坐标函数

The potential functions of incident and scattered waves were expanded into Fourier-Bessel series, and the coefficients of scattering waves field were determined by imposing continuity conditions of stress and displacement at the soil-pile interfaces with the help of a set of cylindrical coordinate systems and in accordance with the Graff's addition theorem.

将倾斜入射波和散射坡的势函数展开成Fourier-Bessel函数的无穷级数的形式，利用一组圆柱坐标系统和Graff加法转换定理，通过施加桩土界面处的应力和位移连续的边界条件，求解出散射波势函数的待定系数，进而得到饱和土体中任意点的位移和应力。

At first, the examples are given to explain a new method in signal processing, in which functions are defined from the viewpoint of multi-scale analysis. Then the authors present "coordinate heft separate" method, discover self-similar structure of points set on plain area; based on this self-similar structure, construct orthogonal complete 2-value function system of high-dimension simplicity; enrich and extend the theory and application of Rademacher function and Walsh function.

首先，举例说明在多尺度分析观点下，信号处理中某些函数定义的新方法；进而提出"坐标分量分离方法"，并由此发现了平面区域上点集坐标数值的自相似结构；在揭示了如此自相似结构的基础上，构造了高维单纯形上的正交完备的二值函数系统；丰富与推广了Rademacher函数及Walsh函数的理论及应用。

For example, if the screen resolution is 640*480, the right-lower corner of the screen is x==639 and y==479. If you want to convert the screen coordinate to window coordinate, use ScreenToClient function.

例如，如果屏幕分辨率是640*480，屏幕右下角的坐标是 x=639 y=479，如果你想屏幕坐标为窗口坐标，用 ScreenToClient 函数。

When they built up the quantum Liouville equation inthe phase-space representaiton and discussed the mathematicaltransformation of the wave functions between the coordinate ormomentum and phase space,Torres-Vega and Frederick alwaysassumed the positive series expansion in coordinate of potentialsof systems.This is obviously incomplete because potentials ofreal systems contains in general negative powers of coordiante.

Torres-Vega和Frederick在建立相空间中的量子Liouville方程以及讨论和推导相空间波函数和坐标或动量空间中的波函数之间的的数学变换时，总是假定体系的相互作用势仅能展成坐标的正项级数，这显然是不全面的，因为实际体系的相互作用往往都含有坐标的负幂项。

Adopting the conformal mapping or rotation axis etc complex methods which areoften used to treat with the hole or cavity problem,a two-dimensional cavity ofeither simply or multiply connected region is projected into the interior of acircle or an annulus.As well as the global coordinate system is turned into thelocal coordinate system.

采用处理孔口问题最常用的映射函数和移轴等复变函数方法，把复杂的单连通区域和某些复连通区域型二维孔洞转化为简单的单位圆内区域或圆环区域，把整体坐标转为局域曲线坐标，而，最终把问题简化归结为一组无穷代数方程组的求解问题。

Crack propagation problems under the influence of the edges of the crack subjected to homogenous loads, the origin of the coordinates subjected to concentrated increasing loads, the central zone of the edges of the crack subjected to homogenous loads, the certain point of the edges of the crack subjected to moving unit step loads, the origin of the coordinates subjected to moving increasing loads Px m, the edges of the crack subjected to instantaneous impulse loads, the edges of the crack subjected to moving concentrated variable loads, the origin of the coordinates subjected to point loads, the edges of the crack subjected to a constant moving concentrated loads and the origin of the coordinates subjected to instantaneously moving impulse loads are studied respectively, and the analytical solutions of dislocation distribution function have been obtained.

同时对裂纹面受均布载荷、坐标原点受集中增加载荷、裂纹面中心区受均布载荷、裂纹面上某点受运动阶跃载荷、坐标原点受运动增加载荷Px m、坐标原点受瞬时冲击载荷、裂纹面受运动集中变载荷、坐标原点受集中载荷、裂纹面受常数运动集中载荷、坐标原点受瞬时运动冲击载荷作用下的裂纹扩展问题分别进行了研究，获得了位错分布函数的解析解。

For acquiring relations between the eigenfunctions of waveguides and tensor Green function, we first take the Fourier transform of Green function. In isotropic media the simplest image function can be expressed in dyadic form, and in anisotropic media in the form of ABA+-ikz0,where A is the coordinate matrix.

