奇异摄动问题的一致收敛离散方法解的一致高阶精度外推

本文讨论基于整体误差一致展开式的一致收敛离散方法解的一致高阶精度外推.将该方法应用于非自共轭问题的Il'in-Allen-Southwell格式,我们得到了二阶一致收敛的外推解,并用数值计算说明该结论.     

椭圆型方程四面体线元的超逼近与外推

重新讨论了三角线元的积分恒等式,使之适用于三维区域的拟一致四面体元,借此证明了椭圆型方程有限元解梯度有超逼近现象,函数值Richardson外推可以提高精度.     

一类拟线性双曲型方程有限元解及其导数的超收敛性

§1.引言关于二阶线性椭圆型方程有限元法的超收敛性研究,已有工作[1]～[6]。本文对于一类拟线性双曲型方程,证明了它的有限元解及其导数具有超收敛性。问题的提法考虑下述混合问题     

四阶方程两点边值问题Hermite有限元解的渐近展式与外推

1引言有限元解的渐近展式是提高微分方程数值解精度的重要工具,比如亏量校正和外推就是建立在有限元解的渐近展式的基础之上．许多作者对此进行了大量的研究(见[1]-[4]),特别是文[1],提出了在研究有限元解的渐近展式中十分有用的能量嵌入技巧．本文利用能量嵌入定理得到了四阶方程两点边值问题Hermite有限元解及其二阶平均导数的渐近展式,进一步我们还讨论了它们的Richardson外推公式．考虑四阶方程两点边值问题     

用有限元方法求解界面特征值问题

用有限元方法计算椭圆型界面特征值问题,实验数据显示近似特征值的变化规律:界面特征值问题中系数的间断性对协调和非协调Crouzeix-Raviart有限元特征值的收敛性并无影响,而且对协调有限元特征值外推以后得到高精度的解,相应的外推值还提供特征值下界;Crouzeix-Raviart元特征值提供特征值下界,这对一般有界区域如"镂空"型区域也成立.另外,还展示近似特征函数的图形.     

最优控制问题的有限元高精度分析及其应用 献给林群教授80华诞

本文简要回顾偏微分方程最优控制问题的有限元高精度分析和基于高精度分析的高效有限元算法的若干研究工作,包括椭圆型方程、抛物型方程最优控制问题的有限元超收敛,椭圆型方程、Stokes方程最优控制问题的混合有限元超收敛,以及基于高精度分析的后验误差估计和自适应有限元方法及有限元外推和校正.本文对近年来上述研究进展进行综述,并展望拟开展的研究工作.     

带第三类边界条件的椭圆型方程的广义Galerkin方法

§1 引言 文[1]和[2]讨论了带第一类边界条件的二阶椭圆型方程的广义差分法(即广义Galerkin方法)。本文主要讨论带第二、三类边界条件的二阶椭圆型方程的广义Galerkin方法,就试探函数空间为分片线性函数,检验函数空间为分片常数的情形,对三角部分证明了广义Galerkin解的存在唯一性,并得到了收敛阶的估计。     

一类椭圆方程很弱解关于区域的连续性

本文讨论了二阶椭圆型方程-△u=f(x,u),x∈Ω的Dirichlet问题u | Ω=0的很弱解u∈W ,r(Ω)(1＜r＜2)关于区域Ω的连续性及很弱边值问题的很弱解的唯一性.     

二阶椭圆型方程组的第三边值问题

本文中,我们讨论二阶非线性一致椭圆型方程组(1.1)在多连通区域上的第三边值问题(问题Ⅲ)。首先,我们证明了调和函数问题Ⅲ解的存在唯一性,并建立了方程组(1.1)问题Ⅲ解的积分表示。然后,使用上述结果,方程组(1.1)问题Ⅲ解的先验估计以及Leray-Schauder定理,我们得到了满足某些条件的二阶非线性椭圆型方程组(1.1)问题Ⅲ的可解性结果。     

ADIF迭代法及其有关问题

§1.引言 本文将考虑二维自共轭二阶椭圆型方程边值问题:其中Ω为有界开域;在闭域Ω上系数P,Q和f Lipschitz连续并有P,Q>0,(x,y)∈Ω。用有限差分法或有限元方法求其数值解,通常导致如下稀疏正定矩阵的线性代数方程组的求解问题:     

