1.School of Mathematics and Statistics, Zaozhuang University , Zaozhuang, 277160, China. 2.School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310018, China. (Received November 08, 2014, accepted March 07, 2015) Abstract. This paper proposes a parallel descent-like prediction-correction method(PDPCM) for structured variational inequalities with three bl...

ERROR ESTIMATES OF A FIRST-ORDER LAGRANGE FINITE ELEMENT TECHNIQUE FOR NONLINEAR SCALAR CONSERVATION EQUATIONS∗ JEAN-LUC GUERMOND† AND BOJAN POPOV† Abstract. This paper establishes a O(h 1 4 ) error estimate in the L∞t (Lx)-norm for the approximation of scalar conservation equations using an explicit continuous finite element technique. A general a priori error estimate based on entropy inequal...

We use Turán type inequalities to give new non-asymptotic bounds on the extreme zeros of orthogonal polynomials in terms of the coefficients of their three term recurrence. Most of our results deal with symmetric polynomials satisfying the three term recurrence pk+1 = xpk − ckpk−1, with a nondecreasing sequence {ck}. As a special case they include a non-asymptotic version of Máté, Nevai and Tot...

Given a graph with n nodes each of them having labels equal either to 1 or 2 (a node with label 2 is called a terminal), we consider the (1,2)-survivable network design problem and more precisely, the separation problem for the partition inequalities. We show that this separation problem reduces to a sequence of submodular flow problems. Based on an algorithm developed by Fujishige and Zhang th...

A stability version of the Blaschke-Santaló inequality and the affine isoperimetric inequality for convex bodies of dimension n≥ 3 is proved. The first step is the reduction to the case when the convex body is o-symmetric and has axial rotational symmetry. This step works for related inequalities compatible with Steiner symmetrization. Secondly, for these convex bodies, a stability version of t...

Given two covar iance matrices R and S for a given elliptically con toured distribution, we show how simple inequalities between the matr ix elements imply that ER(f)< Es(f), e.g., when x = (xil,i ...... i,) is a mult i index vector and f ( x ) = rain max rain max. . .xi l ..... i,, i l i2 i3 or f(x) is the indicator funct ion of sets such as (3 U N U...rx, ...... ~._-<;o, ..... ,~ i l i2 i3

Projection type methods are among the most important methods for solving monotone linear variational inequalities. In this note, we analyze the iteration complexity for two projection methods and accordingly establish their worst-case O(1/t) convergence rates measured by the iteration complexity in both the ergodic and nonergodic senses, where t is the iteration counter. Our analysis does not r...

We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincaré inequalities, to provide a better understanding of the decrease in Fisher Information implied by results of Barron and Brown. We show that if the standardized Fisher Information ever becomes finite then it conver...

We give conditions for an O(1/n) rate of convergence of Fisher information and relative entropy in the Central Limit Theorem. We use the theory of projections in L2 spaces and Poincaré inequalities, to provide a better understanding of the decrease in Fisher information implied by results of Barron and Brown. We show that if the standardized Fisher information ever becomes finite then it conver...

We determine the numbers of integral tetrahedra with diameter d up to isomorphism for all d ≤ 1000 via computer enumeration. Therefore we give an algorithm that enumerates the integral tetrahedra with diameter at most d in O(d5) time and an algorithm that can check the canonicity of a given integral tetrahedron with at most 6 integer comparisons. For the number of isomorphism classes of integra...