Bulletin of the Iranian Mathematical Society
Year:2014 | Volume:40 | Issue:2|Papers Count:17

A matrix PÎCn×n is called a generalized reflection matrix if PH=P and P2=I. An n×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 j be an analytic self-map of the unit disk D. We investigate some operator theoretic properties of bilateral composition operator Cj, T: f®T o f o j on the vector-valued Hardy space Hp (X) for 1£p£+¥. Compactness and weak compactness of Cj, T on Hp (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 x: H®C is an irreducible character (not necessarily linear). Denote by VX (H) the symmetry class of tensors associated with H and X. Let K (T)ÎEnd (VX (H)) be the operator induced by TÎEnd (V). The decomposable numerical range WX (T) of T is a subset of the classical numerical range W (K (T)) of K (T) defined as:WX (T) = {(K (T) x*, x*): x* is a decomposable unit tensor}.In this paper, we study the interplay between the geometric properties of WX (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 WTW and ZTZ 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 GL (S) and GH (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 A * H. Results from the literature are generalized.

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.

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 N) and introduce the notions of I-statistical convergence of order a and I-lacunary statistical convergence of order a, where 0<a<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.

Let G be a finite group and G (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: G @ Sp if and only if |G| = |Sp| and G (G) = G (Sp), where p is a prime.

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. More-over, we apply our main result to obtain strong convergence theorem to a common fixed point of a nonexpansive mapping and solutions of a system of variational inequalities of an inverse strongly mono-tone mapping and strictly pseudo-contractive mapping of Browder-Petryshyn type.

Assume that A, B are Banach algebras and that m: A´B ® B, m¢: A´A ® B are bounded bilinear mappings. We study the relationships between Arens regularity of m, m¢ 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 Ze¢¢ (B**) = B** where e¢¢ 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.

For suitable Banach spaces X and Y with Schauder decompositions and a suitable closed subspace M of some compact operator space from X to Y, it is shown that the strong Banach-Saks-ness of all evaluation operators on M is a sufficient condition for the weak Banach-Saks property of M, where for each xÎX and y*ÎY*, the evaluation operators on M are defined by fx (T)= Tx and yy* (T)= T*y*.

Let R be a commutative ring with identity. A proper ideal P of R is an (n - 1, n)-Fm-prime ((n - 1, n)-weakly prime) ideal if a1, … , anÎR, a1 … anÎP\P m (a1 … anÎP\{0}) implies a1 … ai-1 ai+1 … anÎP, for some iÎ{1, …, n}; (m, n³2).In this paper several results concerning (n - 1, n)-Fm-prime and (n - 1, n)-weakly prime ideals are proved. We show that in a Noetherian domain a Fm-prime ideal is primary and we show that in some well-known rings (n - 1, n)-Fm-prime ideals and (n - 1, n)-prime ideals coincide.