查询词典 intersection theorems

Then several structural theorems of regular power rings and uniform power rings are established respectively and the uniqueness of the multiplication of a regular power ring is proved.

建立了正则幂环与一致幂环的结构定理，并证明了正则幂环的乘法运算的唯一性。

Are also given by constructing Lyapunov function. Finally, by applying the energy methods, Sobolev embedding theorems and bootstrap arguments, the global existence of nonnegative classical solutions to equations with homogeneous Neumann boundary value condition is proved when the space dimension is at most 5. Under certain conditions for the coefficients of the reaction functions, the convergence of the solutions is established for the system with large diffusion coefficients by constructing Lyapunov function.

的正平衡点全局渐近稳定的充分条件；最后，当空间维数不超过5时，应用能量估计、Sobolev嵌入定理和bootstrap技巧证明在齐次Neumann边值条件下非负古典解的整体存在性，并通过构造Lyapunov函数给出当反应函数的系数满足一定条件、扩散系数较大时该模型解的收敛性。

In the end of this chapter,weprove a local nilpotency property of operators on modules(Theorem 2.3.3)whichis one of the main theorems of this work.

这一章的最后主要证明算子作用在模上的一个局部幂零性质（定理2.3.3），它是本工作的主要结果之一。

The reader will need to know some basic finite group theory: the Sylow theorems and how to use them and some elementary properties of permutation groups and solvable and nilpotent groups.

读这本书之前，读者需要一些有限群论的基本知识，如Sylow定理及其应用，置换群，可解群和幂零群的基本性质等等。

WA mathematical model so called "Poincaré Model" is introduced to solve these problems by using the theorems of Euclidean geometry stead of Non Euclidean geometry.

提供一种用模型法证明非欧几何定理的证明方法，在证明中可以使用欧氏几何的定理，从而使学生对非欧几何有更深刻的认

Fixed point theorems act as very important roles in nonlinear functional analysis theory.

不动点理论是非线性泛函分析理论的一个重要组成部分。

The purpose of Chapter 4 is to study the solvability of multi-point boundary value problems at resonance, and establishs some existence theorems under nonlinear growth restriction. Our method is based upon the coincidence degree theory. In Section 1, we consider the same sign case, and in Section 2, discuss the non-same sign case.

第四章研究了具共振条件下二阶非线性微分方程多点边值问题解的存在性，通过使用重合度理论和一些分析技巧，建立了一系列解存在的充分条件，其中在第一节考虑了同号情形，在第二节考虑了异号情形。

Under some conditions we obtain the existence of nontrivial solution by analyzing the best Sobolev embedding constant and by use of the minimax theorems without conditions.

通过使用没有条件的极小极大定理，以及对最佳Sobolev嵌入常数的详细分析，得到了一些具临界Sobolev指数的半线性椭圆系统的真正非平凡解的存在性，并讨论了解的一些性质。

Secondly, Study the basic concepts, theorems , fundamental nature and the computing formula of the interval number.

2研究了区间数有关性质概念、定理的基本性质及运算公式。

The oddness of operators is considered in section 2, some mapping theorems are obtained by using Borsuk's theorem.

这些结果是对Kartsatos and HE Zhen中相应结果的改进。其中第二节中考虑了算子的奇性。

Chimborazo and Cotopaxi, took me by the hand.

越过琴博腊索山和科托帕克西山。

This car is in a good condition.

这辆车的状况很好。