定理

Through the study of this article requires proficiency in differential intermediate value theorem and Taylor's formula to prove, using theorem to solve a number of conclusions related questions, so can a clear understanding of this kind of problem solving ideas.

通过本文的学习，要求熟练掌握微分中值定理和泰勒公式的证明，运用定理结论来解决一些与之相关的问题，使能够明确了解此类问题的解题思路。

According to classical interpolatory theory, two generalized sampling theorems are proposed and two interpolation formula which have stable and highly accurate recovery results are put forward.

根据经典的插值理论提出并证明了二个广义采样定理，在该定理中给出了具有稳定的、高精度恢复结果的采样和内插方式。

In chapter three, we first give the definition of quadratic automata (3. 6 definition), then study their invertibility. 3. 10 theorem gives a sufficient and necessary conditions for weak inverse quadratic form finite automata, and a way to find the one whose weak inverse is quadratic form finite automata.

第三章首先构造了二次型有限自动机类（3.6定义），研究其上的可逆性理论。3.10定理给出了弱逆二次型有限自动机的充要条件及弱原逆的求法、3.12定理则给出了弱可逆二次型有限自动机的充要条件及弱逆的求法。

In chapter 3,we study several kinds of fractional differentiabli-ties,and prove the inverse function theorems and Whitney extendedtheorems concerned to them.

第三章研究几种分数可微性，并证明了与它们相关的反函数定理以及Whitney扩张定理

Let 〓, then:(1)〓, i∈G (2)〓,〓, i∈G The economic meaning of the theorem is that the change of the supply is reverse with the change of the price, the changing rate of the i-th price equals the inverse number of the changing rate of k〓, and the sum of the effect of P〓 to k〓 and the effect of P〓 to c〓 which is weighted by P〓 is 0, i∈G.

定理2.8：(1)〓，i∈G (2)〓，i∈G 此定理的经济含义是任一种产品供给量的变动与该种产品价格的变动呈反向关系；第i种产品价格的变动率等于k〓变动率的相反数，P〓对k〓变化的效应与P〓对c〓变化的效应以P〓加权后的和为0，i∈G。

Chapter 5 deals with the solvable theorem of adaptive inverse optimal control problems for a class of stochastic nonlinear systems driven by Wiener noises of unknown covariance. The systems are depicted by It〓 stochastic differential equations. By using an adaptive backstepping algorithm and stochastic control Lyapunov functions, the designing procedure of control laws of global asymptotic stability in probability and adaptive inverse optimal stabilization in probability are presented systematically. Adaptive control laws and parameter update laws can be obtained at the same time by this design scheme.

在第5章中，针对具有方差不确定Wiener噪声扰动和未知定常参数的随机非线性系统（假设方差的F—范数是一个常数或一个缓慢变化的量，对其进行在线辨识），给出并证明了自适应逆最优控制问题可解定理，基于随机Lyapunov定理和It〓微分规则，采用自适应Backstepping设计方法，系统地设计了全局依概率渐近稳定和自适应逆最优控制策略，这种设计方法可同时获得控制策略和自适应律，计算机数值仿真结果表明该控制算法是有效性的。

In the present work,the existence and uniqueness results aboutperiodic boundary value problems for different kinds of the nonlin-ear periodically perturbed nonconservative systems are establishedthrough the discretization technique,under suitable assumptions,by using global inverse function theorem and result about the ex-istence and uniqueness of periodic solution for nonhomogeneouslyfirst order linear periodic boundary value problem.

本文的第一章概述了在讨论原问题解的存在唯一性过程中以及构造和分析相关的数值求解方法时将要用到的全局反函数定理、有关矩阵特征值的若干重要引理、线性常微分方程非齐次周期问题解的存在唯一性定理和单参数影射方法及有关结论，并简单回顾了已有的证明非线性微分方程周期边值问题解的存在唯一性的方法，其中包括谱理论、最大最小化形式方法、摄动技术和全局反函数理论方法，最后，介绍了两类数值求解非线性微分方程问题的方法。

Moreover, the semiopen mapping theorem, the semiclosed graph theorem and the semibounded inverse theorem are established under some conditions of weaker t-norms.

对MengerPN空间上的线性算子引入β-半有界，β-半开及β-半闭等概念，讨论了它们间的关系，并在较弱的t-模条件下建立了半开射定理，半闭图定理和半有界逆定理。

Based on the Second Desargues Theory and involution theory,a simple drawing method for a conic is presented.

为了使二次曲线的作图更简便，文章以第二笛沙格定理和对合定理为基础，提出了一种新的作图方法。

The irreducibility and unitarizability Theorems in section 1. 2. 4 are useful for our study.

其中§l.2.4节的不可约性定理和酉性定理对我们的研究很有帮助。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