Criterion for Lagrange stability of a class of pendulum-like systems in Hilbert spaces

In this paper, a class of pendulum-like systems in infinite-dimensional Hilbert spaces is investigated. A frequency domain criterion guaranteeing the systems with the property of Lagrange stability is established.     

Constraint qualifications in multiobjective optimization problems: Differentiable case

In this paper, we are concerned with a multiobjective optimization problem with inequality constraints. We introduce a constraint qualification and derive the Kuhn-Tucker type necessary conditions for efficiency. Moreover, we give conditions which ensure the constraint qualification.This work was done while the author was visiting the University of California, Berkeley, California.     

Asymptotic analysis of stochastic programs

In this paper we discuss a general approach to studying asymptotic properties of statistical estimators in stochastic programming. The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs. Asymptotic analysis of the optimal value will be presented in detail. Asymptotic properties of the corresponding optimal solutions are briefly discussed.     

Solution of the planar Newtonian stick–slip problem with the singular function boundary integral method

A singular function boundary integral method (SFBIM) is proposed for solving biharmonic problems with boundary singularities. The method is applied to the Newtonian stick–slip flow problem. The streamfunction is approximated by the leading terms of the local asymptotic solution expansion which are also used to weight the governing biharmonic equation in the Galerkin sense. By means of the divergence theorem the discretized equations are reduced to boundary integrals. The Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers, the values of which are calculated together with the singular coefficients. The method converges very fast with the number of singular functions and the number of Lagrange multipliers, and accurate estimates of the leading singular coefficients are obtained. Comparisons with the analytical solution and results obtained with other numerical methods are also made. Copyright © 2005 John Wiley & Sons, Ltd.     

ERROR ANALYSIS AND GLOBAL SUPERCONVERGENCES FOR THE SIGNORINI PROBLEM WITH LAGRANGE MULTIPLIER METHODS

1. IntroductionIt is well known that contact problems have always occupied a position of special importancein the mechanics of solids. So it attracted particular attention of engineers and computationalexperts. In the last ten years, with the development …     

｜x｜^α的Lagrange插值多项式在零点的收敛速度

S.M.Lozinskii指出了函数｜x｜基于等距节点的Lagrange插值多项式在零点的收敛速度.2000年,M.Revers把S.M.Lozinskii的结果推广到｜x｜~α(0<α1).本文考虑的是把等距节点改为修改的Chebyshev节点,从而把零点处的收敛速度从M.Revers证明的O(n-α)提高O(n-2α).     

Direct simulation of the motion of neutrally buoyant balls in a three-dimensional Poiseuille flow

In a previous article the authors introduced a Lagrange multiplier based fictitious domain method. Their goal in the present article is to apply a generalization of the above method to: (i) the numerical simulation of the motion of neutrally buoyant particles in a three-dimensional Poiseuille flow; (ii) study – via direct numerical simulations – the migration of neutrally buoyant balls in the tube Poiseuille flow of an incompressible Newtonian viscous fluid. Simulations made with one and several particles show that, as expected, the Segré–Silberberg effect takes place. To cite this article: T.-W. Pan, R. Glowinski, C. R. Mecanique 333 (2005).     

Regularized Principal Component Analysis for Spatial Data

In many atmospheric and earth sciences, it is of interest to identify dominant spatial patterns of variation based on data observed at p locations and n time points with the possibility that p > n. While principal component analysis (PCA) is commonly applied to find the dominant patterns, the eigenimages produced from PCA may exhibit patterns that are too noisy to be physically meaningful when p is large relative to n. To obtain more precise estimates of eigenimages, we propose a regularization approach incorporating smoothness and sparseness of eigenimages, while accounting for their orthogonality. Our method allows data taken at irregularly spaced or sparse locations. In addition, the resulting optimization problem can be solved using the alternating direction method of multipliers, which is easy to implement, and applicable to a large spatial dataset. Furthermore, the estimated eigenfunctions provide a natural basis for representing the underlying spatial process in a spatial random-effects model, from which spatial covariance function estimation and spatial prediction can be efficiently performed using a regularized fixed-rank kriging method. Finally, the effectiveness of the proposed method is demonstrated by several numerical examples.     

On the solution of plane boundary-value problems of elasticity in a rectangle

An algorithm for solving plane boundary-value problems of elasticity for a rectangular domain is expounded. The algorithm is based on a complex-valued representation of the general solution to the differential equations of the plane problem and on the use of Lagrange polynomials to satisfy the boundary conditions. The algorithm can quite easily be implemented in a computer program. This is probably the simplest way of solving boundary-value problems of this class __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 1, pp. 97–102, January 2006.     

On the canonical equations of Kirchhoff-Love theory of shells

The paper outlines a procedure to derive the canonical system of equations of the classical theory of thin shells using Reissner’s variational principle and partial variational principles. The Hamiltonian form of the Reissner functional is obtained using Lagrange multipliers to include the kinematical conditions that follow from the Kirchhoff-Love hypotheses. It is shown that the canonical system of equations can be represented in three different forms: one conventional form (five equilibrium equations) and two forms that are equivalent to it. This can be proved by reducing them to the same system of three equations. For problems with separable active and passive variables, partial variational principles are formulated __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 10, pp. 99–107, October 2007.