泛函分析

By employing the local Lipschitz condition and Picard sequence, the local existence-uniqueness of solutions of stochastic functional differential equations of Ito-type is firstly obtained. Furthermore, a continuation theorem for stochastic functional differential equations of Ito-type is given by using stochastic analysis technique and the quasi-boundedness condition. Finally, by establishing some delay differential inequalities and using properties of H_m-functions, a stochastic version of Wintner theorem and the global existence-uniqueness of solutions of stochastic functional differential equations of Ito-type are given. The results generalize the earlier publications.

首先，利用局部Lipschitz条件和Picard序列，获得了伊藤随机泛函微分方程解的局部存在唯一性；其次，利用随机分析技巧和拟有界条件，建立了伊藤随机泛函微分方程解的延拓定理；最后，通过建立一些时滞微分不等式和利用H_m-函数的特性，得到了Wintner定理的随机版本和伊藤随机泛函微分方程解的全局存在唯一性，推广了已有的一些结果。

Each kind of theory and technology about health safeguard can be integrated into a grading describable system. The 5 kinds basic space, which is derived sequentially from topological space, regular space, metric space, measured space and continuous space, are the mathematical base to structure the method of health safeguard.

从泛函分析的角度全面总结了各种健康保障理论与技术，将其统一到一个递级的描述系统中，由拓扑空间、规则空间、度量空间、测度空间和连续空间逐步继承而来的5类基本空间是构造健康保障方法的数学基础。

The first part is to discuss the solvability of Volterra-Stieltjes integral equations.

积分算子理论和积分方程是非线性泛函分析中的一个重要分支。

We established abstract functional spaces, proved that the plastic deformation power rate functional is strict convex and the friction power rate functional and the tensional stress power rate functional are convex. So, strict convexity of the total power rate functional 〓 can be obtained. Further, By nonlinear analysis theory, we proved the existence and uniqueness of minimal point of functional 〓.

本文首先建立了抽象的泛函空间，证明了塑性变形功率泛函是严格凸泛函，摩擦功率泛函和外力功率泛函是凸泛函，从而得到总能耗率泛函的严格凸性，进一步地，利用非线性分析的理论，得到总能耗率泛函有唯一的极小值点。

At last,we conclude the essay and put forward to some new questions and ways by which may be solved(variational inequality and functional analysis).

在文章的最后，对本文进行了总结，并且提出了一些新的问题以及可能解决的方法(变分不等式结合泛函分析的方法)。

The process of our study links some of the most basic questions about C〓 with beautiful classical results from analyticfunction theory. For instance, it is essential Littlewood subordination theorem that assures that composition operators act boundedly on many analytic function spaces. And there are close connections between the compactness of C〓 and the existence of angular derivatives of ψ at points of 〓D. It involves the classical Julia-Careatheodory theorem, Denjoy-Wolff theorem and Nevanlinna counting functions and so on. It makes many old theorems in analytic-function theory getting some new meanings, and bestows upon functional analysis an interesting class of linear operators. This thesis consists of six chapters as follows: Chapter 1 is a preparatory in nature.

从而建立了C〓的算子性质与解析函数论中许多漂亮的经典结果之间的联系，如许多解析函数空间上复合算子的有界性本质上往往是著名的Littlewood从属原理，复合算子的紧性与其诱导映射在边界〓D上的角导数之间有着紧密的联系等等，这样自然而然地涉及到经典函数论中的Julia-Caratheodory定理，Denjoy-Wolff定理及Nevanlinna计数函数等等一些结果，并以此赋予函数论中许多古老问题以新意，同时也为泛函分析提供了一类十分具体的线性算子。

The result that different relaxed systems can reach aggregate equivalence is expanded and analogized with the method of set function in functional space. The existence and necessary conditions for optimal control are obtained.

运用泛函分析空间理论中集值函数，扩展或类推得到了不同松弛系统可达集相同的结论，并且较好地解决了最优控制的存在性及必要条件。

Optimal control ; Copper refining rotary anode furnace ; Heavy oil consuming ; Functional analysis

最优控制；铜精炼阳极炉；重油消耗；泛函分析

In Chapter 3, the prior estimates about the 3-D difference solution and its difference quotients on time space and geometry space are made by means of discrete functional analysis, so that the stability and the convergence of the 3-D difference solution are obtained.

在第三章中，运用离散泛函分析的手段，对三维中子输运方程的差分解及其时间、空间差商进行了先验估计，从而得到了差分解的稳定性和收敛性，也为三维问题的应用研究打下了初步的理论基础。

In this dissertation, we investigate the theory of fuzzy number space and the space of fuzzy-valued continuous functions, the main works of this dissertation are as following: 1. We use some properties of fuzzy numbers to give a generalization of Bolzano theorem in classical analysis to fuzzy number space (E1, d∞).

本文研究了模糊数空间和模糊数值连续函数空间的有关理论，主要内容如下： 1 利用模糊数的相关性质，给出了经典泛函分析中 Bolzano 定理在模糊数空间(E1， d∞)中的推广。

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。