Related papers: Applications of generalized special functions in s…

Except for 1H, 2H, 3He, 4He, and 7Li, originating from the Big Bang, all heavier elements are made in stellar evolution and stellar explosions. Nuclear physics, and in many cases nuclear structure far from stability, enters in a crucial…

The quest to comprehend how nuclear processes influence astrophysical phenomena is driving experimental and theoretical research programs worldwide. One of the main goals in nuclear astrophysics is to understand how energy is generated in…

Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank…

In [Grenier-Nguyen], we introduced so called {\em generators} functions to precisely follow the regularity of analytic solutions of Navier Stokes equations. In this short note, we give a presentation of these generator functions and use…

The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…

General theory of elliptic hypergeometric series and integrals is outlined. Main attention is paid to the examples obeying properties of the "classical" special functions. In particular, an elliptic analogue of the Gauss hypergeometric…

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…

The manuscript reviews progress achieved in recent years in various aspects of nuclear astrophysics, including stellar nucleosynthesis, nuclear aspects of supernova collapse and explosion, neutrino-induced reactions and their possible role…

We introduce the notion of the generalized-analytical function of the poly-number variable, which is a non-trivial generalization of the notion of analytical function of the complex variable and, therefore, may turn out to be fundamental in…

Relativistic energy density functionals have become a standard framework for nuclear structure studies of ground-state properties and collective excitations over the entire nuclide chart. We review recent developments in modeling nuclear…

Surrogate modeling based on Gaussian processes (GPs) has received increasing attention in the analysis of complex problems in science and engineering. Despite extensive studies on GP modeling, the developments for functional inputs are…

I describe in very simple terms the theoretical tools needed to investigate ultra-peripheral nuclear reactions for nuclear astrophysics purposes. For a more detailed account, see arXiv:0908.4307.

Generalized trigonometric functions (GTFs) are simple generalization of the classical trigonometric functions. GTFs are deeply related to the $p$-Laplacian, which is known as a typical nonlinear differential operator. Compared to GTFs with…

This paper studies the equivalence between generalized holomorphic functions (GHF) and complex analytic functions in the framework of Robinson-Colombeau generalized numbers. In every non-Archimedean ring, the use of ordinary series is…

In this article we consider certain types of weighted generalized functions associated with nondegenerate quadratic forms. Such functions and their derivatives are used for constructing fundamental solutions of iterated ultra-hyperbolic…

Generalized superstatistics, i.e., a "statistics of superstatistics," is proposed. A generalized superstatistical system comprises a set of superstatistical subsystems and represents a generalized hyperensemble. There exists a random…

We review different models used for reactions involved in nuclear astrophysics. The reaction rate is defined for resonant as well as for non-resonant processes. For low-density nuclei, we describe the DWBA method, the potential model, the…

This work provides an in-depth mathematical description of the response functions that are used for spatial and spectral analysis of X-ray data. The use of such functions is well-known to anyone familiar with the analysis of X-ray data…

This review focuses on nuclear reactions in astrophysics and, more specifically, on reactions with light ions (nucleons and alpha particles) proceeding via the strong interaction. It is intended to present the basic definitions essential…

The basic concepts of a generalized relativistic density functional approach to the equation of state of dense matter are presented. The model is an extension of relativistic mean-field models with density-dependent couplings. It includes…