查询词典 spherical coordinates

First,The properties of the spherical Bezier Curvesproposed by Ken Shoemake(Spherical Bezier curve of first kind)are listed,such asEndpoint property,Symmetry property,Invariant property under solid motion,Spherical convex hull property,etc.,and the fact that this kind of spherical BezierCurve is devoid of subdivision property is pointed out;Based on subdivision,theconcept of a new kind of spherical Bezier curve(Spherical Bezier curve of secondkind)is proposed.This kind of spherical Bezier curve is continuous differentiable.Furthermore,generalization of Bezier curve on more comprehensive manifolds isdiscussed.2Spherical Chaikin algorithm and general spherical corner-cuttingalgorithm.

首先，文中列举了Ken Shoemake提出的点点生成的球面Bezier曲线(第一类球面Bezier曲线)的性质，如端点性质、对称性质、运动不变性质、球面凸包性质等，并指出这种球面Bezier曲线没有剖分性质；基于细分，文中给出了一种新的球面Bezier曲线(第二类球面Bezier曲线)的构造方法，指出这种曲线是连续可微的；作为这些理论的应用，文中改进了Ken Shoemake提出的球面插值曲线构造方法；进一步，文中探讨了Bezier曲线在更广泛的流形上的推广方法。2球面Chaikin算法和一般的球面割角算法。

The element equations are derived in a fixed current element coordinates which are coincident with the current moving element coordinates. The perturbed moving element coordinates and the variation of the element nodal rotation parameters corresponding to the perturbation of element nodal displacements and rotations referred to the current fixed element coordinates is consistently determined using the first order linearization of the way used to determine the current element coordinates and element nodal rotation parameters corresponding to the incremental element nodal displacements and rotations referred to the global coordinates.

本研究在梁元素当前的变形位置上，利用元素节点的座标及断面方位建立一个移动元素座标并决定元素节点的旋转参数，对应於元素节点旋转参数扰动量的广义节点力为一广义力矩，为推导传统力和力矩与该广义力矩的关系，本研究在一个与当前的移动元素座标重合的固定元素座标上，推导出元素节点在当前固定元素座标的扰动位移和扰动旋转与元素节点旋转参数的扰动量的关系。

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction.

本文围绕地球重力场的球面小波展开及其应用进行研究，在积分逼近与径向基函数概念的基础上引入了球面小波，利用球面小波对重力场展开进行了重新表示，在此基础上进行了球面小波正则化、卫星重力多尺度逼近、航空重力数据向下延拓、重力场球面小波逼近的最小范数性质、两类边值问题的球面小波实用解、球面选择多尺度去噪方法等方面的研究。

In this paper we separate the Hamiltonian into three parts: a spherical symmetry Hamiltonian; a z-component of the angular momentum operator, and a non-spherical symmetric potential as the perturbation operator, and provide a propose method by separating the potential containing squared magnetic field B^2 into two parts spherical symmetric and non-spherical symmetric ones so that the first-order energy correction due to the non-spherical symmetric potential is zero, and the second-order correction due to B^2 can be obtained by a simple variational method.

采用变分法和微扰法相结合的方法，把高强度磁场中氢原子的哈密顿H分为三部分：球对称哈密顿；z分量角动量算符相应部分和非球对称势微扰，并用一种特别规定的分解法将哈密顿H中含磁场平方项的势能分解为球对称与非球对称两部分，且使非球对称部分引起的一级修正能量值为零，并采用一种简便的变分法直接求出B^2对能级的二级修正值。

Based on the Lorentz-Mie theory, the single scattering characteristics of multi-dispersed spherical and multi-layered spherical particles are studied. The extinction coefficients, scattering coefficients, single albedos, single scattering phase functions and asymmetry factors of different clouds are presented. Numerical results for single scattering of spherical and non-spherical particles are obtained in the approximation of geometrical optics. The single scattering phase matrixes of non-spherical aerosols are calculated by using the T matrix method.

