关于Γ-除环

文中首先给出了定理２．２,由它可以行到文献「４」和「５」中关于Γ－域和除Γ－环的一些结果,其次,我们还指出了一个Γ－环是Γ－除环的几个条件。     

两类求解y“=f（x,y）具有极小相位延迟的显式方法

本文提出了两类数值积分二阶周期性初值问题ｙ〃＝ｆ（ｘ，ｙ），ｙ（ｘ０）＝ｙ０，ｙ（ｘ０）＝ｙ０具有检小相位延迟的显式两步法。这些方法推广和改进了文献「１」１－「７」中的某些方法。数值试验表明本文中的某些方法优于「１」－「７」中的某些方法。     

正定型超曲面上的闭曲线与非线性振荡的周期

本文在Ｒ＾ｎ＋１中定义了一类超曲面并讨论了其上闭测地线上度的下界以及Ｈａｍｉｌｔｏｎ系统的周期解的最小周期，这类超曲面比星形超曲面广泛，因而本文结论包括了文献「１」、「２」、「３」中的相应结论。     

具有正负系数中立型时滞差分方程的振动性

本文获得了差分方程（＊）振动的充分条件,对文献「１」的结果进行了有益的推广和补充。     

关于M—矩阵等价表征的注记

「２」指出了「１」的某些错误,并给出了修正的结果。本继续「２」的讨论,给出了Ｍ－矩阵等价表征的进一步结果。     

基于顺序统计量的几何分布特征的进一步结果

用顺序统计量来刻划几何分布的特征已有不少结果，但仍有问题有待解决。本文在文「１」的基础上，针对Ａｒｎｏｌｄ「２」所提问题进行了进一步研究，得到了一些进一步的结果。这些结果同时给出了几何分布的基于顺序统计量的特征。     

所有循环平坦系满足条件（P）的PSF幺半群

本文讨论所有循环平坦系满足条件（Ｐ）的幺半群的“元素－－理想”特征问题,该问题至今仍未获解决,在Ｓ是左ＰＳＦ幺半群的条件下,本文证明了所有循环平坦右Ｓ－系满足条件（Ｐ）当且仅当Ｓ的任意元ｘ或者是右可消元,或者是右零元,当且仅当对Ｓ的任意真右理想Ｉ,或存在ａ∈Ｉ－Ｉａ,或Ｉ中的所有元素均为右零元,该结果改进并推广了「４」、「７」、「８」、「１５」中的部分结果。     

H—空间中单调型集值映象变分不等式解的存在性问题

该文研究了一类具广义单调型集值映象的变分不等式解的存在性问题，结果包含文献「１，８，９」中的相应结果为特例。     

关于Rhoades文章的评注

本文给出了Ｄ－度量空间中的一个不动点定理,并指出了文献「１」中的错误。     

关于迭代序列的子列极限点

本文讨论了度量空间上一个连续自映射在一点处的迭代序列的子列极限点集的结构，所得的结果统一和推广了Ｄｉａｚ和Ｍｅｔｃａｌｆ「１」，Ｍａｉｔｉ和Ｂａｂｕ「２，４」和Ｐａｒｋ「３」的若干结果。     

Generalized genus sequences for misère octal games

Two approaches have been used to solve impartial games with misère play; genus theory, which has resulted in a number of results summarized in [2], and Sibert-Conway decomposition [9], which has been used to solve the octal game 0.77 (known as Kayles). The main aim of this paper is to publish (for the first time) the results archived in [1], extending genus theory beyond the applications to which it has previously been applied. In addition, we extend a result from [6] to misère play by adapting it to use the extended genus theory. The resulting theorems require extensive calculations to verify that their preconditions hold for any particular games. These calculations have been carried out by computer for all two-digit octal games. For many of these games, this has resulted in complete solutions. Complete solutions are presented for four games listed in [8] as unsolved. Received: September 2001     

An averaging method applied to a duffing equation

We approximate a Duffing equation by an averaged system. We solve the system explicitely and draw bifurcation diagrams in dependence of the forcing term. We discuss the goodness of the averaging method, relative to the behavior of the solutions in dependence of involved parameters, by comparing with results obtained in [6,10] for the original Duffing equation.     

On a problem for Wardʼs equation with a Mittag–Leffler potential

We solve a problem for a type of non-linear partial differential equation (“Ward?s equation”). This is an equation arising naturally in the study of Coulomb gases and random normal matrix ensembles [4]. In this paper, we consider a problem for Ward?s equation whose solutions are precisely the well-known Mittag–Leffler functions. Our solution to this problem generalizes certain results obtained in [4].     

