Bulletin of Iranian Mathematical Society
Volume:40 Issue: 2, 2014

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.

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.

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.

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.

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.

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.

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.

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.

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.

In this paper, we introduce the notion of $(m,n)$- algebr aically 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.

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.

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 Keywords: I, statistical convergence, I, lacunary statistical convergence, statistical convergence of order $alpha$