On resonant thermonuclear reaction rate integrals- closed-form evaluation and approximation considerations

The central problem in the theory of stellar nucleosynthesis (and in reaction theory of controlled thermonuclear fusion as well) is the determination of thermonuclear reaction rates. Continuing our preceding paper on closed-form evaluation of nonresonant reaction rate integral (HAUBOLD and JOHN 1978) now we consider a general thermonuclear reaction rate integral involving the full BREIT -WIGNER resonance cross section. Discerning between two cases – energy-independent partial widths and energy-dependent partial width – we evaluate the arising parameter-dependent integrals in closed form by means of MEIJER 's G-functions of one and two variables. At next, by using the BUNJAKOVSKIJ -SCHWARZ inequality we derive global upper bounds for thermonuclear reaction rate integrals with arbitrary admissible values of input parameters. Finally, in case of great values of the characteristic parameter COULOMB barrier energy divided by thermal energy we give an asymptotic representation of the general resonant reaction rate integral.     

A Certain Class of Laplace Transforms with Applications to Reaction and Reaction-Diffusion Equations

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 and the concept of Laplacianness in statistics, α-Laplace and Mittag-Leffler stochastic processes, the concepts of infinite divisibility and geometric infinite divisibility problems in probability theory and certain fractional integrals and fractional derivatives. A number of applications are pointed out with special reference to solutions of fractional reaction and reaction-diffusion equations and their generalizations.     

On fractional kinetic equations

The subject of this paper is to derive the solution of generalized fractional kinetic equations. The results are obtained in a compact form containing the Mittag-Leffler function, which naturally occurs whenever one is dealing with fractional integral equations. The results derived in this paper provide an extension of a result given by Haubold and Mathai in a recent paper (Haubold and Mathai, 2000). This revised version was published online in July 2006 with corrections to the Cover Date.     

Downscaling daily precipitation time series using a combined circulation- and regression-based approach

The aim of this paper is to introduce a new conditional statistical model for generating daily precipitation time series. The generated daily precipitation can thus be used for climate change impact studies, e.g., crop production, rainfall–runoff, and other water-related processes. It is a stochastic model that links local rainfall events to a continuous atmospheric predictor, moisture flux, in addition to classified atmospheric circulation patterns. The coupled moisture flux is proved to be capable of capturing continuous property of climate system and providing extra information to determine rainfall probability and rainfall amount. The application was made to simultaneously downscale daily precipitation at multiple sites within the Rhine River basin. The results show that the model can well reproduce statistical properties of daily precipitation time series. Especially for extreme rainfall events, the model is thought to better reflect rainfall variability compared to the pure CP-based downscaling approach.     

Solution of Generalized Fractional Reaction-Diffusion Equations

This paper deals with the investigation of a closed form solution of a generalized fractional reaction-diffusion equation. The solution of the proposed problem is developed in a compact form in terms of the H-function by the application of direct and inverse Laplace and Fourier transforms. Fractional order moments and the asymptotic expansion of the solution are also obtained.     

Computational aspects of the gravitational instability problem for a multicomponent cosmological medium

The paper presents results for deriving closed-form analytic solutions of the non-relativistic linear perturbation equations, which govern the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model. Mathematical methods to derive computable forms of the perturbations are outlined.Presented at the 2nd UN/ESA Workshop, held in Bogotá, Colombia, 9-13 November, 1992.