BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY
Year:2010 | Volume:36 | Issue:2|Papers Count:20

The notion of an action of a locally compact quantum group on a von Neumann algebra is studied from the amenability point of view. Various Reiter’s conditions for such an action are discussed. Several applications to some specific actions related to certain representations and corepresentaions are presented.

An ideal I of an exchange ring R is separative provided that for all A, B  Î FP(I), 2A @= A Å B @ 2B implies that A @ B. We prove that I is separative if and only if so is the ideal of all (triangular) matrices over I. Further, we investigate diagonal reduction over such ideals. Comparability of modules over such ideals are studied as well.

Mirror-symmetric matrices have important applications in studying odd/even-mode decomposition of symmetric multiconductor transmission lines (MTL). In this paper, we propose an iterative algorithm to solve the mirror-symmetric solution of matrix equation AXB + CY D = E. With it, the solvability of the equation over mirror-symmetric X, Y can be determined automatically. When the equation is consistent, its solution can be obtained within finite iteration steps, and its least-norm mirror-symmetric solution can be obtained by choosing a special kind of initial iteration matrices. Furthermore, the related optimal approximation problem is also solved. Numerical examples are given to show the efficiency of the presented method.

We discuss the invariant properties of curvatures effected by the Matsumoto’s C or L-process. We find equivalent conditions on curvatures by comparing the difference between the corresponding curvatures of closely related connections. As an application, Matsumoto’s L-process on Randers manifold is studied. Shen’s connection can not be obtained by using Matsumoto’s processes from other connections. This leads us to two new processes which we call Shen’s C and L-processes. We study the invariant properties of curvatures under Shen’s processes.

We introduce the notion of LMIP ( A), where A is a Banach space, I is an index set and 1 £ p <¥. We find necessary and sufficient conditions for which LMIP ( A) is a Banach algebra and investigate amenability of this Banach algebra. Applications to lP(S) (1 £ p <¥), where S is a Brandt semigroup, are also given.

Let M be a finitely generated module over a regular local ring (R, n), and let M = {Mi} be an n-stable filtration on M. As a consequence of a recent result by Rossi and Sharifan in [14], we prove that if the i-th Betti numbers of M and (grM({M}) coincide with each other, then for each j ³ i the j-th Betti numbers of them are the same and Syzi(M) is a Koszul module provided that Syzi(grM(M) is component wise linear.

We introduce a new adaptive updating technique of the barrier parameter in the celebrated Mehrotra's predictor-corrector algorithm for linear optimization. Our new technique enables us to prove the polynomial iteration complexity of Mehrotra's algorithm without any safeguards. Encouraging computational results using Lipsol software package are reported.

Let k be an integer greater than 2 and n1, . . . , nk be a sequence of positive integers with at most one of them being equal to 1. Let qn1,...,nk be a graph consisting of k paths, having only their endpoints in common. We characterize all sequentially Cohen-Macaulay graphs of this type. We also show for these types of graphs the notions of vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent.

We formulate the operational Tau method for the two dimensional linear Fredholm integral equations of the second kind. Some theoretical results are given to simplify application of the Tau method, and then existence and uniqueness of solution for these equations are investigated. We also estimate error of the proposed method and give some numerical examples to demonstrate its accuracy in finding solutions.

Let G be the special linear group SL (3, q), where q is power of a primep. Here, we show that P has a linear constituent with multiplicity one for each irreducible characterand Sylow p-subgroup P of G. Furthermore, if cf (G) is the vector space of class functions of G, we show that the restriction of a subset of irreducible characters ofG on P is a basis for the vector space of class functions defined onP spanned by {f | f Î cf (G)}.

Let I, J be ideals of a commutative Noetherian ring R and lett be a non–negative integer. Let M be an R–module such that ExtR t(R/I, M) is a finite R–module. If t is the first integer such that the local cohomology module with respect to (I, J) is non– (I, J) –cofinite, then we show that HomR (R/I, Ht I,J(M)) is finite. Also, we study the finiteness of Ext R i(R/I, HtI,J (M)), for i=1, 2. In addition, for a finite R–module M, we show that the associated primes of HI,J t(M) have an equal grade, when t=inf {i|Hi I, J(M)  ¹0}.

We establish the Brunn-Minkowski-type inequality for Lp-dual mixed volumes of star duality of mixed intersection bodies.

We introduce the notion of nilpotent p.p. rings, and prove that the nilpotent p.p. condition is preserved over polynomial rings and skew polynomial rings.

We derive the first and second variation formulas for exponentially harmonic maps between Finsler manifolds, and prove that there is no non-degenerate stable exponentially harmonic map between a compact convex hypersurface of the Euclidean space and any compact Finsler manifold.

We extend the study of Chebyshev centers in pre-Hilbert C*-modules by considering the C*-algebra valued map defined by ½x½=<x, x>1/2. We prove that if T is a remotal subset of a pre-Hilbert C*-module M, and F Í M is star-shaped at a relative Chebyshev center c of T with respect to F, then ½x-qT (x)½2 ³ ½x-c½2+½c-qT (c)½2 (x  Î F). The uniqueness of Chebyshev center follows from this inequality. This is a generalization of a well-known result on Hilbert spaces.

We introduce and investigate some new subclasses of close-to-convex and quasi-convex functions with respect to 2k-symmetric conjugate points. Such results as inclusion relationships, integral representations, convolution properties, integral preserving properties, growth and covering theorems for these function classes are proved. The results presented here would provide extensions of those given in earlier works. Several other new results are also obtained.

We deal with the initial-boundary value problem for a quasilinear degenerate parabolic equation with inhomogeneous density and absorption, which appears in a number of applications to describe the evolution of diffusion processes, in particular non-Newtonian flow in a porous medium. We discuss the extinction of solution and the finite speed of propagation of perturbations.

We present a simple and elementary method for computing the Kostka numbers. We use this method to give compact formulas for K p,m in some special cases.

We give upper bounds for the regularity of edge ideal of some classes of graphs in terms of invariants of graph. We introduce two numbers a’ (G) and n (G) depending on graph G and show that for a vertex decomposable graphG, reg (R/I (G)) £ min{a’ (G), n (G)} and for a shellable graph G, reg (R/I (G))£n (G). Moreover, it is shown that for a graphG, where Gc is a d-tree, we have pd (R/I (G)) =maxvÎV (G) {degG (v)}.

We shall establish two fixed point theorems for contractive multifunctions in a non-empty and closed subset of a complete metric space with certain assumptions.