R.K. SAXENA Department of Mathematics and Statistics, Jai Narain Vyas University Jodhpur 342001, INDIA A.M. MATHAI Department of Mathematics and Statistics, McGill University, 805 Sherbooke Street West, Montreal, CANADA H3A 2K6 H.J. HAUBOLD Office for Outer Space Affairs, United Nations, P.O. Box 500, A-1400 Vienna, AUSTRIA Abstract. The subject of this paper is to derive the solution of genera...

In this paper we give generalization of Opial-type inequalities by using generalized fractional integral operator involving generalized Mittag–Leffler function. We deduce some results which already have been proved. Also we consider n -exponential convexity of some non-negative differences of inequalities involving Mittag-Leffler function and deduce their exponential convexity and log-convexity.

The complex nature of damage in ceramic matrix composites (CMCs) renders conventional methods of measuring quantitative fracture properties impractical. This paper is the first of twopart series that assesses the feasibility of using the J-integral with full-field deformation data from Digital Image Correlation (DIC) to characterize toughness in continuous fiber SiC/SiC CMC laminates. It provid...

We define the determinantal divisor rank of an integral matrix to be the number of invariant factors which equal 1. Some properties of the determinantal divisor rank are proved, which are analogous to known properties of the usual rank. These include the Frobenious inequality for the rank of a product and a relation between the rank of a submatrix of a matrix and that of its complementary subma...

Abstract— We present an a-posteriori method for computing rigorous upper and lower bounds of the J-integral in two dimensional linear elasticity. The J-integral, which is typically expressed as a contour integral, is recast as a surface integral which yields a quadratic continuous functional of the displacement. By expanding the quadratic output about an approximate finite element solution, the...

One of the methods for solving definite integrals is modified trapezoid method, which is obtained by using Hermit interpolation [J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, Second Edition, Springer-Verlag, 1993]. In this article we intend to make a quadrature method for solving the linear integral equations such as repeated trapezoid and repeated Simpson quadrature by using repea...

In a recent paper Richards and Zheng compute the determinant of a matrix whose entries are given by beta-type integrals, thereby generalising an earlier result by Dixon and Varchenko. They then use their result to obtain a generalisation of the famous Selberg integral. In this note we point out that the Selberg-generalisation of Richards and Zheng is a special case of an integral over Jack poly...

Proof: Jf there exists a closed integral curve, then both r* and C* are in the kernel of F*, so F*0. If there is no closed integral curve, let r' be a cycle without contact.3 Any integral curve of F meets r' infinitely often; let P be a point of accumulation of these intersections. We may then construct a C' closed curve C' which differs from the integral curve only in an arbitrarily small neig...

‎in this paper, based on [a. razani, v. rako$check{c}$evi$acute{c}$ and z. goodarzi, nonself mappings in modular spaces and common fixed point theorems, cent. eur. j. math. 2 (2010) 357-366.] a fixed point theorem for non-self contraction mapping $t$ in the modular space $x_rho$ is presented. moreover, we study a new version of krasnoseleskii's fixed point theorem for $s+t$, where $t$ is a cont...

A matrix A = (a~j) has the Edmonds--Johnson property if, for each choice of integral vectors dl, d,., b~, b~, the convex hull of the integral solutions of dt~-x~-d2, bt~-Ax~-b.~ is obtained by adding the inequalities cx~_[~], where c is an integral vector and cx~_J holds for each solution of da~_x~_d2, b~_Ax~_b.. We characterize the Edmonds--Johnson property for integral matrices A which satisf...