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We discuss various recent advances on weak forms of the Twin Prime Conjecture.

Number Theory · Mathematics 2019-11-01 James Maynard

This is a short survey on the connection between general extension theories and the study of realizations of elliptic operators A on smooth domains in R^n, n > 1. The theory of pseudodifferential boundary problems has turned out to be very…

Analysis of PDEs · Mathematics 2014-11-04 Gerd Grubb

The theoretical expectations for the supersymmetric particle spectrum is reviewed and a brief overview on present constraints on supersymmetric models from collider experiments is presented. Finally, we discuss the discovery potential of…

High Energy Physics - Phenomenology · Physics 2007-05-23 Ralf Hempfling

In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.

Number Theory · Mathematics 2013-03-15 Ilgar Sh. Jabbarov

In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.

Geometric Topology · Mathematics 2007-05-23 Sze Kui Ng

We survey recent results on the representation theory of symplectic reflection algebras, focusing particularly on connections with symplectic quotient singularities and their resolutions, spaces of representations of quivers, and on…

Representation Theory · Mathematics 2007-12-11 Iain Gordon

This is a survey talk on the study of Gel'fand-Dorfman bialgebras.

Quantum Algebra · Mathematics 2007-05-23 Xiaoping Xu

In this paper, we give a survey of a geometrical theory of Jacobi forms of higher degree. And we present some geometric results and discuss some geometric problems to be investigated in the future.

Number Theory · Mathematics 2007-05-23 Jae-Hyun Yang

These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.

Classical Analysis and ODEs · Mathematics 2007-05-23 Stephen Semmes

We construct a model of the cubic connectedness locus.

Dynamical Systems · Mathematics 2021-02-16 Alexander Blokh , Lex Oversteegen , Vladlen Timorin

Schauder estimates hold in nonuniformly elliptic problems under optimal assumptions on the growth of the ellipticity ratio.

Analysis of PDEs · Mathematics 2024-12-17 Cristiana De Filippis , Giuseppe Mingione

The problem of estimating the probability of a random process reaching a certain level is well known. In this article, two-sided estimates are established for the probability that a regenerative process reaches a high level. Two auxiliary…

Probability · Mathematics 2025-10-29 Kateryna Akbash , Ivan Matsak , Oleg Zakusylo

We develop structure theory of finite Lie conformal superalgebras.

Quantum Algebra · Mathematics 2007-05-23 Davide Fattori , Victor G. Kac , Alexander Retakh

In this paper we study the hemi-slant submanifolds of cosymplectic manifolds. Necessary and sufficient conditions for distributions to be integrable are worked out. Some important results are obtained in this direction.

Differential Geometry · Mathematics 2016-03-07 Mehraj Ahmad Lone , Mohamd Saleem Lone , Mohammad Hasan Shahid

This is a survey on Kawaguchi-Silverman conjecture.

Algebraic Geometry · Mathematics 2023-11-28 Yohsuke Matsuzawa

We derive a new bound for some bilinear sums over points of an elliptic curve over a finite field. We use this bound to improve a series of previous results on various exponential sums and some arithmetic problems involving points on…

Number Theory · Mathematics 2013-08-23 Omran Ahmadi , Igor E. Shparlinski

We construct relatively bounded toroidal and toric models of relatively bounded fibrations over curves.

Algebraic Geometry · Mathematics 2026-03-06 Caucher Birkar

Existence, regularity and location of solutions to quasilinear singular elliptic systems with general gradient dependence are established developing a method of sub-supersolution. The abstract theorems involving sub-supersolutions are…

Analysis of PDEs · Mathematics 2025-08-11 Abdelkrim Moussaoui

The hypothesis concerning the off-site continuum existence is investigated from the point of view of the mathematical theory of sets. The principles and methods of the mathematical description of the physical objects from different off-site…

General Physics · Physics 2007-06-04 A. V. Novikov-Borodin

Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.

Combinatorics · Mathematics 2017-03-02 Andrei K. Svinin