相关论文: Fox's H-Functions: A Gentle Introduction Through A…
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…
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…
The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended to cover Tsallis statistics (Tsallis, 1988) and more general cases of distribution functions. An analytical study of respective thermonuclear functions is being…
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…
Stars are gravitationally stabilized fusion reactors changing their chemical composition while transforming light atomic nuclei into heavy ones. The atomic nuclei are supposed to be in thermal equilibrium with the ambient plasma. The…
As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. In this paper mathematical/statistical techniques for deriving…
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…
In the theory of thermonuclear reaction rates, analytical evaluation of thermonuclear functions for non-resonant reactions, including cases with cut-off and depletion of the tail of the Maxwell-Boltzmann distribution function were…
This article gives an brief outline of the applications of generalized special functions such as generalized hypergeometric functions, G-functions and H-functions into the general area of nuclear energy generation and reaction rate theory…
The method for the evaluation of the non-resonant thermonuclear function in the Maxwell-Boltzmann case with depleted tail is discussed. Closed forms of the analytical results are obtained in computational format, and written in terms of the…
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…
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 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…
We are interested in electrons kinetics in a stellar atmosphere to validate or invalidate the usually accepted hypothesis of thermalisation of electrons. For this purpose, we calculate the velocity distribution function of electrons by…
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…
This paper deals with a general class of integrals, the particular cases of which are connected to outstanding problems in astronomy and physics. Reaction rate probability integrals in the theory of nuclear reaction rates, Kr\"atzel…
The distribution function of the relative velocity in a two-body reaction of nonrelativistic uncorrelated particles is derived for general cases of given distribution functions of single particle velocities. The distribution function is…
In this paper, the expression of the relativistic Maxwell-J\"uttner velocity distribution was deduced in a detailed and didactic way. This distribution was compared with the well-known Maxwell-Boltzmann distribution, which does not take…
In view of the role of reaction equations in physical problems, the authors derive the explicit solution of a fractional reaction equation of general character, that unifies and extends earlier results. Further, an alternative shorter…
Two representations of the extended gamma functions $\Gamma^{2,0}_{0,2}[(b,x)]$ are proved. These representations are exploited to find a transformation relation between two Fox's $H$-functions. These results are used to solve Fox's…