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A new concept of convex set and its some characteristic properties This paper give a new definition, the support direction of a boundary point of convex set.

2复杂网格的Buffon概率在积分几何中，运动公式是一些定义在定区域与动区域交集上的几何函数的积分公式。

In chapter three, we prove that there exist solutions to the Ky Fan variation inequality, as the set-valued mappings are defined on spheres in infinite dimensional Banach spaces or odd dimensional Euclidean spaces, following from these theorems, we obtain some fixed point theorems for set-valued mappings defined on a sphere. When G is an approximate compact convex subset of E, or G is a almost quasi-convex set-valued mapping, we prove that there exist solutions to and type generalized Ky Fan variation inequality, following these theorems, we prove several best approximation theorems and coincidence theorems involving two set-valued mappings and two different spaces. In chapter four, we first present a new Simplicial algorithm for computing the Leray - Schauder fixed points, the algorithm can solve the set-valued nonlinear complementarily problem. We give a condition to guarantee the computation proceeding in a bounded region. We present integer-labeling algorithms for computing fixed points of some set-valued mappings, the best approximation points and solutions to a kind of set-valued variation inequalities.

第四章给出了计算定义在非凸集上的非自映射的Leray-Schauder不动点的算法，而现有的不动点算法都是计算凸集的上半连续集值自映射的不动点；给出了保证计算有界的一个充分条件，我们的条件大大弱于Mdrrill条件，我们的算法也可用来计算Eaves不动点；给出了集值非线性互补问题存在解的一个充分条件，此时可利用Leray-Schauder不动点算法来求解；向量标号算法以往是计算集值映射不动点的唯一有效算法，我们给出用整数标号算法计算一类集值映射的Kakutani 不动点的算法；定义在紧凸集上的连续映射不一定有不动点，但一定有最近点，最近点是不动点概念的推广，我们给出了计算最近点的算法；集值映射变分不等式尚无有效的求解算法，我们给出求解一类集值映射变分不等式的算法。

In the second we give the necessary and sufficient conditions for strict convexity of power function of exponential family in the discrete case.

在第二个问题中，我们给出了在离散的情形下，指数族势函数严凸的充分必要条件。

In this paper, we use Constant Rank Theorem to give some convexity results for a class of ...

本文中，我们将利用常秩定理对一类Hessian方程给出几个凸性的结果。

We all know it's difficult to convince them to give up the plan.

我们都知道说服他放弃计划是很困难的。

We all know that it is difficult to convince him to give up the plan.

我们都知道说服他放弃计划是很困难的。

He's convincing,I'll give him that.

他说的挺像真的，我相信他

They give it its bite, its convincingness, its seriousness.

它们赋予了这个运动尖锐透彻，另人信服，严肃认真的特点。

In addition, some modifications on several computational methods are also presented. Using LMTO method the electronic structure of several systems are studied, and some results are obtained. They are: The ideal Nb (100) surface has three surface states, the multi-layer relaxed surface has two surface states. The surface energy of the ideal surface is higher than that of the relaxed surface, that means that the multi-layer relaxed surface is more stable than the former one, which supports the LEED results. The mono-layer relaxed Ag (111) surface is the most stable one among several" stable surface models"presented by several researchers. The surface energy of Ag (111) surface is higher than that of surface Ag (001), which supports some experimental results such as different reaction rate at different surface orientations for the same material. The surafce states of Si (111) surface not only locate near the Fermi level, but also in the valence band, which agrees well with Cohen's conclusion. Si (111)-H is an effective model for analysing the surface states and H adsorbed on the back surface is a good method for improving the convincingness of the results obtained on thinner slab models. The surface stability depends on three different kinds of MoSi〓(001) surfaces, the surface with mono-layer Si is the most stable one, and the surface with Mo at the first layer is the most unstable one among them. These are consistant with the Kemoda's experimental results. The valence bands of clean or K adsorbed CdTe (111) surface agrees well with the synchrotron radiation studies. The surface of CdTe (111) consists of four kinds of surface models which show different surface electronic structures and different surface structure stabilities. The conclusion agrees well with Wu's experimental work. The different absorbed alkali metals on the CdTe (111) surface give different adsorption characteristics which have relations not only with the valence electrons, but also with the core ones of the alkali metals. The electonic structures of Si-C alloys are different from that of Si-Ge alloys, and the energy band gaps of Si-C alloys do not increase linearly with Carbon concentration, our conclusion supports Alexander's results, but conflicts with Soref's one.

现分述如下： LMTO方法及其应用方面：1）通过对Nb（100）表面电子态分析发现清洁理想表面有三个表面态，多层弛豫表面有两个表面态；表面能大小说明多层弛豫表面更稳定，支持了LEED结果。2）通过对采用不同方法获得的几种不同Ag（111）表面稳定结构的表面能计算分析，给出了单层弛豫表面为Ag（111）表面的最稳定结构；从Ag（111）单层弛豫表面和Ag（001）表面的表面能比较，发现了Ag（001）表面表面能要比Ag（111）小的，表明了同种物质不同表面取向将表现出不同物理、化学性质，这是与实验中得出的结论是吻合的，3）通过对Si（111）表面态分析，不仅发现了Si（111）表面不仅具有居于费米能级附近的悬挂键所对应的表面态，而且还有很多表面态位于价带能量范围内，与Cohen等结果一致，H饱和slab模型背表面相当于增加了slab层的厚度，是一有效的变相增加slab层厚的方法，弛豫表面较清洁理想表面价带谱们低能端的少许移动，预示着总能降低，说明弛豫表面较清洁理想表面稳定。4）MoSi〓具有三种表面，从费米能级上态密度值大小得到单层Si表面最稳定，Mo原子为表层原子的表面最不稳定，双层Si原子表面居中的结论，这与Kemoda等人实验结果是一致的。5）通过对CdTe（111）表面表面电子态、表面结构稳定性及表面H、碱金属吸附的电子结构系列研究，不仅得出了CdTe（111）清洁及碱金属K吸附价带谱与同步辐射光电子谱相吻合的结果，而且发现了CdTe（111）表面具有四类不同原子近邻特征，表现出四类不同的表面结构及电子结构特征：不同表面态分布、不同的表面结构稳定性（表层原子与次层原子成三键有一悬挂键的表面要比表层原子与次层原子成一键有三悬挂键稳定（与Wu等人实验结果一致））、不同的H吸附特性。

I'm gonna give you a muscle relaxant so your body doesn't convulse.

我会帮你注射肌肉迟缓剂以防止抽筋

Those who loved reading were obliged to send for their books from England; the members of the junto had each a few

那些喜欢看书的人就得从英国购书，讲读俱乐部的的成员每人都有几本。

Three fourths of the earth's surface is covered with water.

地球表面的四分之三被水覆盖着。