Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 ‎Finite iterative methods for solving systems of linear matrix equations over reflexive and anti-reflexive matrices 295 323 498 EN Mehdi Dehghan Prof. Masoud Hajarian Department of Mathematics Faculty of Mathematical Sciences Shahid Beheshti University, G.C., Evin, Tehran 19839 Iran Journal Article 2012 09 28 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 Bilateral composition operators on vector-valued Hardy spaces 325 337 499 EN Hamid Rezaei Yasouj University Journal Article 2011 09 20 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 Periodically correlated and multivariate symmetric stable‎ ‎processes related to periodic and cyclic flows 339 355 500 EN Afshin Parvardeh Academic Professor Sareh Goliforushani Academic Professor Ahmad Reza Soltani Academic Professor Journal Article 2011 02 13 ‎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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 Improvements of two preconditioned AOR iterative methods for Z-matrices 357 371 501 EN Mohsen Hasani Islamic Azad University Davod Khojasteh Salkuyeh University of Guilan Journal Article 2011 11 26 ‎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.‎
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 Ostrowski type inequalities for functions whose derivatives are preinvex 373 386 502 EN Imdat Işcan Giresun University Journal Article 2012 04 18 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 On the decomposable numerical range of operators 387 398 503 EN Yousef Zamani Sahand University of Technology Sima Ahsani Sahand University of Technology Journal Article 2012 04 10  ‎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 Society 1017-060X 40 2 2014 04 01 WZ factorization via Aba y-Broyden-Spedicato algorithms 399 411 504 EN Effat Golpar-Raboky University of Qom null N. Mahdavi-Amiri Sharif University of Technology null Journal Article 2012 07 27 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 A graphical difference between the inverse and regular semigroups 413 421 505 EN Ayoub Gharibkhajeh Islamic Azad university North-Tehran Branch Hossein Doostie Science and Research, Islamic Azad University Tehran- Iran Journal Article 2012 11 28 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 Gorenstein global dimensions for Hopf algebra actions 423 431 506 EN Qunxing Pan Department of Mathematics, Nanjing Agricultural University Faqun Cai Department of Economic Management, Nanjing College of Chemical Technology Journal Article 2012 05 30 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 \$(m,n)\$-algebraically compactness and \$(m,n)\$-pure injectivity 433 445 507 EN Mahmood Behboodi Isfahan University of Technology Atefeh Ghorbani Isfahan University of Technology Seyed Hossein Shojaee Isfahan university of technology Journal Article 2012 09 16 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 A Stochastic algorithm to solve multiple dimensional Fredholm integral equations of the second kind 447 458 508 EN Rahman Farnoosh School of Mathematics, Iran University of Science and Technology. Mahboubeh Aalaei School of Mathematics, Iran University of Science and Technology. Journal Article 2012 07 30 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 On \$I\$-statistical and \$I\$-lacunary statistical convergence of order \$alpha\$ 459 472 509 EN Pratulananda Das Jadavpour University Ekrem Savas Istanbul Commerce University Journal Article 2012 08 03 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 A characterization of the symmetric group of prime degree 473 480 510 EN Qingliang Zhang School of Sciences, Nantong University, 226007, Nantong, P. R. China Jinhua Wang School of Sciences, Nantong University, 226007, Nantong, P. R. China Weijun Liu School of Sciences, Nantong University, 226007, Nantong, P. R. China Journal Article 2012 07 29 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 Approximating fixed points of nonexpansive mappings and solving systems of variational inequalities 481 504 511 EN Hossein Piri Department of Mathematics, University of Bonab, Bonab 5551761167, Iran Journal Article 2013 01 04 ‎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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 Arens regularity of bilinear forms and unital Banach module spaces 505 520 512 EN kazem Haghnejad Azar Faculty member of Mohghegh Ardabili Universsity Journal Article 2011 10 22 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.
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 Weak Banach-Saks property in the space of compact operators 521 530 513 EN B. Khadijeh Moosavi Islamic Azad University, Bafgh Branch S. Mohammad Moshtaghioun Yazd University Journal Article 2012 10 12 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^*.\$‎
Iranian Mathematical Society (IMS) Bulletin of the Iranian Mathematical Society 1017-060X 40 2 2014 04 01 On generalisations of almost prime and weakly prime ideals 531 540 514 EN Mahdieh Ebrahimpour ‎University ‎of Vali-e-Asr Journal Article 2012 11 16 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.