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Due to the restriction of computational complication and precision,WRM boundary collocation method can only be used to simulate temperature fields of single-particle model,as for the case of some more complicated particle geometry shape it is very hard to obtain sufficient approximation solutions.Thus,BEM is adopted to analyze the thermal conduction problem of composites with particle of arbitrary geometry.

由于受计算复杂程度和计算精度的限制，采用加权残值法只能分析单夹杂问题，且对于更复杂的夹杂形状很难得到良好的近似解，因此接下来采用边界元方法分析了具有任意形状夹杂复合材料的温度场问题。

Secondly, for the boundary correspondence of affine stretch on hyperbolic regions, we prove that the above conclusion is also true. Finally, we pose a sufficient and necessary condition for the same conclusion.

最后利用退化的四边形序列，给出了拟对称同胚的极值拟共形延拓的最大伸缩商、四边形模之比的上确界及拟对称同胚的边界伸缩商三者相等的一个充要条件。

The dissertation is mainly concerned with research of necessary and sufficient boundary integral equations and nonsingular boundary element method.

本文主要研究充要边界积分方程和无奇异边界元方法。

In this paper,the existence of multiple positive solutions for a class of fourth-order p-Laplacian operator singular boundary value problems is discussed by using the fixed point index,and some sufficient conditions are given such that the problem has at least two positive solutions.

利用不动点指数理论研究了一类含 p-Laplace算子的四阶奇异边值问题的多重正解的存在性，给出了至少存在两个正解的条件，改进了不久前其他作者的相关研究。

The existence of solutions to a type of nonlinear ordinary differential equations four-point boundary value problems with p-Laplace operator was studied by means of the extension of Mawhin s continuation theorem with sufficient conditions obtained for the existence of solution.

利用Mawhin连续引理的推广形式，研究一类具 p-Laplace算子的非线性常微分方程四点边值问题解的存在性，得到了方程解存在的充分条件。

Applied Green's function, the differential equations will be transformed into the equivalent of integral equations, sufficient conditions for existence and uniqueness of positive solutions for fourth-order nonlinear singular continuous boundary value problems with p-Lapacian operator are obtained.

文中，利用格林函数，将微分方程转化成等价解的积分方程，给出了该奇异非线性四阶p-Lapacian微分方程边值问题的正解的存在及惟一性的一个充要条件。

Transforming the boundary value problem with p-Laplace operator into operator equation, giving propriety conditions for different value of p,and using an extension of Mawhin s continuation theorem,the existence of solution of a boundary value problem with p-Laplace operator is proved, and the sufficient conditions for solution existence are obtained.

将具p-Laplace算子的边值问题转化成算子方程，对于p的不同取值给出适当的条件。利用Mawhin连续引理的推广形式，证明了一类具p-Laplace算子的微分方程边值问题解的存在性，得到了一系列解存在的充分条件

We have also found the sufficient and necessary conditions for the solvability of the above boundary value problem.

本文将在文[2]所建立的方程(1)的广义解一般表达式的基础上，讨论边界条件更为一般的斜微商问题，建立这一问题的解的表达式、问题的指标同解

FR conjugate gradient methods with perturbations are proposed. The global convergence property of the first method is proved under the condition of main directions' sufficient descent. Whereas, in the proof of the convergence for the other two methods, we only need main directions' descent. Importantly and quite interesting, boundedness conditions such as objective function being bounded below, boundedness of level set are not needed. Chapter 5 presents a version of Dai-Yuan conjugate gradient method with perturbations.

在主方向充分下降的条件下证明了第一个方法的全局收敛性，而后两个方法的收敛性是在主方向下降的条件下证明的，这些收敛性证明的一个共同特征就是不需要目标函数有下界或水平集有界等有界性条件，第5章采用Wolfe或Armijo步长规则提出了带扰动项的Dai-Yuanabbr。

On the basis of the coincident relation between a radar signal and a radar ambiguity function, an arbitrary bounded two-dimensional function of intergrable square is presented as a necessary and sufficient condition for radar ambiguity function.

本文基于雷达信号和雷达模糊度函数间的一致关系，提出了任意平方可积的二维有界函数是雷达模糊度函数的充要条件，并且指出它包括了Wilcox提出的离散的可实现条件。

Warden: That's a beautiful dog, but don't bring her again.

那是条漂亮的狗，但是不要再把她带来了。

You get up in the morning – no hangover!

你第二天早上起来的时候—不会宿醉！