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In Chapter 2 and Chapter 3, we give the solutions of integral form on Orbifold T〓/Z〓(N=3, 4, 6). These solutions include all the projection operators which have minimal trace and the induced matrices of which are continuous functions of kq. In terms of this kind of solution one can construct various closed form of solutions.

在第二章和第三章中我们给出了T〓/Z〓（N=3，4，6）上的以积分形式表达的解，这些解包括所有具有最小迹且诱导矩阵是kq参量连续函数的投影算子，并且可以由它进而构造各种有限形式的解。

The solutions of two plane strain basic problems can be used to obtain the analytic solutions of two subproblems through the continuity condition of displacement.The theoretical solutions for the stress distribution in...

进一步地，基于两个弹性力学平面应变基本问题的解，采用结构力学的求解思想，由位移连续条件分别求得了两个子问题的解，最后由叠加原理得到了原问题的理论解。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

The conformal flat space-time solutions in electromagnetic and scalar theory are shown,and the indefiniteness of the plane-symmetric solutions and the method for defining a noncontinuous field by the intersection of multi-solutions are demonstrated.

文摘：给出电磁场和标量场在共形平直时空中的解，发现了平面对称解的不确定性及由多重解的交集来定义一个非连续场的方法。

In Chapter 1, we use the upper and lower solutions method, the bootstrap technique and the Schauder fixed point theorem to investigate the existence of periodic solutions and the asymptotic behavior of general time-dependent solutions for periodic reaction-diffusion systems of the following three types:(1) Quasimonotone nondecreasing system;(2) Mixed quasimonotone system;(3) A nonquasimonotone 2-system. The boundary conditions are assumed to be either the Dirichlet condition or linear Robin conditions.

在第一章，我们应用上、下解方法，bootstrap技巧和Schauder不动点定理考察如下三类周期反应扩散方程组的周期稳态解的存在性和一般的时变解的渐近性态：（1）拟单增系统；（2）混拟单调系统；（3）一个非拟单调2-系统，其边界条件是Dirichlet条件或线性Robin条件。

There are three motheds generally: to seek equational solutions to analysis;to seek the numerical solutions of equtions; solutions\' qualitative analysis.

通常有三种方法：求出方程的解析解；求方程的数值解；对解的性态进行定性分析。

There are three motheds generally: to seek equational solutions to analysis;to seek the numerical solutions of equtions; solutions qualitative analysis.

本文第四章中运用定性分析的方法研究了一类四阶时滞微分方程解的无条件稳定性。

The thought based on the hyperbola function method is extended,and more explicit and exact solutions are successfully derived,including shock wave type solutions with break point and exponential function type solutions .

在此基础上又对双曲函数法的思想进行了推广，从而获得了其更多的显式精确解，包括间断型激波解和指数函数型解。

Concretely, firstly with Timoshenko beams, the fundamental formulae of solutions of dynamical equations, boundary conditions and initial conditions have been transformed by Laplace transformation. Secondly, in the Laplace regions , we gain the analytical solutions of impact forces at the impact contact points, shear and maximum inverse stress of beams. Then, by using Durbin numerical inverse method, we gain the numerical solutions of Timoshenko beams under various restriction conditions. Moreover, the graphs about impact forces at the impact contact points, shear and maximum inverse stress of beams can be obtained too.

把Timoshenko梁力学模型动力学方程的基本解形式、边界条件以及初始条件进行Laplace变换，在Laplace区域得到了冲击接触处的冲击力、整个梁的最大弯曲应力和剪力的解析解，然后利用Durbin数值反演的方法得到了各种约束条件下的Timoshenko梁模型时间-空间的数值解，得到了冲击接触处的冲击力、梁各处的最大弯曲应力和剪力的曲线图。

In this thesis, we study two problems: the existence results of solutions for generalized vector quasi-equilibrium problems and Hlder continuity of solutions to generalized vector equilibrium problems. The detailed contents are listed as following:In Hausdorff topological vector space, we discuss the existence results of solutions for three types of generalized vector quasi-equilibrium problem (GVQEP1,(GVQEP2) and (GVQEP3), for short respectively.

本文主要研究了两类问题：广义向量拟平衡问题解的存在性以及广义向量平衡问题解的Hlder连续性，具体内容如下：在Hausdorff向量拓扑空间中，讨论了三类广义向量拟平衡问题(GVQEP1)，(GVQEP2)和(GVQEP3)解的存在性定理。

There are two types of gold deposits in this area, namely altered rock type and quartz vein type.

本区金矿床包括两种类型：柴胡栏子金矿床为蚀变岩型金矿；莲花山和红花沟金矿床属石英脉型。

You were home and it was two weeks ago.

你回到了家里。当时是两周前。