In this paper, we are concerned with random sampling of an n dimensional integral point on an (n−1) dimensional simplex according to a multivariate discrete distribution. We employ sampling via Markov chain and propose two “hit-and-run” chains, one is for approximate sampling and the other is for perfect sampling. We introduce an idea of alternating inequalities and show that a logarithmic sepa...

Let n k denote the number of times the kth largest distance occurs among a set S of n points. We show that if S is the set of vertices of a convex polygone in the euclidean plane, then n1+2n2~3n and n2<~n +n 1. Together with the well-known inequality n~<~n and the trivial inequalities n~>~O and n2>~O, all linear inequalities which are valid for n, n 1 and n2 are consequences of these. Similar r...

It is customary to formulate the inequalities of the "Verzerrungssatz" type for analytic functions w—f(z), schlicht in the unit circle, with reference to a specific normalization. The two normalizations mainly used are: (a) f(z) is finite in \z\ < 1 , /(O) = 0 , /'(O) = 1; (b) ƒ(z) has a pole at 2 = 0 with the residue 1. If we want to obtain inequalities which are independent of any particular ...

In this paper, we propose an inexact alternating direction method with square quadratic proximal  (SQP) regularization for  the structured variational inequalities. The predictor is obtained via solving SQP system  approximately  under significantly  relaxed accuracy criterion  and the new iterate is computed directly by an explicit formula derived from the original SQP method. Under appropriat...

Using formal logic, many iproblems from the general area of linear inequalities co~ be expressed in the elementary theory o f addition on the real numbers (EAR). We describe a method for eliminatit~ quantiflers in EAR which has been programmed arm demonstrate its usefulness in solving some problems related to linear programming. In the area o f mechanical mathematics this kind o f approach has ...