An improvement on the positivity results for 2-stage explicit Runge-Kutta methods

In this paper, we investigate the positivity property for a class of 2-stage explicit Runge-Kutta (RK2) methods of order two when applied to the numerical solution of special nonlinear initial value problems (IVPs) for ordinary differential equations (ODEs). We also pay particular attention to monotonicity property. We obtain new results for positivity which are important in practical applications. We provide some numerical examples to illustrate our results.     

A general solution for static piezothermoelastic problems of crystal class 6mm solids

In this paper, a general solution for three-dimensional static piezothermoelastic problems of crystal class 6mm solids is presented. The general solution involves four piezoelastic potential functions and a piezothermoelastic potential function, of which four piezoelastic potential functions are governed by weighted harmonic differential equations. Compared with the general solution given by Ashida et al., in which seven potential functions are introduced, the general solution proposed in the present paper is more rigorously derived. Moreover, it has a simple form and is convenient for application. As an illustrative example, the problem of a pyroelectric half-space subjected to axisymmetric heating is studied. Numerical results of displacements stresses, electric potential and electric displacements are obtained for a cadmium selenide half-space. Thermally induced displacements and stress distribution are compared with those obtained for the same material without piezoelectric and pyroelectric effects. Project supported by the National Natural Science Foundation of China (19872060).     

Structural analysis of certain linear operators representing chemical network systems via the existence and uniqueness theorems of spectral resolution. VI*

The present Part VI of this series of articles provides a mathematical and methodical link between (i) fundamental methodology in the repeat space theory (RST), which is referred to as the approach via the aspect of form and general topology and which has universal unifying power to handle additivity problems of molecules that have many identical moieties, and (ii) frontier electron theory of reactivity indices. Using theoretical tools required to link (i) and (ii), we establish a theorem from which the Generalized Alpha Existence Theorem (a theorem essential in the RST and proved in the previous Part V) directly follows. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 389–400, 2001     

A CONSTRAINT QUALIFICATION FOR CONVEX PROGRAMMING

1. IntroductionLet X be the n-dimensional Euclidean space Rad. Denote the transpose of the columnvector y by yT. Suppose that R7 and nit R= are the n-dimensional vector sets with nonnegative and positive components, whose elements are denoted by y 3 0 and y > 0, respectively.Write R for the nonnegative real number set.Consider a nondiffereatiable convex programming problem:We assume that f(x), gi(x),..', g.(x) are finite reaLvalued continuous, convex functions on X, but not necessarily d…     

A QP-free constrained Newton-type method for variational inequality problems

Received January 5, 1997 / Revised version received November 19, 1997 Published online November 24, 1998     

Block-Projections Algorithms with Blocks Containing Mutually Orthogonal Rows and Columns

In this paper we present an algorithm which, for a given (sparse) matrix, constructs a partition of its set of row-indices, such that each subset of this partition (except the last one obtained) contains indices which correspond to mutually orthogonal rows. We then use such decompositions in some classes of block-projections methods, previously extended by the author to general inconsistent linear least-squares problems. Numerical experiments on an inconsistent and rank-deficient least-squares model problem are described in the last section of the paper.     

Economic Characterization of Reciprocal Isoperimetric Control Problems Revisited

Theorem 2.1 of Caputo (Ref. 1) linking the optimal solution functions and optimal value functions of reciprocal pairs of isoperimetric control problems is correct, but requires stronger assumptions than those used explicitly to establish its veracity. One such set of stronger assumptions is provided in this note.     

The boundary element method applied to elastic contact problems with friction

In the current paper the boundary integral equations (BIE) for elastic contact problems with friction are derived from the incremental virtual work principle. After introducing contact conditions of adhesion and slip into BIE all variants on boundary are made to discretize by quadratic isoparametric boundary element. In the current paper not only an auto-increment loading law is presented but also the iterative calculation laws for open, slip and adhesion condition are given. The results of numerical examples are satisfactory.     

A production system with two job classes,changeover times and revisitation

This paper, motivated by the need to predict performance of production systems with random arrivals, setup times and revisitation, presents an imbedded Markov chain analysis of the underlyingM/G/1 queue with two customer classes, changeover times and instantaneous Bernoulli feedback. It is assumed that jobs are scheduled according to the exhaustive alternative priority queue discipline. Expressions for the mean waiting time and the nonsaturation condition are derived under two different priority assignments to the repeat customers. Sojourn times under these priority assignments are shown to possess a convex ordering. Results of the study are also applicable to data communication networks that operate under cyclic switching mechanisms. Research supported in part by Natural Sciences and Engineering Research Council of Canada.     

Comparison theorems for diffusion processes

We prove comparison theorems for diffusion processes onR ^d. From these theorems we derive lower and upper bounds for the transition probabilities of a diffusion process. In contrast to the known estimates for fundamental solutions of parabolic equations our bounds do not depend on the moduli of continuity of the coefficients of the differential operator.