Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices295323498ENMehdi DehghanProf.Masoud HajarianDepartment of Mathematics
Faculty of Mathematical Sciences
Shahid Beheshti University, G.C.,
Evin, Tehran 19839
IranJournal Article20120928A 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Bilateral composition operators on vector-valued Hardy spaces325337499ENHamid RezaeiYasouj UniversityJournal Article20110920Let $T$ 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Periodically correlated and multivariate symmetric stable processes related to periodic and cyclic flows339355500ENAfshin ParvardehAcademic ProfessorSareh GoliforushaniAcademic ProfessorAhmad Reza SoltaniAcademic ProfessorJournal Article20110213In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Improvements of two preconditioned AOR iterative methods for Z-matrices357371501ENMohsen HasaniIslamic Azad UniversityDavod Khojasteh SalkuyehUniversity of GuilanJournal Article20111126In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Ostrowski type inequalities for functions whose derivatives are preinvex373386502ENImdat IşcanGiresun UniversityJournal Article20120418In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401On the decomposable numerical range of operators387398503ENYousef ZamaniSahand University of TechnologySima AhsaniSahand University of TechnologyJournal Article20120410 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401WZ factorization via Abay-Broyden-Spedicato algorithms399411504ENEffat Golpar-RabokyUniversity of QomnullN. Mahdavi-AmiriSharif University of TechnologynullJournal Article20120727Classes 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401A graphical difference between the inverse and regular semigroups413421505ENAyoub GharibkhajehIslamic Azad university North-Tehran BranchHossein DoostieScience and Research, Islamic Azad University Tehran- IranJournal Article20121128In 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. Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Gorenstein global dimensions for Hopf algebra actions423431506ENQunxing PanDepartment of Mathematics, Nanjing Agricultural UniversityFaqun CaiDepartment of Economic Management, Nanjing College of Chemical TechnologyJournal Article20120530Let $H$ 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. Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401$(m,n)$-algebraically compactness and $(m,n)$-pure injectivity433445507ENMahmood BehboodiIsfahan University of TechnologyAtefeh GhorbaniIsfahan University of TechnologySeyed Hossein ShojaeeIsfahan university of technologyJournal Article20120916In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401A Stochastic algorithm to solve multiple dimensional Fredholm integral equations of the second kind447458508ENRahman FarnooshSchool of Mathematics, Iran University of Science and Technology.Mahboubeh AalaeiSchool of Mathematics, Iran University of Science and Technology.Journal Article20120730In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401On $I$-statistical and $I$-lacunary statistical convergence of order $alpha$459472509ENPratulananda DasJadavpour UniversityEkrem SavasIstanbul Commerce UniversityJournal Article20120803In 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401A characterization of the symmetric group of prime degree473480510ENQingliang ZhangSchool of Sciences, Nantong University, 226007, Nantong, P. R. ChinaJinhua WangSchool of Sciences, Nantong University, 226007, Nantong, P. R. ChinaWeijun LiuSchool of Sciences, Nantong University, 226007, Nantong, P. R. ChinaJournal Article20120729Let $G$ 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Approximating fixed points of nonexpansive mappings and solving systems of variational inequalities481504511ENHossein PiriDepartment of Mathematics,
University of Bonab, Bonab 5551761167, IranJournal Article20130104A 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Arens regularity of bilinear forms and unital Banach module spaces505520512ENkazem Haghnejad AzarFaculty member of Mohghegh Ardabili UniverssityJournal Article20111022Assume 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.Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401Weak Banach-Saks property in the space of compact operators521530513ENB. Khadijeh MoosaviIslamic Azad University, Bafgh BranchS. Mohammad MoshtaghiounYazd UniversityJournal Article20121012For 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 $psi_{y^*}(T)= T^*y^*.$Iranian Mathematical Society (IMS)Bulletin of the Iranian Mathematical Society1017-060X40220140401On generalisations of almost prime and weakly prime ideals531540514ENMahdieh EbrahimpourUniversity of Vali-e-AsrJournal Article20121116Let $R$ 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.