Related papers: {\Delta}- convergence on time scale
The galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future Large Scale Structure surveys. The precision demanded by these Stage IV surveys requires the use of second…
The main goal of galaxy surveys is to map the distribution of the galaxies, for the purpose of understanding the properties of this distribution and its implications for the content and the evolution of the universe. However, in order to…
Two new criteria, that involve the microscopic dynamics of the system, are proposed for the identification of clusters in continuum systems. The first one considers a residence time in the definition of the bond between pairs of particles,…
This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is…
This chapter reviews several quantities that have been proposed in scattering theory to characterize the temporal aspects of one dimensional collisions: the dwell time, the delay time, the decay time, and times characterizing transient…
We consider new models of dark energy with finite time future singularities, by introducing the pressure density as a function of the scale factor. This approach gives acceptable phenomenological models of dark energy, practically…
This thesis focuses on characterizing the distribution of points and galaxies using multifractal analysis. In this attempt the main emphasis is on calculating the Minkowski-Bouligand fractal dimension (Dq) of the distribution of points over…
We put forward a new view of relativity theory that makes the existence of a flow of time compatible with the four-dimensional block universe. To this end, we apply the creation-discovery view elaborated for quantum mechanics to relativity…
Some properties of $m$-density points and density-degree functions are studied. Moreover the following main results are provided: \vskip2mm \begin{itemize} \item {\it Let $\lambda$ be a continuous differential form of degree $h$ in…
In order to study large variations or fluctuations of finite or infinite sequences (time series), we bring to light an 1868 paper of Crofton and the (Cauchy-)Crofton theorem. After surveying occurrences of this result in the literature, we…
We study the Cauchy problem for the relativistic Boltzmann equation near relativistic Maxwellians in the whole space. The purpose of this article is to handle hard potentials, and for initial data with finite $L^\infty$ norm, to construct…
We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog…
We discuss some old results due to Abel and Olivier concerning the convergence of positive series and prove a set of necessary conditions involving convergence in density.
The following is a short report about recent work on discrete physics/mathematics on the Planckscale and the use of the concept of ''random graphs'' in this business, appearing in the group21-proceedings (Gosslar 1996)
Three similar convergence notions are considered. Two of them are the long established notions of convergent dynamics and incremental stability. The other is the more recent notion of contraction analysis. All three convergence notions…
Some types of statistical convergence such as statistical order and deferred statistical convergences have been studied and investigated in Riesz spaces, recently. In this paper, we introduce the concept of deferred statistical convergence…
In this paper, using the concept of natural density, we have introduced the notion of rough statistical convergence which is an extension of the notion of rough convergence in a partial metric space. We have defined the set of rough…
After calculating the Dushnik-Miller dimension of Minkowski spaces to be countable infinity, we define a novel notion of dimension for ordered spaces recovering the correct manifold dimension and obtain a corresponding obstruction for the…
We consider the relative entropy between vacuum states of two different theories: a conformal field theory (CFT), and the CFT perturbed by a relevant operator. By restricting both states to the null Cauchy surface in the causal domain of a…
This paper studies a Boltzmann-Nordheim equation in a slab with two-dimensional velocity space and pseudo-Maxwellian forces. Strong solutions are obtained for the Cauchy problem with large initial data in an $ L^1 \cap L^{\infty} $ setting.…