为了得到波导管的本征函数和格林张量函数的一些关系，我们首先对格林函数作富氏变换，它的象函数在各向同性介质波导中以并矢形式作为最简单的表达方法，而在充有各向异性介质波导中可以表为ABA~+e~的形式，这里A是坐标矩阵。

It is found thatthe fractal dimension D=1.25 corresponds to the lowest criticalcoupling constant αc=1.9,D=1.73 corresponds to the highest criticalratio of dielectric constants ηc=0.163,and when D≤1.145 bipolaronscan not exist at any rate.In chap,4,we will propose a novelapproach to the calculation of the exciton ground-state energy for thestrong-coupling case.Different from all previous methods,the wavefunction of the phonon part is assumed to take a form related to thewave function of the relative motion.We obtain the exciton energy bysolving the derived integrodifferential equation rather than select ahydrogen-like form to minimize the energy expectation.

结果发现，分数维的维数D＝1.25对应最小的临界的电-声耦合常数(αo＝1.9)，D＝1.73对应最大的临界的介电常数比(ηc＝0.163)，当分数维的维数D≤1.145时，双极化子无论如何也不可能存在，在第四章中，我们将提出一种新颖的变分方法来计算强耦合的激子-声子系统的基态能，不同于以前所有的方法，我们取声子的波函数与相对运动波函数有关的形式，而不是假定一个固定的关于相对运动坐标r的函数形式，得到相对运动波函数所满足的非线性的微分积分方程，我们数值求解这个微分积分方程得到系统基态能，而不是选择一个类氢原子的波函数变分使得能量的期待值最小。

Based on the propagation and transformation law of Wigner distribution function through a general axially nonsymmetrical optical system,investigated is the transform relationship of WDF between the input and the output planes of a pair of cylindrical lenses system which is used widely in optical signal processing .

基于维格纳分布函数在一般非轴对称系统的传播和变换规律，讨论了在光学信息处理系统中常用的双柱透镜系统输入和输出面WDF之间的变换关系，在直角坐标中给出了联系该系统相空间坐标的维格纳分布函数的坐标变换关系式和等价的矩阵表示。

Address the characteristics of non-uniform speed transmission, position function control and transmission ratio function control were presented to realize electronic gearbox. The differences between position function curve interpolation and general NC interpolation were analyzed. Considering the effect of uncontrollable continuous principal motion, interpolation slope and position function precompensation interpolation were presented. The relationship among interpolation, servo dynamic response and transmission precision was studied. The coordinate linkage relationship and electronic gearbox scheme in noncirclar gear hobbing were studied.

对电子齿轮箱实现非匀速比传动进行了研究，提出了位置函数控制与传动比函数控制两种非匀速比传动关系的实现方法；对位置函数控制方式，分析了位置函数曲线的插补与普通数控插补方法的区别，提出了插补斜率的概念与位置函数曲线的预补偿插补方法；对非匀速比电子齿轮箱传动精度进行研究，得出了插补精度、伺服系统动态性能指标与传动精度之间的关系；研究了非圆滚齿加工坐标联动的非匀速比传动关系，列出了多种可以满足要求的电子齿轮箱传动方案。4。

The absorption and distribution of chromium were studied in ryeusing nutrient culture technique and pot experiment.

采用不同浓度K2CrO4(0，0.4，0.8和1.2 mmol/L)的Hoagland营养液处理黑麦幼苗，测定铬在黑麦体内的亚细胞分布、铬化学形态及不同部位的积累。

By analyzing theory foundation of mathematical morphology in the digital image processing, researching morphology arithmetic of the binary Image, discussing two basic forms for the least structure element: dilation and erosion.

通过分析数学形态学在图像中的理论基础，研究二值图像的形态分析算法，探讨最小结构元素的两种基本形态：膨胀和腐蚀；分析了数学形态学复杂算法的基本原理，把数学形态学的部分并行处理理念引入到家实际应用中。