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With the solutions of the biharmonic equation at boundary value in a semi-infinite stripe,a weighted energy function is established.

对半无限带状区域上双调和方程边值问题建立了能量衰减估计，证明了以方程的解建立的加权能量随着与区域有限端距离的增长，该能量呈指数式衰减。

ABSTRACT For an infinite soft ferromagnetic elastic crack material, the controlling equation for the plane problem is derived based on the linear theory of Pao and Yeh. Then it is reduced to a biharmonic equation combined with a harmonic equation.

对处于面内磁场中的含穿透裂纹无限大软铁磁弹性体，本文基于Pao和Yeh的磁弹性耦合线性化理论，通过推导，把问题的控制方程表示成一个重调和方程和一个调和方程，而得到问题的复势解。

In this paprer, the usual notions of superlinearity and sublinearity for Biharmonic problems $\Delta^2 u + c\Delta u =f $ are given a local form and extended to infinite nonlinearities.

在本文中，我们给出了双调和超线性和次线性问题$\Delta^2 u + c\Delta u =f $的一个局部形式且扩展为不定的非线性形式。

Ringel realized positive parts of semisimple Lie algebras in the framework of Ringel-Hall algebras. The main result of this thesis is to build a geometric and topological model over triangulated categories such as derived categories and stable module categories of repetitive algebras. We defines a Lie bracket by Euler characteristics of constructible subsets and thus realizes infinite dimensional Lie algebras of various types with non-degenerated bilinear form.

本文的主要结果是在导出范畴和重复代数的稳定模范畴等三角范畴水平上建立相应的几何-拓扑模型，并利用相应可构集的欧拉示性数定义了一个Hall代数的交换子乘法，从而在三角范畴水平上实现了一大类无限维李代数的整体构造，并且这类李代数本质上都具有非退化的不变双线性型。

The topics covered include: cooperative stochastic games; noncooperative stochastic games; sequencing games; games arising form linear infinite programming problems; network formation, costs and potential games; potentials and consistency in transferable utility games; the nucleolus and equilibrium prices; population uncertainty and equilibrium selection; cost sharing; centrality in social networks; extreme points of the core; equilibrium sets of bimatrix games; game theory and the market; and transfer procedures for nontransferable utility games.

包括的题目包括︰合作的随机的比赛； noncooperative随机的比赛；排序比赛；出现的比赛形成线的无限的编程问题；网路阵式，费用和潜在的比赛；用可转让的效用游戏的潜能和一致；核仁和均衡价格；人口不确定和均衡选择；费用分享；在社群网里的centrality；核心的极端点；均衡bimatrix 比赛；运筹学和市场；并且转移不可过户的效用比赛的程式。

The boon space Si say:Newton established astronomy because of discovering gravitational theory, because of carry on light of resolve but established the optics of science, established mathematics of science because of establishing binomial equation axioms and infinite theories, established the mechanics of science because of knowing the man's natural character of the mechanics.

恩格斯说：牛顿由于发现了万有引力定律而创立了天文学，由于进行光的分解而创立了科学的光学，由于创立了二项式定理和无限理论而创立了科学的数学，由于认识了力学的本性而创立了科学的力学。

Newton to humanity's contribution is huge, just like Engels said:"Newton as a result of invented law of universal gravitation to establish the science astronomy; As a result of has carried on the light decomposition, but established the science optics; As a result of established the binomial theorem and the infinite theory established the science mathematics; As a result of has known the strength essence, but established the science mechanics".

牛顿对人类的贡献是巨大的，正如恩格斯所说："牛顿由于发明了万有引力定律而创立了科学的天文学；由于进行了光的分解，而创立了科学的光学；由于创立了二项式定理和无限理论而创立了科学的数学；由于认识了力的本质，而创立了科学的力学"。

The line graph of further complete bipartite graph(infinite graph of n≥6) is extendable graph.

进一步完全二部图(n≥10的无限图)的线图是可扩圈图。

The nonlinear stability of three-dimensional disturbances for the Blasius boundary layers is studied. We adopted here the high accuracy method of using the expansions in orthogonal functions along the normal direction and the effective algebraic mapping to deal with the problem in the infinite region. The initial solutions of two-dimensional harmonic waves are given by Landau expansion, and the mean-flow-distortion is calculated by the approximation equation.

运用Landau展开给出了二维谐波的初始解、通过求解线性PSE而得到TS波和C型亚谐扰动的初始站值、以及近似地模拟初始站的均流变形值，以此为初始条件，并结合迭代-预估校正方法来实现非线性PSE的求解和推进，详细地研究了非平行边界层三维扰动C型失稳过程。

As we become conscious of the harmony in our soul, our apprehension of the blissfulness of the spirit of the world becomes universal, and the expression of beauty in our life moves in goodness and love towards the infinite.

当我们认识了我们灵魂深处的和谐时，我们对于这个世界精神上的极乐境界的体会就会变得普通，我们生活中表现出的美在美德中活跃起来，爱达到无限的境地。

I will endeavour to find you some assistance.

我尽力帮你找人帮忙。

At first I only know bruck is the idol of American younglings, afterwards I returned back to Taiwan ,even in Beijing last year ,I saw her poster everywhere, I was so surprised at her charm.

起初我只晓得布鲁克雷德丝是美国少男少女崇拜的偶像，后来回台湾，甚至去年在北京，居然也四处看见她的海报，才惊讶她的魅力之大。