定理的

This paper presents the new bound theorems in structural limit analysis developed on the basis of the generalized variational principle. The approximate limit factors determined from the new bound theorems are closer to the exact limit factor than the ones obtained from the classical bound theorems.

本文给出在极限分析的一般变分原理[1]的基础上发展起来的极限乘子的新的上、下限定理[10]，由这个新的上、下限定理决定的极限乘子的上、下限比经典的上、下限定理给出的更为靠近准确解。

Then we deeply studied the completeness of LP . Consequently, we established:(1) The completeness theorem of LP with truth-value in finite Lukasiewiczchain;(2) The completeness theorem of LP with truth-value in complete and atomic lattice implication algebras;(3) The completeness theorem of LP with truth-value in injective lattice implication algebras.

建立了：（1）基于Lukasiewicz有限链的格值命题逻辑系统LP的完备性定理；（2）基于完备的且原子的格蕴涵代数的格值命题逻辑系统LP的完备性定理；（3）基于内射的格蕴涵代数的格值命题逻辑系统LP的完备性定理。

Secondly,we firstly study the properties of functions with values in a uni-versal Clifford algebra 〓,and we obtain the following very important basictheorems in universal Clifford analysis:Cauchy's integral formula,Cauchy's inte-gral theorem,the mean value theorem,the three versions of the maximum mod-ulus theorem,the Taylor's expansion,the Laurent's expansion and the residuetheorem etc..All of these results generalized the classical results.

第二，本文所讨论的各种函数性质以及所得的结果都在泛Clifford代数〓上所做的工作，它一方面包含了从前在泛Clifford代数〓上所做的工作，所得到的结果更广泛、更漂亮、更自然，另一方面，本文也是迄今为止第一次建立起来了在泛Clifford分析中与经典函数论相对照处基础地位的LR正则函数在特异边界上的Cauchy积分公式、Cauchy积分定理、平均值定理、极大模原理的三种表达形式、Taylor展式、Laurent展式留数定理等深刻的结果。

The structure theorem is obtained by defining "ternary ordered partition method" which is used to choose the test-sets of the first $k$ tests, and by defining two operations and two relations on feedback sequences; The isomorphism classification theorem is strictly proved by virtue of the structure theorem, thus the complicated problem of discussing $3^k$ possible search domains is reduced to the relatively easy problem on $k+1$ representative search domains; By the techniques of "super-coin construction method" and "image-union method", the search problem on $k+1$ representative search domains is reduced to the simple verification of several conditions on finite space of small cardinality.

通过引入用于选取前$k$次试验的试验集的"三元有序剖分法"以及关于反馈序列的两种运算和两种关系，得到了结构定理；基于结构定理严格地证明了同构类定理，从而将必须针对$3^k$个搜索域的复杂问题转变为讨论$k+1$个具代表性的搜索域的相对简单的问题；通过"构造超币法"和"并像法"等技术手段，将关于$k+1$个具代表性的搜索域的搜索问题转化为简单的关于势非常小的有限空间的几个条件的验证问题。

In Chapter Two, Liapunov functional method and Liapunov function method with Razumikhin techniques are employed to obtain some delay independent stability results for the Cohen-Grossberg neural networks with multiply delays.

在第三章中，我们首先对一般的无时滞Cohen-Grossber神经网络模型建立了几个稳定性定理，即文中定理3.3.1-3.3.4。从其中推论可看出负的自联接起着很大的稳定化网络的作用。然后我们考虑了一般的Hopfiel神经网络模型，运用单调动力系统理论，在对激发函数做出很弱的假定下获得了与时滞相关的稳定性结果，并对时滞的大小给出很多的估计，文中定理3.4.3。

In order to study vector-valued optimization problem, in chapter 5, a class of vector -valued function, that is, uniformly same-order set-valued function is introduced , which includes the separated functions as its proper subset; without hypothesis of convexity, new minimax theorem and saddle point theorem for uniformly same-order set-valued function are established. Next, by employing Ky Fan\'s lemma and H-KKM mapping , several existence results for generalized vector equilibrium problem established.

为了研究向量优化问题，作为可分函数的推广，第五章引入了一致同阶集值函数类，在没有凸性条件的假设下，对一致同阶集值函数建立了新的极小极大定理与鞍点存在定理；利用H-KKM映射，对一般向量均衡问题建立了(来源：A73BcbC论文网www.abclunwen.com)几个存在性定理；最后讨论了集值向量均衡问题系统，利用集值映射的拟凸性，在较弱的条件下证明了解的存在性。

Firstly, the generalization of Fan-Ha section theorem and a general vector variational inequality without convexity assumption and minimax theorem of vector-valued function are obtained. Then, the quasi-montone vector variational inequality problem is concerned. Cx-quasi-monotone operator is defined in topological vector space, inner point of a closed convex set K is introduced, the relation between inner point and relative algebraic interior point is given, an existence result for quasi-monotone vector variational inequality is obtained.

第三章主要研究了向量变分不等式和极小极大定理(来源：3282AB83C论文网www.abclunwen.com)，建立了广义的Fan-Ha截口定理、新的向量变分不等式与极小极大定理，并在拓扑向量空间中定义了C_x-拟单调算子，引入了闭凸集K的inner点，给出了inner点与相对代数内点的关系，利用innK_c代替K的拓扑内部，建立了新的拟单调向量变分不等式。

Recently, Professor Liu Wen and his associates study the strong law of large numbers for Markov chain fields on trees. But for the nonhomogeneous Markov chain fields ,they only study the even-odd Markov chain and non-symmetric Markov chain. However, this article goes in the normal nonhono-geneous Markov chain fields and gets a class of limit theorems for the functions of two variables of finite nonhomogeneous Markov chain fields. Some limit theorems on the frequences of states and ordered state couples are obtained by several corollaries.

最近刘文教授及其合作者对树上的马氏链场的极限定理作了研究，对于非齐次马氏链场，仅对其中的奇偶马氏链场和非对称马氏链场作了研究，本文讨论了一般的非齐次马氏链场的极限性质，得到了关于Caylay树上有限非齐次马氏链场二元泛函的一类极限定理，作为推论得到了关于状态与状态序偶出现频率的极限定理。

Chapter 6 is contributed to studying the convergence properties of pariwise NQD random sequences. We extend the Kolomogrov-type inequality, Baum and Katz complete convergence, the three series theorem, Marcinkiewicz strong law of large number and Jamison theorem.

第六章研究两两NQD列的收敛性质，首先给出两两NQD列的Kolmogorov型不等式，进而讨论它的若干收敛性质，获得了与独立情形一样的Baum和Katz完全收敛定理；几乎达到独立情形著名的Marcinkiewicz强大数定律，三级数定理，推广了著名的Jamison定理。

In view of these, the second part of this paper presents two sufficient conditions and two mixed type duals for the generalized fractional programming only under-convexity assumptions. These sufficient conditions apply to a broader class of mathematical programming problems.The results about weak duality, strong duality and strictly reverse duality arealso presented under more suitable conditions.

鉴于此，本文的第二部分，我们仅在函数—凸性假设下，给出了广义分式规划的二个最优性充分条件，这些充分条件较文献中的相关的条件有更广泛的适用性；同时还给出了混合型对偶，并且在适当的条件下，给出了相应的弱对偶定理、强对偶定理，以及严格逆对偶定理。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。