基于洛伦茨-米理论研究了服从一定尺寸分布的球形和多层球形粒子的单次散射特性，计算了各种不同类型云层的消光系数、散射系数、单次散射反照率、单次散射相函数以及不对称因子；利用几何光学方法计算了球形、非球形粒子的单次散射特性；利用T矩阵方法计算了非球形气溶胶的单次散射相矩阵。

Considering non-spherical particles, starting from particle size distribution, the concept of the number of equivalent spherical particles was put forward, and the theory formula to calculate mass concentration of non spherical panicles was derived. The validity of the formula for non-spherical particles was verified. On this basis, aerosol mass concen-trations algorithm baaed on the number of equivalent spherical particles was proposed.

考虑非球形颗粒，从颗粒群粒度分布概念出发，提出了统计意义上的等效球形颗粒数概念，给出了非球形颗粒物质量浓度的理论公式，并利用该理论公式阐明了OPC测量非球形颗粒物质量浓度计算公式的合理性，进而给出了基于等效球形颗粒数的悬浮颗粒物的质量浓度算法。

Second, based on the spherical vector wave function in uniaxial anisotropic medium, and the first, second, third and fourth spherical Bessel functions satisfy the same differential equation and recursive formula. The scattering fields in terms of spherical vector wave function from a uniaxial anisotropic spherical shell and an anisotropic uniaxial-coated conducting sphere by a plane wave are derived. The electromagnetic fields in uniaxial anisotropic medium and free space can be expressed in terms of spherical vector wave functions in uniaxial anisotropic media and isotropic medium.

二、在建立均匀各向异性单轴介质球矢量波函数理论的基础上，利用二阶线性偏微分方程的性质和第一、第二、第三和第四类球Bessel函数满足相同的微分方程和递推关系，我们分别研究了单轴介质球壳和单轴介质涂覆导体球对平面波的电磁散射特性，首先给出了各个区域的电磁场用球矢量波函数来表示的解析表达式，进而利用电磁场在边界上满足电磁场切向连续的边界条件和球谐函数的正交性，得出了各向异性单轴介质球结构中电磁场用球矢量波函数表示的系数所满足的矩阵方程。

Several types of processes and characteristics of super-fine SSP are analyzed and compared, they are high frequency plasma spherical method, direct current plasma spherical method, carbon pole electrical arc spherical method, gas burnt flame spherical method, high temperature fused quartz jet and chemo synthesis spherical method.

本文对国内的研究开发现状和国际球形石英粉的生产现状进行了分析研究；分析比较了高频等离子球化法、直流等离子体球化法、碳极电弧球化法、气体燃烧火焰球化法、高温熔融喷射以及化学合成球化法的工艺特点。

In this paper, the author reviewed the nonorthogonal coordinates one-way wave migration methods using tilted coordinates, curvilinear coordinates, and elliptic coordinates.

从倾斜坐标系、曲线坐标系和椭圆坐标系3个方面详细阐述了非正交系单程波偏移方法。

First, in the horizontal positioning accuracy aspect of total-station instrument, point out the importance of direction, distance to correct calculation and coordinates to convert, give coordinates calculated formula of single intersection point of non-symmetry type of horizontal curve, deduce to square–error's calculated formula of horizontal coordinates and point space by polar coordinates positioning methods, and analyze the main influence factor of square–error.

首先，在全站仪的平面定位精度方面，指出方向、距离归化计算和坐标转换的重要性，给出单交点非对称型平曲线坐标的计算公式，导出极坐标定位法平面坐标和点位中误差的计算公式，并分析中误差的主要影响因素。

"The operators will suffer a temporary decrease in the number of consumers and short message services as people may not like having to provide their ID cards for a phone number," Xu Junqi, vice-dean with the Policy-Making Institute of the Telecommunications Research Centre under MII, said yesterday.

信息产业部下属的通信决策研究院副主任徐俊其昨天说：&实行手机实名制后，人们可能不太情愿用身份证注册手机号，所以通信运营商会暂时面临用户减少和短信用户减少的问题。&

I don't believe in make-believe!

我不相信这些虚构的故事。