求解stokes问题的一个新的非协调混合元格式

构造一个新的非协调混合元格式求解stokes问题,证明了该元满足B-B条件,并且有2阶收敛速度.     

The Order Completion Method for Systems of Nonlinear PDEs: Pseudo-topological Perspectives

By setting up appropriate uniform convergence structures, we are able to reformulate the Order Completion Method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs. As an application, we obtain existence and uniqueness results for the solutions of arbitrary continuous, nonlinear PDEs.      

Charge-conserving electron density averaging for a set of nuclear configurations

The Löwdin-Inverse Löwdin Transformation (LILT) technique combined with the Diophantine Density Matrix Purification (DDMP) method is suggested for a charge-preserving density averaging approach for a range of nuclear configurations.     

Quadratic spline-on-spline

Recently Dolezal and Tewarson [2], and Papamichael and Soares [3] have considered the cubic spline-on-spline for the purpose of the approximating the derivatives y⁽²⁾,y⁽³⁾, and y⁽⁴⁾. In this paper their ideas have been extended and the quadratic spline-on-spline has been established for the same purpose. This technique yields better results than the traditional process using a single quadratic spline.     

A mixed algorithm for the calculation of rapidly varying fluid flows: The impulsively started circular cylinder

A mixed discrete Fourier transform-Finite difference algorithm is developed and used for the calculation of rapidly changing viscous fluid flows past a circular cylinder. The numerical approach has been designed to overcome certain difficulties arising for high Reynolds number simulations. The foremost advantage of the technique lies in its fast calculations of the convolution sums portraying the convective terms of the governing equations. Third-order spatial discretizations and fourth-order time marching are implemented. New schemes are proposed for the boundary conditions at the solid wall and at large distances. The techniques are tested on a case study with other schemes (summarized by Roache¹) in order to obtain an optimal choice. Definite indications on the stability and accuracy of boundary condition schemes are achieved. Support for the statement of dominant importance of boundary conditions is also given. A comparison of computational results with experimental data is presented for the case study of the flow past an impulsively started cylinder at Reynolds number 20. The time development of the symmetrical zone of recirculation, which is formed at an early stage of the flow, has been studied for 300 ≤ Re ≤ 9500 by means of the proposed algorithm. Computational results, comparisons with experimental data² and discussion of upper limits of validity of the procedure will be presented in a companion paper.     

关于n阶微分方程边值问题（Ⅲ）——奇摄动的渐近展开

本文研究n阶非线性过值问题(NB)的奇异摄动。在较一般的条件下,应用高阶微分不等式理论证明了摄动解的存在性,并给出了摄动解直到n阶导函数的一致有效渐近展开式,推广和改进了已有的结果。     

The range of the p-Laplacian

We prove that for λ ≥ 0, p ≥ 3, there exists an open ball B L²(0,1) such that the problem

− (|u′|^p−2 u′)′ − λ|u|^p−2u = f, in (0,1)

, subject to certain separated boundary conditions on (0,1), has a solution for f B.     

On a characterization of the exponential distribution by spacings

Summary LetX be a non-negative random variable with probability distribution functionF. SupposeX _i,n (i=1,…,n) is theith smallest order statistics in a random sample of sizen fromF. A necessary and sufficient condition forF to be exponential is given which involves the identical distribution of the random variables (n−i)(X _i+1,n−X_i,n) and (n−j)(X _j+1,n−X_j,n) for somei, j andn, (1≦i<j<n). The work was partly completed when the author was at the Dept. of Statistics, University of Brasilia, Brazil.     

An approach to high-speed micro-HPLC

The possibility of high-speed micro-HPLC has been investigated using a short micro-column (35 mm × 0.5 mm i.d.) packed with 3 μm ODS particle. The results indicate that this approach has considerable potential for good separations with short analysis time. A typical example shows only three minutes is required with a plate count of 3,800 to separate seven PAHs.     

Necessary and sufficient optimality conditions for a class of nonsmooth minimization problems

The purpose of this paper is to derive, in a unified way, second order necessary and sufficient optimality criteria, for four types of nonsmooth minimization problems: thediscrete minimax problem, thediscrete l ₁-approximation, the minimization of theexact penalty function and the minimization of theclassical exterior penalty function. Our results correct and supplement conditions obtained by various authors in recent papers.