相关论文: The Path to Recent Progress on Small Gaps Between …

Studies of galaxy evolution at optical and near-infrared wavelengths have reached an interesting point in their historical development and the arrival of a new millenium provides an appropriate occasion to review the overall direction in…

Some recent developments in the theory of quantum spin systems are reviewed.

This mini-review provides a perspective on recent progress and emerging directions aimed at utilizing and controlling in-plane optical polarization, highlighting key application spaces where in-plane near-field tip responses have enabled…

We discuss applications of minimal surfaces to comparison geometry.

Ways to access transversity through asymmetry measurements are reviewed. The recent first extraction and possible near future extractions are discussed.

Definition of the number of prime numbers in the given interval

Using evaluations of the difference between consecutive primes we develop another way of estimating of the number of primes in the interval $(n, 2n)$. We also discuss the ultra Cramer conjecture, $p_{n+1} - p_n = O(log^{1+\epsilon}p_n)$…

We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.

This is a review article on the development of the probe and enclosure methods from past to present, focused on their central ideas together with various applications.

This is a survey on Kawaguchi-Silverman conjecture.

This is a very brief report on recent developments on the Dirichlet problem for the minimal surface system and minimal cones in Euclidean spaces. We shall mainly focus on two directions: (1) Further systematic developments after…

In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.

We present effective upper bounds on the symmetric bilinear complexity of multiplication in extensions of a base finite field Fp2 of prime square order, obtained by combining estimates on gaps between prime numbers together with an optimal…

In this paper, using the well known fact that the series of reciprocals of primes diverges, we obtain a general inequality for gaps of consecutive primes that holds for infinitely many primes. As it is shown the key ingredient for this…

In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.

Comparative prime number theory is the study of the {\em{discrepancies}} of distributions when we compare the number of primes in different residue classes. This work presents a list of the problems being investigated in comparative prime…

The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings…

We present a variety of prime-generating constructions that are based on sums of primes. The constructions come in all shapes and sizes, varying in the number of dimensions and number of generated primes. Our best result is a construction…

This article is partly a survey and partly a research paper. It tackles the use of Groebner bases for addressing problems of numerical semigroups, which is a topic that has been around for some years, but it does it in a systematic way…

The goal of this note is to prove a compact embedding result for spaces of forward rate curves. As a consequence of this result, we show that any forward rate evolution can be approximated by a sequence of finite dimensional processes in…