定理

WIMP-Based electronic teaching systems can not meet teachers' requirements of natural and efficient interaction, especially continuous drawing and writing in geometry teaching. In this paper, an intelligent pen-based whiteboard system for dynamic geometry visualization is designed and implemented.

计算机辅助教学系统目前已在教学中大量应用，然而，基于WIMP界面范式的电子课件系统，无法满足教师在课堂教学互动中需要与用户界面自然、高效、连续性交互的需求，尤其是几何教学中连续书写板书、自由勾画图形、动态几何定理演示等。

In chapter one, by using a competely continuous operator on cone and the Krasnoselskii fixed point theorem, we study the existence of positive periodic solutions of differential equations with impulses and delays, and some sufficient conditions will be given.

第一章讨论了一类具脉冲时滞微分方程周期正解的存在性，通过建立锥上的全连续算子，利用Krasnoselskii不动点定理，得到了存在周期正解的若干充分条件。

In view of continuous function problems, it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem. Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收效，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收效的证明。

In view of continuous function problems,it is first proved that the-ES algorithm based on uniform distribution converges in probability in a weaker condition by means of the central limit theorem.Then it is proved that the-ES algorithm which adopts the general continuous random variables as its variable operators converges in probability.

针对连续函数优化问题，利用中心极限定理，在较弱的条件下，首先证明了基于均匀分布的-ES算法依概率收敛，然后给出了采用一般连续性随机变量作为变异算子的-ES算法依概率收敛的证明。

That not only could be extended to the continuous random varia- ble,but also the theorem of maximum information measure could be extended to the continuous random variable, which unified the measurement arithmetic of information between distributed random variable and continuous ran- dom variable,and gave two validating models to the information entropy of the continuous random variable in the last.

用公理化的方法，推导出了有限分布列的离散型随机变量的信息量系，不仅将它推广到连续型随机变量，而且将信息量系的最大信息量定理推广到连续型随机变量，统一了离散型和连续型随机变量的信息度量算法。最后利用得出的结论对连续型随机变量信息熵给出两个验证性算例。

Theorem If and are continuous on an open set S, then at each point of S.

定理 若和在开集S连续，则对于S的每一点有。

Being based on the acknowledgement of continuum medium hypothesis, it has made an analysis of some general movements of macro material, which points out that there are a series non-consistence problems in logic in the Cauchy's stress theory and Stokes's stress hypothesis, etc.

除了指出 Cauchy 的两个应力定理， Stokes 应力假设等存在的逻辑不自洽问题，并产生的原因进行了系统分析以外，演绎地构造了连续介质物质模型严格假设下的完整形式表述体系，并且演绎地导得这个演绎体系必然导致三维物质流形，在三维 Euclid 空间中恒为超定。

On the basis of Muskhelishvili's complex function theory, an auxiliary field of mixedmode crack was accomplished, and then using Betti's reciprocal work theorem, a path independent contour integral method for stress intensity factors of mixed-mode crack was obtained.

本文用复变函数理论推导出裂纹的辅助场，并用Betti功互等定理给出求解混合型裂纹应力强度因子的远场围绕积分法。

The paper gives a conjectural model of utility function on Non-Euclidean space, and proves this possibility, as well as a solution to Edgeworth contract curve and indifference function by utilizing the proposed model.

这个定理给从那以后的经济学，带来了极大的困难。①许多人试图否定阿罗的结论，但都没有成功。②我们总结了前人的

The first part is the preparatory knowledge, introducing the contracting mapping principle which through the basis of vector and matrix norm, derivative and differential theorem of mean to thorough understanding the nature of soluble for nonlinear equations.

第一部分为预备知识，重点介绍压缩映象原理。通过引入向量与矩阵范数，导数与微分中值定理，以求深入理解非线性方程组可解性的基本理论。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新