查询词典 laplace beltrami operator

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

The Laplace Transform; The Region of Convergence for Laplace Transforms; The Inverse Laplace Transform; Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot; Properties of the Laplace Transform; Analysis and Characterization of LTI Systems Using the Laplace Transform; System Function Algebra and Block Diagram Representations; The Unilateral Laplace Transform..

教学内容：拉普拉斯变换；拉普拉斯变换收敛域；拉普拉斯反变换；由零极点图对傅立叶变换进行几何求值；拉普拉斯变换性质；常用拉普拉斯变换对；用拉普拉斯变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边拉普拉斯变换。

Mastery: The Laplace Transform, The Region of Convergence for Laplace Transforms, The Inverse Laplace Transform, Properties of the Laplace Transform, Some Laplace Transform Pairs; Analysis and Characterization of LTI Systems Using the Laplace Transform, System Function Algebra and Block Diagram

基本要求：掌握拉普拉斯变换定义，拉普拉斯变换收敛域，拉普拉斯反变换，拉普拉斯变换性质，用拉普拉斯变换分析和表征线性时不变系统，系统函数的代数属性与方框图表示；熟悉常用拉普拉斯变换对，单边拉普拉斯变换；了解由零极点图对傅立叶变换进行几何求值。

Mastery: The Laplace Transform, The Region of Convergence for Laplace Transforms, The Inverse Laplace Transform, Properties of the Laplace Transform, Some Laplace Transform Pairs; Analysis and Characterization of LTI Systems Using the Laplace Transform, System Function Algebra and Block Diagram Representations;Roth Criterion;Mason Equation of the Signal Flow Graphs.

基本要求：掌握拉普拉斯变换定义，拉普拉斯变换收敛域，拉普拉斯反变换，拉普拉斯变换性质，用拉普拉斯变换分析和表征线性时不变系统，系统函数的代数属性与方框图表示，罗斯判别，信号流图的梅森公式；熟悉常用拉普拉斯变换对，单边拉普拉斯变换；了解由零极点图对傅立叶变换进行几何求值。

The Laplace Transform; The Region of Convergence for Laplace Transforms; The Inverse Laplace Transform; Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot; Properties of the Laplace Transform; Analysis and Characterization of LTI Systems Using the Laplace Transform; System Function Algebra and Block Diagram Representations; The Unilateral Laplace Transform.;Roth rule ;Signal Flow Graphs.

教学内容：拉普拉斯变换；拉普拉斯变换收敛域；拉普拉斯反变换；由零极点图对傅立叶变换进行几何求值；拉普拉斯变换性质；常用拉普拉斯变换对；用拉普拉斯变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边拉普拉斯变换；罗斯准则；信号流图。

Op1 + op2 The addition operator will add two numbers. op1 - op2 The subtraction operator will subtract two numbers. op1 * op2 The multiplication operator will multiply two numbers. op1 / op2 The division operator will divide two numbers. op1 % op2 The modulus operator will return the remainder of the division of two integer operands. op1 xx op2 The exponentiation operator will raise op1 to the power of op2.++op1 The pre-increpment operator will increase the value of op1 first, then assign it. op1++ The post-increment operator will increase the value of op1 after it is assigned.--op1 The pre-decrement operator will decrease the value of op1 before it is assigned. op1-- The post-decrement operator will decrease the value of op1 after it is assigned.

op1 + op2 对两个数值做加法操作 op1 - op2 对两个数值做减法操作 op1 * op2 对两个数值做乘法操作 op1 / op2 对两个数值做除法操作 op1 % op2 求两个整型数值的余数 op1 xx op2 求幂操作：求 op1 的 op2 次幂++op1 前加操作： op1 的值先增加，然后将值赋给自身 op1++后加操作： op1 的值先赋给自身，再增加值--op1 前减操作： op1 的值先减少，然后将值赋给自身 op1—后减操作： op1 的值先赋给自身，再减少值

The Laplace Transform; The Region of Convergence for Laplace Transforms; The Inverse Laplace Transform; Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot; Properties of the Laplace Transform; Analysis and Characterization of LTI Systems Using the Laplace Transform; System Function

教学内容：拉普拉斯变换；拉普拉斯变换收敛域；拉普拉斯反变换；由零极点图对傅立叶变换进行几何求值；拉普拉斯变换性质；常用拉普拉斯变换对；用拉普拉斯变换分析和表征线性时不变系统；系统函数的代数属性与方框图表示；单边拉普拉斯变换。

Then we sharpen the images with Laplace operator. In the course of edge detection, we detect images' edge by using Roberts operator, Sobel operator, Robinson operator, LoG operator and Canny operator, and compare the results of images' edge. The result shows, Canny edge detection operator precede other operators obviously.

在对图像进行边缘检测时，对经过预处理过的人脸图像分别用Roberts边缘算子、Sobel边缘算子、Robinson边缘算、LoG边缘算子、Canny边缘算子进行边缘检测，然后，对边缘检测算子进行了研究改进，并对检测结果进行了讨论比较，结果表明，Canny边缘算子的检测结果明显优于其它几个算子。

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。

Since Leptokurtosis, skewness and fat-tail are always used to depict market risk, this paper introduces the improved Laplace distribution to risk management of stock portfolio. Empirical results show, improved Laplace distribution and asymmetric Laplace distribution are similar for estimating Leptokurtosis, while improved Laplace distribution is better for estimating skewness.In order to analyze the correlation between return distribution and volatility, the thesis uses ARCH-M Models to simulate the return series of China's Stock Market and developed markets ao as to discover the relation between investment return and time-varying risk.

对尖峰、厚尾、偏态的刻画有助于正确估计市场风险，本文将改进型Laplace分布引入到股票组合的风险管理中，实证结果发现，改进型Laplace分布和非对称Laplace分布对尖峰、厚尾的刻画效果接近；而非对称Laplace分布对负偏性考察不足，改进型Laplace分布的拟合结果能够准确地反映股指收益的负偏态，这也正是改进型Laplace分布相对于传统的非对称Laplace分布的优势所在。

The network space is the typical form of abstract space when it comes to the digital stage.

网络空间是抽象空间数字化阶段的典型形式。

The Notarial System,as the system of judicial certification in our country,is both the constructor and the defender of social credit system,It has its special value and function in the social honesty.

公证制度作为我国司法证明制度，既是社会信用体系的建设者，同时也是社会信用的捍卫者，在诚信中有其特殊的价值和功能。