Related papers: "Killing Mie Softly": Analytic Integrals for Reson…
The comments of Guseinov on our recent paper (Czech. J. Phys., 52 (2002)1297) have been analyzed critically. It is shown that his comments are irrelevant and also unjust. In contrast to his comment, it is proved that the presented formulae…
Mathematical functions, which often appear in mathematical analysis, are referred to as special functions and have been studied over hundreds of years. Many books and dictionaries are available that describe their properties and serve as a…
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
One-dimensional quantum scattering from a local potential barrier is considered. Analytical properties of the scattering amplitudes have been investigated by means of the integral equations equivalent to the Schrodinger equations. The…
The Airy integral and Bessel functions are of significant in mathematical description of spectral distribution of different types of radiation produced by relativistic charged particles moving in synchrotron and in periodical macro- and…
We carry out the asymptotic analysis of repulsive ensembles of N particles which are discrete analogues of continuous 1d log-gases or beta-ensembles of random matrix theory. The ensembles that we study have several groups of particles which…
Dose calculation for radiotherapy with protons and heavier ions deals with a large volume of path integrals involving a scattering power of body tissue. This work provides a simple model for such demanding applications. There is an…
We establish a general semiparametric Bernstein-von Mises theorem for Bayesian nonparametric priors based on continuous observations in a periodic reversible multidimensional diffusion model. We consider a wide range of functionals…
We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin-Selberg integrals). This leads to: (i) a way to classify of such integrals, based on the classification…
In this present paper our aim is to deal with two integral transforms which involving the Gauss hypergeometric function as its kernels. We prove some compositions formulas for such a generalized fractional integrals with k Bessel function.…
This work studies scattering-induced elastic wave attenuation and phase velocity variation in 3D untextured cubic polycrystals with statistically equiaxed grains using the theoretical second-order approximation (SOA) and Born approximation…
Recent work of Bornemann has uncovered hitherto hidden integrable structures relating to the asymptotic expansion of quantities at the soft edge of Gaussian and Laguerre random matrix ensembles. These quantities are spacing distributions…
This paper concerns mathematical formulation of well-known MUltiple SIgnal Classification (MUSIC)-type imaging functional in the inverse scattering problem by an open sound-hard arc. Based on the physical factorization of so-called…
Many questions of fundamental interest in todays science can be formulated as inference problems: Some partial, or noisy, observations are performed over a set of variables and the goal is to recover, or infer, the values of the variables…
We suggest scattering experiments which implement the concept of ``protective measurements'' allowing the measurement of the complete wave function even when only one quantum system (rather than an ensemble) is available. Such scattering…
We use the tridiagonal representation approach to solve the radial Schr\"odinger equation for the continuum scattering states of the Kratzer potential. We do the same for a radial power-law potential with inverse-square and inverse-cube…
We give a necessary and sufficient condition for symmetric infinitely divisible distribution to have Gaussian component. The result can be applied to approximation the distribution of finite sums of random variables. Particularly, it shows…
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
The computation of integrals is a fundamental task in the analysis of functional data, which are typically considered as random elements in a space of squared integrable functions. Borrowing ideas from recent advances in the Monte Carlo…
A method for analytic continuation of imaginary-time correlation functions (here obtained in quantum Monte Carlo simulations) to real-frequency spectral functions is proposed. Stochastically sampling a spectrum parametrized by a large…