Related papers: A dispersion function for the regularized kappa di…
Based on the $\kappa$-deformed functions ($\kappa$-exponential and $\kappa$-logarithm) and associated multiplication operation ($\kappa$-product) introduced by Kaniadakis (Phys. Rev. E \textbf{66} (2002) 056125), we present another…
This tutorial provides an introduction to Palm distributions for spatial point processes. Initially, in the context of finite point processes , we give an explicit definition of Palm distributions in terms of their density functions. Then…
The aim of this paper is to find the necessary and sufficient conditions and inclusion relations for Pascal distribution series to be in the classes SP_{p}({\alpha},\b{eta}) and UCV_{p}({\alpha},\b{eta}) of uniformly spirallike functions.…
The concern of the present paper is the design of efficient numerical schemes for a specific Fokker-Planck equation describing the dynamics of energetic particles occurring in thermonuclear fusion plasmas (runaway electrons for example). In…
In this paper, we obtain a $(p,\nu)$-extension of the Whittaker function $M_{\kappa,\mu}(z)$ by using the extended confluent hypergeometric function of the first kind $\Phi_{p,\nu}(b;c;z)$ introduced in Parmar et al. [J. Classical Anal. 11…
We investigate the possibility of diagnosing the degree of departure from the Maxwellian distribution using single-ion spectra originating in astrophysical plasmas in collisional ionization equilibrium. New atomic data for excitation of Fe…
We have developed an analytic model to describe coupling of plasma and neutral fluids in the partially ionized heliosphere plasma medium. The sources employed in our analytic model are based on a $\kappa$-distribution as opposed to the…
In this paper, we present the $\alpha$-$\eta$-$\mathcal{F}$ and $\alpha$-$\kappa$-$\mathcal{F}$ composite fading distributions. The two distributions generalize the two well-known composite fading distributions, namely the…
Certain types of electro-magnetic waves propagating in a plasma can undergo a mode conversion process. In magnetic confinement fusion, this phenomenon is very useful to heat the plasma, since it permits to transfer the heat at or near the…
Numerical underflow and overflow are major hurdles for rolling-out the modeling and simulation infrastructure for temperatures below about 50 K. Extending the numeric precision is computationally intensive and thus best avoided. The root…
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…
The $\alpha$-$\eta$-$\kappa$-$\mu$ is one of the most generalized and flexible channel models having an excellent fit to experimental data from diverse propagation environments. The existing statistical results on the envelope of…
We present the main features of the mathematical theory generated by the \kappa-deformed exponential function exp_{\kappa}(x)=(\sqrt{1+\kappa^2 x^2}+\kappa x)^{1/\kappa}, with 0<\kappa<1, developed in the last twelve years, which turns out…
This article reviews two currently available analytic models of the dielectric function of a plasma consisting of quantum particles interacting via Coulomb forces, namely the Random Phase Approximation (RPA) and the Standard (Simple)…
The generalized Fermi-Dirac functions and their derivatives are important in evaluating the thermodynamic quantities of partially degenerate electrons in hot dense stellar plasmas. New recursion relations of the generalized Fermi-Dirac…
In this paper a new generalization of the hyper-Poisson distribution is proposed using the Mittag-Leffler function. The hyper-Poisson, displaced Poisson, Poisson and geometric distributions among others are seen as particular cases. This…
We present parton distribution functions which include a quantitative estimate of its uncertainties. The parton distribution functions are optimized with respect to deep inelastic proton data, expressing the uncertainties as a density…
Aims. Optically thin plasmas may deviate from thermal equilibrium and thus, electrons (and ions) are no longer described by the Maxwellian distribution. Instead they can be described by $\kappa$-distributions. The free-free spectrum and…
We investigate kinetic entropy-based measures of the non-Maxwellianity of distribution functions in plasmas, i.e., entropy-based measures of the departure of a local distribution function from an associated Maxwellian distribution function…
In Bayesian inference, an unknown measurement uncertainty is often quantified in terms of a Gamma distributed precision parameter, which is impractical when prior information on the standard deviation of the measurement uncertainty shall be…