For two-player games of perfect information such as Checker, Chess, Go, etc., we introduce “uniqueness” properties. For any game position, we say roughly that it has a uniqueness property (or, a unique solution property) if a winning strategy (if it exists) is forced to be unique. Depending on the way that winning strategy is forced, a uniqueness property is classified as (bi-)weak, (bi-)strong...

This work concerns the study of existence and uniqueness to heat equation with fractional Laplacian dierentiation in extended Colombeau algebra.

This is a survey paper on the subject of strong uniqueness in approximation theory. MSC: 41A52, 41A50, 41A65

In this paper we extend recent results on the existence and uniqueness of solutions of ODEs with non-smooth vector fields to the case of martingale solutions, in the StroockVaradhan sense, of SDEs with non-smooth coefficients. In the first part we develop a general theory, which roughly speaking allows to deduce existence, uniqueness and stability of martingale solutions for L-almost every init...

General boundary value problems are considered for general parabolic (in the Douglas–Nirenberg–Solonnikov sense) systems. The dependence of solution uniqueness classes of these problems on the geometry of a nonbounded domain is established. The dependence of solution uniqueness classes of the first boundary value problem for a second-order parabolic equation in an unbounded domain on the domain...

this paper is devoted to the study of establishing sufficient conditions forexistence and uniqueness of positive solution to a class ofnon-linear problems of fractional differential equations. the boundary conditionsinvolved riemann-liouville fractional order derivative and integral. further, the non-linear function $f$ containfractional order derivative which produce extra complexity. thank to...

The paper investigates a method for identifying risky records within a microdata file. The method, Special Uniques Identification, involves inferring population uniqueness for a set of key variables from sample uniqueness for a collapsed form of that key variable set. The method is shown to be useful with being considerably higher probability of than the probability of population uniqueness giv...