Related papers: On forbidden sets
Assuming a lower bound on the dimension, we prove a long standing conjecture concerning the classification of global solutions of the obstacle problem with unbounded coincidence sets.
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
The purpose of this paper is twofold. Firstly, the new matrix domains are constructed with the new infinite matrices and some properties are investigated. Furthermore, dual spaces of new matrix domains are computed and matrix…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
Let $\mathbb{F}_q$ be a finite field with $q=p^n$ elements. In this paper, we study the number of solutions of equations of the form $a_1 x_1^{d_1}+\dots+a_s x_s^{d_s}=b$ with $x_i\in\mathbb{F}_{p^{t_i}}$, where $b\in\mathbb{F}_q$ and…
There has been a great deal of research on graphs defined on algebraic structures in the last two decades. In this paper we begin an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
This is an expository paper on the largest size of equilateral sets in finite-dimensional normed spaces.
We prove a lemma that is useful to get upper bounds for the number of partitions without a given subsum. From this we can deduce an improved upper bound for the number of sets represented by the (unrestricted or into unequal parts)…
We survey classical and recent results on exponents of Diophantine approximation. We give only a few proofs and highlight several open problems.
We consider the problem of identifying discontinuous doping profiles in semiconductor devices from data obtained by different models connected to the voltage-current map. Stationary as well as transient settings are discussed and a…
We provide a list of (mainly unsolved) problems in ordered and orderable groups. These were originally compiled 10 years ago by the last two authors. New problems have been added to the list. Progress on some of these is noted and…
The work studies some Difference equations, which are connected with Mejer's function.
There has been always an ambiguity in division when zero is present in the denominator. So far this ambiguity has been neglected by assuming that division by zero as a non-allowed operation. In this paper, I have derived the new set of…
Given two points in the plane, and a set of "obstacles" given as curves through the plane with assigned weights, we consider the point-separation problem, which asks for the minimum-weight subset of the obstacles separating the two points.…
In this paper, we study non-linear differential equations associated with Legendre polynomials and their applications. From our study of non- linear differential equations, we derive some new and explicit identities for Legendre…
We prove a general result on irregularities of distribution for Borel sets intersected with bounded measurable sets or affine half-spaces.
An assortments of `species' of families of subsets of a set and some of their properties are investigated, with an eye on the logic and limit role they may play as `relaxed parallels' to ultrafilters.
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
In this paper we propose an extension of Defeasible Logic to represent and compute three concepts of defeasible permission. In particular, we discuss different types of explicit permissive norms that work as exceptions to opposite…