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91.
F.G. Mitri 《Ultrasonics》2010,50(6):541-543
The aim of this short communication is to report that Gegenbauer’s (partial-wave) expansion, that may be used (under some specific conditions) to represent the incident field of an acoustical (or optical) high-order Bessel beam (HOBB) in spherical coordinates, anticipates earlier expressions for undistorted waves. The incident wave-field is written in terms of the spherical Bessel function of the first kind, the gamma function as well as the Gegenbauer or ultraspherical functions given in terms of the associated Legendre functions when the order m of the HOBB is an integer number. Expressions for high-order and zero-order Bessel beams as well as for plane progressive waves reported in prior works can be deduced from Gegenbauer’s partial-wave expansion by appropriate choice of the beams’ parameters. Hence the value of this note becomes historical. In addition, Gegenbauer’s expansion in spherical coordinates may be used to advantage to model the wave-field of a fractional HOBB at the origin (i.e. z = 0). 相似文献
92.
Djurdje Cvijovi? 《Applied mathematics and computation》2010,215(11):4040-740
In a recent paper Dattoli and Srivastava [3], by resorting to umbral calculus, conjectured several generating functions involving harmonic numbers. In this sequel to their work our aim is to rigorously demonstrate the truth of the Dattoli-Srivastava conjectures by making use of simple analytical arguments. In addition, one of these conjectures is stated and proved in more general form. 相似文献
93.
入射平面电磁波的球面波函数展开是求解不同圆球结构的平面波散射问题的重要工具,相关文献分别利用场的坐标分解和矢量势法得到了入射平面波的球面波函数的两种不同形式的展开式.利用偏微分方程边值问题解的存在唯一性定理,给出了这两种展开式的等价性的一个简洁的解析证明,并进行了数值验证. 相似文献
94.
Said Mesloub 《Mathematical Methods in the Applied Sciences》2010,33(1):57-70
In this paper, we study a nonlocal mixed problem for a nonlinear hyperbolic equation. Based on some a priori estimates and some density arguments, we prove the well posedness of the associated linear problem. The existence and uniqueness of the weak solution of the nonlinear problem are then established by applying an iterative process based on the obtained results for the linear problem. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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In this work we consider a system of partial differential operators D
1,D
2 on K=[0,+[×R, whose eigenfunctions are the functions (x,t), (x,t)K, =((R0)×N)(0×[0,+[), which are related to the Laguerre functions for ((R 0)×N)(0,0) and which are the Bessel functions for (0×[0,+[). We provide K and with a convolution structure. We prove a Lévy–Khintchine formula on K, which permits us to characterize dual convolution semigroups on . 相似文献
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This paper is concerned with representations of split orthogonal and quasi-split unitary groups over a nonarchimedean local field which are not generic, but which support a unique model of a different kind, the generalized Bessel model. The properties of the Bessel models under induction are studied, and an analogue of Rodier's theorem concerning the induction of Whittaker models is proved for Bessel models which are minimal in a suitable sense. The holomorphicity in the induction parameter of the Bessel functional is established. Local coefficients are defined for each irreducible supercuspidal representation which carries a Bessel functional and also for a certain component of each representation parabolically induced from such a supercuspidal. The local coefficients are related to the Plancherel measures, and their zeroes are shown to be among the poles of the standard intertwining operators. 相似文献