Related papers: {\Delta}- convergence on time scale
We describe a framework to build distances by measuring the tightness of inequalities, and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the H\"older ordinary and reverse…
Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness has been achieved. As in case of sequential compactness, one…
Cosmological implications of the observed large-scale peculiar velocities are reviewed, alone or combined with redshift surveys and CMB data. The latest version of the POTENT method for reconstructing the underlying three-dimensional…
In this paper we introduce new distributions which are solutions of higher-order Laplace equations. It is proved that their densities can be obtained by folding and symmetrizing Cauchy distributions. Another class of probability laws…
We outline a relation between the densities for the $\beta$-ensembles with respect to the Jacobi weight $(1-x)^a(1+x)^b$ supported on the interval $(-1,1)$ and the Cauchy weight $(1-\mathrm{i}x)^{\eta}(1+\mathrm{i}x)^{\bar{\eta}}$ by…
A conformal gauge theory is used to describe and unify myriad electromechanical and magnetomechanical coupling effects observed in solid continua. Using a space-time pseudo-Riemannian metric in a finite-deformation setup and exploiting the…
In this article, we study the unique determination of convection term and the time-dependent density coefficient appearing in a convection-diffusion equation from partial Dirichlet to Neumann map measured on boundary.
The goal of these notes is to fill some gaps in the literature about random walks in the Cauchy domain of attraction, which has been in many cases left aside because of its additional technical difficulties. We prove here several results in…
In this paper we study some basic properties of strong {\lambda}- statistical convergence of sequences in probabilistic metric (PM) spaces. We also introduce and study the notion of strong {\lambda}-statistically Cauchyness. Further…
The theory of the calculus of variations was recently extended to the more general time scales setting, both for delta and nabla integrals. The primary purpose of this paper is to further extend the theory on time scales, by establishing…
I present recent progress in theoretical modelling of cosmological density--velocity relations in the weakly nonlinear regime. The relations are local, based on rigorous perturbation theory and include the effects of smoothing of the…
This paper introduces the correlation-of-divergency coefficient, c-delta, a custom statistical measure designed to quantify the similarity of internal divergence patterns between two groups of values. Unlike conventional correlation…
We introduce two time: deterministic Newton time-stream t and stochastic time-epoch $\tau$. The relation of uncertainty for time-epoch of physical events $\Delta\tau\Delta D \geq c_1,\eqno(*)$ where $c_1=const$, is proved. The function…
In this research article, we have primarily focused on the circumstantial investigation of deferred statistical convergence of sequences and investigated some fundamental results compatible with the structure of a probabilistic normed…
The main objective of this paper is to present recurrence relations for the generalized poly-Cauchy numbers and polynomials. This is accomplished by introducing the concept of generalized m-poly-Cauchy numbers and polynomials. Additionally,…
The relative entropy and chi-squared divergence are fundamental divergence measures in information theory and statistics. This paper is focused on a study of integral relations between the two divergences, the implications of these…
A variant of the divergence theory for vacuum-condensation developed in a previous communication is analyzed from the viewpoint of a 'time' asymmetric law in vacuum. This law is found to establish a substantial distinction between…
In the second section, we introduce dense unital magmas and show that a near-ring is dense if and only if it has a positive element smaller that unity. In the third section, we discuss magma-valued metric spaces. The density property of the…
Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to…
These lectures cover various aspects of the statistical description of cosmological density fields. Observationally, this consists of the point process defined by galaxies, and the challenge is to relate this to the continuous density field…