泛函分析

Other semirings arise naturally in such diverse areas of mathematics as combinatorics, functional analysis, topology, graph theory, Euclidean geometry, probability theory, commutative and noncommutative ring theory, optimization theory, discrete event dynamical systems, automata theory, formal language theory and the mathematical modeling of quantum physics and parallel computation systems.

在许多不同的数学领域存在着其它形式的半环，比如组合学，泛函分析，拓扑学，图论，欧式几何，概率论，交换和非交换环，优化论，离散动力系统，自动化理论，形式语言理论，量子物理的数据模型和并行计算系统。

A precise background theory of computational mechanics is formed. Saint-Venant's principle is discussed in chain model by means of this precise theory. The classical continued fraction is developed into operator continued fraction to be the constrictive formulation of the chain model.

用泛函分析的双空间理论为计算力学构造了一个严密的背景理论，以此在链式模型上讨论圣文南原理，同时将传统的连分数扩展为算子连分式作为链式模型的本征关系式。

Convexity and convex function have extensive applications in functional analysis, optimal theory, and mathematical economy.

凸性和凸函数在不等式、泛函分析、最优理论、运筹学、控制论及数理经济学等应用数学领域都有很多应用。

Some equivalent conditions for unique ergodicity are included in theorem 6 and theorem 7 and the methods of the proof of theorem 7 is from functional analysis.

定理6及定理7给出唯一遍历的等价条件，定理7的证明采用的是泛函分析的方法。

Every existence theorem of them is proved, respectively.

本文所获的一些结果不仅是非线性泛函分析领域中一系列重要定理的推广，而且它们为随机微分方程、随机积分方程及随机算子方程的研究提供重要的工具。

Firstly, according to electromagnetic field theory, the 2-dimensional (2-D) mathematical model of a three phase squirrel-cage Y802-2 induction motor is developed. Then general equations can be deduced from finite element discrete and functional analysis. The motor's 2D solving region of electromagnetic field is given based on the boundary conditions and assumption conditions of the squirrel-cage induction motor. Through finite element mothod and inner–outer convergence method, magnetic field distributions and magnetic forces of bars can be calculated in following rotor conditions: health rotor, one single broken bar, two adjacent broken bars, two broken bars with one good interval, two broken bars with two good interval and four adjacent broken bars.

本文首先根据电磁场理论建立Y802-2型三相笼型感应电动机二维电磁场的数学模型，并对其进行了有限元离散以及泛函分析，推导出总体方程；在基本假设和边界条件基础上，给出笼型感应电动机二维电磁场的求解区域，然后应用有限元并结合内外双收敛方法，对样机稳态运行进行数值计算，得出电机在转子完好、一根导条断裂、连续两根导条断裂、间隔一根两根导条断裂、间隔两根两根导条断裂及连续四根导条断裂六种情况下的磁场分布和导条所受电磁力的变化情况。

At present, nonlinear functional analysis has been one of the most important branch of learning in modern mathematics.

目前，非线性泛函分析已经成为现代数学中的一个重要分支。

The purpose of this paper is to investigate some subjects about nonlinear functional analysis.

中文摘要：这篇文章的目的是研究非线性泛函分析的一些课题。

By using the functional analysis theory, the existence and uniqueness of solution are proved.

利用泛函分析理论，证明了系统解的存在性和唯一性。

Nonlinear functional analysis is an important branch of mathematics, and it can explain several kinds of natural phenomena.

非线性泛函分析是数学中的一个重要分支，因其能很好的解释自然界中的各种各样的自然现象受到了国内外数学界和自然科学界的重视。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。