Related papers: A problem of Stanislaw Saks
By the methods of the synthetic geometry we investigate properties of objects generated from a complete quadrangle and a line, which lies in its plane. We start with a problem from the book of Sharygin "Problems in Plane Geometry". We…
Despite remarkable achievements in its practical tractability, the notorious class of NP-complete problems has been escaping all attempts to find a worst-case polynomial time-bound solution algorithms for any of them. The vast majority of…
The representation of the solution of some Backward Stochastic Differential Equation as an infinite series is obtained. Some exactly solvable examples are considered.
This paper provides an efficient solution approach to the screen-line counter location problem (SCLP), which is a counter location problem with the constraint that the traffic between OD pairs must be observed at least once. This paper…
A polynomial algorithm is obtained for the NP-complete linear ordering problem.
These lecture notes are meant to accompany two lectures given at the CDM 2016 conference, about the Kadison-Singer Problem. They are meant to complement the survey by the same authors (along with Spielman) which appeared at the 2014 ICM. In…
In this paper, we present a converse to a version of Skoda's $L^2$ division theorem by investigating the solvability of $\bar{\partial}$ equations of a specific type.
Kotlarski's theorem (see H. Kotlarski. Bounded Induction and Satisfaction Classes. Mathematical Logic Quarterly, vol. 32, 31-34, 1986, P. 531--544.) formalized in $WKL_0$.
We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.
The ATSP polytope can be expressed by asymmetric polynomial size linear program.
Presentation of a Method for determining whether a problem 3Sat has solution, and if yes to find one, in time max O(n^15). Is thus proved that the problem 3Sat is fully resolved in polynomial time and therefore that it is in P, by the work…
We present the history and previous approaches to the proof of Stirling's series. We use a different procedure, based on the asymptotic analysis of the difference equation $\Gamma(z+1)=z\Gamma(z)$. The method reproduces Stirling's series…
We consider the problem of satisfiability of sets of constraints in a given set of finite uniform hypergraphs. While the problem under consideration is similar in nature to the problem of satisfiability of constraints in graphs, the…
We study, with the help of a computer program, the Polish Algorithm for finite terms satisfying various algebraic laws, e.g., left distributivity a(bc) = (ab)(ac). While the termination of the algorithm for left distributivity remains open…
We explore the resolution of claims problems with history. At a given period of time, a group of agents holds claims over an insufficient endowment, as they did in previous periods. The solution to the present-period problem might be…
We consider the Schr\"odinger-Poisson-Slater (SPS) system in $\R^3$ and a nonlocal SPS type equation in balls of $\mathbb R^3$ with Dirichlet boundary conditions. We show that for every $k\in\mathbb N$ each problem considered admits a nodal…
We answer negatively a 2014 problem of Yang and Chen on Romanoff type representations. Sharp results involving their problem were also obtained in this article.
In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…
A variant of the well-known Knapsack Problem is studied in this paper, where pairs of items are conflicting, and cannot be selected at the same time. This configures a set of hard constraints. The problem, which can be used to model real…
In this paper we obtain four new parametric ideal solutions of the Tarry-Escott problem of degree 7, that is, of the simultaneous diophantine equations, $\sum_{i=1}^8x_i^r=\sum_{i=1}^8y_i^r,\;r=1,\,2,\,\dots,\,7$. While all the known…