Related papers: A problem of Stanislaw Saks
We give a solution to a part of Problem 1.60 in Kirby's list of open problems in topology thus answering in the positive the 1987 conjecture by J.Przytycki concerning the existence of knots without matched diagrams.
The initial motivation of this text was to provide an up to date translation of the monograph [45] written in french by the first author, taking account of more recent developments of infinite dimensional dynamics based on the…
Extends previous work on a quintic-solving algorithm to equations of the eighth-degree.
The exact solution of the Cauchy problem of the linear theory of elasticity is given in the paper, when the initial data belong to a specific class of functions.
We prove the existence of classical solutions to parabolic linear stochastic integro-differential equations with adapted coefficients using Feynman-Kac transformations, conditioning, and the interlacing of space-inverses of stochastic flows…
We determine a general link between two different solutions of the MaxEnt variational problem, namely, the ones that correspond to using either Shannon's or Tsallis' entropies in the concomitant variational problem. It is shown that the two…
The k-satisfiability problem is a well-known task in computational complexity theory. In this paper approach for it's solving is introduced.
In this paper, we prove the infinitely many solutions to a class of sublinear Schr\"{o}dinger-Poisson equations by using an extension of Clark's theorem established by Zhaoli Liu and Zhi-Qiang Wang.
This document is an exposition of an assortment of open problems arising from the exact enumeration of (perfect) matchings of finite graphs. Roughly half have been solved at the time of this writing; see the document "Twenty Open Problems…
Solutions of Lee Smolin Five Great Problems from his book {\it The Trouble with Physics: the Rise of String Theory, the Fall of a Science, and What Comes Next} are described. This solutions is obtained only from the properties of…
We discuss a fast approximate solution to the associated classical -- classical orthogonal polynomial connection problem. We first show that associated classical orthogonal polynomials are solutions to a fourth-order quadratic eigenvalue…
We find a solution of Sincov's inequality. Further, we prove that in the differentiable case we can interpret such solution as a differentiable manifold in the original sense of Lang. This allows to generalize the notion of atlas and…
We obtain a small improvement of Gallagher's larger sieve and we extend it to higher dimensions. We also obtain two interesting upper bounds for the number of solutions to polynomial congruences.
Waring's classical problem deals with expressing every natural number as a sum of g(k) k-th powers. Recently there has been considerable interest in similar questions for nonabelian groups, and simple groups in particular. Here the k-th…
In this paper we study local and global well-posedness of the following Cauchy problem: $$ \bigg \{ \begin{array}{rl} i\partial_t\Psi+\frac{1}{2}\Delta_{x}\Psi = A_0\Psi +\alpha |\Psi|^{\gamma-1}\Psi, & (t,x)\in\R\times\R,\\…
A modified $k$-deck of a graph $G$ is obtained by removing $k$ edges of $G$ in all possible ways, and adding $k$ (not necessarily new) edges in all possible ways. Krasikov and Roditty asked if it was possible to construct the usual $k$-edge…
Given k similarity classes of invertible matrices, the Deligne-Simpson problem asks to determine whether or not one can find matrices in these classes whose product is the identity and with no common invariant subspace. The first author…
We study the complexity of local search for the Boolean constraint satisfaction problem (CSP), in the following form: given a CSP instance, that is, a collection of constraints, and a solution to it, the question is whether there is a…
I survey problems concerning Lindelof spaces which have partial set- theoretic solutions.
In this note, we discuss two problems of S\'{a}rk\"{o}zy (2001). In particular, we prove an optimal result on sumsets of sparse subset of primes.