Due to huge increase in the records and dimensions of available databases pattern mining in large databases is a challenging problem. A good number of parallel and distributed FP mining algorithms have been proposed for large and distributed databases based on frequency of item set. Not only the frequency, regularity of item also can be considered as emerging factor in data mining research. Cur...

A topological space X is said to be completely regular if whenever F is a nonempty closed set and x ∈ X \F , there is a continuous function f : X → [0, 1] such that f(x) = 0 and f(F ) = {1}. A completely regular space need not be Hausdorff. For example, ifX is any set with more than one point, then the trivial topology, in which the only closed sets are ∅ and X, is vacuously completely regular,...

This paper is devoted to the study of intuitionistic fuzzy topological spaces. In this paper an intuitionistic fuzzy regular weakly generalized closed set and intuitionistic fuzzy regular weakly generalized open set are introduced. Some of its properties are studied. Also we have provided some applications of intuitionistic fuzzy weakly generalized closed set namely intuitionistic fuzzy rwT1/2 ...

In this paper, a new kind of sets called regular μ-generalized closed (briefly rμg-closed) sets are introduced and studied in a topological space. Some of their properties are investigated. Finally, some characterizations of almost μ-regular, almost μ-normal and mildly μ-normal spaces have been given.

A closed κ0-curve is a closed regular curve of class C r (r ≥ 2) in the Euclidean 3-space having constant curvature κ0 > 0. We present various examples of nonplanar closed κ0-curves of class C , which are composed of n arcs of circular helices. The construction of c starts from the spherical image (= tangent indicatrix) c of c, which then has to be a closed regular curve of class C on the unit ...

In this notes unbounded regular operators on Hilbert C∗-modules over arbitrary C∗-algebras are discussed. A densely defined operator t possesses a densely defined adjoint operator if the graph of t is an orthogonal summand. Moreover, for a densely defined operator t the graph of t is orthogonally complemented if and only if t is regular. For a given C∗-algebra A any densely defined A-linear clo...