查询词典 resolvent operator

Through the Radon transformation of the normally ordered Wigner operator we introduce two mutually conjugate intermediate coordinate- momentum representations. Based on them we construct the appropriate quantum phase space theory which includes the new Wigner operator adapting to this space and construct the appropriate generalized Fredholm operator equation and then find its solution. We then deriving the Hermite polynomials operator identities by applying the Fredholm equation. We also reveal the connection between the generalized Wigner operator and the 2-dimension normal distribution in statistics, which is useful to study the quantum tomogram. As the application of the entanglement Husimi operator theory we calculate the Wigner function and the Husimi function of the one- and two-mode combination squeezed state , study their characters through drawing the three-dimensional graphics.

由正规序Wigner算符的拉登变换引入了两个互为共轭的中介坐标-动量表象，在此基础上我们建立了相应的量子相空间理论，其中包括引入适合该空间的新的Wigner算符；并在该表象的基础上，建立了广义Fredholm算符方程，求出了它的解，并运用该方程导出有关厄米多项式的算符公式；揭示广义Wigner算符与统计学中的随机变量的二维正态分布形式上的相似，这对于研究量子态的tomogram(是英文Tomography的派生词)有用。

The paper gives a detailed introduction to the classification and mothed of image edge detection from the traditional point of view,that is,the robert operator based on the maximum gradient detection,the sobel operator,the prewitt operator,the canny orerator,the laplancan operator based on the detection of second derivative of the zero-crossing point and then log operator.The paper makes a summary and analysis to the principles and applications,advantages and disadvantages of each algorithms and operators. Especially the canny operator.

本文首先介绍了图像边缘检测在国内外的发展，图像边缘检测的重要性及意义，阐述了图像边缘检测的原理，从传统的角度详细介绍了的图像边缘检测的分类及方法，即基于检测梯度最大值的robert算子，sobel算子，prewitt算子，canny算子，基于检测二阶导数的零交叉点的laplacan算子及log算子，对各种算法和算子的原理及用法及优缺点做了总结和分析尤其是canny算子。

In this paper, we first give an example that the bilateral weighted shift operator in c_0space is hypercyclic operator and first solve the existence problem of hypercyclic operator in c_0or c_0(Z space . And then we investigate the property of weighted shift operator in c_0 space and an important property of the hypercyclic vector of weighted shift operator in c_0 space and c_0 space. At last we give the concept of weak hypercyclic operator and weak hypercyclic vector , and give the equivalence between the weak hypercyclicity and the hypercyclicity in l~1 space.

本文首先给出了c_0空间上的一个双边左加权移位算子是超循环算子的一个例子，首次解决了c_0 或c_0(Z 空间中超循环算子的存在性问题；接下来分别研究了c_0和c_0空间上的加权移位算子的性质以及c_0和c_0空间上的加权移位算子的超循环向量的一个重要性质，最后提出了弱超循环算子和弱超循环向量的概念，并且给出了I~1空间中弱超循环性与超循环性的等价性。

VC prepared by an image processing procedures : it can achieve image edge detection and contour extraction, Edge Detection Operator : Robert operator, bobel operator, prewitt operator, kirsch operator, gauss - laplace operator. Hough line detection, contour extraction, seed testing and contour tracking.

用VC编写的一个图像处理的程序：它可以实现图像的边缘检测和轮廓提取，边缘检测算子包括：Robert算子、bobel算子、prewitt算子、kirsch算子、gauss－laplace算子。hough直线检测、轮廓提取、种子检测和轮廓跟踪。

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。

First we prove that all points on the imaginary axis except for zero belong to the resolvent set of the operator corresponding to the model, second prove that 0 is an eigenvalue of the operator and its adjoint operator with geometric multiplicity and algebraic multiplicity one,last by using theabove results we obtain that the time-dependent solution of the model str.

