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In this paper the natural boundary reduction for some elliptic boundary value problems with concave angle domains and its natural boundary element methods are investigated.

本文研究凹角型区域椭圆边值问题的自然边界归化及其边界元法。

Part II, the artificial boundary condition and its numerical methods based on natural boundary reduction for a hyperbolic initial boundary value problem in an infinite domain with a concave angle is investigated.

第二部分，研究一类具有凹角的无界外区域的双曲型初边值问题基于自然边界归化的人工边界条件及其数值方法。

Based on the correlation of the Guadalupian and Lopingian conodont zones of the Salt Range, Pakistan with those of South China, the Amb Formation and the lower part of the Wargal Formation in the Salt Range, Pakistan are Late Guadalupian in age. The Guadalupian/Lopingian boundary is in the lower part of the Wargal Formation, and the Wuchi-apingian/Changhsingian boundary is in the lower part of the Chhidru Formation. The Permian/Triassic boundary is in the Kathwai Member of the Mianwali Formation.

根据华南与盐岭地区瓜达鲁普统和乐平统的牙形类化石带对比，可以确定Amb组和Wargal组底部的时代为瓜达鲁普世晚期，瓜达鲁普统与乐平统的界线位于Wargal组下部，吴家坪阶与长兴阶的界线位于Chhidru组的下部，而二叠与三叠系的界线位于Mianwali组下部的Kathwai段之内。

Take the method of "subarea" and "conjunction" to segment the whole request model to three parts. Making use of boundary continuousness between medium and lining structure at stress and displacement, construct a wave function that can satisfy the stress boundary condition at horizontal surface by the scattering of SH-waves in circular part. And then, availing of the wave function, conjoin the circular part into the semi-circular hollow space at common boundary. The problem can be reduced to solve the question that can only meet the condition of "conjunction". Finally, the solution of the problem can be summarized to a series of algebraic equations and solved numerically by truncating the finite terms of the infinite algebraic equations.

采用"分区"与"契合"的方法，将整个求解区域分割成三部分，利用介质与衬砌结构在边界上的应力、位移的连续性，构造一个可以自动满足水平界面上应力边界条件的圆域对SH波散射的波函数；再利用这一波函数将圆域与半圆形凹陷半空间的"公共边界"进行"契合"，将问题简化成对一个只需满足'契合'边界条件的散射问题的求解；最终归结为对一组无穷代数方程组的求解问题，利用截断有限项的方法对其进行计算。

In this thesis, we apply Coulomb's law and propose an external force to overcome the problem of traditional ACM that can not capture the cavities of an object. Assume that each node of a snake has its own electric charge, and the object boundary has opposite electric charge. Then object boundary will attract the nodes of the snake. This helps the contour easily to move to the object boundary.

本论文中，我们运用库仑定律的观念，提出了一个运用局部引力作为外力的方法，用以克服传统主动性轮廓模型在凹面处收敛不佳的缺点；假设物件边界带电，而主动性轮廓模型的结点带与物件边界相异之电荷，则物件边界会吸引著主动性轮廓模型各结点，使得模型曲线更容易靠近物件边界。

Compared with the known results,the nonlinearity is allowed to change sign and is involved with the first-order derivative explicitly.In particular,the boundary condition includes the Dirichlet boundary condition and Robin boundary condition.

与现有工作相比，我们所考虑的动力方程不但非线性项可变号，而且包含一阶导数项，所考虑的边值条件更具一般性，比如可以包含Dirichlet及Robin边值条件等。

In order to bypass the difficulty of discretizing the boundary r or the Lebesgue discontinuous set Su in the Mumford-Shah model, we use an edge-detector function and a threshold value to induce a thin-belt where the image boundary lie in and displace the length of the boundary by the area of the thin-belt approximatively.

为避免在离散化Mumford-Shah模型中的边界Γ或Lebesgue不连续集S_u的困难，我们借助边界检测算子和门限值，确定图像边界所在的窄带区域，用窄带区域面积近似边界的长度。

Initial boundary value problem of two dimensional unsteady diffusion equations is solved in this paper. By using time-dependent fundamental solution of two dimensional diffusion equations and the extension of double layer potential, we establish virtual boundary integral expression of diffusion equations. Then virtual boundary element method is used to implement the numerical computation.

本文在求解二维非定常扩散方程的初边值问题时，利用二维扩散方程与时间有关的基本解，基于双层位势的延拓，建立二维扩散方程的虚边界积分表达式，然后利用虚边界元法进行数值计算。

This invention discloses a preparation method for anti-corrosion rare earth magnet material characterizing that it takes the optimized grain-boundary phase design as the starting point on the basis of a dual alloy method to select Nd base alloy with high crystal forming ability as the assist alloy and reduces the temperature of the press mold blank in a quartz container to room temperature from over grain-boundary phase melting point with the water extraction way to get enough cooling rate and guarantee the non-grain-boundary phase, compared with the material of the same composition prepared by ordinary method, the weightlessness of this invented material reduces over 30% after testing the weightlessness of the material by laying it for 96 hours under 121deg.C, 2 atmosphere and 100% humid environment to show the advanced performance of anti-corrosion.

本发明公开了一种耐腐蚀稀土永磁材料的制备方法，其特征是它在双合金法制备工艺的基础上，以优化晶界相设计为出发点，选取具有较高非晶形成能力的Nd基合金为辅合金，并在烧结回火时将置于耐高温石英容器中的压型坯件，从晶界相熔点以上以水淬冷却的方式降温至室温，以达到足够的冷却速率，确保得到非晶晶界相，根据本发明制得的耐腐蚀稀土永磁材料，通过测量在121℃、2个大气压以及100％湿度环境下放置96小时后材料的失重情况，结果显示本发明得到的材料与常规方法制备的相同成分的稀土永磁材料相比失重减少了30％以上，充分证明其具备了更优越的耐腐蚀性能。可广泛应用于电子、汽车、计算机、电力、机械、能源、环保、国防、医疗器械等领域。

This is a kind of evolutionary elliptic free boundary problems, in which the free boundary changes with time and at each fixed time the unknown function satisfies a boundary value problem for an equation of elliptic type.

详细本文分两部分。第一部分讨论拟定常电加工问题。这是一类发展型的椭圆自由边界问题，其自由边界依赖于时间的变化而不断演化，在每一固定时间，未知函数满足椭圆型方程的边值问题。

This is not an ordinary box, which is used as a background picture of the dialog box, very pretty.

详细说明：这可不是一个一般的对话框，它是用图片作为背景的对话框，非常好看。

Conceal me what I am,and be my aid for such disguise as haply shall become the form of my intent.

遮掩我的身份，帮助我，我的面具将成为我的目的。