解空间

Inspired by this section, in section 5.2,we explore some basic topological degree properties of A-proper mapping in Menger pn-space. By its homotopy invariance, we prove the existence of solution for some equations.

受这节内容的启发，在第5.2节，我们首次在Menger pn-空间中研究了A-proper映射的拓扑度理论，并利用其同伦不变性获得了几类方程解的存在性。

By solving the Schrodinger equation and using the boundary conditions of delta function, We can get the Buttiker scattering Matrix.

通过解薛定谔方程求得自旋空间的波函数，再由边界条件确定波函数的振幅，进而求出散射矩阵。

To research the propagation characteristics of travelling wave along transmission line in depth, the authors establish a mathematical model of travelling wave along lossless transmission line with the format of discrete time and space mesh lines, derive the stable condition and boundary condition of the wave equations using numerical solution of partial differential equation, and attempt the simplification of the boundary condition to realize full decoupling of voltage and current.

为深入研究行波在配电线路上的传播特性，建立了时间-空间网格线离散格式的无损传输线行波数学模型，采用偏微分方程的数值解法推导了波动方程的稳定条件和边界条件，并尝试对边界条件进行简化，以实现电压和电流的完全解耦。

Finally, we give some examples.In Chapter 3, The existence of a bounded global attactor for Olmstead model with homogeneous Dirichlet boundary condition is proved under some condition on the parameters.

本章分四个部分，第一部分是对问题的概述；第二部分讨论了扩散系数对具有无穷时滞的一维竞争扩散系统的空间一致定态解的稳定性的影响，将扩散系数d作为分支参数，我们证明了从d_0处当d

At last, we are concerned with the global existence and asymptotic behavior of smooth solution to the initial boundary value problem for the bipolar hydrodynamic model with the Neumann and Dirichlet boundary condition in the one-dimensional case, respectively. The difficulties from the coupled action between electrons and holes are carefully dealt with.

另外，本文也深入研究一维空间双极半导体流体动力学模型初边值问题光滑解的整体存在性及其衰减性，分别讨论了两类在实际应用中重要的边值条件，克服了由于电子和空穴之间的耦合作用所带来的困难。

By using the spatial finite sine and cosine transform, and the temporal Laplace transform, the existence of the analytic solutions of its initial-boundary problems in a boundedspace domain with Dirichlet and Neumann boundary conditions is derived.

利用空间有限的sine或cosine变换及时间Laplace变换，给出了该方程有限区间上带Dirichlet和Neumann边界条件的两类初边值问题的解析解。

The CSD algorithm is shown to be efficient design method for complex system in parallel, and can search out better design for mixed continuous/discrete system in very reasonable number of system analysis compared to traditional optimization method, and is able to deal with the issue of dynamic design requirements.

并行子空间设计算法不仅有效地实现了并行设计思想，而且与传统的优化算法相比，CSD算法降低飞机系统分析的次数，找到系统全局最优解的概率也较高。另外，它还能成功地解决含有离散/连续混合变量的设计优化问题，以及具有处理工程设计中设计要求动态变化的能力。

Chapter 6, consider a coupled generalized KdV-Burgers equation. In section 6.2, we study the initial-boundary value problem in the semi-unbounded domain, the existence of global solutions and global attractors is proved by means of a uniform priori estimate for time. In section 6.3, the Cauchy problem by using the weighted space, the existence of the global attractors for a coupled generalized KdV-Burgers in an semi-unbounded domain is proved.

第六章，考虑了一类广义耦合的KdV-Burgers方程，在第二节中讨论了半无界区域上的初边值问题，证明了整体光滑解和整体吸引子的存在性；在第三节中讨论了Cauchy问题，利用加权函数和加权空间上的插值8不等式，证明了半无界区域上整体吸引子的存在性。

In this thesis, the virtual boundary integral equation is based on double layer potential with the virtual density to be determined on virtual boundary. Since this integral equation related to double layer potential only involves the computation of the normal derivative and second normal derivative of fundamental solution, the exponential integral function is not involved in it, so numerical computation for the exponential integral function is avoid.

本文则基于双层位势，引入虚拟矩密度函数来建立虚边界积分方程，并首先对时间变量进行解析积分，在虚、实边界上采用常单元和等额配点离散，该方程只涉及含基本解的法向导数及其二阶法向导数项的计算，对时间变量进行解析积分后，不会出现对指数积分函数的空间变量的积分计算。

In order to test the efficient and possibility of the method, main vibration features about space double layer has been calculated based on this method, comparing this with the precise solution of finite element method,...

为检验这种方法的有效性和可行性，用这种方法计算了空间双层子结构的主要振动特性，并将所得结果与有限元精确解进行对比，表明了这种方法不仅适用于简单对接情况也适用于高度赘余连接的情况，并且具有良好的综合精度。

I didn't watch TV last night, because it .

昨晚我没有看电视，因为电视机坏了。

Since this year, in a lot of villages of Beijing, TV of elevator liquid crystal was removed.

今年以来，在北京的很多小区里，电梯液晶电视被撤了下来。