Analytical Solutions of Electromagnetic Fields from Current Dipole Moment on Spherical Conductor in a Low-Frequency Approximation

We analytically derive the solutions for electromagnetic fields of electric current dipole moment, which is placed in the exterior of the spherical homogeneous conductor, and is pointed along the radial direction. The dipole moment is driven in the low frequency f = 1 kHz and high frequency f = 1 GHz regimes. The electrical properties of the conductor are appropriately chosen in each frequency. Electromagnetic fields are rigorously formulated at an arbitrary point in a spherical geometry, in which the magnetic vector potential is straightforwardly given by the Biot- Savart formula, and the scalar potential is expanded with the Legendre polynomials, taking into account the appropriate boundary conditions at the spherical surface of the conductor. The induced electric fields are numerically calculated along the several paths in the low and high frequeny excitation. The self-consistent solutions obtained in this work will be of much importance in a wide region of electromagnetic induction problems.

Train crossing modeling based on measurements and best numerical approximation in subway tunnels

Communication based train control systems （CBTC） must work even in the worst situation-- train crossing. This paper models the propagation characteristics in one of the most common and piv- otal scenarios--train crossing in subway tunnels which is rarely mentioned in previous publications. Firstly, measurements for train crossing scenario at 2.4 GHz in a real subway line in Madrid have been made. The field measurement is the most reliable way to reveal the propagation characteristics involving shadowing effect and fast fading. Moreover, to precisely describe the fast fading distribu- tion and eliminate the inevitable weak points of traditional fitting way, a best numerical approxima- tion method using Legendre orthogonal polynomials has been proposed. Comparisons show that this method works better and is of greater physical significance. Finally, a complete statistical model is given and all the coefficients can be applied by system designers for the link and system level simu- lations.

测试你的网球IQ

网球当然是一项让人全身心放松的运动,但如果你拥有了过人的网球IQ,让头脑与身体一起运动,不仅会令你处处占得先机,更会让你充分领略网球这项“智慧运动”的非凡乐趣。那么,你会用脑子打球吗?双打策略问题1: 很多初学者在同伴发球时会对自己处于网前的位置感到不自在。他们不敢确定哪个球自己该接,从而赢得这1分,相反只能躲在边线上而对这一分毫无贡献(见图1)。

The recurrence relations for the spheroidal functions

The integrable properties of the spheroidal equations are investigated. The shape-invariance property is proved to be retained for the spheroidal equations, for which the recurrence relations are obtained. This is the extension of the recurrence relation of the Legendre polynomials.

Evaluate More General Integrals Involving Universal Associated Legendre Polynomials via Taylor's Theorem

Abstract A few important integrals involving the product of two universal associated Legendre polynomials Pl＇m＇, （x）,Pk＇n＇（x）and x2a（1-x2）-p-1,xb（1± x）-p-1and xc（1-x2）-p-1（1 ± x）axe evaluated using the operator form of Taylor＇s theorem and an integral over a single universal associated Legendre polynomial. These integrals are more general since the quantum numbers are unequal, i.e.l＇ ≠ k＇ and m＇≠ n＇ .Their selection rules are a/so given. We also verify the correctness of those integral formulas numerically.