在集中力和集中力偶作用下不同弹性材料圆形界面的裂纹问题

运用推广的Schwarz延拓原理结合对复应力函数的奇性主部分析,求解一类有集中荷载的平面弹性问题,十分有效。文[1]用此方法研究了同种材料的弹性问题。本文把它推广于在集中力和集中力偶作用下不同弹性材料的圆形界面上有多条裂纹的情形,求出了几种典型情况复应力函数的封闭解,算出了应力强度因子,并由此导出一系列特殊解答,其中两个在文[1]、[6]中找到一致结果。     

Propagation of Density-Oscillations in Solutions to the Compressible Navier-Stokes-Poisson System

Concerning a bounded sequence of finite energy weak solutions to the compressible Navier-Stokes-Poisson system （denoted by CNSP）, which converges up to extraction of a subsequence, the limit system may not be the same system. By introducing Young measures as in [6, 15], the authors deduce the system （HCNSP） which the limit functions must satisfy. Then they solve this system in a subclass where Young measures are convex combinations of Dirac measures, to give the information on the propagation of density-oscillations. The results for strong solutions to （CNSP） （see Corollary 6.1） are also obtained.     

N[a,b]类中边界Nevanlinna-Pick插值(I)

用所谓的Hankel向量方法求解N[a,b]函数类中带边界插值数据的Nevanlina-Pick插值(BNP(N[a,b]))问题,并建立BNP(N[a,b])问题与[a,b]上的某种带约束条件的Hausdorff矩量问题之间等价的可解条件以及解之间明确的一一对应关系.这使得当BNP(N[a,b])问题有多解时,能通过带约束条件的矩量问题的可解性准则和解获得BNP(N[a,b])问题的可解性准则和解的参数化描述,而在唯一解的情况下,通过BNP(N[a,b])问题解的存在唯一性准则和唯一解来获得带约束条件的     

Conservation laws for conformally invariant variational problems

We succeed in writing 2-dimensional conformally invariant non-linear elliptic PDE (harmonic map equation, prescribed mean curvature equations,..., etc.) in divergence form. These divergence-free quantities generalize to target manifolds without symmetries the well known conservation laws for weakly harmonic maps into homogeneous spaces. From this form we can recover, without the use of moving frame, all the classical regularity results known for 2-dimensional conformally invariant non-linear elliptic PDE (see [Hel]). It enables us also to establish new results. In particular we solve a conjecture by E. Heinz asserting that the solutions to the prescribed bounded mean curvature equation in arbitrary manifolds are continuous and we solve a conjecture by S. Hildebrandt [Hil1] claiming that critical points of continuously differentiable elliptic conformally invariant Lagrangian in two dimensions are continuous.     

Solving generalized equations via homotopies

Global Newton methods for computing solutions of nonlinear systems of equations have recently received a great deal of attention. By using the theory of generalized equations, a homotopy method is proposed to solve problems arising in complementarity and mathematical programming, as well as in variational inequalities. We introduce the concepts of generalized homotopies and regular values, characterize the solution sets of such generalized homotopies and prove, under boundary conditions similar to Smale’s [10], the existence of a homotopy path which contains an odd number of solutions to the problem. We related our homotopy path to the Newton method for generalized equations developed by Josephy [3]. An interpretation of our results for the nonlinear programming problem will be given.     

An investigation of the impact and penetration of solids of revolution into soft earth

The numerical method proposed earlier in [1] is developed to solve problems of the impact and penetration of rigid and deformable bodies of revolution into soft soil, which are described by Grigoryan's model [2]. The effect of the surface Coulomb friction, the bulk compressibility and the shear strength of soft soil on the forces of resistance and contact pressures in the contact zone is analysed. The results of numerical solutions of problems in a coherent formulation are compared with analytical relations and experimental data on the determination of the forces and coefficients of resistance to the penetration of impactors of different shapes into soft soil.     

Solvability via viscosity solutions for a model of phase transitions driven by configurational forces

This article is concerned with an initial-boundary value problem for an elliptic-parabolic coupled system arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel. This model was proposed in Alber and Zhu (2007) [4], and investigated in Alber and Zhu (2006) [3] the existence of weak solutions which are defined in a standard way, however the key technique used in Alber and Zhu (2006) [3] is not applicable to multi-dimensional problem. One of the motivations of this study is to solve this multi-dimensional problem, and another is to investigate the sharp interface limits. Thus we define weak solutions in a way, which is different from Alber and Zhu (2006) [3], by using the notion of viscosity solution. We do prove successfully the existence of weak solutions in this sense for one-dimensional problem, yet the multi-dimensional problem is still open.