首先证明在虚轴上除了0以外其他所有点都属于该算子的豫解集，其次证明0是对应于该系统的主算子及其共轭算子的几何与代数重数为1的特征值，由此推出该系统的时间依赖解当时刻趋向于无穷时强收敛于系统的稳态解。

Though comparing Canny operator and center B spline dyadic wavelet, the following conclusion is proven in this dissertation: a Center B spline function has tight support and Canny operator hasn't. b Center B spline function asymptotic convergence to Gaussian function and the derivative of Center B spline function asymptotic convergence to Canny operator. c The derivative of fourth order center spline B function is more suitable as a optimal edge detector than Canny operator. d Center B spline function can balance the smoothing and approximation of original data, and the fourth center B spline function is the only optimal solution of two order smoothing problem. e The error between the valve of time-frequency uncertainty of the fourth center B spline function and the lower bound of time-frequency uncertainty does not exceed 0.143% of the lower bound. f The derivative of center spline B function can construct a stability dyadic wavelet and can give a fast algorithm for multiscale edge detection, but Canny operator can do neither.

作者给出了Canny算子与中心B样条二进小波严格的比较证明，得出如下结论：a中心B样条函数具有紧支集，Canny算子不具有紧支集。b中心B样条函数的极限收敛于高斯函数，中心B样条函数的导数收敛于Canny算子。c四阶中心B样条函数的导数比Canny算子更接近最佳边缘检测滤波器。d中心B样条函数比高斯函数更能兼顾对原函数平滑和逼近的折中要求，并且四阶中心B样条函数是二阶逼近问题的唯一最优解。e四阶中心B样条函数的时频测不准关系值与时频测不准关系下界的逼近误差不超过0.143％。f中心B样条函数的导数可以构成稳定的二进小波，存在快速的多尺度算法；而Canny算子不构成稳定的二进小波，无法给出快速的多尺度算法。

The generalized ordered weighted averaging operator is ob tamed by combining the ordered weighted averaging operator and the generalized mean operator. Based on the GOWA operator, the generalized uncertain ordered weighted averaging operator is proposed.

该算子将有序加权平均算子和广义平均算子相结合而成的广义有序加权平均算子推广到不确定的环境中，提出了一个广义不确定有序加权平均算于。

The instrument software has the function of demonstration of basic knowledge of Digital Image Processing, i.e., it performs the functions of real-time collection and images saving, color change (brightness, binarization, RGB separation etc.), geometrical transform, edge detection (Robert arithmetic operator, Sobel arithmetic operator, Prewitt arithmetic operator, LOG arithmetic operator, Canny arithmetic operator etc.), gray-scale image enhancement (histogram equalization, averaging filtering, median filtering), and binary mathematical morphology management (erosion, dilation, opening, closing, objects marking, Euler number calculation).

该测试仪的软件部分包含数字图像处理课程所涉及的一些基础知识的演示，具体包括图像的实时采集与保存、颜色变换(灰度化、二值化、R、G、B颜色分量的分离等)、几何变换、边缘检测(Robert、Sobel、Prewitt、LOG、Canny)、灰度图像增强(直方图均衡化、均值滤波、中值滤波等)、二值图像操作(腐蚀、膨胀、开启、闭合、对象标注、欧拉数计算)等功能。

In chapter one,the backgrounds and current situation of operator theory in Banach space are introduced and the preliminaries of Banach space are given.In chapter two,we study the existence and uniqueness of fixed point for decreasing strict-set-contraction operator in product space.Under the weak continuous condition,we obtain the existence and uniqueness of fixed point for decreasing operator and we give an application of these results; In chapter three,we get several positive fixed point theorems of decreasing operator and the existence and uniqueness theorems of positive fixed point for operator C=A+B,C=D-A in real Banach space where the order is decided by a normal cone; In chapter four,we obtained some existence and uniqueness theorems of fixed point for some mixed monotone operators in semi-ordered Banach space.

在第一章中，主要介绍了半序Banach空间非线性算子的研究历史背景、现状以及半序Banach空间中的预备知识；在第二章中，我们利用半序方法研究了Banach乘积空间中严格集压缩减算子不动点存在唯一性问题，在弱连续的条件下，得到了不动点的存在唯一性和迭代收敛性，同时，给出了它们的一些应用；在第三章中，我们建立了拟弱连续减算子的正不动点定理，并证明了算子C=A+B，C=D-A的正不动点存在唯一性定理；在第四章中，我们得到了半序Banach空间中混合单调算子的不动点存在性及唯一性定理。

Yet, Edith says, there was always money in the bank.

但是Edith说，她的银行户口里面总是有钱。

We have created a series of files that resolve this problem--one for each day of the 40 days of purpose.

我们制作一系列的档案去解决这问题---一个为标竿40天中的每一天。