Related papers: A strong uniqueness theorem for planar vector fiel…

In a previous article the authors determined the best-known upper bound for the cardinality of the image set for several classes of functions, including planar functions. Here, we show that the upper bound cannot be tight for planar…

We study singular solutions to the fractional Laplace equation and, more generally, to nonlocal linear equations with measurable kernels. We establish B\^ocher type results that characterize the behavior of singular solutions near the…

A slip on a paper concerning near-vector spaces is fixed. New characterization of near-vector spaces determined by finite fields is provided and the number (up to the isomorphism) of these spaces is exhibited.

We prove that if a subset of the d-dimensional vector space over a finite field is large enough, then it contains many k-tuples of mutually orthogonal vectors.

We prove a uniqueness theorem for a large class of functional equations in the plane, which resembles in form a classical result of Aczel. It is also shown that functional equations in this class are overdetermined in the sense of Paneah.…

We introduce a notion of planar algebra, the simplest example of which is a vector space of tensors, closed under planar contractions. A planar algebra with suitable positivity properties produces a finite index subfactor of a II_1 factor,…

A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Holder solvability of semilinear equations and a strong similarity…

We prove local unique solvability of the wave equation for a large class of weakly singular, locally bounded space-time metrics in a suitable space of generalised functions.

A family of quantum fields is said to be strongly local if it generates a local net of von Neumann algebras. There are few methods of showing directly strong locality of a quantum field. Among them, linear energy bounds are the most widely…

This paper contributes to the solution of the Poincare problem, which is to bound the degree of a (generalized algebraic) leaf of a (singular algebraic) foliation of the complex projective plane. The first theorem gives a new sort of bound,…

In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic Newton equation with an external potential $V$, $V\in C^2$. Using known results,…

We show that every valued differential field has an immediate strict extension that is spherically complete. We also discuss the issue of uniqueness up to isomorphism of such an extension.

First, a new sufficient condition for uniqueness of weak solutions is proved for the system of 2D viscous Primitive Equations. Second, global existence and uniqueness are established for several classes of weak solutions with partial…

Finite collections of point masses contained in some bounded domain produce a unique field in the exterior domain, which means that the associated basis functions (often called ``fundamental solutions'') are independent. A new proof of this…

We present a study on strong t-continuity and measure of discontinuity on PN spaces. As an application, we prove a fixed point theorem for a self mapping on PN spaces by means of measure of discontinuity.

In this work we prove uniqueness result for an implicit discrete system defined on connected graphs. Our discrete system is motivated from a certain class of spatial segregation of reaction-diffusion equations.

In this paper we shall find some sufficient conditions for a uniqueness polynomial to be a strong uniqueness polynomial, as this type of problem was never investigated by researchers earlier.We also exhibit some examples to substantiate our…

In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type $\tto$ factors arising from countable discrete groups. We give simple criteria for…

In this paper, first some results of [5] are extended for subadditive separating maps between C(X;E) and C(Y;E), such that E is a unital Banach algebra. Then we give some conditions under which a strongly subadditive map has a unique fixed…

We introduce and study a new class of differential fields in positive characteristic. We call them separably differentially closed fields and demonstrate that they are the differential analogue of separably closed fields. We prove several…