Related papers: {\Delta}- convergence on time scale
Global hyperbolicity is a central concept in Mathematical Relativity. Here, we review the different approaches to this concept explaining both, classical approaches and recent results. The former includes Cauchy hypersurfaces, naked…
We introduce the concept of a class of equivalence of molecular clouds represented by an abstract spherically symmetric, isotropic object. This object is described by use of abstract scales in respect to a given mass density distribution.…
Some new reverses of the Cauchy-Schwarz inequality in inner product spaces are presented in this paper.The results obtained here complement the recent work of the references.
Complex nonequilibrium systems are often effectively described by a `statistics of a statistics', in short, a `superstatistics'. We describe how to proceed from a given experimental time series to a superstatistical description. We argue…
Cauchy's condensation test allows to determine the convergence of a monotone series by looking at a weighted subseries that only involves terms of the original series indexed by the powers of two. It is natural to ask whether the converse…
In 2013, Komatsu introduced the poly-Cauchy numbers, which generalize Cauchy numbers. Several generalizations of poly-Cauchy numbers have been considered since then. One particular type of generalizations is that of…
Self-consistent theory for concentrated electrolytes is developed. Oscillatory decay of the charge-charge correlation function with the decay length that shows perfect agreement with the experimentally discovered and so far unexplained…
In this paper some links between the density of a set of integers and the density of its sumset, product set and set of subset sums are presented.
We discuss various space-time metrics which are compatible with Einstein's equations and a previously suggested cosmology with a finite total mass. In this alternative cosmology the matter density was postulated to be a spatial delta…
We critically discuss the measure of very short time intervals. By means of a Gedankenexperiment, we describe an ideal clock based on the occurrence of completely random events. Many previous thought experiments have suggested fundamental…
We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…
Quantum mechanical effects related to the recently developed projective theory of relativity are considered. It is shown that at cosmological time intervals the light velocity increases and the atomic units of length and time are shrinking.…
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…
We report a recent developement on the theory of upper conical densities. More precicely, we look at what can be said in this respect for other measures than just the Hausdorff measure. We illustrate the methods involved by proving a result…
Multivariate density moments (correlators) of arbitrary order are obtained for the multiplicative self-similar cascade. This result is based on the calculation by Greiner, Eggers and Lipa (reference [1]) where the correlators of the…
We consider the Cauchy problem on nonlinear scalar conservation laws with a diffusion-type source term related to an index $s\in \R$ over the whole space $\R^n$ for any spatial dimension $n\geq 1$. Here, the diffusion-type source term…
Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
The aim of this note is to complement and extend some recent results on Whitley's indices of thinness and thickness in three main directions. Firstly, we investigate both the indices when forming $\ell_p$-sums of Banach spaces, and obtain…
Superclusters are a convenient way to partition and characterize the large scale structure of the Universe. In this Letter we explore the advantages of defining superclusters as watershed basins in the divergence velocity field. We apply…