对偶的

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

By Lagrange dual and scalarization of vector optimization, characterizations of solutions for which objective mapping satisfies weak convexity conditions are shown. The strongly and weak dual theorems for generalized subconvex-like mapping are obtained.

通过适当定义对偶问题和向量优化问题的标量化研究各解之间的关系，刻画目标映射满足弱凸性条件的优化问题解的特征，在目标映射是广义锥次类凸的条件下给出有关的对偶定理。

In the paper, the basic theory, the key technology of New GPS is investigated. The framework of GPS knowledge base is constructed based with databases based on the general matrix model and Inference Mechanisms based on the duality principle of New GPS.

本文通过对新一代GPS 的理论基础、关键技术的分析和研究，依据新一代GPS 的通用矩阵模型和对偶性原理，研究并提出了GPS 知识库的基本框架，GPS 知识库由基于通用GPS(来源：A31BC论文网www.abclunwen.com)矩阵模型搭建的数据库和基于对偶性原理设计的知识推理机构组成。

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。

The main work of this thesis is that basing on the documents of [77] , [78] , [79] , [80] , [81] probe into the applications of the duality theory in the macroeconomic analysis combining with some important problems in the modern economics, at the same time especially pay attention to the microfoundation of the macroanalysis.

本文的主要工作就是在[77]，[78]，[79]，[80]，[81]等文的基础上，以数学规划中的对偶理论做为基本数学工具，结合现代经济学研究的几个重大课题深入系统地探讨了对偶理论在宏观经济分析中的应用，同时也特别注重了宏观分析赖以存在的微观基础。

The relation between the nondegeneracy of their primal-dual optimal solutions and their strictly complementary optimal solutions is characterized, and then the conditions in which the solutions of a pair of primal and dual conic programmings are unique respectively are obtained.

从几何的观点描述一对原始-对偶锥规划可行域的极点，给出原始-对偶非退化的最优解与严格互补的最优解之间的关系，从而得到锥规划最优解唯一的条件。

At last, By using the factorization properties of cyclotomic polynmials on finite fields and the construction characteristic of cyclic codes, we present the relation of the period distribution of cyclic codes and the period distribution of their dual codes, establish the explicit formula for the number of the codewords without inner-period of the cyclic codes and their dual codes, find the method for computing the dimension and the period distribution of narrow-sense primitive BCH codes,and study the inverse question of period distribution of cyclic codes.

最后，利用有限域上分圆多项式的分解特性和循环码的构造特点，揭示了循环码的周期分布与其对偶码周期分布之间的内在联系，确定了一般循环码及其对偶码内无内周期码字的精确计数公式，决定了狭义本原BCH码的维数与周期分布，讨论了循环码周期分布的反问题。

In chapter two,based on the ultraviolet/infrared scale separation of the connection decomposition variables,we proposed that at the classic level the strong-coupling limit of the Yang-Mills theory vacuum behaves as a black hole with regard to colors.With this idea,we prove that there exists a dual superconductor solution for the strongly-coupled Yang-Mills theory,whose vacuum is made up of a many-body system of magnetic charges. A dual Abelian-Higgs model,with a Higgs vacuum constant added has been derived from the gluonic field part of SU(2)QCD based on the Faddeev-Niemi decomposition and random-order assumptions.The scale potential Vhas the Mexico-hat form.

第二章基于联络分解变量的紫外/红外分离，提出杨-米尔斯理论真空的强耦合极限表现为一个经典场论意义下色空间的黑洞，并证明在强耦合极限下该理论存在对偶超导体解，其非微扰真空可由磁荷的多粒子体系构成，借助规范场的Faddeev-Niemi分解，由SU(2)QCD的胶子部分推导出一个含有黑格斯真空常数的有效对偶阿贝尔-黑格斯模型，标量势V具有Mexico-hat形式，计算出Ginzburg-Landau参数为κ=/=(8/9)/(1/2)，，这与最近T。

First,the 3-d dynamic equations in cylindrical coordinate for transversely isotropic saturated soil were transformed into a group of governing differential equations with 1-order by the technique of Fourier expanding with respect to azimuth,and the state equation was established by Hankel integral transform method,furthermore the transfer matrixes within layered media were deriv...

首先，通过方位角的Fourier变换，将圆柱坐标系下横观各向同性饱和土的三维动力方程转化为一阶常微分方程组，基于径向Hankel变换，建立问题的状态方程，求解状态方程后得到传递矩阵；其次，利用传递矩阵，结合层状饱和地基的边界条件、排水条件及层间接触和连续条件，给出了任意简谐激振力作用下层状横观各向同性饱和地基动力响应的通解；然后，按混合边值问题建立层状饱和地基上弹性圆板非轴对称振动的对偶积分方程，并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程，并给出了算例。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。