Related papers: Density functions of periodic sequences
We analyze the structure of the Fundamental Measure Theory for the free energy density functional of hard sphere mixtures. A comparative study of the different versions of the theory, and other density functional approaches, is done in…
We study the existence of densities for distributions of piecewise deterministic Markov processes. We also obtain relationships between invariant densities of the continuous time process and that of the process observed at jump times. In…
Diagonal lines in symbolic recurrence plots are closely related to the identification and characterization of specific biprolongable words within a sequence. In this paper we focus on the recurrence plot of a fixed point of a uniform binary…
Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation…
Classical density functional theory (DFT) is a statistical mechanical theory for calculating the density profiles of the molecules in a liquid. It is widely used, for example. to calculate the density distribution of the molecules in the…
The point process of vertices of an iteration infinitely divisible or more specifically of an iteration stable random tessellation in the Euclidean plane is considered. We explicitly determine its covariance measure and its pair-correlation…
We examine the state of statistical equilibrium attained by a uniformly forced condensable substance subjected to advection in a periodic domain. In particular, we examine the probability density function (\pdf{}) of the condensable…
Position probability distribution of a set of massive mutually exclusive particles in one dimension has been defined. Examples with a given two mutually exclusive particles system are considered. It is emphasized that quantum particles at…
In some particular cases we give criteria for morphic sequences to be almost periodic (=uniformly recurrent). Namely, we deal with fixed points of non-erasing morphisms and with automatic sequences. In both cases a polynomial-time algorithm…
In this paper we study the density in the real line of oscillating sequences of the form $$ (g(k)\cdot F(k\alpha))_{k \in \mathbb{N}} ,$$ where $g$ is a positive increasing function and $F$ a real continuous 1-periodic function. This…
This paper considers the problem of characterizing the simplest discrete point sets that are aperiodic, using invariants based on topological dynamics. A Delone set whose patch-counting function N(T), for radius T, is finite for all T is…
We study densities of functionals over uniformly bounded triangulations of a Delaunay set of vertices, and prove that the minimum is attained for the Delaunay triangulation if this is the case for finite sets.
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
Deriving exact density functions for Gibbs point processes has been challenging due to their general intractability, stemming from the intractability of their normalising constants/partition functions. This paper offers a solution to this…
A set of bi-orthogonal potential-density basis functions is introduced to model the density and its associated gravitational field of three dimensional stellar systems. Radial components of our basis functions are weighted integral forms of…
Wavefunction correlations and density matrices for few or many particles are derived from the properties of semiclassical energy Green functions. Universal features of fixed energy (microcanonical) random wavefunction correlation functions…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
Starting from a result of Stewart, Tijdeman and Ruzsa on iterated difference sequences, we introduce the notion of iterated compositions of linear operations. We prove a general result on the stability of such compositions (with bounded…
Mesoscopic theory for soft-matter systems that combines density functional and statistical field theory is derived from the microscopic theory by a systematic coarse-graining procedure. Within the framework of this theory we obtain the…
Let $\mathcal{M}$ be a set with $M$ elements, let $\psi :\mathcal{M}\to\mathcal{M}$ be a bijective involution, and let~$\boldsymbol{\mathcal{X}}_{\psi}$ be the set of sequences $(x_1,\dots,x_M)\in\mathcal{M}^M$ with the property that…