A notion of closure operator with respect to a functor U is introduced. This allows us to describe a number of mathematical constructions that could not be described by means of the already existing notion of closure operator. Some basic results and examples are provided. Mathematics Subject Classification (1991). 18A22, 18A32, 06A15.

the aim of this paper is to study the categorical relations betweenmatroids, goetschel-voxman’s fuzzy matroids and shi’s fuzzifying matroids.it is shown that the category of fuzzifying matroids is isomorphic to that ofclosed fuzzy matroids and the latter is concretely coreflective in the categoryof fuzzy matroids. the category of matroids can be embedded in that offuzzifying matroids as a simul...

The least common ancestor on two vertices, denoted , , is a well defined operation in a directed acyclic graph (dag) . We introduce , a natural extension of , for any set of vertices. Given such a set , one can iterate in order to obtain an increasing set sequence. being finite, this sequence has always a limit which defines a closure operator. Two equivalent definitions of this operator are gi...

‎We present some inequalities for operator space numerical radius of $2times 2$ block matrices on the matrix space $mathcal{M}_n(X)$‎, ‎when $X$ is a numerical radius operator space‎. ‎These inequalities contain some upper and lower bounds for operator space numerical radius.

The distribution function for the first eigenvalue spacing in the Laguerre unitary ensemble of finite size may be expressed in terms of a solution of the fifth Painlevé transcendent. The generating function of a certain discontinuous linear statistic of the Laguerre unitary ensemble can similarly be expressed in terms of a solution of the fifth Painlevé equation. The methodology used to derive ...

Let M^2n be a hoph hypersurfaces with parallel ricci operator and tangent to structure vector field in Sasakian space form. First, we show that structures and properties of hypersurfaces and hoph hypersurfaces in Sasakian space form. Then we study the structure of hypersurfaces and hoph hypersurfaces with a parallel ricci tensor structure and show that there are two cases. In the first case, th...

We consider the question of taking transitive closures on top of pure relational systems (Sybase and Ingres in this case). We developed three kinds of transitive closure programs , one using a stored procedure to simulate a built-in transitive closure operator, one using the C language embedded with SQL statements to simulate the iterated execution of the transitive closure operation, and one u...