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81.
N. S. Kazak E. G. Katranji I. A. Utkin A. A. Ryzhevich A. N. Khilo 《Journal of Applied Spectroscopy》2004,71(5):697-701
The phenomenon of self-diffraction of Bessel light beams (BLB) in a nonlinear liquid medium has been studied experimentally and theoretically for the first time. Diffraction maxima which do not correspond to integer orders for an induced periodic structure have been registered. It has been shown that the appearance of these maxima is due to the initial BLB modulation, which can be caused by the departure of the axicon refracting surface from the ideal conical surface, as well as by the imperfection of the form of the Gaussian beam incident on the axicon. 相似文献
82.
Shy-Der Lin 《Journal of Mathematical Analysis and Applications》2004,294(2):399-411
The main object of this paper is to investigate several general families of hypergeometric polynomials and their associated single-, double-, and triple-integral representations. Some known or new consequences of the general results presented here, involving such classical orthogonal polynomials as the Jacobi, Laguerre, Hermite, and Bessel polynomials, and various other relatively less familiar hypergeometric polynomials, are also considered. Each of the integral representations, which are derived in this paper, may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials. 相似文献
83.
84.
B.J. Stoyanov R.A. Farrell J.F. Bird 《Journal of Computational and Applied Mathematics》1994,50(1-3):533-543
Asymptotic expansions of certain finite and infinite integrals involving products of two Bessel functions of the first kind are obtained by using the generalized hypergeometric and Meijer functions. The Bessel functions involved are of arbitrary (generally different) orders, but of the same argument containing a parameter which tends to infinity. These types of integrals arise in various contexts, including wave scattering and crystallography, and are of general mathematical interest being related to the Riemann—Liouville and Hankel integrals. The results complete the asymptotic expansions derived previously by two different methods — a straightforward approach and the Mellin-transform technique. These asymptotic expansions supply practical algorithms for computing the integrals. The leading terms explicitly provide valuable analytical insight into the high-frequency behavior of the solutions to the wave-scattering problems. 相似文献
85.
N.M. Temme 《Numerical Algorithms》1997,15(2):207-225
Airy-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing the asymptotic series. One method is based on expanding the coefficients of the asymptotic series in Maclaurin series. In the second method we consider auxiliary functions that can be computed more efficiently than the coefficients in the first method, and we do not need the tabulation of many coefficients. The methods are quite general, but the paper concentrates on Bessel functions, in particular on the differential equation of the Bessel functions, which has a turning point character when order and argument of the Bessel functions are equal. 相似文献
86.
Random Motions at Finite Speed in Higher Dimensions 总被引:1,自引:0,他引:1
Alexander D. Kolesnik 《Journal of statistical physics》2008,131(6):1039-1065
We present a general method of studying the transport process
, t≥0, in the Euclidean space ℝ
m
, m≥2, based on the analysis of the integral transforms of its distributions. We show that the joint characteristic functions
of
are connected with each other by a convolution-type recurrent relation. This enables us to prove that the characteristic function
(Fourier transform) of
in any dimension m≥2 satisfies a convolution-type Volterra integral equation of second kind. We give its solution and obtain the characteristic
function of
in terms of the multiple convolutions of the kernel of the equation with itself. An explicit form of the Laplace transform
of the characteristic function in any dimension is given. The complete solution of the problem of finding the initial conditions
for the governing partial differential equations, is given.
We also show that, under the standard Kac condition on the speed of the motion and on the intensity of the switching Poisson
process, the transition density of the isotropic transport process converges to the transition density of the m-dimensional homogeneous Brownian motion with zero drift and diffusion coefficient depending on the dimension m.
We give the conditional characteristic functions of the isotropic transport process in terms of the inverse Laplace transform
of the powers of the Gauss hypergeometric function. Some important models of the isotropic transport processes in lower dimensions
are considered and some known results are derived as the particular cases of our general model by means of the method developed. 相似文献
87.
Paweł Keller 《Numerical Algorithms》2007,46(3):219-251
We propose a general method for computing indefinite integrals of the form
where g is a smooth function, and k is a function that contains a singular factor or is rapidly oscillatory. The only assumption on k is that it satisfies a linear differential equation with polynomial coefficients. The approximate value of the integral is
given in terms of Chebyshev coefficients of functions that form a solution of a certain system of differential equations.
As an illustration, we present effective algorithms for computing indefinite integrals of the functions g(t)|t–d|
α
e
i
ω
t
, g(t)log|t–d| e
i
ω
t
, g(t) t
α
J
ν
(ct).
相似文献
88.
89.
Complexity of Gaussian-radial-basis-function networks, with varying widths, is investigated. Upper bounds on rates of decrease of approximation errors with increasing number of hidden units are derived. Bounds are in terms of norms measuring smoothness (Bessel and Sobolev norms) multiplied by explicitly given functions a(r,d) of the number of variables d and degree of smoothness r. Estimates are proven using suitable integral representations in the form of networks with continua of hidden units computing scaled Gaussians and translated Bessel potentials. Consequences on tractability of approximation by Gaussian-radial-basis function networks are discussed. 相似文献
90.
V. A. Abilov F. V. Abilova M. K. Kerimov 《Computational Mathematics and Mathematical Physics》2009,49(7):1103-1110
Two estimates useful in applications are proved for the Fourier-Bessel integral transform in L 2(?+) as applied to some classes of functions characterized by a generalized modulus of continuity. 相似文献