Related papers: An optimal bound on the solution sets of one-varia…
We investigate the least number of palindromic factors in an infinite word. We first consider general alphabets, and give answers to this problem for periodic and non-periodic words, closed or not under reversal of factors. We then…
In this paper, we consider the multiplicity of solutions for a class of Kirchhoff type problems with sub-linear and critical terms on an unbounded domain. With the aid of Ekeland's variational principle and the concentration compactness…
If an infinite non-periodic word is uniformly recurrent or is of bounded repetition, then the limit of its periodicity complexity is infinity. Moreover, there are uniformly recurrent words with the periodicity complexity arbitrarily high at…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
Three problems about recovery of a high-frequency free term in the one-dimension wave equation with homogeneous initial-boundary conditions by some information about partial asymptotics of its solution have been solved. It is shoun, that…
We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \begin{equation*} \label{eq-1} \begin{gathered} {u^{\prime \prime}}(t)+f(t, u(t))=0,\ 0<t<T, \\…
Some approach to the solution of boundary value problems for finding functions, which are analytical in a wedge, is proposed. If the ratio of the angle at the wedge vertex to a number \pi is rational, then the boundary value problem is…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
We extend Robust Optimization to fractional programming, where both the objective and the constraints contain uncertain parameters. Earlier work did not consider uncertainty in both the objective and the constraints, or did not use Robust…
The Maximum Flow Problem with Conflict Constraints is a generalization that adds conflict constraints to a classical optimization problem on networks used to model several real-world applications. In the last few years several approaches,…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
Classes of polynomial differential equations of degree n are considered. An explicit upper bound on the size of the coefficients are given which implies that each equation in the class has exactly n complex periodic solutions. In most of…
Using variational methods, we establish the existence of infinitely many solutions to an elliptic problem driven by a Choquard term and a singular nonlinearity. We further show that if the problem has a positive solution, then it is bounded…
We prove that bounded solutions to an overdetermined fully nonlinear free boundary problem in the plane are one dimensional. Our proof relies on maximum principle techniques and convexity arguments.
We introduced the notation of a set of prohibitions and give definitions of a complete set and a crucial word with respect to a given set of prohibitions. We consider 3 particular sets which appear in different areas of mathematics and for…
In this paper, by using Krasnoselskii's fixed point theorem in a cone, we study the existence of single and multiple positive solutions to the three-point integral boundary value problem (BVP) \begin{equation*} \label{eq-1} \begin{gathered}…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
We prove existence and regularity of solutions to degenerate and singular elliptic free boundary problems, where the volume of the positivity set of the solution is prescribed.
We consider a randomized algorithm for the unique games problem, using independent multinomial probabilities to assign labels to the vertices of a graph. The expected value of the solution obtained by the algorithm is expressed as a…