对偶定理

By using these convergence theorems,it presents the Silverman-To-eplitz regular theorem and Samaratunga-Sember theorem on the Abelian topologicalgroups,the Vitali-Hahn-Saks theorem on algebras and the weak sequentially completenesstheorem of 〓-dual spaces of sequence spaces,etc.

这是抽象分析中的两个基本定理。作为应用，给出了Abelian拓扑群上的Silverman-Toeplitz正则性定理、Samaratunga-Sember定理、代数上的Vitali-Hahn-Saks定理，以及序列空间的〓对偶空间之弱序列完备性定理等。

In the second chapter, this problem is converted into a dual problem, i.e.

第二章把原规划转化为一个对偶问题，即无约束极大化问题，推广和证明了这个对偶问题的一些性质和基本定理。

Furthermore, the proof of correctness of CalcCycleTime is also the proof of the existence of cycle time, the existence of generalized eigenvectors, and the duality theorem.

本论文中给出的CalcCycleTime算法的正确性证明同时是周时存在性、广义特征向量存在性和对偶定理的证明。

Based on the duality theorem of linear programming, the directional derivatives of the objective function can be expressed as a linear programming which is very important in the practical calculation for nonmono tone line search subproblems.

基于线性规划的对偶定理，目标函数的方向导数可以表示成线性规划问题，这在实际计算非单调线搜索子问题时是非常重要的。

Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

Note on relation of seminorm and norm in vector space;2. The functional representation of some seminorms such as the continuous seminorms, the beundedseminorms and the lower semicontinuous seminorms are given out.

给出了局部凸空间上连续半范数，有界半范数和下半连续半范数等的泛函表示，应用这些表示定理，我们得到了Banach－Mackey空间的一个全局特征和囿空间的对偶特征，最后还给出了局部凸空间理论中一些重要定理的简化证明。

A new definition on canonical convex multiplier is given with a canonical dual method for the primal problem. Some examples are illustrated.

给出了凸乘子定义，对偶定理和搜寻全局最优点的方法，并通过一些例子加以演示。

We introduce the notion of characteristic pairs and give the definition of dual characteristic pairs of Dirac structures on Lie bialgebroids. Using the dual characteristic pairs, we give the if and only if conditions for which a maximally isotropic subbundle of the double of a Lie bialgebroid is a Dirac structure.

本文在李双代数胚上，引入了Dirac结构的特征对并给出对偶特征对的概念，利用对偶特征对，给出李双代数胚double的极大迷向子丛是Dirac结构的充要条件；其次，分别利用特征对与对偶特征对，将可约Dirac结构分为第一类可约与第二类可约，在此基础上，建立Poisson流形的两类对应约化定理。

In the sense of weak effective solution,the problems of Lagrange duality and saddle point are discussed under the convexlike condition.An alternative theorem of the system containing a semidefinite constraint of a matrix function is established at first.

首先在似凸条件下建立了一个含矩阵函数半定约束系统的择一性定理，由此得到多目标半定规划及其在弱有效解意义下的Lagrange对偶理论，包括弱对偶、强对偶和逆对偶等。

Apply those properties to find the self-dual code of length 66, we got new extremal self-dual [66,33,12] code with β=32 for w1 and at least 50 inequivalent extremal self-dual [66,33,12] codes with .

我们推广Harada[4]的一个建构自对偶码的定理，Harada[4]的方法在[2n，n]， n为偶数的条件下方可成立，而我们推广出的定理可以适用於n为奇数的情况。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。