Related papers: Fractional calculus, completely monotonic function…
Anisotropic patchy particles have become an archetypical statistical model system for associating fluids. Here we formulate an approach to the Kern-Frenkel model via classical density functional theory to describe the positionally and…
We introduce fractional flat space, described by a continuous geometry with constant non-integer Hausdorff and spectral dimensions. This is the analogue of Euclidean space, but with anomalous scaling and diffusion properties. The basic tool…
The L-fractional derivative is defined as a certain normalization of the well-known Caputo derivative, so alternative properties hold: smoothness and finite slope at the origin for the solution, velocity units for the vector field, and a…
We study non-linear additive functionals of stationary Gaussian fields over anisotropically growing domains in $\mathbb{R}^d$, including spatiotemporal settings, and establish Gaussian and non-Gaussian limit theorems under non-separable…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
From the data analysis we defined distribution function against the population on the level of various structure units, namely regions, federal districts and the country on the whole. We have studied peculiarities of the distribution…
The subject of fractional calculus has witnessed rapid development over past few decades. In particular the area of fractional differential equations has received considerable attention. Several theoretical results have been obtained and…
We derive necessary and sufficient conditions for a continuous bounded function $f: R\to C$ to be a characteristic function of a probability measure. The Cauchy transform $K_f$ of $f$ is used as analytic continuation of $f$ to the upper and…
The recently proposed universal relations between the moments of the polydispersity distributions of a phase-separated weakly polydisperse system are analyzed in detail using the numerical results obtained by solving a simple density…
We study the problem of constructing a probability density in 2N-dimensional phase space which reproduces a given collection of $n$ joint probability distributions as marginals. Only distributions authorized by quantum mechanics, i.e.…
Dynamical properties of spherically symmetric galaxy models where both the stellar and total mass density distributions are described by the Jaffe (1983) profile (with different scale-lenghts and masses), are presented. The orbital…
In the paper we discuss two questions about smooth expanding dynamical systems on the circle. (i) We characterize the sequences of asymptotic length ratios which occur for systems with H\"older continuous derivative. The sequences of…
In this paper we define distance expanding random dynamical systems. We develop the appropriate thermodynamic formalism of such systems. We obtain in particular the existence and uniqueness of invariant Gibbs states, the appropriate…
This paper generalizes recent proposals of density forecasting models and it develops theory for this class of models. In density forecasting, the density of observations is estimated in regions where the density is not observed.…
Rosenfeld's fundamental measure theory for lattice models is given a rigorous formulation in terms of the theory of Mobius functions of partially ordered sets. The free-energy density functional is expressed as an expansion in a finite set…
The paper considers probability distribution, density, conditional distribution and density and conditional moments as well as their kernel estimators in spaces of generalized functions. This approach does not require restrictions on…
In the context of the study of the properties of the mutual mass distribution of the bright and dark matter in elliptical galaxies, present a family of two-component, spherical, self-consistent galaxy models, where one density distribution…
This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of transcendental…
It is argued that the evolution of complex phenomena ought to be described by fractional, differential, stochastic equations whose solutions have scaling properties and are therefore random, fractal functions. To support this argument we…
We examine the fractional derivative of composite functions and present a generalization of the product and chain rules for the Caputo fractional derivative. These results are especially important for physical and biological systems that…