查询词典 spherical bessel function

The mutual connection that analyses Bessel beam of light and Bessel-Gauss beam of light theoretically reachs distinction, beam of light of Bessel of numeric imitate ideal and Bessel-Gauss beam of light are in the radial light intensity of aleatoric plane distributings, and the influence that smooth waist radius and syntonic antrum antrum grow pair of output Bessel-Gauss beam of light.

梗概： 理论分析Bessel光束和Bessel-Gauss光束的相互联系及区别，数值模拟理想Bessel光束和Bessel-Gauss光束在任意平面的径向光强分布，以及光腰半径和谐振腔腔长对输出Bessel-Gauss光束的影响。

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。

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。

The lens axicon is based on the use of the spherical aberration of the mirror surfaces,which is inexpensive and easy to manufacture into a element with large apertures as compared with diffractive axicons,refractive cone axicons,and earlier lens axicons with aspheric surfaces;the opaque disk can offer the Bessel beams with long non-diffracting distances,and the diameter of the central peak is adjusted by choosing the focal length of the collimating lens;the tunable fluidic conical lens is a new device for generating Bessel beams,which can obtain the Bessel beams with different parameters by varying the refractive indexes of the solution which is filled in the device.

双透镜轴棱锥法主要基于透镜球面像差的运用，与衍射轴棱锥、折射轴棱锥和早期的非球面轴棱锥相比，具有加工简单、便宜，易于制作大尺寸的特点；不透明障碍物法得到的贝塞尔光束具有很长的无衍射距离，其直径可通过选择不同焦距的准直透镜来得到调节；可调流体轴棱锥是一种产生贝塞尔光束的新型器件，它可以很容易地通过改变注入器件的液体的折射率来得到不同参量的贝塞尔光束。

In chapter 3, the author considers that approximate value of Bessel fuctions and transcendental equations are main ob stacle to realize computer simulation for isolated well principle. The character of Bessel functions are studied, new approximate values of Bessel function are set forth.

第3章中，针对"割离井法"微机实现的难点——贝塞尔函数的渐近计算和超越方程的合理求解，研究了贝塞尔函数的性质，提出了新的贝塞尔函数的渐近式，并采用ZEROIN法完成了超越方程的求解，最后编制出新的"割离井法"计算程序。

In chapter 3, the author considers that approximate value of Bessel fuctions and transcendental equations are main ob stacle to realize computer simulation for isolated well principle. The character of Bessel functions are studied, new approximate values of Bessel function are set forth.

第3章中，针对&割离井法&微机实现的难点——贝塞尔函数的渐近计算和超越方程的合理求解，研究了贝塞尔函数的性质，提出了新的贝塞尔函数的渐近式，并采用ZEROIN法完成了超越方程的求解，最后编制出新的&割离井法&计算程序。

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。

A backer of an Afghan law that critics say legalizes marital rape has rejected the international outcry as foreign meddling.

饱受批评的一项法律的拥护者说合法化的婚内暴力不会受国际舆论的干涉。

Years ago, a ancient Egyptian fleet went to the Land of punt for seeking a kind of flavor named "myrrh", and aromatic plants which has dense exotic style for the queen Hatshepsut.

3500年前的一个古埃及的舰队到&彭特之地&寻找一种叫没药的香料。