Related papers: The Path to Recent Progress on Small Gaps Between …
Assuming the Riemann hypothesis, this article discusses a new elementary argument that seems to prove that the maximal prime gap of a finite sequence of primes p_1, p_2, ..., p_n <= x, satisfies max {p_(n+1) - p_n : p_n <= x} <=…
This popular article provides a short summary of the progress and prospects in Weather and Climate Modelling for the benefit of high school and undergraduate college students and early career researchers. Although this is not a…
We investigate the question of which growth rates are possible for the number of periodic points of a compact group automorphism. Our arguments involve a modification of Linnik's Theorem, concerning small prime numbers in arithmetic…
This is an expository article to accompany my two lectures at the CDM conference. I have used this an excuse to make public two sets of notes I had lying around, and also to put together a short reader's guide to some recent joint work with…
In the present work we investigate the largest possible gaps between consecutive numbers which can be written as the difference of two primes. The best known upper bounds are the same as those concerning the largest possible difference of…
The aim of this paper is to report on recent development on the conformal fractional Laplacian, both from the analytic and geometric points of view, but especially towards the PDE community.
Numerous research studies have been investigated on proxy signatures over the last decade. This survey reviews the research progress on proxy signatures, analyzes a few notable proposals, and provides an overall remark of these proposals.
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…
The talk contains a brief introduction string theory, followed by a discussion of some of the recent developments.
In this short note we briefly review some recent developments in understanding discrete torsion. Specifically, we give a short overview of the highlights of a group of recent papers which give the basic understanding of discrete torsion.…
We prove explicit versions of Cram\'er's theorem for primes in arithmetic progressions, on the assumption of the generalized Riemann hypothesis.
We give an overview of different approaches to measuring the similarity of, or the distance between, two graphs, highlighting connections between these approaches. We also discuss the complexity of computing the distances.
Starting with the Brezis-Browder principle, we give stronger versions of many variational principles and minimal element theorems which appeared in the recent literature. Relationships among the elements of different sets of assumptions are…
This is a quick survey on some recent works done in the field of random maps.
A review of recent developments in the analyses of supersymmetric dark matter is given.
Prime numbers are one of the most intriguing figures in mathematics. Despite centuries of research, many questions remain still unsolved. In recent years, computer simulations are playing a fundamental role in the study of an immense…
Statistical distribution of the primes in an arithmetic progression is considered. The estimation of prime numbers is given and combinatorial methods are used to calculate the twin primes on the available interval. The distribution and…
Substantial progress in the field of the Local Interstellar Medium has been largely due to recent launches of space missions, mostly in the UV and X-ray domains, but also to ground-based observations, mainly in high resolution spectroscopy.…
The soft topological spaces and some their related concepts have stud- ied in [7]. In this paper, we introduce and study the notions of soft connected topological spaces after a review of preliminary definitions.
In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.