基本域

The soundness and completeness theorem of this method were proved at last. This part consists of the following points: 1. The properties of the indecomposable extremely simple form of LP were discussed, the theorem shown that every logical formula of LP was equals of a generalized conjunction normal form. 2. The method for judging a logical formula is a indecomposable extremely simple form or not was discussed, the necessary and sufficient conditions of a logical formula with not more than three implicative connective being a indecomposable extremely simple form was given. 3. The α-resolution fields of the indecomposable extremely simple form of LP were discussed, some elementary results were obtained. 4. The automated reasoning method based on the resolution principle of classical logic was discussed, the author given a method to describe the set of clauses by using a matrix, and translated the resolution of two clauses to column operations of this matrix.

二、关于格值命题逻辑系统LP中α-自动推理方法的研究 1、对LP中不可分极简式的性质进行了研究，证明了LP中任何一个格值逻辑公式等值于一个广义合取范式； 2、对LP中不可分极简式的判定方法进行了研究，讨论了含有不超过3个蕴涵运算的格值逻辑式为不可分极简式的充分必要条件； 3、对LP中不可分极简式的α-归结域进行了研究，得到了一些基本结果； 4、对经典逻辑中基于归结原理的自动推理方法进行了研究，给出了用符号矩阵表示子句集合的一种方法，把不同的归结过程转换成矩阵的列变换。

In this paper, we introduce the algorithm of Schoof-Elkies-Atkin to compute the order of elliptic curves over finite fields. We give out a fast algorithm to compute the division polynomial f〓 and a primitive point of order 2〓. This paper also gives an improved algorithm in computing elliptic curve scalar multiplication. Using the method of complex multiplication, we find good elliptic curves for use in cryptosystems, and implemented ElGamal public-key scheme based on elliptic curves. As a co-product, we also realized the algorithm to determine primes using Goldwasser-Kilian's theorem. Lastly, the elliptic curve method of integer factorization is discussed. By making some improvement and through properly selected parameters, we successfully factored an integer of 55 digits, which is the product of two 28-digit primes.

本文介绍了计算有限域上椭圆曲线群的阶的Schoof-Elkies-Atkin算法，在具体处理算法过程中，我们给出了计算除多项式f〓的快速算法和寻找2〓阶本原点的快速算法；标量乘法是有关椭圆曲线算法中的最基本运算，本文对[Koe96]中的椭圆曲线标量乘法作了改进，提高了其运算速度；椭圆曲线的参数的选择直接影向到椭圆曲线密码体的安全性，文中利用复乘方法构造了具有良好密码特性的椭圆曲线，并实现了椭圆曲线上ElGamal公钥体制；文中还给出了利用Goldwasser-Kilian定理和椭圆曲线的复乘方法进行素数的确定判别算法；最后讨论了利用椭圆曲线分解整数的方法并进行了某些改进，在PC机上分解了两个28位素数之积的55位整数。

Experimental results show the recognition rate of the method is 95%for a known expresser and 72% for a novel expresser. Aiming at the shortcomings of optical flow technique,two improved optical flow algorithms are presented.One way is to introduce forward and backword constraint eqution and Hessian matrix of optical flow equation is computed.The well- posedness of each point of local neighbourhood is examined and the weight of Lucas-Kanade's method is defined as the reciprocal of the conditioning number of its Hessian Matrix.

3针对传统光流法的缺点，分别提出了两种不同的改进方法：其一为引入前向-后向光流方程，计算其Hessian矩阵，把Hessian矩阵条件数的倒数作为Lucas-Kanade光流法的加权阵，可有效消除局部邻域中不可靠约束点，同时提高基本约束方程解的稳定性；其二为针对传统光流法只适用于刚体运动的特点，在扩展约束光流方程的基础上引入了div-curl样条函数作为扩展光流约束方程的附加约束条件，给出了一阶和二阶div-curl样条约束下光流的数值解。

The first chapter introduces the trust region method , quadratic model and conic model.

第一章主要简介了信赖域方法的基本思想、二次模型和锥模型的研究状况。

In this paper, with the framework of non-equilibrium thermodynamic separation theory, a mathematical model of nonlinear chromatography is established according to the actual chromatography processes based on the three basic theorems, Lagrangian-Eulerian description, continuity axiom and local equilibrium assumption.

本文在梁恒等建立的非平衡热力学分离理论的框架下，以Lagrangian-Eulerian描述、连续性公理和局域平衡假设三大基本法则为基础，建立了一种制备色谱理论模型。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用"超平面"的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的"平移"方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

In chapter two, some necessary and basic materials of the finite field arithmetic theory and elliptic curve cryptosystems theory are introduced.

第二章给出有限域运算和椭圆曲线密码体制理论的基本知识和相关性质。

With the emphasis on the results obtained by the author, the basic scheme of the finite field theory and elliptic curve cryptosystems theory is sketched.

全文在强调作者所取得研究成果的同时给出了有限域运算理论和椭圆曲线密码体制理论的基本框架。

Among his contributions the most significant is to justify the theorem of the impossibility of the Paretian liberal that there is no a social decision function that meets unrestricted domain, Paretian principle and minimal liberty simultaneously, which helped him win the Nobel Prize on economics.

而他影响最大的贡献是证明了帕累托自由的不可能，后者为他赢得诺贝尔经济学奖奠定了基础，其基本含义指不存在一种可以同时满足无限制域、帕累托原则和最低限度的自由这三个条件的社会决策函数。

Many. I first analyze what is simulacra of the third order, and then indicates the laxity of the third order through a discussion of the relationship among simulacra, idea and mimesis. Based on a reinterpretation of the metaphor of cave, I demonstrate the generation and nature of simulacra, their relationship with humans and cognitive functions, thus defining a basic theoretical field for the discussion of simulacra.

论文首先分析什么是第三秩序的仿像，在此基础上通过仿像与理念、模仿之间关系的论述表明第三秩序的松动性，进而重新解读洞穴隐喻，展现仿像的制作、仿像的性质、仿像与人的关系、仿像的认识功能等，划定了仿像探讨的基本论域。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。