BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
Year:2008 | Volume:34 | Issue:2|Papers Count:10

A difficulty in solving linear Diophantine systems is the rapid growth of intermediate results. Rosser’s algorithm for solving a single linear Diophatine equation is an efficient algorithm that effectively controls the growth of intermediate results. Here, we propose an approach to generalize Rosser’s algorithm and present two algorithms for solving systems of linear Diophantine equations. Then, we show that the generalized approach provides us with a new formulation of the LDSSBR of Chou and Collins and a more efficient implementation of Rosser’s approach. The new formulation also enables us to propose an efficient algorithm for solving rank one perturbed linear Diophantine systems based on the LDSSBR, and to improve and extend the class of integer ABS algorithms for solving linear Diophantine systems.

In finite groups the probability that two randomly chosen elements commute or randomly ordered n-tuples of elements mutually commute has recently attracted interest by many authors. There are some classical results estimating the bounds for this kind of probability so that the knowledge of the whole structure of the group can be more accurate.The same problematic has been recently extended to certain classes of infinite compact groups in [2], obtaining restrictions on the group of the inner automorphisms. Here such restrictions are improved for a wider class of infinite compact groups.

Let Irr(G) be the set of irreducible complex characters of a finite group G and cd(G)={x(1) | x Î 2 Irr(G)} be the set of irreducible character degrees of G. The question: Given the set cd(G), what can be said about the structure of G? have been studied by several people. In case cd(G)={1,m}, for some integer m, the basic tools for studying the question can be found in Chapter 12 of the well known book of Isaacs [8]. Isaacs proved in Theorem 12.5 and Corollary 12.6 the following results. Theorem A. Let G be a finite group and cd(G) = {1,m}. Then, at least one of the followings occurs: (a) G has an abelian normal subgroup of index m.

Here, we consider a composite iterative process for two finite families of Lipschitzian mappings in a real Banach space. Our results mainly improve and extend the recent results of [S.S. Chang, Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 129 (2001) 845-853], [Y.J. Cho, J.I. Kang, H. Zhou, Approximating common fixed points of asymptotically nonexpansive mappings, Bull. Korean Math. Soc. 42 (2005) 661-670] and some others.

Here, we present a new complete lift metric for which every infinitesimal fiber-preserving conformal transformation on the tangent bundle induces an infinitesimal projective transformation on the base manifold. Moreover, this correspondence gives rise to a homomorphism between Lie algebras. Also, we introduce an almost product structure on the tangent bundle and show that it is a product structure if and only if the corresponding Riemannian metric is of constant curvature.

Let R, S be rings with identity and M be a unitary (R, S)-bimodule. We characterize homomorphisms and derivations of the generalized matrix ring T =(or sm), and provide a triangular representation of the differential polynomial ring T[b; d].

Abstract. The notion of strongly quotient graph was introduced by Adiga et al. [3]. Here, we show that some well known families of graphs are strongly quotient graphs. We also establish an upper bound for the energy of a strongly quotient graph with respect to the distance matrix.

Abstract. Let A and B be Banach algebras and M be a Banach (A,B)-module. Then, T =[OA BM] equipped with the usual 2x 2 matrix operations, obvious internal module actions and the Banach space norm || [oa bm] || = ||a||A + ||m||m + ||b||B is a triangular Banach algebra. We show that T is biflat if and only if A and B are biflat and M = 0, where M is an essential (A,B)-module, that is, AM-= M= MB-. A similar result is obtained on biprojectivity.

We obtain some new sharp results for some new analytic functional spaces defined with the help of Bergman metric ball.

We study a simple new method to find a numerical solution for the special class of Systems of Non-linear Volterra integrodifferential Equations (SNVE). To this end, we will present our method based on matrix form of SNVE. The corresponding unknown coefficients of our method is determined using computational aspects of matrices. Finally, accuracy of the method is verified by presentation of some numerical computations.