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In a paper [8] the authors classify entropy into three categories, as a thermodynamics quantity, as a measure of information production, and as a means of statistical inference. An entropy measure introduced by Mathai falls into the second and third categories. It is shown that this entropy measure is the same whether the variables involved are real or complex scalar, vector, or matrix variables. If the entropy measure is optimized under some moment-like conditions then one can obtain various types of densities which are applicable in different areas. Unlike Tsallis' entropy [9], it does not need an intermediary escort distribution to yield the desired results. Calculus of variation can be directly applied to obtain the desired results under Mathai's entropy. Tsallis' entropy, which is the basis of the area of non-extensive statistical mechanics, is a modified version of the ?-generalized entropy of Havrda-Charvat considered in [7]. Various types of distributions that can be obtained through optimization of Mathai's entropy, are illustrated in this paper., Comment: 7 pages

Thermal Doppler broadening of spectral profiles for particle populations in the absence or presence of potential fields are described by kappa distributions. The kappa distribution provides a replacement for the Maxwell-Boltzmann distribution which can be considered as a generalization for describing systems characterized by local correlations among their particles as found in space and astrophysical plasmas. This paper presents all special cases of kappa distributions as members of a general pathway family of densities introduced by Mathai., Comment: 10 pages

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, namely the Maxwell-Boltzmann distribution, the pathway distribution, and the Mittag-Leffer distribution. We emphasize the utilization of Meijer G-function and Fox H-function which are special functions of mathematical physics., Comment: 8 pages

The paper utilizes data from the SuperKamiokande solar neutrino detection experiment and analyses them by diffusion entropy analysis and standard deviation analysis. The result indicates that solar neutrinos are subject to Levy flights (anomalous diffusion, superdiffusion). Subsequently, the paper derives the probability density function, represented as Fox H-function, and the governing fractional diffusion equation (fractional Fokker-Planck Equation) for solar neutrino Levy flights., Comment: 13 pages. arXiv admin note: substantial text overlap with arXiv:1209.1520

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 probability integral, Kraetzel transform, and pathway transform are explored. It is shown that the common thread in these connections is the H-function representations. The pathway parameter is shown to be connected to the fractional order in fractional integrals and fractional differential equations., Comment: 14 pages

This paper reviews briefly the history of the Michelson experiment, invented and performed for the first time in the Astrophysical Observatory Potsdam in 1881. The paper draws attention to the International Michelson Colloquium, held from April 27 to April 30, 1981 in Potsdam (Germany). This paper is an attempt to reconsider a scientific event organized 40 years ago, as the follow-up to Einsteinss Centenary in 1979, for Michelsons experiment done 140 years ago., Comment: 9 pages, 8 figures

In 1910 Einstein published a crucial aspect of his understanding of Boltzmann entropy. He essentially argued that the likelihood function of any system composed by two probabilistically independent subsystems {\it ought} to be factorizable into the likelihood functions of each of the subsystems. Consistently he was satisfied by the fact that Boltzmann (additive) entropy fulfills this epistemologically fundamental requirement. We show here that entropies (e.g., the $q$-entropy on which nonextensive statistical mechanics is based) which generalize the BG one through violation of its well known additivity can {\it also} fulfill the same requirement. This fact sheds light on the very foundations of the connection between the micro- and macro-scopic worlds., Comment: 5 pages including 2 figures

In 1990 the United Nations in cooperation with the European Space Agency initiated the organization of a series of annual Workshops on Basic Space Science for the benefit of astronomers and space scientists in Asia and the Pacific, Latin America and the Caribbean, Africa, Western Asia, and Europe. This article summarizes accomplishments of these Workshops and their follow-up projects., Comment: 13 pages, LaTeX, 1 Postscript figure attached, 1 Postscript table attached, to appear in Annals of the New York Academy of Sciences

The physical principles and the mathematical structure involved in deriving an analytical representation of the internal structure of the sun are discussed. For a two-parameter family of a non-linear matter density distribution, the run of mass, pressure, temperature, and luminosity throughout the sun are expressed in terms of Gauss' hypergeometric function. The system of differential equations governing hydrostatic equilibrium and energy conservation for the sun generates another field of application of special functions.

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 probability integrals for nuclear reactions in the cases of nonresonant, modified nonresonant, screened nonresonant and resonant cases are given. These are expressed in terms of H-functions, G-functions and in computable series forms. Computational aspects are also discussed.

This paper examines a number of analytic models which can describe the gravitationally stabilized fusion reactor of the Sun. An analytical multiparameter model is shown to reproduce various structure parameters such as density, mass, pressure and temperature throughout the solar core, which have been obtained by solving numerically the system of solar structure differential equations. For simplicity, numerical and analytical results are discussed in detail for a two-parameter model.

Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized solar fusion reactor. We assume a matter density distribution varying non-linearly through the central region of the Sun. The analytic solutions of the differential equations of mass conservation, hydrostatic equilibrium, and energy conservation, together with the equation of state of the perfect gas and a nuclear energy generation rate $\epsilon=\epsilon_0 \rho^nT^m$, are given in terms of Gauss' hypergeometric function. This model for the structure of the Sun gives the run of density, mass, pressure, temperature, and nuclear energy generation through the central region of the Sun. Because of the assumption of a matter density distribution, the conditions of hydrostatic equilibrium and energy conservation are separated from the mode of energy transport in the Sun.

Physical principles and mathematical structure involved in deriving an analytical representation of the internal structure of the Sun is discussed. For a two-parameter family of a non-linear matter density distribution, the run of mass, pressure, temperature, and luminosity throughout the Sun is presented in terms of Gauss' hypergeometric function. The system of differential equations governing hydrostatic equilibrium and energy conservation for the spherical Sun is proved to be a laboratory for the application of special functions., Comment: 18 pages LaTeX

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 majority of reactions among nuclei leading to a nuclear transformation are inhibited by the necessity for the charged participants to tunnel through their mutual Coulomb barrier. As theoretical knowledge and experimental verification of nuclear cross sections increases it becomes possible to refine analytic representations for nuclear reaction rates. Over the years various approaches have been made to derive closed-form representations of thermonuclear reaction rates (Critchfield 1972, Haubold and John 1978, Haubold, Mathai and Anderson 1987). They show that the reaction rate contains the astrophysical cross section factor and its derivatives which has to be determined experimentally, and an integral part of the thermonuclear reaction rate independent from experimental results which can be treated by closed-form representation techniques in terms of generalized hypergeometric functions. In this paper mathematical/statistical techniques for deriving closed-form representations of thermonuclear functions will be summarized and numerical results for them will be given. The separation of thermonuclear functions from thermonuclear reaction rates is our preferred result. The purpose of the paper is also to compare numerical results for approximate and closed-form representations of thermonuclear functions. This paper completes the work of Haubold, Mathai, and Anderson (1987).

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 such as the energy generation in a simple stellar model and nuclear reaction rates in non-resonant and resonant as well as screened non-resonant

The paper presents results for deriving closed-form analytic solutions of the evolution of inhomogeneities in a homogeneous spatially flat multicomponent cosmological model. Mathematical methods to derive computable forms of the perturbations are outlined.