Quenched large deviation principle for words in a letter sequence

When we cut an i.i.d. sequence of letters into words according to an independent renewal process, we obtain an i.i.d. sequence of words. In the annealed large deviation principle (LDP) for the empirical process of words, the rate function is the specific relative entropy of the observed law of words w.r.t. the reference law of words. In the present paper we consider the quenched LDP, i.e., we condition on a typical letter sequence. We focus on the case where the renewal process has an algebraic tail. The rate function turns out to be a sum of two terms, one being the annealed rate function, the other being proportional to the specific relative entropy of the observed law of letters w.r.t. the reference law of letters, with the former being obtained by concatenating the words and randomising the location of the origin. The proportionality constant equals the tail exponent of the renewal process. Earlier work by Birkner considered the case where the renewal process has an exponential tail, in which case the rate function turns out to be the first term on the set where the second term vanishes and to be infinite elsewhere. In a companion paper the annealed and the quenched LDP are applied to the collision local time of transient random walks, and the existence of an intermediate phase for a class of interacting stochastic systems is established.     

Testing for causality in the Richardson arms race model

This paper shows that the Hsiao test can be used to test the causal implication of the Richardson model demonstrating arms race between U.S. and the U.S.S.R. in the presence of China. The impact of Strategic Arms Limitation Talks (SALT I) upon the arms race of the U.S. and the U.S.S.R. is also examined. Two conclusions can be drawn from this study: First, it was found that it was the growth in the U.S.S.R. armament that ‘Granger caused’ the growth in U.S. arms spending over the period from 1952 to 1981. Second, there seems little evidence that SALT I has had any impact upon the armaments of either the U.S. or the U.S.S.R..     

Numerical Simulation of Crack Growth

In recent years the X-FEM based on the partition of unity method and the strong discontinuity approach (SDA) have shown to be powerful tools to model crack growth. Both methods model the crack surface by introducing additional d.o.f.. In the X-FEM the nodes in the mesh around a crack are globally enhanced with new d.o.f. while in in the SDA the new d.o.f. are commonly introduced as internal ones. Thus the jump displacement fields are constant across elements. Therefore the d.o.f. can be condensed on element level which results in jumps in the displacement field at element edges. In this contribution the strong discontinuity approach is used approximating the displacement jump linearly across the crack length similar as e.g. in [3]. New additional nodes of the cracked elements that lie on the element edges are introduced but are not considered as internal nodes but remain global. Thus crack path continuity is automatically given. These global d.o.f. approximate the discontinuous part of the displacement field. The sum of the aforementioned part and the continuous displacement field represent the total displacement field including a possible jump. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

网络外部性条件下差异化双边平台买者参与问题

双边平台存在的基础是参与的用户,因此用户的分配是双边市场上各利益主体最关心的问题。为研究用户分配问题,本文在具有差异性的竞争双边市场上,建立了两阶段的双边平台竞争模型。第一阶段使用Rubinstein讨价还价模型对卖者的参与人数进行分配,利用讨价还价顺序描述卖者进入的先后顺序;第二阶段分别在平台利润最大化和社会福利最大化两种情况下,刻画买者对平台的规模偏好,并求均衡的市场份额。通过此模型分析竞争性平台差异化的情况下,网络外部性系数对平台均衡市场份额以及市场利益相关者利得的影响。研究表明:在考虑平台利润最大化的情况下,买者参与人数受卖者规模与网络外部性系数的影响,平台规模并非越大越好;在考虑社会福利最大化的情况下,买者的网络外部性系数与买者参与人数不相关,但与总社会福利正相关。     

天然心瓣关闭机理研究

本文在二维模型假定的基础上,从一个新的角度,通过理论分析和实验研究,解决了心脏瓣膜在射血加速相的部分关闭机理以及旋涡在瓣关闭中的作用这两个心瓣关闭机理研究中长期以来一直悬而未决的问题,并指出了窦(或瓣叶后空腔)对有效瓣膜关闭的决定性作用.此外,本文还研究了瓣长、频率等对瓣运动的影响.估计本文的研究对人工心瓣的研制有一定参考作用.     

