算出

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。

Its main tasks are to deal with binary images, gray scale processing, and the use of Sobel, Canny, Roberts, Laplacan operator of four digital image edge detection, the results show that: Roberts operator more precise positioning, but more sensitive to noise, Sobel operator son of gray-scale images with low noise gradient has a better detection of the effect of Laplacian can be detected in the vast majority of the edge did not appear at the same time the basic pseudo-edge, the edge can be precisely targeted, Canny operator is the traditional first-order differential operator in one of the best operator to detect the best edge detection, edges clear, make clear at a glance.

主要工作包括图像的二值处理，灰度处理，并运用Sobel、Canny、Roberts、Laplacan四个算子实现数字图像边缘检测，结果表明：Roberts 算子定位比较精确，但对噪声比较敏感，Sobel算子对灰度渐变低噪声的图像有较好的检测效果，拉普拉斯算子可以检测出绝大部分边缘，同时基本没有出现伪边缘，可以精确定位边缘，Canny算子是传统一阶微分算子中最好的算子之一，检测边缘检测的效果最好，边缘轮廓清晰，使人一目了然。问题补充：摘要英文翻译，不要在线翻译的，是在线等！急啊！！！！谢谢！！！！

In this paper,four aspects of the above problems were studied:Firstly, the problem of solving continuous linear operator equation inseparable Hilbert space is studied .

通过把第一类连续不适定算子方程转换为等价的无穷维方程组，然后利用投影法，给出了解存在唯一的充要条件；给出了连续线性不适定算子方程解析解，解决了不适定情况下解的表示问题，由此给出了算子方程的数值求解公式；进一步证明了，在解不唯一情况下，此表达式给出的解为算子方程的最小范数解，同时表示出了连续线性不适定算子方程的解集。

The introduction of displacement operator, derivation operator, integral operator and the operator, such as differential calculus operator and the definition of the form of computing, will be applied to similar derivation formula gives Newton a Kete Si formula and Bernstein theorem Law said the operator, and form is derived; linear differential equations is the operator solution.

有没有高手可以帮我翻译下这段话啊？？？引入位移算子、求导算子、积分算子和差分算子等微积分算子的定义及其形式运算，将其应用于近似求导公式；给出牛顿一柯特斯公式和伯恩斯坦定理的算子法表示，并进行形式推导；给出线性常微分方程的算子解法。

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。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

As an extension, we also obtain some sufficient and necessary conditions under which M_c is left Fredholm and left Weyl for some left invertible operator C, respectively.In chapter 2, the sufficient and necessary condition under which the difference of two idempotent operators on infinite dimensional Hilbert spaces is Fredholm (in-vertible) is discussed. In addition, some equivalent conditions under which products and differences of projections in a C~*-algebra are Moore-Penrose invert-ible are obtained.

来源：Ae5BCab论7a文网www.abclunwen.com对给定的算子对，给出存在左可逆算子C使得M_C左可逆的充要条件；存在可逆算子C使得M_C左可逆的充要条件；存在左可逆算子C使得M_C是左Fredholm算子的充要条件；存在可逆算子C使得M_C是左Fredholm算子的充要条件；存在左可逆算子C使得M_C是左Weyl算子的充要条件；存在可逆算子C使得M_C是左Weyl算子的充要条件。

We also give all positive self-adjoint extensions ofsingular differential operators,and all positive self-adjoint operators generated by theproducts of differential expressions 〓,where l is an nth order differentialexpression.The result that each positive self-adjoint operator is not necessarily theform of operator product 〓.This answers an open problem proposed by theauthors recently.

我们也给出了奇型微分算子的所有正自伴扩张形式及乘积微分算式〓所诱导的所有正自伴算子形式，证明〓所诱出的正自伴算子不必须是由算子乘积〓为l所生成的算子）的形式，从而回答了作者新近提出的一个公开问题。

This chapter defines the conceptsof P linear operator,〓 linear operator and 〓 linear operator by extending theconcepts of P matrix,〓 matrix and 〓 matrix to the linear operator from thelinear space of symmetric matrices to itself.In this chapter,we also present a path-following method and a potential reduction method for solving general linear matrixcomplementary problems,and analyzes their computational complexities undersuitable assumptions.

本章将第二章中给出的P矩阵、〓矩阵及P矩阵的概念推广到由实对称矩阵构成的向量空间到其自身的线性算子L上，得到了P线性算子、〓线性算子及P线性算子的概念，给出了求解一般线性矩阵互补问题的路径跟踪法和势函数约减法，并在L为P线性算子的假设下分析了这些算法的计算复杂性。

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。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。