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espanolResolvemos el problema de Cauchy para la ecuacion de las ondas en n dimensiones utilizando propiedades elementales de las funciones de Bessel. EnglishWe solve the Cauchy problem for the n-dimensional wave equation using elementary properties of the Bessel functions.

La carga topológica de una onda electromagnética CT, está relacionada con su distribucion espacial en el frente de onda. Ondas electromagnéticas con un factor acimutal exp(ilq) en su fase, tienen CT entera (l=m) o no entera (l=M). Estas ondas electromagnéticas con un valor definido de carga topológica pueden ser producidas en el régimen visible utilizando máscaras tenedor holográficas generadas por computador. En este artículo se estudia mediante simulaciones numéricas la red triangular formada en el régimen de intensidad de Fraunhofer de haces Bessel-Gauss con CT entera y no entera que han difractado sobre una rendija en forma triangular para determinar su signo y su magnitud. También se presentan los resultados experimentales de la intensidad en campo lejano obtenidos al difractar una onda luminosa Bessel-Gauss con CT entera y no entera a través de una rendija triangular equilátera. Argumentos cualitativos parciales han sido expuestos para explicar el fenómeno de difracción de estos haces con carga topológica. Aquí se presentan argumentos cualitativos y cuantitativos que permiten explicar todos los resultados de la difracción por una abertura triangular de haces con carga topológica obtenidos ya sea por simulación numérica o mediante su realización experimental. The topological charge TC of an electromagnetic wave is relate with their wavefront spatial distribution. Electromagnetic waves with factor azimuthal exp(ilq) in its phase, have TC integer (l=m) or non-integer (l=M). These electromagnetic waves with a well-defined of TC can be produced in the visible regime by computer generated holographic masks with fork shaped. In this paper, we study the formed triangle lattice distribution in the intensity Fraunhofer regime using numerical simulations of the Bessel-Gauss beams with integer and non-integer TC. The beam is diffracted by equilateral triangular aperture to measure both their sign and magnitude. In addition, we showed the experimental results of the intensity in far field regime product of diffraction of Bessel-Gauss beams with integer and non-integer TC by the equilateral triangular aperture. Partial and qualitative explanations have been proposed for the diffraction of electromagnetic beams with topological charge. This paper presents a complete analysis for qualitative and quantitative explanation of diffraction of a beam with topological charge by a triangular aperture. The results of such diffraction are obtained by numerical simulation or experimentally.

In this note, two aspects in relation to distribution involving general functions are considered. Firstly, the distribution of the sum and also the ratio of two independent radom variables with densities including ∅2 (a1,.... an; S; λ1 x, .. , λn x) and ψ2 (p ; b1 ..., bn ; t1 u .... tn y) is dealt with. The speciol case of n=2 is considered. Also, the distribution oI the sum of variables with ∅2 and ∅3 as their densities is obtained. The second aspect is estimation. In ∅2 , a parameter is estimated and the estimate is put in the closed form in terms of the general function ψ2. Also, the Bayes estimate in the distribution involving the Bessel function Ip(cx) is obtained and is expressed in terms of another general function FA.

In this paper, a general distribution derived from a generalized Bessel function, together with a generalized Beta distribution are discussed. An alternate method for obtaining the distribution of the sum of n independent random variables for the first distribution is obtained. Three of the parameters in this distribution are estimated by different methods under certain conditions. Distribution of maxima and mínima are also considered. For the generalized Beta distribution, esti mates are put in closed form in terms of the generalized hypergeometric function FA.