黎曼流形上的法坐標

<正> 1952年P.Hartman和A.Wintner建立了下述定理:設連續函數E(u,ν),F(u,ν),G(u,ν)在點(0,0)的鄰域內满足條件     

n-2型黎曼空间的等距对应

<正> §1.导言一个正则的 n 维黎曼空间,若恰有 p 个函数独立的不变量,便称为 p 型的,这样的空间,我们将用 R(n,p)表之.此定义创自 T.Y.Thomas,他并详尽地研究了特殊情况:n=2,p=0,1,2.本文作者假定两个 R(n,n—2)具有结构相同的两组不变式 I_1,     

玻璃腐蚀与离子交换原理

<正> 一、玻璃腐蚀原理影响玻璃腐蚀程度的因素相当多,综合起来可归纳为两大类:玻璃本身的化学稳定性和侵蚀玻璃的外界介质。玻璃的化学稳定性取决于组成玻璃的各种成份及其性质。纯硅玻璃是由[SiO_4]~(-4)四面体组成的,     

SOME THEOREMS ON THE SPACES OF QUASI-CONSTANT CURVATURE

The present paper is devoted to determining the metric g for an n-dimensional (n≥4) Riemannian manifold (M, g) of quasi-constant curvature [1]. By the way, we have identified the space of quasi-constant curvature with the k-special conformally flat space of K. Yano & B. Y. Chen [8]. Based upon the results so obtained, we have completely determined the canonical metric for such a space to admit the relevant field X as geodesic field, and the geometric structure for (M, g) to be a recurrent space of quasi-constant curvature. Also we have examined the validity of our results just obtained for a 3-dimensional conformally flat space of quasi-constant cvrvature. Besides, we have deduced some global properties for a complete manifold of quasi-constant curvature, which may be useful in applications.     

关于容许全脐超曲面正交族的Einstein流形

The aim of the present paper is to study globally the Riemannian manifold admitting two or more mutually orthogonal families of totally umbilical hypersurfaccs of which each is Einsteinian. This paper consists of four parts: (i) to establish anew the canonical form of the metric of (M,g) admitting p (p≥2) families of mutually orthogonal totally umbilical hypcrsurf aces from the standpoint of global differential geometry; (ii) to prove in a n-dimensional (n>2) Einsteinian manifold E_n of nonvanishing scalar curvature there doesn't exist one family of compact totally geodesic Einsteinian hypersurfaces (Theorem 1);(iii) to prove in a n-dimensional (n≥5) Einsteinian manifold E_n of nonnegative scalar curvature R there don't exist two orthogonal families of totally umbilical but not geodesic complete Einsteinian hypersurfaces (Theorem Ⅱ);(iv) to show that a n-dimensional (n≥5) Riemannian manifold of negative constant scalar curvature R.     

关于两个n-1型黎曼空間的等距对应

一个具有正定线素的黎曼空间V_n,若有n-1个函数独立的绝对不变量,常称为n-1型的.将这些不变量取作变数y~2…,y~n,此空间的线素便可写成     

拟定曲率空间上的几个定理

The present paper is devoted to determining the metric g for an n-dimension-al (n≥4) Riemannian manifold (M, g) of quasi-constant curvature [1]. By the way, we have identified the space of quasi-constant curvature with the κ-special conformally flat space of K.Yano & B.Y.Chen [8]. Based upon the results so obtained, we have completely determined the canonical metric for such a space to admit the relevant field X as geodesic field, and the geometric structure for (M, g) to be a recurrent space of quasi-constant curvature. Also we have examined the validity of our results just obtained for a 3-dimensional conformally flat space of quasi-constant cvrvature. Besides, we have deduced some global properties of a complete manifold of quasi-constant curvature, which may be useful in applications.     

低周疲劳随机损伤过程的有限元模拟

讨论了一种低周疲劳下随机损伤演变过程 数值模拟方法，借助于Ｌｅｍａｉｔｒｅ＆Ｄｕｆａｉｌｌｙ给出的代表性体元的微观力学模型，建立了损伤与微裂纹尺寸的关系，采用随机初始损伤反映材料中固的的微缺陷，将所得模型与有限元结合对低周疲劳损伤过程进行了数值模拟。     

表面裂纹平板应力强度因子的杂交应力元-线弹簧模型方法

本文采用基于杂交应力元和线弹簧模型相结合的方法,计算表面裂纹平板的应力强度因子。结果表明,本文解和三维有限元解吻合很好,与基于位移元和线弹簧模型相结合的解相比,具有更高的精度和较宽的适用范围。