On Sets Defining Few Ordinary Lines

On Sets Defining Few Ordinary Circles

An ordinary circle of a set P of n points in the plane is defined as a circle that contains exactly three points of P. We show that if P is not contained in a line or a circle, then P spans at least [Formula: see text] ordinary circles. Moreover, we determine the exact minimum number of ordinary circles for all sufficiently large n and describe all point sets that come close to this minimum. We...

On the Number of Ordinary Lines Determined by Sets in Complex Space

Kelly’s theorem states that a set of n points affinely spanning C3 must determine at least one ordinary complex line (a line passing through exactly two of the points). Our main theorem shows that such sets determine at least 3n/2 ordinary lines, unless the configuration has n − 1 points in a plane and one point outside the plane (in which case there are at least n− 1 ordinary lines). In additi...

On bD-Sets and Associated Separation Axioms

Fixed point theorems for $alpha$-$psi$-contractive mappings in partially ordered sets and application to ordinary differential equations

‎In this paper‎, ‎we introduce $alpha$-$psi$-contractive mapping in partially ordered sets and construct fixed point theorems to solve a first-order ordinary differential equation by existence of its lower solution.

On Connections between Information Systems, Rough Sets and Algebraic Logic

In this note we remark upon some relationships between the ideas of an approximation space and rough sets due to Pawlak ([9] and [10]) and algebras related to the study of algebraic logic — namely, cylindric algebras, relation algebras, and Stone algebras. The paper consists of three separate observations. The first deals with the family of approximation spaces induced by the indiscernability r...