly prime ideals are proved. We show that in a Noetherian domain a $Phi_m$-prime ideal is primary and we show that in some well known rings $(n-1,n)$-$Phi_m$-prime ideals and $(n-1,n)$-prime ideals coincide.
Quasi-local ring,prime ideal,almost prime ideal,$(n-1,n)$-weakly prime ideal,n)$-$\Phi_m$-prime ideal
http://bims.iranjournals.ir/article_514.html
http://bims.iranjournals.ir/article_514_6d6ae9529874c4c6f84dc631664e5962.pdf