Related papers: Densities in Fabry's theorem
The evolution of density perturbations is analysed in a modified theory of gravity with a nonminimal coupling between curvature and matter. We consider the broken degeneracy between the choices of matter Lagrangian for a perfect fluid,…
Several examples of generalized number systems are constructed to compare various conditions occurring in the literature for the prime number theorem in the context of Beurling generalized primes.
Density-power-based divergences are known to provide robust inference procedures against outliers, and their extensions have been widely studied. A characteristic of successful divergences is that the estimation problem can be reduced to…
Weak limits as the density tends to infinity of classical ground states of integrable pair potentials are shown to minimize the mean-field energy functional. By studying the latter we derive global properties of high-density ground state…
In this work, we consider different forms of relativistic perfect fluid Lagrangian densities, that yield the same gravitational field equations in General Relativity. A particularly intriguing example is the case with couplings of the form…
Recently a new type of cosmological singularity has been postulated for infinite barotropic index $w$ in the equation of state $p=w \rho$ of the cosmological fluid, but vanishing pressure and density at the singular event. Apparently the…
Can quantum theory be seen as a special case of a more general probabilistic theory, similarly as classical theory is a special case of the quantum one? We study here the class of generalized probabilistic theories defined by the order of…
The extension of the density functional theory (DFT) to include pairing correlations without formal violation of the particle-number conservation condition is described. This version of the theory can be considered as a foundation of the…
The curvature singularity in viable f(R) gravity models is examined when the background density is dense. This singularity could be eliminated by adding the $R^{2}$ term in the Lagrangian. Some of cosmological consequences, in particular…
Fourth - order gravity theories have received much interest in recent years thanks to their ability to provide an accelerated cosmic expansion in a matter only universe. In these theories, the Lagrangian density of the gravitational field…
A density-matrix formalism is developed based on the one-particle density-matrix of a single-determinantal reference-state. The v-representable problem does not appear in the proposed method, nor the need to introduce functionals defined by…
By combining the upper and lower bounds to the free energy as given by the Gibbs inequality for two systems with the same intermolecular interactions but with external fields differing from each other only in a finite region of space Gamma,…
In this article, we examine the theorem of Mattila establishing rectifiability for regular sets in the setting of strictly convex, finite-dimensional Banach spaces.
We are interested in the tail behavior of the pdf of mass density within the one and $d$-dimensional Burgers/adhesion model used, e.g., to model the formation of large-scale structures in the Universe after baryon-photon decoupling. We show…
In this paper we present some basic uniqueness results for evolutive equations under density constraints. First, we develop a rigorous proof of a well-known result (among specialists) in the case where the spontaneous velocity field…
Let $f: B^n \rightarrow {\mathbb R}$ be a $d+1$ times continuously differentiable function on the unit ball $B^n$, with $\max_{z\in B^n} \Vert f(z) \Vert=1$. A well-known fact is that if $f$ vanishes on a set $Z\subset B^n$ with a non-empty…
In two dimensions, Gallagher's theorem is a strengthening of the Littlewood conjecture that holds for almost all pairs of real numbers. We prove an inhomogeneous fibre version of Gallagher's theorem, sharpening and making unconditional a…
Let $K$ be a field of characteristic zero over which every diagonal form in sufficiently many variables admits a nontrivial solution. For example, $K$ may be a totally imaginary number field or a finite extension of a $p$-adic field.…
This paper investigates a local central limit theorem for a normalized sequence of random variables belonging to a fixed order Wiener chaos and converging to the standard normal distribution. We prove, without imposing any additional…
We present a new lower bound on the Bowen-Radin maximal density of radius-R ball packings in the m-dimensional hyperbolic space, improving on the basic covering bound by factor \Omega(m(R+\ln m)) as m tends to infinity. This is done by…