卷积定理

We give several sufficient conditions of NA and NSD properties of random variables, compare the closeness of distribution functions of order statistics between NA and independent rv's, investigate properties of NSD defined by supermodular functions, study the dependence structure of stationary Markov process and order statistics and their spacings from two samples, establish stochastic comparisons of order statistics of heterogeneous rv's in the hazard rate and the reversed hazard rate orders, and give the first analytic proof of the closure property of the up shifted likelihood ratio order under convolution.

给出判定一组随机变量NA性质的几个充分条件，并给出NA和独立随机变量的次序统计量之间"贴近性"的比较，系统地研究基于特殊函数类所定义的NSD负相依概念，给出一些判别NSD性质的结构定理和一些有用概率不等式。系统研究平稳马氏过程的相依结构。研究两样本次序统计量及其问题隔的相依结构。在失效率、反向失效率序和似然序意义下给出非齐次随机变量次序统计量的比较。给出上漂移似然序卷积封闭性的第一个解析证明。

This paper discusses the Noether theorem of complete singular integral equation which containsboth the convolution kernel and the Cauchy kernel, and comes up with the Noether theoremwhich is similar to the Fredholm integral equation, the convolution equation and the singularintegral equation.

本文讨论了既含卷积核又含Cauchy核的完全奇异积分方程的Noether定理，得到了与Fredholm积分方程、卷积型积分方程、奇异积分方程相类似的Noether定理。

Stability and convergence of the model are proven by means of the weak convergence theorem of generalized function and the convolved integration theory.

由广义函数弱收敛定理和卷积理论，证明所提出的非局部连续模型具备收敛性和稳定性。

Aimed to the differential equation in form of convolution and the functional presented by M. E. Gurtin, the matrix operator which includes the differential equation and the boundary condition is proved self-adjoint, furthermore a general variational principles in form of convolution and the preparation theorem are given and proved.

针对M.E.Gurtin提出的含卷积运算的抛物型偏微分方程及其对应的泛函，运用泛函势算子理论，从理论上证明了含卷积运算的抛物型偏微分方程及其边界条件所对应的矩阵算子有势，进而给出并证明了具有普适意义的含卷积运算的变分定理及预备定理。

This paper describes various methods of analog modulation based on Convolution Theorem and Hilbert Transform unitedly to simplify the theoretical analysis in the" communication principle" course.

本文基于信号处理概念中的卷积定理和希尔伯特变换统一地描述各种模拟调制方式(括DSB，SSB，AM，FM)原理，旨在简化"通信基础"课程中关于模拟调制理论的分析。

Firstly, a balance equation is erected, And then,on the basis of the predecessor formula and with the Convolution Theorem and Fourier inverse transforms,a semi-analytical solution of the velocity response in time-domain under semi-sine exciting force is given.

建立成层土中桩纵向振动平衡方程，利用卷积定理和傅立叶逆变换求得半正弦脉冲激振作用下桩顶速度响应的半解析解。

The hand back image is captured by the device made by ourselves. The articular skin texture is segmented and located by utilizing Canny operator. According to convolution theorem, the fast match algorithm of two articular skin textures is given.

利用自主设计的采集装置获得手背图像，由Canny算子分割并定位手指背关节皮纹，根据卷积定理，对要测试的两背关节皮纹进行快速配准，以相关分类器作为判据，检验两者是否为同一模式。

A human model using polynomial convolution surface is presented which is modeled by articulated skeletons convolved with some kernel function. The convolution surface and curve correspondence theorem under orthogonal projection is presented. The human contour is approximated with a convolution curve and 3D human pose can be estimated using a nonlinear optimization algorithm.

首先建立了一种新颖的多项式密度卷积曲面人体模型，该模型由连接体线骨架与某种卷积核卷积而成，整个曲面是一张连续曲面，调节多项式和半径参数可以让人体任意变形；给出了正交投影下卷积曲面和曲线对应的概念和相关定理，为二维的图像轮廓和三维人体模型之间建立对应关系；根据正交投影下卷积曲面与曲线对应定理，用卷积曲线去逼近人体的图像轮廓曲线，从而估计和恢复出三维人体运动姿态。

In chapter 3, we introduce a new family of functions with negative coefficients T,...

第五章根据α螺旋形函数的定义及算子D~λ定义一族新的解析函数类S_α，导出族中函数的积分表达式；研究了S_α中函数的某种积分运算及卷积定理。

By using a soil modeling of three axes symmetry and considering three dimensions wave effect ,the longitudinal vibration characterisitic is analyzed on condition that a vertical force being harmonious and stimulating force is loaded upon the whole newel stake in the damping soil of homogeneous and detained material.

从三维轴对称土模型出发，考虑桩周土体的三维波动效应，对均质滞回材料阻尼土中完整端承桩在垂直协和激振力作用下的纵向振动特性进行分析，求解得到桩顶频域响应解析解、复刚度和速度导纳，利用卷积定理和傅里叶逆变换，求得半正弦脉冲激振力作用下桩顶速度导纳时域响应半解析解。

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。