A method to compute the transitive closure, a transitive opening and a transitive approximation of a reflexive and symmetric fuzzy relation is given. Other previous methods in literature compute just the transitive closure, some transitive approximations or some transitive openings. The proposed algorithm computes the three different similarities that approximate a proximity for the computation...

In this paper, we consider finite flag-transitive affine planes with a solvable automorphism group. Under a mild number-theoretic condition involving the order and dimension of the plane, the translation complement must contain a linear cyclic subgroup that either is transitive or has two equal-sized orbits on the line at infinity. We develop a new approach to the study of such planes by associ...

Consider two horizontal lines in the plane. A pair of a point on the top line and an interval on the bottom line defines a triangle between two lines. The intersection graph of such triangles is called a simple-triangle graph. This paper shows a vertex ordering characterization of simple-triangle graphs as follows: a graph is a simple-triangle graph if and only if there is a linear ordering of ...

For any odd prime power q, all (q&q+1)th roots of unity clearly lie in the extension field Fq6 of the Galois field Fq of q elements. It is easily shown that none of these roots of unity have trace &2, and the only such roots of trace &3 must be primitive cube roots of unity which do not belong to Fq . Here the trace is taken from Fq6 to Fq . Computer based searching verified that indeed &2 and ...

A partial linear space is a pair $(\mathcal{P},\mathcal{L})$ where $\mathcal{P}$ non-empty set of points and $\mathcal{L}$ collection subsets called lines such that any two distinct are contained in at most one line, every line contains least points. proper when it not or graph. group automorphisms $G$ acts transitively on ordered pairs collinear non-collinear precisely transitive rank 3 In thi...

Let PG(r, q) be the projective space of dimension r over GF (q). A k–cap K̄ in PG(r, q) is a set of k points, no three of which are collinear [10], and a k–cap is said to be complete if it is maximal with respect to set–theoretic inclusion. The maximum value of k for which there is known to exist a k–cap in PG(r, q) is denoted by m2(r, q). Some known bounds for m2(r, q) are given below. Suppose ...

Given that A is longer than B, and that B is longer than C, even 5-year-old children can infer that A is longer than C. Theories of reasoning based on formal rules of inference invoke simple axioms ("meaning postulates") to capture such transitive inferences. An alternative theory proposes instead that reasoners construct mental models of the situation described by the premises in order to draw...