对偶的

A new SVM is presented in this paper to solve the approximately linear separable problem of pattern recognition:First,we transform the two convex hulls which are made up of the approximately separable training set to make them separable;Second,we can figure out a separating hyperplane by halving the nearest points method or maximal margin method;Then,we get the approximately linear SVM by solving the dual problem of maximal margin method.

对模式分类中的近似线性可分问题提出了一种新的近似线性支持向量机：先对近似线性分类中的训练集所形成的两类凸壳进行了相似变形，使变形后的凸壳线性可分，再用平分最近点和最大间隔法求出理想的分划超平面，然后再通过求解最大间隔法的对偶问题得到基于相似压缩的近似线性SVM。

Then, the system is linearized by variational approach, the local null controllability is proved by applying a generalized implicit function theorem and combining the good property of the solution mapping.

首先通过对系统线性化，构造泛函，利用对偶方程，给出控制函数具体形式的办法得到系统的逼近能控性；然后采用变分方法对系统线性化，再结合解映射好的性质，应用推广的隐函数定理，证明系统的局部零能控性；最后利用局部零能控性和逼近能控性结合给出系统零能控的结论。

In chapter 4, Based on the orthogonality relations and duality of C-algebras, we study the decompositions of C-algebras, and give a Fourier inversion formula on C-algebras, which generalizes the Fourier inversion formula on the center of a finite group algebra over complex. As an application, we characterize the integral closure of C-algebras over the ring of integers, and show a necessary and sufficitient condition for elements of C-algbras being algbraic integral over integers.

第四章 我们应用C-代数的正交性及对偶性刻画了C-代数的一个分解，给出了C-代数上这个完全分解的Fourier反演公式，从而推广了Z分解的Fourier反演公式；作为Fourier反演公式的一个应用，我们刻画了Z在整数环Z上的整闭包，进一步我们研究了C-代数在整数环Z上的整闭包，给出了C-代数在整数环Z上为整元的一个充要条件。

The high resolution image of full hole can be obtained from the being processed imaging logging information, and the morphological features about intersecting lines of fracture face and borehole present monocyclic sine curve.

成像测井数据经处理后可得到全井壁高分辨率的图像，而裂缝面与井筒的交线在图像上的形态特征呈现为单周期的正弦曲线，应用哈夫变换的点－线对偶性拾取图像中的裂缝角度等信息，可得到较好的处理结果。

Besides, the reduction of the dispersion part of potential leads to a lower critical temperature and higher in-plane part of molecular dipole moment; however, because the reduced critical temperature is relatively small compared with that of a 3D system, disappearance of the critical point has not been observed in the quasi-2D SM system within practical scope of the simulation.

尽管受到插入困难的限制，本文没有直接发现随着色散作用的减小汽液共存消失的现象，但根据对模拟结果的分析及对偶极作用的讨论，本文猜测这种情况在更小的色散作用和更低的温度下仍然是会发生的。

In chapter 4, the case of risk asset allocation with allowed sell and restricted short sell is discussed, especially in case of restricted short sell, the efficient frontier piecewise partition is determined by using duality theory in parametric quadratic programming. And the concept of tripartition is introduced, economic meaning stated and algorithm to determine efficient frontier proposed.

特别对限制卖空的证券组合，应用参数二次规划对偶性理论解决了有效边缘曲线分片划分的问题，并引入了三元分割的概念，解释其经济意义，同时给出确定有效边缘的算法；对于协方差矩阵是奇异的情况，利用矩阵分块技术，得到不同情形下有效边缘的解析表达式，并用直观的几何图形描述，克服了M-V模型在实证分析中遇到的困难。

The 1-generator quasi-cyclic codes and their duals are the most frequently encountered QC codes in the literature. Séguin discusses the construction and the enumeration of 1-generator QC codes in the special case where the prime factorization of x~m — 1 is the same in IF_qn as in IF_q.

单生成元的拟循环码及其对偶码是拟循环码中研究最多的一种。Séguin在要求x~m-1在F_q及F_中具有相同的分解的条件下，讨论了单生成元的拟循环码的结构及计数。

In the fist part, considering the game theoretical aspect of generalized Cohen's forcing C in dependence of ideal / on ω, Generalized a result of Sharp in Combinatorics on Ideals and Axiom A(The Journal of Symbolic Logic,1994), we argue that if J is a regular p*-ideal then C do not satisfy Axiom A.

第一部分通过讨论ω上的理想J的广义Cohen's力迫C的博弈论性质，我们推广了Sharp在论文Combinatorics on Ideals and Axiom A(The Journal of Symbolic Logic，1994)中的一个主要结果——如果U是一个超滤，则其对偶理想J=U~*所作成的广义Cohen's力迫C不满足力迫公理A，我们进一步证明了如果J是一个正则的p~*-ideal则C不满足力迫公理A。

Using operator-theoretic-methods, we give some characterizations for a dual generalized frame of a generalized frame in a separable Hilbert space H. We also prove a result concerning two strongly disjiont generalized frames.

本文研究了可分的Hilbert空间H中的广义框架，运用算子理论方法，研究了可分的Hilbert空间H中广义框架的性质，给出了广义框架的对偶广义框架的一些刻画，并且证明了两个广义框架是强非交的一个充分必要条件。

The highlight of the DCL algorithm is that we have studies hidden variables structure estimation with own parameters, which form more general case of curve data submanifold. As the application of information geometry learning algorithm for supervised neural networks, we have given detailed algorithm implementment of DCL algorithm for mixture of experts, and stochastic multilayer percetron.

其中我们所作重要的工作是把结果推广到隐变量本身带参数结构的弯曲数据子流形的情形，采用了由场变换所形成的数据子流形估计中，辅助量本身是一个带参数的量，根据对偶梯度流公式，给出了学习算法实现的具体形式。

It has been put forward that there exists single Ball point and double Ball points on the symmetrical connecting-rod curves of equilateral mechanisms.

从鲍尔点的形成原理出发，分析对称连杆曲线上鲍尔点的产生条件，提出等边机构的对称连杆曲线上有单鲍尔点和双鲍尔点。

The factory affiliated to the Group primarily manufactures multiple-purpose pincers, baking kits, knives, scissors, kitchenware, gardening tools and beauty care kits as well as other hardware tools, the annual production value of which reaches US$ 30 million dollars.

集团所属工厂主要生产多用钳、烤具、刀具、剪刀、厨具、花园工具、美容套等五金产品，年生产总值3000万美元，产品价廉物美、选料上乘、质量保证，深受国内外客户的青睐