相关论文: The Path to Recent Progress on Small Gaps Between …
In the present work we prove a number of surprising results about gaps between consecutive primes and arithmetic progressions in the sequence of generalized twin primes which could not have been proven without the recent fantastic…
There are several centrality measures that have been introduced and studied for real world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness…
We verify the Hardy-Littlewood conjecture on primes in quadratic progressions on average. The results in the present paper significantly improve those of a previous paper of the authors(arXiv:math.NT/0605563).
In the recent preprint [3], Goldston, Pintz, and Y{\i}ld{\i}r{\i}m established, among other things, $$ \liminf_{n\to\infty}{p_{n+1}-p_n\over\log p_n}=0,\leqno(0) $$ with $p_n$ the $n$th prime. In the present article, which is essentially…
In a recent work Friedlander studied the problem of how large consecutive prime gaps should be in order that the sum of the reciprocals should be divergent. Supposing a very deep Hypothesis, a generalization of the Hardy--Littlewood prime…
Some recent results in supersymmetric grand unified theories are reviewed.
In the present work we prove a common generalization of Maynard-Tao's recent result about consecutive bounded gaps between primes and on the Erd\H{o}s-Rankin bound about large gaps between consecutive primes. The work answers in a strong…
We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions.
We give an overview of publications on partial actions and related concepts, paying main attention to some recent developments.
We study whether several consecutive prime gaps can all be relatively large at the same time, or is it possible that all are squares or perfect powers, or perhaps none of them are squares? A few related results and problems are also…
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
We prove the existence of primitive sets (sets of integers in which no element divides another) in which the gap between any two consecutive terms is substantially smaller than the best known upper bound for the gaps in the sequence of…
We survey recent developments on the Restriction conjecture.
One field of particular interest in Number Theory concerns the gaps between consecutive primes. Within the last few years, very important results have been achieved on how small these gaps can be. The strongest of these results were…
This is an extension and background to a talk I gave on 9 October 2013 to the Brown Graduate Student Seminar, called `A friendly intro to sieves with a look towards recent progress on the twin primes conjecture.' During the talk, I mention…
We review recent progress at the Centre for Cold Matter in developing atom chips. An important advantage of miniaturizing atom traps on a chip is the possibility of obtaining very tight trapping structures with the capability of…
The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.
The aim of this survey article is to cover most of the recent research on preopen sets. I try to present majority of the results on preopen sets that I am aware of.
This paper is simply a collection of process diagrams for further use and reference. These are diagrams about different approaches to research.