函数

This is my last OpenGL for a project to use the "three-dimensional vector space / point" and related functions, they can use a definition of space vector / points, for the vector translation, zooming and rotation, the use of correlation function can also achieve two vector by the fork, get a Vectors absolute length of a vector unit, received a 3:00 decision vector perpendicular to the plane, a space to be the distance between two points, two vector to be the plot points, to be the angle between two vectors, such as operating for the use of user-friendly, each function is detailed Notes, it is particularly important if the calculation vector plot points, fork also took note, we hope to have useful.

这是我过去进行一个OpenGL项目时使用到的"三维空间向量/点"类及相关函数，使用它们可以定义一个空间向量/点，实现向量的平移，缩放和旋转等，使用相关函数还可以实现两向量的叉乘，得到一个向量的绝对长度，将一个向量单位化，得到一个三点决定的平面的垂直向量，得到空间中两点的距离，得到两向量的点积，得到两向量的夹角等操作，为方便用户的使用，每个函数都有详细的注释，特别重要的向量计算如点积，叉乘还有相关说明，希望对大家有所用处。

By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polynomials with the complex argument for the constitutive parameter.

应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式。

By using the expansion of spherical wave functions for a cylindrical wave function and with the help of the theory of hypergeometric functions, the Sommerfeld type integral contained in the electromagnetic fields is expressed as a rapidly and absolutely convergent series of spherical wave functions; and the coefficients of the series are the Legender Polyno...

应用圆柱波函数的球面波展开式和超几何函数理论，场分量中的索末菲尔德型积分被表示成快速、绝对收敛的球面波函数系展开式；展开系数是以物性参数为复宗量的勒让德多项式。

Analytical expressions for electromagnetic fields of a vertical or horizontal electric dipole over the finitely conducting plane are derived subject to the boundary conditions; Sommerfeld type integral contained in Hertz potential is expressed as the sum of two parts: zeroth order Hankel function and an absolutely convergent series of spherical Hankel function.

在此边界条件下，推导出有限导电平面上垂直和水平电偶极子电磁场的解析表达式；赫芝位函数中的索末菲型积分被表达成零阶汉克尔函数与绝对收敛的球汉克尔函数级数之和的形式。

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。

Three intersection functions,such as adjacent node set,node-arc angle set and connected node set,were presented,and based on the shortest path method proposed by Dijkstra,a road guide sign model was built by using the intersection functions.

结合路网的拓扑结构，定义了用于确定指路标志的状态函数集，给出了3个描述路网拓扑特征的交叉口函数：邻近结点集、结点-弧段夹角集和连通结点集，基于Dijkstra最短路径的思想，运用交叉口函数建立了城镇指路标志的标识模型：以待标识城镇为中心，在城镇的影响区域内，通过向外搜索交叉口邻近结点集来确定指路标志的设置，并使每个结点上标识的路径都是最优的。

It is proved that the least squareestimators of linear estimable functions of regression coefficients areadmissible under matrix loss and minimax. The necessary and sufficientexistence conditions are derived for the uniformly minimum riskequivariant estimators of linear estimable functions ofregression coefficients under an affine group and a transitive group oftransformations respectively. It is also proved that there are no UMREestimators ofthe covariance matrix and variance under an affine groupof transformations and quadratic loss functions.

本文证明了回归系数的线性可估函数的最小二乘估计是极小极大的且在矩阵损失函数下是可容许的；还分别在仿射变换群和平移群下导出了存在回归系数的线性可估函数的一致最小风险同变估计的充要条件，并证明了在仿射变换和二次损失下不存在协方差阵和方差的 UMRE 估计。

These application examples indicate that the direct method derived in this paper simplifies the process of constructing the Airy function in specific plane problems.

这些例子说明，利用本文的观察法可以将某些平面问题应力函数构造的过程简单化。关键词双调和函数， Airy应力函数，弹性力学平面问题

A stress function involving several unknown co efficients was constructed in the solution process, and the stress and displacement expressions were obtained through traditional Airy stress function methodology. After the fixed end boundary condition was treated with two methods, the unknown coefficients in stress function were determined with stress and displacement boundary conditions, and the analytical solutions were achieved.

在求解过程中，构造了一个含待定系数的应力函数，通过Airy应力函数解法，给出了应力和位移的表达式，对固支端边界条件采用两种处理办法，利用应力和位移边界条件，确定应力函数中的待定系数，得到了应力和位移的解析解结果。

A methodology of noise-like key generation is presented. Chaotic process of tentmap function is used as a deterministic generation of noise-like key, image storage and retrieval are completed in a algebraic form. A mathematics model of noise-like chaotic coding memory is constructed, meanwhile the basic mechanism of circulant convolution and circulant correlation in image information storage and retrieval are demonstrated.

在详细阐明数字序列和字母序列的1-D映射函数设计方法的基础上，利用构造出的1-D映射的稳定周期环和不稳定极限环完成了存储和联想记忆功能，为了识别有关的输入信息，提出了映射函数直接控制的方法；在此基础上，提出了一种1-D映射型混沌神经网络模型，该网络本身不当作一个"黑箱"处理，网络的参数值由网络中实现的映射函数来确定，该网络模型具有联想记忆、容错性、模式识别和奇异滤波等一系列智能信息处理的基本功能。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。