Related papers: Fractional calculus, completely monotonic function…
Assuming the separable augmented density, it is always possible to construct a distribution function of a spherical population with any given density and anisotropy. We consider under what conditions the distribution constructed as such is…
If the augmented density of a spherical anisotropic system is assumed to be multiplicatively separable to functions of the potential and the radius, the radial function, which can be completely specified by the behavior of the anisotropy…
This paper presents a set of new conditions on the augmented density of a spherical anisotropic system that is necessary for the underlying two-integral phase-space distribution function to be non-negative. In particular, it is shown that…
General criteria to check the positivity of the distribution function (phase-space consistency) of stellar systems of assigned density and anisotropy profile are useful starting points in Jeans-based modeling. Here we substantially extend…
Following the seminal result of An & Evans, known as the central density slope-anisotropy theorem, successive investigations unexpectedly revealed that the density slope-anisotropy inequality holds not only at the center, but at all radii…
A connection between fractional calculus and statistical distribution theory has been established by the authors recently. Some extensions of the results to matrix-variate functions were also considered. In the present article, more results…
The fundamental measure density functional theory for hard spheres is generalized to binary mixtures of arbitrary positive and moderate negative non-additivity between unlike components. In bulk the theory predicts fluid-fluid phase…
A method is presented for finding anisotropic distribution functions for stellar systems with known, spherically symmetric, densities, which depends only on the two classical integrals of the energy and the magnitude of the angular…
Fractional calculus is an effective tool in incorporating the effects of non-locality and memory into physical models. In this regard, successful applications exist rang- ing from signal processing to anomalous diffusion and quantum…
The exact universal functional of integer charge leads to an extension to fractional charge asymptotically when it is applied to a system made of asymptotically separated densities. The extended functional is asymptotically local and is…
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
We introduce notions of absolutely continuous functionals and representations on the non-commutative disk algebra $A_n$. Absolutely continuous functionals are used to help identify the type L part of the free semigroup algebra associated to…
It is shown that calculus can apply on a fractal structure with the condition that the infinitesimal limit of change of the variable is larger than the lower cut-off of the fractal structure, and an assumption called local decomposability.…
In classical density (or density-functional) estimation, it is standard to assume that the underlying distribution has a density with respect to the Lebesgue measure. However, when the data distribution is a mixture of continuous and…
Density perturbations in cosmology, i.e. spherically symmetric adiabatic perturbations of a Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime, are locally exactly equivalent to a different FLRW solution, as long as their wavelength is…
Recently, some intriguing results have lead to speculations whether the central density slope -- velocity dispersion anisotropy inequality (An & Evans) actually holds at all radii for spherical dynamical systems. We extend these studies by…
The standard method to generate dynamical models with a finite extent is to apply a truncation in binding energy to the distribution function. This approach has the disadvantages that one cannot choose the density to start with, that the…
In this paper, we prove the strict monotonicity in the parameter $\rho$ of the Mittag-Leffler functions $E_\rho(-t^\rho)$ and $t^{\rho -1}E_{\rho,\rho}(-t^\rho)$. Then, these results are applied to solve the inverse problem of determining…
In this work, we construct a fractional matter sector for general relativity. In particular, we propose a suitable fractional anisotropy function relating both the tangential and radial pressure of a spherically symmetric fluid based on the…
This paper presents two families of phase-space distribution functions (DFs) that generate scale-free spheroidal mass densities in scale-free spherical potentials. The `case I' DFs are anisotropic generalizations of the flattened f(E,L_z)…