The Convergence of the Spectral Scheme for Solving Two-Dimensional Vorticity Equations

Much work has been done for the spectral scheme of the P.D.E. The author proposed a technique to prove the strict error estimation of the spectral scheme for the K.D.V.-Burgers equation. In this paper, the technique is generalized to two-dimensional vorticity equations. Under some conditions, the error estimation implies the convergence. The more smooth the solution of the vorticity equations, the more accurate the approximate solution.     

Problem of an elastic half-plane with a crack emerging orthogonally at the boundary

The problem of the half-plane, in which a finite crack emerges orthogonally at the boundary, is studied. On the edges of the crack a self-balancing load is applied. A detailed investigation is carried out for an integral equation with respect to the unknown derivative of the displacement jump, to which the problem can be reduced. The exact solution of the integral equation is constructed with the aid of the Mellin transform and the Riemann boundary value problem for the halfplane. The asymptotic behavior of the solution at both ends of the crack is elucidated. First the asymptotic behavior of the solution at the point of emergence of the crack is obtained and the dependence of this asymptotic behavior on the type of the load is established. For a special form of the load one obtains a simple expression of the stress intensity coefficient. In the case of a general load, the asymptotic behavior is used for the construction of an effective approximate solution on the basis of the method of orthogonal polynomials. As a result, the problem reduces to an infinite algebraic system, solvable by the reduction method.Translated from Dinamicheskie Sistemy, No. 4, pp. 45–51, 1985.     

On a lower and upper bound for the curvature of ellipses with more than two foci

Let a set of points in the Euclidean plane be given. We are going to investigate the levels of the function measuring the sum of distances from the elements of the pointset which are called foci. Levels with only one focus are circles. In case of two different points as foci they are ellipses in the usual sense. If the set of the foci consists of more than two points then we have the so-called polyellipses. In this paper we investigate them from the viewpoint of differential geometry. We give a lower and upper bound for the curvature involving explicit constants. They depend on the number of the foci, the rate of the level and the global minimum of the function measuring the sum of the distances. The minimizer will be characterized by a theorem due to E. Weiszfeld together with a new proof. Explicit examples will also be given. As an application we present a new proof for a theorem due to P. Erd?s and I. Vincze. The result states that the approximation of a regular triangle by circumscribed polyellipses has an absolute error in the sense that there is no way to exceed it even if the number of the foci are arbitrary large.     

Derivation of the particle dynamics from kinetic equations

The microscopic solutions of the Boltzmann-Enskog equation discovered by Bogolyubov are considered. The fact that the time-irreversible kinetic equation has time-reversible microscopic solutions is rather surprising. We analyze this paradox and show that the reversibility or irreversibility property of the Boltzmann-Enskog equation depends on the considered class of solutions. If the considered solutions have the form of sums of delta-functions, then the equation is reversible. If the considered solutions belong to the class of continuously differentiable functions, then the equation is irreversible. Also, the so called approximate microscopic solutions are constructed. These solutions are continuous and they are reversible on bounded time intervals. This analysis suggests a way to reconcile the time-irreversible kinetic equations with the timereversible particle dynamics. Usually one tries to derive the kinetic equations from the particle dynamics. On the contrary, we postulate the Boltzmann-Enskog equation or another kinetic equation and treat their microscopic solutions as the particle dynamics. So, instead of the derivation of the kinetic equations from the microdynamics we suggest a kind of derivation of the microdynamics from the kinetic equations.     

Nonstationary boundary problem for model kinetic equations at critical parameters

Nonstationary solutions of the model kinetic equation at critical values of the motion of the wall (the boundary of the half-space occupied by gas) are studied. The characteristic equation is obtained by separating the variables. The eigenfunctions and the eigenvalue spectrum are found in the distribution space. A solution to the equation is expandable over the eigenfunction basis. The Rayleigh problem is considered as an application. The distribution function is continuous in the plane of the wall-motion parameters, including the closed curve of critical parameter values. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 116. No. 2, pp. 305–320. August. 1998.