可变形体的有限转动参数和回转磁效应

本文的第一部份将Synge[2]关于转动变换的推导用张量公式表达,进一步阐明作者在文[7]中所求得正交变换式的几何意义.文中并讨论转轴矢量的张量性质.文中后一部份应用拖带坐标系描述法讨论回转磁效应(Einstein-de Haas效应),建立一个求变形体中求磁化体力矩的简单公式.     

计算渠道横断面面积的一种方法

在渠道测量中,为了计算挖填土施工量,需要就每一横断面分别计算出各挖方部份面积(如图1中阴影部份Ⅰ所示)和各填方部分面积(如图1中阴影部分Ⅱ、Ⅲ所示).计算工作通常是在画出各横断面图后进行的.计算方法可采用分块法、梯形法、方格法等多种.但采用这些方法计算,做起来一般都比较繁杂.由于渠道横断面的个数通常都比较多,因而就更显得这一工作繁重了.     

能行连续泛函

<正> 本文讨论了部份递归函数族,部份递归泛函和能行运算的一些拓扑性质,定义了连续泛函和能行连续泛函的概念,证明了能行连续泛函与部份递归泛函的等价性,讨沦了能行连续泛函与能行运算的异同.     

空间机构的向量分析——Ⅲ空间机构运动学

用简单的向量代数方法对第Ⅰ部份和第Ⅱ部份所讨论的空间机构进行瞬时运动学分析.     

Yang-Mills规范场的存在性、可解性(一)

应用数学机械化方法研究欧氏空间中$SU(2)$ Yang-Mills规范场的存在性问题.首先对YM--方程的结构进行了讨论,说明YM--方程由它的奇部份和偶部份联立组成.对于YM--方程构造了一类线性微分变换,称之为$SU(2)$规范场的示性变换.经示性变换,将非线性的YM--方程的奇部份变为一组Laplace方程,实现了$SU(2)$规范场方程的线性化.从而证明了$SU(2)$规范场存在3个独立的Yang-Mills规范场.     

开曲面的凸性判别条件(三)

<正> 在本文的(一)、(二)两部份给出了开曲面成为凸曲面的两个判别方法,即定理1、2、它们给出的充分必要条件中除了要求曲面π在周界以外的点,即 intπ的点有对π的局部支持平面外,另一个要求的特点是在π的一部份点上存在着一个平面,这平面对π的另一部份点有某种关系.现在我们试把另一个要求的特点改为讨论一条直线和π有多少交点而来建立另一判别方法.     

可靠性(Ⅲ)

设我们要研究产品的两个参数X、Y.按技术文件规定生产一批n个产品.每一个产品的X、Y值可以用XY平面上的一点(X,Y)来表示.这一批n个产品的参数表现为XY平面的n个点.我们把XY平面的某一部份划分为很多小矩形格子.统计(X,Y)落在每一个小矩形格子中的相对频数.在每一个小矩形格子上建立一个直方柱,使直方柱的体积表示(X,Y)落在该矩形格中的相对频数.当按技术文件生产极多产品时,这些矩     

部分埋入水中悬臂圆柱体的弯曲自由振动

本文作者讨论了部份埋入水中悬臂圆柱体的弯曲自由振动,给出了柱水偶联体系振型函数的精确解和以行列式表示的频率方程.指出了水的效应等价一个附加分布质量,因此,水中柱体振动频率低于无水时柱体振动频率.     

关于Fuzzy一致空间的一个注记

本文讨论F-映射的Fuzzy一致连续性和F一致结构关于F映射的逆像,从而把[1]中相应部份推广到更一般的情况。     

非线性系统的能控性分布与解耦问题(Ⅰ)

在应用近代微分几何方法研究非线性系统的过程中,已经引入的(A,B)不变分布概念,是与线性系统几何理论中的(A,B)不变子空间概念相对应的。对(A,B)不变分布的性质及其应用于非线性系统的干扰解耦已有许多讨论。本文的目的是对非线性系统引入另一类分布——能控性分布,并用来研究非线性系统的解耦问题。全文分两部份。第Ⅰ部份主要是引入能控性分布的概念并讨论其性质。第Ⅱ部份则应用Ⅰ的结果讨论解耦问题。     

Dynamics of Bianchi Type I Solutions of the Einstein Equations with Anisotropic Matter

We analyze the global dynamics of Bianchi type I solutions of the Einstein equations with anisotropic matter. The matter model is not specified explicitly but only through a set of mild and physically motivated assumptions; thereby our analysis covers matter models as different from each other as, e.g., collisionless matter, elastic matter and magnetic fields. The main result we prove is the existence of an ‘anisotropy classification’ for the asymptotic behaviour of Bianchi type I cosmologies. The type of asymptotic behaviour of generic solutions is determined by one single parameter that describes certain properties of the anisotropic matter model under extreme conditions. The anisotropy classification comprises the following types. The convergent type A₊: Each solution converges to a Kasner solution as the singularity is approached and each Kasner solution is a possible past asymptotic state. The convergent types B₊ and C₊: Each solution converges to a Kasner solution as the singularity is approached; however, the set of Kasner solutions that are possible past asymptotic states is restricted. The oscillatory type D₊: Each solution oscillates between different Kasner solutions as the singularity is approached. Furthermore, we investigate non-generic asymptotic behaviour and the future asymptotic behaviour of solutions. Submitted: October 28, 2008.; Accepted: January 26, 2009.     

