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It reduces a boundary valueproblem of elliptic equation to a singular integral equation on the boundary containing the finitepart of divergent integrals in the sense of distrib...

本文是在导师冯康教授指导下完成的，作者谨在此对他表示衷心的感谢。

As known, using the porential theory Green's tormulae and the fundamental solutions wecan reduce the harmonic and biharmonic elliptic boundary value problems to integral equationson the boundary.

我们熟知，利用位势理论或由Green公式及基本解出发区域内调和及重调和边值问题可归化为边界上的积分方程。

In 1970s, boundary value problems with equivalued surface are put forward. Andit is important to study them to solve practical problems. Li Ta-tsien and his partnersdo systematic research on them, especially study certain kind of elliptic boundary valueproblem with equivalued surface on the domain with thin layer.

二十世纪七十年代提出了一类等值面边值问题，它对于解决实际问题起到了非常重要的作用，李大潜等人对其进行了比较系统的研究，特别的对在具有薄层的区域上的椭圆型等值面边值问题进行了探讨。

Test and analysis show that, the distribution patterns of the tangent veloctiy fields in the big cone area and the small cone area, which are comprised of para-free vortex and para-forced vortex, are basically identical without a change of the radius of the boundary surface; with the increase of the angle of the small cone, the para-free vortex area decreases and the para-forced vortex area increases, and the emulsifiability of the fluid drips increases with the increase of velocity gradient; the tangent velocity increases with the increase of inlet flow, and the maximum tangent velocities of both the big cone area and the small cone area are 4.94 times of the inlet flow; and the maximum tangent velocity increases with the increase of the split ratio and with the radius of the boundary surface not changed.

试验分析表明，大锥段和小锥段切向速度分布规律基本相同，均由准自由涡和准强制涡构成，分界面半径rm没有变化；随着小锥角θ的增加，准自由涡区缩小，准强制涡区扩大，速度梯度增加会加大液滴的乳化程度；随入口流量增加，切向速度增大，经拟合得出大锥段和小锥段的最大切向速度均为入口流量的4.94倍；分流比加大，分界面半径基本不变，最大切向速度增加。

The last time when the valves open and close the boundary condition equation and heating systems in the other boundary condition equations, one-dimensional unsteady flow equations of motion and the joint solution of continuity equation, we can find the non-dimensional opening when the valve changes, heating system to calculate changes in surface pressure.

上回阀启闭时的边界条件方程与供热系统中的其它边界条件方程、一维不定常流动的运动方程和连续方程联解，就可以求出当止回阀无量纲开度变化时，供热系统各计算截面压力的变化情况。

Under the appropriate assumptions, the asymptotic solutions of the problem with different forms are obtained according to the multiple number of the root of some equation, which is satisfied by the boundary value of the reduced problem, by giving the general expressions for the coefficients of outer solution expansion and the corresponding boundary conditions.

在适当的假设下，通过给出外部解展开式系数及其对应边界条件的一般表达式，根据退化问题的边值作为某方程的根的重数，得到了此问题不同形式的渐近解。

Secondly, the analytic expressions of the error band boundary line for the s model of line segment are deduced, the parameter equations of the error band boundary are gotten.

考虑实用性和合理性，将线元看成离散点的集合，将线的不确定性看成点的不确定性的聚合体，将线元的位置不确定性模型看成以各点误差椭圆的长半轴E为半径的误差圆的聚合体，建立了以线元上任意点处的误差椭圆的长半轴E为带宽的线元不确定性ε模型。

Based on the good essential boundary condition processing capability of radial point interpolation meshless method, as well as the better computing efficiency of Element-free Galerkin method, the mixed method coupling EFG and RPIM is used to deal with the essential boundary condition.

基于径向基点插值无网格方法良好的本质边界条件处理能力，以及无网格伽辽金方法较好的计算效率，应用混合元法耦合两种无网格方法进行了本质边界条件的处理，数值算例结果表明：混合元法简明有效，计算概念清晰，易于编程计算。

In this thesis, we propose a self-detecting algorithm for the nodes of a wireless sensor network to determine the event boundary in the presence of faulty nodes. The nodes exchange messages and execute the algorithm in parallel to determine whether they are located on the boundary of an event.

在这篇论文中，主要的目的是在一个无线感测网路环境下，如果当事件发生时，每一个感测节点如何透过单纯的资料交换和平行演算法来达到自我侦测并且判断出本身是否位於事件的边缘。

On the basis of the above references, this paper attempts to make use of cone compression and expansion fixed point theorem, Mnch fixed point theorem and fixed point index theorem to discuss a special kind of singular boundary value problem-Lidstone boundary value problem.

主要包括以下三个方面的内容：第一章考虑了Banach空间中2n阶奇异边值问题正解的存在性，其中f在t=0，1处具有奇异性这里θ表示Banach空间E中的(来源：faABC论文网www.abclunwen.com零元。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。