相关论文: The $\kappa$-cookbook: a novel generalizing approa…
Previously, the author offered a plasma-like description of quantum phenomena. This article offers a new criterion of approximation of probability density functions of quantum theories by sums of $\delta$-functions with integer coefficients…
In this chapter we will argue that studying such multi-scale multi-science systems gives rise to inherently hybrid models containing many different algorithms best serviced by different types of computing environments (ranging from…
This paper presents an extensive survey of regular distributions in natural and social sciences. The survey includes studies from a wide scope of academic disciplines, in order to create an inventory of the different mathematical functions…
We develop a self-consistent quasilinear theory for the relaxation of electromagnetic kinetic plasmas, and demonstrate that the mean distribution functions of both electrons and ions tend to relax to a universal $v^{-5}$ tail. Large-scale…
In this work, standard methods of the mixed thin-shell foramlism are refined using the framework of Colombeau's theory of generalized functions. To this end, systematic use is made of smooth generalized functions, in particular…
We consider a thermal particle which is diffusing in velocity-space and in a weakly confining potential characterized by the inverse hyperbolic sine function of the particle velocity $v$ and the control parameter $v_c$. The stationary state…
To estimate cosmological parameters from a given dataset, we need to construct a likelihood function, which sometimes has a complicated functional form. We introduce the copula, a mathematical tool to construct an arbitrary multivariate…
Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial…
We present new analytical distribution functions for anisotropic spherical galaxies. They have the density profiles of the gamma-models, which allow a wide range of central density slopes, and are widely used to fit elliptical galaxies and…
The pseudopotential method is used to derive electron hole structures in a suprathermal plasma having a regularized $\kappa$ probability distribution function background. The regularized character allows the exploration of small $\kappa$…
A new method is presented for assigning distributional curvature, in an invariant manner, to a space-time of low differentiability, using the techniques of Colombeau's `new generalised functions'. The method is applied to show that…
In this paper, we propose an optimization-based mechanism to explain power law distributions, where the function that the optimization process is seeking to optimize is derived mathematically, then the behavior and interpretation of this…
In this paper we derive the maximum entropy characteristics of a particular rank order distribution, namely the discrete generalized beta distribution, which has recently been observed to be extremely useful in modelling many several…
We establish sufficient conditions for the existence, and derive explicit formulas for the $\kappa$'th moments, $\kappa \geq 1$, of Markov modulated generalized Ornstein-Uhlenbeck processes as well as their stationary distributions. In…
We revisit effective scenarios for the origin of heavy tails in stationary velocity distributions. A first analysis combines localization with diffusive acceleration. That gets realized in space plasmas to find the so-called…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
The Copula is widely used to describe the relationship between the marginal distribution and joint distribution of random variables. The estimation of high-dimensional Copula is difficult, and most existing solutions rely either on…
Field emission data are often represented on a Fowler--Nordheim plot but a new empirical equation has been recently proposed to better analyze experiments. Such an equation is based on approximations of the Murphy and Good model and…
In tabular Markov decision processes (MDPs) with perfect state observability, each trajectory provides active samples from the transition distributions conditioned on state-action pairs. Consequently, accurate model estimation depends on…
We describe a statistical method to avoid biased estimation of the content of different particle species. We consider the case when the particle identification information strongly depends on some kinematical variables, whose distributions…