查询词典 duality theorem

Through study on Rernel operation nature of duality relation ,the definition of quotient set for every duality relation was presented.

通过对二元关系核运算性质的研究，定义出任何一个二元关系的商集。

Through a study on kernel operation nature of duality relation , the definition of quotient set for every duality relation was presented.

通过二元关系核运算性质的研究，定义出任何一个二元关系的商集。

In this thesis, we defined duality Fuzzy relation in a pointwise Fuzzy set by a set of duality Fuzzy point. Then we defined Fuzzy congruence and Fuzzy rough set in Fuzzy semigroups.

本文把二维模糊点作成的集合定义为一个点态化模糊集上的模糊二元关系，进一步定义模糊同余关系，并通过它又定义点态化模糊集上模糊粗糙子集，并研究了它们的一些性质。

Chapter 4,based on strong efficiency rather than efficiency or weak effi-ciency,discusses the similar problem to chapter 3.The concepts of strongsupremum and strong infimum for the set in finite-dimensionalEuclidean space are given,s-conjugate functions and s-subdifferentials theory is developed,by means of which,the duality problem ofmulitobjectivre programming for strong efficient solutions or called absoluteoptimal solutions is analysed,and a new duality theory-s-conjugateduality theory is proposed.

第四章，基于强有效性而不是有效性和弱有效性，给出了类似于第三章的结果，提出了有限维欧氏空间中集合的强上、下确界等概念，研究了点集映象的强共轭函数和强次微分问题，建立了点集映象的s-共轭函数及其s-次微分理论，并借助于这一理论，讨论了多目标规划关于绝对最优解或称强有效解的对偶性问题，建立了基于强有效性的s-共轭对偶理论。

In this paper,some approximate optimal solutions and an augmented Lagrangian function in nonlinear programming were introduced,duality map and duality problems based on the augmented Lagrangian function were established, relationship between the approximate optimal solutions of augmented Lagrangian function and primal problem was discussed.

介绍了几种近似最优解和增广拉格朗日函数，建立了基于增广拉格朗日函数的对偶映射和相应的对偶问题，讨论了增广拉格朗日函数的几种近似解和原问题的几种近似解的关系，得到的结果推广了一些已有的结论。

Firstly, this paper definited pseudometric d for n -foldproduct of σ-algebra A of subsets of a given set X , and definited indicator function ; secondly, gave the concept of differentiable of set function at S° and concept of partial derivative at S° with respect to the ith argument Si through indicator function, and defound the weak efficient solution of and optimality necessary condition; Finally, obtained three weak duality results and strong duality results under generalized convexity conditions.

首先，对已知集X的子集的σ-代数A的n-折积A^n，定义了伪度量d，给出了相应的特征函数〈h，Is〉；其次，通过特征函数给出了集函数在S 可微的定义及集函数在S 关于第i个变量Si的偏导数定义；给出了多目标规划问题的弱有效解概念及的最优性必要条件；最后，分别在目标函数和约束函数的3种较弱凸性条件下，研究n-集函数多目标规划问题的对偶问题，获得了3个弱对偶结果和强对偶结果。

This paper studies the duality in the structure of his thought, his literary character, and his mutually interacting traditional and anti-traditional mentalities by analyzing the duality of the society of the Meiji Age and the Taisho Age.

文章从明治、大正时代社会的二重性出发，分析了作为时代代表作家的森鸥外在思想结构、文学性格上的二重性，其传统与反传统的互制心理。

Based on the third kind of wave-particle duality and the harmonious unifying of three kinds of wave-particle duality[6], we discussed the materiality of the electromagnetic element-wave.

基于"第三种波粒二象性"以及"三种波粒二象性的和谐统一"[6]，我们对"电磁基波"的物质性又作了进一步讨论。

With the similarity between electromagnetical fields and structural mechanics, the electronic E and magnetic H are considered as two duality variables. With the variational principle, the system is introduced into symplectic geometry of Hamiltonian duality equations.

根据电磁场问题与结构力学的类比关系，把电场量E和磁场量H作为二类变量，通过变分原理寻求一般条件下的解法，将体系导入Hamilton对偶方程的辛几何形式，给出了电磁波导的Hamilton辛体系，并给出了辛本征值问题的表达形式。

The duality feature of the acceptation individual in the ancient Chinese comes form the duality of glosseme.

存在于词义个体的静态和动态的不同运动状态中，存在于词义语言义和言语义的语义转化中。

Don't listen to their haver, nothing of that sort.

别听他们胡说八道，根本就没那回事。

But bank's shares trade below their book value, suggesting that investors are skeptical.

但是，银行股票以低于账面价值的价格交易，这一点反应了投资者的怀疑。