Related papers: On Erd\"os--Szekeres problem and related problems
We discuss alternative iteration methods for differential equations. We provide a convergence proof for exactly solvable examples and show more convenient formulas for nontrivial problems.
A proof of Sendov's conjecture is given.
New (infinitely many) rational approximants to \zeta(3) proving its irrationality are given. The recurrence relations for the numerator and denominator of these approximants as well as their continued fraction expansions are obtained. A…
We give a new and short proof of a theorem on k-hypertournament losing scores due to Zhou et al. [G. Zhou, T. Yao, K. Zhang, On score sequences of k-tournaments, European J. Comb., 21, 8 (2000) 993-1000.]
This is the English translation of the short note where the first nontrivial tetrahedron relation (solution of the Zamolodchikov tetrahedron equation) with variables on the edges was presented.
In the present paper we introduce old and new results related to St\"ormer theorem about Pell equations. Moreover we give four types of applications of these results.
We present a new general, complete closed-form solution of the Stark problem in terms of Weierstrass elliptic and related functions. With respect to previous treatments of the problem, our analysis is exact and valid for all values of the…
In this paper some new ways of generalizing perfect numbers are investigated, numerical results are presented and some conjectures are established.
We prove an analog of the Szemer\'edi-Trotter theorem in the plane for definable curves and points in any o-minimal structure over an arbitrary real closed field $\mathrm{R}$. One new ingredient in the proof is an extension of the well…
We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.
We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the…
The full causal ladder of spacetimes is constructed, and their updated main properties are developed. Old concepts and alternative definitions of each level of the ladder are revisited, with emphasis in minimum hypotheses. The implications…
Some of the conclusions of an improved JWKB method by Eleuch H., Rostovtsev Y. V. and Scully M. O., EPL, 89 (2010) 50004 are clarified. The degree of approximation to exact solutions is quantitatively assessed. The improved JWKB method is…
In this paper we attack the Erdos-Straus conjecture by means of the structure of its solutions, extending and improving the results of a previous paper. Using previous results and supported by the works of Elsholtz and Tao and Monks and…
We study the Cauchy problem of the Schr\"odinger-Korteweg-de Vries system. First, we establish the local well-posedness results, which improve the results of Corcho, Linares (2007). Moreover, we obtain some ill-posedness results, which show…
The paper presents several new sufficient conditions, as well as new equivalent criteria for the classical Riemann Hypothesis. Noteworthy are also other statements and remarks about $\zeta$ to be found throughout the paper.
A class of generalized Schr\"{o}dinger elliptic problems involving concave-convex and other types of nonlinearities is studied. A reasonable overview about the set of solutions is provided when the parameters involved in the equation assume…
The experimental and theoretical issues and challenges for extracting the neutron-neutron scattering length are discussed. Particular emphasis is placed on recent results and their impact on the field. Comments are made regarding current…
A new technique was recently developed to approximate the solution of the Schroedinger equation. This approximation (dubbed ERS) is shown to yield a better accuracy than the WKB-approximation. Here, we review the ERS approximation and its…