广义坐标

The main advantages of EGGLE include:the fixed neighborhood parameter k,only one time for constructing neighborhood graph and geodesic distance matrix,only needing to choose generalized Gaussian functions many times for constructing many Laplacian matrixes,obtaining multiple independent low-dimensional coordinate sets, independently training multiple classifiers,and combining classification results of these component classifiers to produce the final identification.

3提出了一种基于GGLE的集成判别算法，该算法的主要优点是：近邻参数k固定，邻接矩阵和测地线距离矩阵都只构造一次，只需要多次选择广义高斯型函数构造多个拉普拉斯矩阵，获取多个独立的低维空间坐标集合，独立学习分类器，集成分类识别。

Making use of the elementary matrix form of stereohomology, this work presents a theoretical framework with the approximately axiomatized form in computer graphics especially the three dimensional reconstruction based on homogeneous coordinates, and the analytical forms of projection and reconstruction with generalized meaning have been obtained, in which the Moore-Penrose pseudo-inverse of the camera matrix is employed.

通过给出的中心投影和平行投影等的解析解，提出计算机图形学、尤其是三维重建方面，基于齐次坐标表象的公理化的理论框架，并由此得到采用Moore-Penrose广义逆的、具有较为一般意义的投影与重建过程的解析表达式。

For the four laterals simply supported plate, the transverse deflection of plate is expanded over the modal shapes, the electroelastic model with self-sensing actuators plate is given, and the current is considered as output variable of measurement equation. Generalized modal coordinates being state variables, LQG and H∞control is proceeded using the state space equation.

将板的横向位移按模态展开，对配置压电自感作动器的薄板建立了模型，给出以广义模态坐标为状态变量的状态方程和以传感电流为输出的观测方程，在此基础上，对系统进行了LQG控制和H∞控制。

In chapter 4, by AREELS, the Generalized Oscillator Strength Density Spectra were measured in the energy region from 56 to 66eV, with the incident energy 2. 5 keV and energy resolution 80 meV, at scattering angles from 0°to 6°, corresponding to the momentum transfer K〓=0.03~2. 01 a. u. The Fano profile parameters f〓 and q for the optically allowed transition 〓(0, 1)〓P°and the optically forbidden transitions 〓(1, 0)〓S〓and 〓(1, 0)〓D〓 were obtained as a function of K〓. With the hyperspherical coordinate wavefunctions, the dynamical correlation are discussed qualitatively. So, a new experimental way to study dynamical electron correlation effect is opened.In chapter 5, the widely used R-matrix theory was introduced. Then, the GOSDS for the optically allowed excitation series (1s〓)〓S〓→〓(0, 1)〓P°(n=2-4) were calculated by this method, and the Fano profile parameters f〓 and q were obtained sequently. So the electron correlation effect can be described by these parameters quantitatively, and the theoretical results were compared with our AREELS experimental results.

在第四章中，实验上，同样使用角分辨的高能量分辨快电子能量损失谱仪，在2.5keV电子入射能量和80meV的能量分辨下，测量了0°到6°散射角下的He原子双电子激发态在56~66eV的广义振子强度密度谱，这种情况，0°~6°对应的动量转移范围K〓=0.03~2.01a.u。，得到了光学允许跃迁的双电子激发态〓（0，1）〓P〓和光学禁戒跃迁的双电子激发态〓（1，0）〓S〓、〓（1，0）〓D〓的Fano线形参数f〓，q等随动量转移变化的曲线；观测到了几个强度很弱、能级很窄的光学允许和禁戒跃迁双电子激发态，用前人准确的理论结果进行了标识；通过比较弱共振〓（1，0）〓S〓和〓（-1，0）〓S〓的强度随动量转移K〓的变化规律，结合超球坐标理论计算的波函数，定性地阐述了在电子碰撞散射过程中它们各自不同的动力学电子关联效应，发展了一套在实验上研究电子关联效应的新方法。

InSection 2,we give several sufficient conditions for the existence of one solution,multiplesolutions and infinitely many solutions of the Sturm-Liouville bvps via the generalizedpolar coordinates.Then in Section 3,the existence of positive solutions are proved undersuperlinearity,sublinearity and many other conditions by a fixed point theorem in cones.Our results have generalized those in many articles.A detailed discussion of periodic solu-tions of a kind of functional differential equations with high-order Laplacian-like operatorcan be found in Section 4 and this subject has not been studied before.

在第二节，我们定义了一种新的坐标变换-广义极坐标，并利用它讨论了p-Laplacian算子和Laplacian-型算子的Sturm-Liouville边值问题，分别得到了存在一个解、多个解、无穷多个解的多个充分条件；第三节研究p-Laplacian算子的Sturm-Liouville边值问题正解的存在性与多重性，采用的是锥上的不动点定理，全面推广了这一方面已有的结果；对目前研究较少的高维Laplacian-型算子及带有Laplacian-型算子的泛函微分方程的周期解问题，我们在第四节做了一些研究，这也是拓扑方法的一个应用。

By employing coordinate transformation, the overall generalized displacement vector relevant to the motion of pad and axle journal is converted into axle journal displacement vector in a local motion coordinate system, and the oil film force in a partial motion coordinate system is obtained by solving the dynamic characters of a fixed bush bearing.

通过坐标变换，将瓦块和轴颈运动相关的全局广义位移矢量转换为局部动坐标系下轴颈的位移矢量；利用求解固定瓦轴承动力特性的方法求得的局部动坐标系下的油膜力。

The spontaneous emission spectrum of a novel wiggler with its magnetostatic-fiele indepen dent of the axialcoordinate is calculated by means of generalized Bessel functions,and the re sult is analysed.

利用广义Bessel函数计算出了ShlomoPinhas提出的磁场与纵向坐标无关的摆动器的自发辐射谱，并对结果进行了分析。

In the third chapter,We study some geometric properties and spectral propertiesof the Jacobi operator on a solvable extension G of Heisenberg groups H.In the firstsection,we give the definition of G and some fundamental geometric properties on G.Inthe second section,we discuss the Integrability of certain subbundles and the geometricstructure of the induced foliations in case of integrability.In the third section,we studythe spectral properties of the Jacobi operator of G.

可解李群与类对称空间亦密切相关，Damcek-Ricci空间即是广义Heisenberg的一可解扩张李群，在第三章中，我们构造且研究了Heisenberg群的一可解扩张李群G的几何性质，第一节讨论了G的曲率，李指数映射，整体坐标等基本几何性质；第二章研究了TG的某些子丛的可积性及可积时诱导叶片的几何结构；第三节给出了G的Jacobi算子的特征值和相应的特征子空间。

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。