查询词典 uniqueness theorem

Chapter 2 deals with some refinements of the central limit theorem for a class of non-uniformly hyperbolic dynamical systems called Young\'s system, such as local central limit theorem and so-called Berry-Esseen theorem giving the rate of convergence in the central limit theorem.

在第二、三章中，我们考虑一类重要的非一致双曲动力系统的统计性质-中心极限定理，及其进一步的精细结果如局部中心极限定理，带有收敛速度的中心极限定理。

On the other hand , illuminated by close relation between harmonic maps and sumanifold theory, we have also researched in-depth about some relative problems in submanifolds theory which include: the estimate of heat kernel and eigenvalue and it geometric application of submanifolds with or without boundary; many kinds of pinching problem of submanifolds which include the rigidity theorem, topological sphere theorem, differential sphere theorem and topological finite theorem.

另外，鉴于调和映照与子流形之间的密切关系，我们还要深入研究子流形几何中与之相关的一些问题，主要包括：带边与不带边子流形的热核与特征值估计及其几何应用；子流形的刚性定理、拓扑球定理、微分球面定理、拓扑有限性定理等各类Pinching问题。

The positive periodic solution of functional differential equation with infinite delay is deeply concentrated these years, some scholars study this subject by means of Lyapunov theorem, Schauder fixed point theorem, and cone extending and compression theorem (from thesis -[5]), and they obtain the existence theorem of positive periodic solution.

近年来，无穷时滞泛函微分方程的周期解问题受到广泛关注，一些学者应用Lyapunov泛函方法，Schauder不动点方法，以及非线性泛函分析中的锥拉伸锥压缩方法(见[1]-[5])，研究了无穷时滞泛函微分方程的周期解的存在性问题。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

And guided by Schur theorem, many of the Schur theorem inference arises, formed a complete theoretical system Schur theorem. Schur theorem and put many of its reasoning applied to the unitary matrix and the similarity matrix eigenvalue of proof onto.

在Schur定理的指导下，许多关于Schur定理的推论便产生了，并且形成了一个完整的Schur定理理论体系，把Schur定理和它的许多推论推广到了酉矩阵的相似和矩阵的特征值的证明上来。

By employing the theorem on existence and uniqueness of solutions, the existence and uniqueness of path is proved. A method of solving ordinary differential equation systems is proposed to get the trajectory of SVM solutions.

利用微分方程组的存在唯一性定理，我们得到了路径的存在唯一性，并给出了一种常微分方程组的近似解法求解SVM解的路径。

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。

A new type of polar decomposition—weighted polar decomposition of matrices is presented and defined. Aim at this new matrix decomposition, we prove its uniqueness theorem and obtain its uniqueness conditions, and also investigate the best approximation property of weighted unitary polar factor.

矩阵的极分解和广义极分解一直是矩阵分析研究的重要内容，本文中我们对其进行了横向扩展，提出并定义了一种新的极分解形式—矩阵的加权极分解。

We prove the existence theorem of rationed with Borel points for meromorphic functions in the unit circle, discuss the operations of algebroid functions and the existence theorem of Nevanlinna direction of algebroid function dealing with mutiple values, and obtain some uniqueness theorems dealing with mutiple values of algebroid functions.

证明了单位圆内限定Borel点的亚纯函数的存在性定理，讨论了代数体函数的运算性质以及涉及重值的Nevanlinna方向的存在性定理，得到了一些涉及重值的代数体函数的唯一性定理； 2。

In this paper, we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence, uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations.

利用混合单调凝聚算子的耦合不动点定理，给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。

Liapunov—Schmidt method is one of the most important method in the bifurcation theory.

Liapunov—Schmidt方法是分叉理论的最重要方法之一。

Be courteous -- even when people are most discourteous to you .

要有礼貌──即使当別人对你最不礼貌的时候。