对偶性

The available camera self-calibration is based on the image of the dual absolute quadric, but its elements have so large differences in magnitude that solutions are extremely sensitive to noise.

现有的自定标技术一般都是基于对偶绝对二次曲面像，由于对偶绝对二次曲面像元素在数量级上相差较大，在求解时必然会导致鲁棒性较差。

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。

The discussion produces some useful result:theconvergence of bounded subfeasible solution sequence and the convergence to zero of thesubfeasible dual gap.

在引入摄动的思想下，针对受摄动KKT系统，首先证明了以上四个规划问题中线性规划及其Wolfe对偶问题解的存在性，在此基础上得到一个关于其有界次可行序列收敛和次可行对偶间隙收敛到0的重要结论。

There are three classes of dual polyhedral links which can be explored: the tetrahedral link is self-dual, the hexahedral and octahedral link, as well as the dodecahedral and icosahedral link are dual to each other.

从手性角度考虑，对偶变换具有手性保持的特征，十个多面体链环分为六组对偶多面体链环。

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。

As a consequence, we make a conclusion that the dual Toeplitz operator is normal if and only if the range of the symbol lies on a line.

在此基础上研究了对偶Toeplitz算子的正规性，得到了对偶Toeplitz算子是正规算子的充分必要条件。

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。

Moreover, we give some dual properties of these problems, and on this basis, we present a dual algorithm for solving the nonconvex conic model trust-region subproblem.

论文分析了这些问题的对偶性质，在此基础上，通过对偶提出了求解锥模型信赖域子问题的算法，同时证明了算法的全局收敛性以及局部Q-超线性收敛性，并给出了一些数值算例以说明算法的有效性。

Increase of the regularity of interpolating scaling functions efficiently improves the approximation power of systems, moreover, that of dual scaling functions markedly enhances the smoothness of duals and improves the frequency characteristics of analysis filters in passband and stopband.

内插尺度函数正则度的增加有效提高了系统的逼近能力，对偶正则度的提高显著增加了对偶尺度函数、对偶小波的光滑性，改善了分析滤波器组的通带、阻带特性。冗余度在一定意义下制约了小波系统的性能。

The main aims of this disseration are to extend the complex self-dual grav-itational theory-the Ashtekar theory in four dimensional spacetime and este-bhsh a parametric self-dual gravitational theory in order to solve the problemof reality conditions in the Ashtekar theory.

本文的主要目的是推广四维时空的复自对偶引力理论-阿西特卡理论，建立一个参数化的自对偶引力理论，进而解决阿西特卡理论中面临的至关重要的实性条件问题。

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。