相关论文: Special functions and pathways for problems in ast…
A.M. Mathai is Emeritus Professor of Mathematics and Statistics at McGill University, Canada, and Director of the Centre for Mathematical and Statistical Sciences, India. He has published over 300 research papers and more than 25 books on…
A brief description and results of A.M. Mathai's research programme on statistics and probability, initiated in the 1970s, and its relation to physics is given.
We presented background information about various entropies in the literature. The pathway idea of Mathai (2005) is shown to be inferable from the maximization of a certain generalized entropy measure and established connections to…
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 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…
These notes were originally prepared as additional material for the lessons I have given at the summer school Gamma-ray Astrophysics and Multifrequency: Data analysis and astroparticle problems, organized by the Department of Physics of the…
This paper summarizes a presentation for a panel discussion on "The Future of Astrostatistics" held at the Statistical Challenges in Modern Astronomy V conference at Pennsylvania State University in June 2011. I argue that the emerging…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
In this review, an overview of the recent history of stochastic differential equations (SDEs) in application to particle transport problems in space physics and astrophysics is given. The aim is to present a helpful working guide to the…
Previous and present "academic" research aiming at atomic scale understanding is mainly concerned with the study of individual molecular processes possibly underlying materials science applications. Appealing properties of an individual…
We give an abridged account of a continued string of studies in condensed matter physics and in complex systems that span five decades. We provide links to access abstracts and full texts of a selected list of publications. The studies were…
Since their introduction in the early sixties, the R\'enyi entropies have been used in many contexts, ranging from information theory to astrophysics, turbulence phenomena and others. In this note, we enlighten the main connections between…
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
Dozens of research centers, foundations, international organizations and scientific societies, including the Institute of Mathematical Statistics, have joined forces to celebrate 2013 as a special year for the Mathematics of Planet Earth.…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques…
Recent modern space missions deliver invaluable information about origin of our universe, physical processes in the vicinity of black holes and other exotic astrophysical objects, stellar dynamics of our galaxy, etc. On the other hand,…
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…
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…
Abridged: The golden age of astrophysics is upon us with both grand discoveries (extra-solar planets, dark matter, dark energy) and precision cosmology. Fundamental understanding of the working of stars and galaxies is within reach, thanks…