广义坐标

By solving the SturmLiouville eigen-equation in the barycentric coordinate, the generalized sine and cosine functions in the triangular domain are constructed. Properties of these functions are systematically investigated by visualization and theoretical derivation.

本文通过求解重心坐标下的Sturm-Liouville特征方程，构造出了三角区域的广义正弦函数和广义余弦函数，并通过可视化与理论推导相结合的方法系统的研究了这两组函数的性质。

By solving the Sturm-Liouville eigen-equation in the barycentric coordinate, the generalized sine and cosine functions in the triangular domain are constructed. Properties of these functions are systematically investigated by visualization and theoretical derivation.

本文通过求解重心坐标下的Sturm-Liouville特征方程，构造出了三角区域的广义正弦函数和广义余弦函数，并通过可视化与理论推导相结合的方法系统的研究了这两组函数的性质。

Area coordinates and general Duffycoordinates are employed to transform the singular integrals of the Time-Domain Electric Field Integral Equation into non-singular integrals, which can be accurately and efficiently evaluated by dividing the transformed domain of integration into sub-domains.

摘要该文首先利用参数坐标和广义Duffy坐标变换将时域电场积分方程的奇异性积分转换成非奇异性积分，然后根据时间基函数的特点将该积分转换成可以快速精确计算的分区域积分。

Through the Radon transformation of the normally ordered Wigner operator we introduce two mutually conjugate intermediate coordinate- momentum representations. Based on them we construct the appropriate quantum phase space theory which includes the new Wigner operator adapting to this space and construct the appropriate generalized Fredholm operator equation and then find its solution. We then deriving the Hermite polynomials operator identities by applying the Fredholm equation. We also reveal the connection between the generalized Wigner operator and the 2-dimension normal distribution in statistics, which is useful to study the quantum tomogram. As the application of the entanglement Husimi operator theory we calculate the Wigner function and the Husimi function of the one- and two-mode combination squeezed state , study their characters through drawing the three-dimensional graphics.

由正规序Wigner算符的拉登变换引入了两个互为共轭的中介坐标-动量表象，在此基础上我们建立了相应的量子相空间理论，其中包括引入适合该空间的新的Wigner算符；并在该表象的基础上，建立了广义Fredholm算符方程，求出了它的解，并运用该方程导出有关厄米多项式的算符公式；揭示广义Wigner算符与统计学中的随机变量的二维正态分布形式上的相似，这对于研究量子态的tomogram(是英文Tomography的派生词)有用。

Based on the improved local piston theory , this paper presents the matrix expression of generalized aerodynamic forces expressed by the generalized coordinates.

基于改进的当地流活塞理论，推导了用模态坐标表示的弹性振动翼面的非定常广义气动力表达式。

Based on homogeneous approximation, a robust control law is designed, which drives generalized coordinates of the closed loop system to the origin exponentially and generalized velocities to the origin asymptotically.

基于齐次展开的思想，给出了一种鲁棒控制器设计方法，使得闭环系统的广义位置坐标指数镇定，广义速度渐近镇定。

Besides all six degrees of freedom of ship rigid body, other inportant generalized freedom such as aircushion pressure, freedom of seals and generalized coordinates of structural vibration are also included in the model in accordance with the nature of hybrid catamaran.

分析模型中除了船舶刚体运动的六个自由度外，还包括了其它重要的广义自由度-气垫压力、围裙运动的自由度以及结构各阶振形所对应的主坐标。

A generalized Gaussian Laplacian eigenmap algorithm based on geodesic distance is proposed,which incorporates geodesic distance and generalized Gaussian function into the original Laplacian eigenmap algorithm.GGLE algorithm can adjust the similarities between nodes of neighborhood graph,and can preserve the different degrees of local properties by using super-Gaussian function,Gaussian function or sub-Gaussian function.Moreover,GGLE can avoid the deficiency of Euclidean distance by using geodesic distance when neighborhoods of data points are enlarged for preserving more neighborhood relations.Experimental results show that the global low-dimensional coordinates obtained by GGLE have different clustering properties and different degrees of preserving local neighborhood structures when different generalized Gaussian functions are used to measuring the similarities between high-dimensional data points.(3) An ensemble-based discriminant algorithm based on GGLE is proposed.

该算法将测地线距离和广义高斯函数融合到传统的拉普拉斯特征映射算法中，可以调整近邻图结点间的相似度，通过选择超高斯、高斯或者次高斯函数来实现不同程度的近邻局部特性的保持；而且当需要保持更多的近邻关系使得数据点邻域增大时，采用测地线距离可以避免欧氏距离度量不合理的缺陷；实验结果表明在用不同的广义高斯函数度量高维数据点间的相似度时，局部近邻结构保持的程度是不同的，GGLE获得的全局低维坐标也呈现出不同的聚类特性。

In the dq0 coordinates a new definition of generalized instantaneous reactive current is proposed, and methods of resolution and measurement of generalized instantaneous reactive current components are also presented.

瞬时无功功率和瞬时无功电流定义是快速无功补偿和有源滤波的理论基础，本文提出了在dqO坐标下广义瞬时无功电流的新定义，并给出了广义瞬时无功电流各分量的分解方法和测量方法。

Included are the measurements of the tooth profile deviation of a shaving cutter based on the generalized polar coordinate method, and of the helix deviation of the shaving cutter using curvature method to automatically identify the boundary points; the measurements of the tooth profile of a modified hobbing cutter, and of deviation of contact line of the hobbing cutter by means of the generalized cylindrical coordinate method; the measurement of the deviation of tooth profile of a non-linear worm .

这些测量包括：①基于广义极坐标法的剃齿刀齿廓误差测量，以及采用&曲率法&自动识别界点的剃齿刀螺旋线误差的测量；②修形滚刀的齿廓测量，以及基于广义圆柱坐标法的滚刀啮合误差的测量；③非线性蜗杆的齿廓误差测量。

The concept of equivalent rotationally rigidity is offered and the formula of rotationally rigidity is obtained.

主要做了如下几个方面的工作：对伸臂位于顶部的单层框架—筒体模型进行分析，提出了等效转动约束的概念和转动约束刚度的表达式。

Male cats normally do not need aftercare with the exception of the night after the anesthetic.

男猫通常不需要善后除了晚上的麻醉。