一类小周期椭圆方程的三重尺度渐近分析

利用三重尺度方法对一类小周期椭圆方程进行了三重尺度渐近展开分析,构造了对应的三重尺度形式渐近展开式,得到了均匀化常数和均匀化方程.在形式渐近展开的基础上,构造了对应边值问题解的三重尺度渐近近似解,并分析了对应三重尺度形式渐近误差估计.     

一个非线性波动方程的计算机代数-摄动解*

本文采用计算机代数-摄动法讨论一个非线性波动方程的Caychy问题高阶渐近解,将特征坐标变形与重整化方法相结合,消除直接展开解的长期项,并利用计算机代数软件进行符号运算,得到该问题的四项摄动解,所得的渐近解与数值解的比较表明:对较小的ε,两者相吻合;对较大的ε(如ε=0.25),两者也相当符合。     

第五类Painlevé方程解的渐近性态分析

本文用比较直接的方法研究Painleve方程的渐近解和连同公式:(1)先求出数值解,然后用最小二乘法拟合出最佳渐近解;(2)根据最佳渐近解的表达形式,用谐波平衡法得到振荡渐近解与参数之间的依赖关系,即连同公式．当参数α,β,γ和δ满足一些条件时,对一般实的第五类Painleve方程,我们找出了振荡渐近解和连同公式．     

On boundary value problems for the domain exterior to a thin or slender region

In this paper a method for obtaining uniformly valid asymptotic expansions of the solution of the boundary value problems in domains exterior to thin or slender regions is given. This approach combines the Tuck's method, based on the use of a suitable co-ordinates system with the method given by Handelsman and Keller yielding complete uniform asymptotic expansion of the solution for slender body problems. Our method avoids the determination of the extremities of the segment containing singularities; it is pointed out that this last problem is a pure geometrical one and independent of solving concrete boundary value problems in the given domain.     

Recursive parameter estimation: asymptotic expansion

This paper is concerned with the asymptotic behaviour of estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The results of the paper can be used to determine the form of the recursive procedure which is expected to have the same asymptotic properties as the corresponding non-recursive one defined as a solution of the corresponding estimating equation. Several examples are given to illustrate the theory, including an application to estimation of parameters in exponential families of Markov processes.     

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.     

非线性阻尼作用下标准线性固体粘弹性Ⅲ型破裂的解析解

把非线性Rayleigh阻尼引入标准线性固体粘弹性介质的Ⅲ型破裂的控制方程中,此方程是一个偏微分积分方程;首先设法消去积分项,得到一个三阶非线性偏微分方程,然后用小参数摄动法,得出线性化的各阶渐近控制方程;把每一个具有变系数的三阶线性控制方程分解为弹性部分及剩余部份,而前者的解析解为已知,后者是一个二阶变系数线性偏微分方程;它化不成Mathieu方程,也化不成Hill方程,故采用WKBJ的方法得出其渐近的解析解。     

Analysis of the hypotheses used when constructing the theory of beams and plates

The solution of the two-dimensional problem of the theory of elasticity for a strip and the three-dimensional one for a plate are formulated by simple iterations and using asymptotic estimates with respect to a small parameter. These problems arc solved in the literature by reducing the two-dimensional and three-dimensional problems to one-dimensional and two-dimensional ones, respectively, using the semi-inverse Saint-Venant's method [1, 21. It is assumed that the solution obtained by the semi-inverse method has an error of the order of the relative size of the small domain of the applied self-balanced load. The treatment of the hypotheses, introduced in the semi-inverse method, as a selection of the respective initial approximation of the method of simple iterations enables the solution process to be formalized and provides an estimate of the error. The classical theory of beams and plates is supplemented by a solution of the boundary-layer type. The procedure is illustrated by solving the problem of a strip with an applied concentrated load. An additional solution for a rectangular plate, together with the solution of a biharmonic equation, enables three boundary conditions to be satisfied on each free end surface.     

On the application of the method of matching asymptotic expansions to a singular system of ordinary differential equations with a small parameter

We consider a bisingular initial value problem for a system of ordinary differential equations with a single small parameter, the asymptotics of whose solution can be constructed in the form of power-logarithmic series on several boundary layers and an external layer. To use the method of matching asymptotic expansions, we prove theorems that permit one to make the passage between two adjacent layers and obtain a uniform estimate of the approximation to the solution by a composite asymptotic expansion.