解空间

The second component of this thesis is about the setup of oriented molecule photodissociation and the theoretical treatment. We primarily discussed the steric distribution, the probability of electron transition and the angular distribution of photofragment of the molecules in orientation field.

论文的第二部分是我们建造的利用Brute-force场使分子取向的光解实验装置和相应的理论处理，主要讨论了分子在取向电场中的空间排布、电子跃迁、和光解碎片的角分布。

Based on constraint satisfaction,an entirely feasible scheduling is obtained by constraint propogation technology and heuristic repair method and is regarded as initial solution for tabu search algorithm.Current solution is optimized by neighborhood transformation on a critical path.The final optimizal solution is improved by adopting a global neighborhood swapping strategy.

该算法基于约束满足思想，通过约束传播技术和启发式修复算法，得到可行调度作为禁忌搜索算法的初始解；再进行关键路径上的邻域变换，优化当前解；并采用一种全局邻域交换策略，扩大搜索空间，改善优化结果。

In the solution of the problems in algebraic equation, differential equation and integral equation, we usually resort the sotution of equation to the fixed point of mapping in metric space. The contraction mapping principle can be used to solve many problems of the existence and uniqueness of equation solution.

在代数方程、微分方程和积分方程的求解问题中，通常把所求的解归结为度量空间中映射的不动点，然后应用压缩映象原理来统一处理许多方程解的存在性和唯一性问题。

As for the existence of positive solutions, the cone theory and the fixed point index of condensing mapping are employed, and the results of the existence of positive solutions are obtained in the case of superlinear and sublinear. The conclusions extend and improve the existence theorem which Lou Ben-dong extablished in 1996 about the question of Sturm-Liouville of Banach spaces.

三、对于正解存在性问题，我们应用凝聚映射的不动点指数理论，分别在超线性与次线性情形下进行讨论，获得了一些正解存在的结果，主要结果推广和改进了1996年Lou Ben-dong对Banach空间Sturm-Liouville问题所建立的存在性定理。

The second kind of Fredholm integral equation for the pile was established in terms of the fundamental solution, the compatibility conditions and the free wave field.

利用半空间饱和土的基本解和自由波场解及桩、土间变形协调条件，建立了桩土共同作用的第二类Fredholm积分方程。

In this dissertation,we consider the following nonlinear singular partial differentialequation in complex domain 〓where u=uis a unknow function,Fis a holomorphic function withrespect to the variables〓.

本文主要考虑的问题是复空间中的非线性全特征型奇性偏微分方程解的性质，即考虑如下偏微分方程〓的解的性质，其中〓为未知函数，F是一个关于变量〓〓的已知全纯函数。

Chapter 4,based on strong efficiency rather than efficiency or weak effi-ciency,discusses the similar problem to chapter 3.The concepts of strongsupremum and strong infimum for the set in finite-dimensionalEuclidean space are given,s-conjugate functions and s-subdifferentials theory is developed,by means of which,the duality problem ofmulitobjectivre programming for strong efficient solutions or called absoluteoptimal solutions is analysed,and a new duality theory-s-conjugateduality theory is proposed.

第四章，基于强有效性而不是有效性和弱有效性，给出了类似于第三章的结果，提出了有限维欧氏空间中集合的强上、下确界等概念，研究了点集映象的强共轭函数和强次微分问题，建立了点集映象的s-共轭函数及其s-次微分理论，并借助于这一理论，讨论了多目标规划关于绝对最优解或称强有效解的对偶性问题，建立了基于强有效性的s-共轭对偶理论。

On the whole, we do as follows: Firstly, we list some conceptions and lemmas for later use. Secondly, we define δ-fine partitions for infinite interval and integral of vector-valued functions on infinite interval, and discuss the properties of integral, and characterize its primitives...

主要包括以下五部分内容：在第一部分中，我们介绍了本文所用到的基本概念和引理；在第二部分中，通过定义无穷区间上δ-精细的分法，我们给出了无穷区间上向量值函数的积分的定义，并讨论其性质，还给出了原函数的刻划；在本文的第三部分中，我们着重讨论了无穷区间上向量值函数积分的收敛定理；在本文的在第四部分中，我们首先应用无穷区间上向量值函数积分的收敛定理给出了常微分方程整体广义解的存在性定理，其次应用强积分对Banach空间常微分方程广义解进行了讨论；最后，在第五部分中，我们将模糊积分推广到无穷区间上并给出了其数值计算方法。

Based on the basic solutions of the pressure response of point source in infinite space, pressure responses at any point in a horizontally infinite reservoir are studied.

以无限空间点源压力响应的基本解为基础，研究了水平方向无限大油藏在任意位置的压力响应，从测压点位置、等价压力点、多解性的解决办法等方面探讨了水平分支井的试井解释方法。

For different polynomials g, if the characteristic polynomial of a n matrix A is irreducible, then we get some theorems to determine matrix equations g =A solvable; if it is reducible, then, to see n-dimension space vectors M over a field F as F-module, we use module theory to determine these equations solvable such that it is simpler and clearer to investigate these questions.

对于不同多项式g，当n阶矩阵A的特征多项式为不可约的，我们给出了矩阵方程g=A有解的判定定理；当A的特征多项式为可约的，把域F上的n维线性空间M作为由A导出的F -模，我们利用模论知识来决定矩阵方程g=A有解性，从而使这一问题变了简单，研究思路更加清晰。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失