相关论文: A versatile integral in physics and astronomy
An overview is presented on statistical techniques for the analytic evaluation of integrals for non-resonant, non-resonant depleted, non-resonant cut-off, non-resonant sccreened, and resonant thermonuclear reaction rates. The techniques are…
Superstatistics and Tsallis statistics in statistical mechanics is given an interpretation in terms of Bayesian statistical analysis. Subsequently superstatistics is extended by replacing each component of the conditional and marginal…
The pathway model for the real scalar variable case is re-explored and its connections to fractional integrals, solutions of fractional differential equations, Tsallis statistics and superstatistics in statistical mechanics, reaction-rate…
Possible modification in the velocity distribution in the non-resonant reaction rates leads to an extended reaction rate probability integral. The closed form representation for these thermonuclear functions are used to obtain the stellar…
Needed for cosmological and stellar nucleosynthesis, we are studying the closed-form analytic evaluation of thermonuclear reaction rates. In this context, we undertake a comprehensive analysis of three distinct velocity distributions,…
In reaction rate theory, in input-output type models and in reaction-diffusion problems when the total derivatives are replaced by fractional derivatives the solutions are obtained in terms of Mittag-Leffler functions and their…
Nuclear reactions govern major aspects of the chemical evolution of galaxies and stars. Analytic study of the reaction rates and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction…
New integral formulas involving the Meijer $G$-function are derived using recent results concerning distributional characterisations and distributional transformations in probability theory.
We present an analytic proof of the integrals for astrophysical thermonuclear functions which are derived on the basis of Boltzmann-Gibbs statistical mechanics. Among the four different cases of astrophysical thermonuclear functions, those…
Nuclear reactions govern major aspects of the chemical evolution od galaxies and stars. Analytic study of the reaction rates and reaction probability integrals is attempted here. Exact expressions for the reaction rates and reaction…
The major problem in the cosmological nucleosynthesis is the evaluation of the reaction rate. The present scenario is that the standard thermonuclear function in the Maxwell-Boltzmann form is evaluated by using various techniques. The…
A class of Laplace transforms is examined to show that particular cases of this class are associated with production-destruction and reaction-diffusion problems in physics, study of differences of independently distributed random variables…
The reaction rate probability integral is extended from Maxwell-Boltzmann approach to a more general approach by using the pathway model introduced by Mathai [Mathai A.M.:2005, A pathway to matrix-variate gamma and normal densities, Linear…
Integral representations of hypergeometric functions proved to be a very useful tool for studying their properties. The purpose of this paper is twofold. First, we extend the known representations to arbitrary values of the parameters and…
The averages of ratios of characteristic polynomials det(lambda - X) of N x N random matrices X, are investigated in the large N limit for the GUE, GOE and GSE ensemble. The density of states and the two-point correlation function are…
In general, while obtaining the probability density function of sums and products of shifted random variables, ordinary analytical methods such as Fourier and Mellin transforms tend to provide integrals which cannot be expressed in terms of…
In this paper we study the integral of type \[_{\delta,a}\Gamma_{\rho,b}(x) =\Gamma(\delta,a;\rho,b)(x)=\int_{0}^{\infty}t^{x-1}e^{-\frac{t^{\delta}}{a}-\frac{t^{-\rho}}{b}}dt.\] Different authors called this integral by different names…
The current status of optical potentials employed in the prediction of thermonuclear reaction rates for astrophysics in the Hauser-Feshbach formalism is discussed. Special emphasis is put on $\alpha$+nucleus potentials. A novel approach for…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
We present a list of formulae useful for Weyl-Heisenberg integral quantizations, with arbitrary weight, of functions or distributions on the plane. Most of these formulae are known, others are original. The list encompasses particular cases…