It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

            In this paper, the Normality set  will be investigated. Then, the study highlights some concepts properties and important results. In addition, it will prove that every operator with normality set has non trivial invariant subspace of  .

This paper deals with the F-compact operator defined on probabilistic Hilbert space and gives some of its main properties.

Let A ⊆ V(H) of any graph H, every node w of H be labeled using a set of numbers; , where d(w,v) denotes the distance between node w and the node v in H, known as its open A-distance pattern. A graph H is known as the open distance-pattern uniform (odpu)-graph, if there is a nonempty subset A ⊆V(H) together with  is the same for all . Here  is known as the open distance pattern uniform (odpu-) labeling of the graph H and A is known as an odpu-set of H. The minimum cardinality of vertices in any odpu-set of H, if it exists, will be known as the odpu-number of the graph H. This article gives a characterization of maximal outerplanar-odpu graphs. Also, it establishes that the possible odpu-number of an odpu-maximal outerplanar graph i

This paper presents a hybrid approach for solving null values problem; it hybridizes rough set theory with intelligent swarm algorithm. The proposed approach is a supervised learning model. A large set of complete data called learning data is used to find the decision rule sets that then have been used in solving the incomplete data problem. The intelligent swarm algorithm is used for feature selection which represents bees algorithm as heuristic search algorithm combined with rough set theory as evaluation function. Also another feature selection algorithm called ID3 is presented, it works as statistical algorithm instead of intelligent algorithm. A comparison between those two approaches is made in their performance for null values estima

A new type of the connected domination parameters called tadpole domination number of a graph is introduced. Tadpole domination number for some standard graphs is determined, and some bounds for this number are obtained. Additionally, a new graph, finite, simple, undirected and connected, is introduced named weaver graph. Tadpole domination is calculated for this graph with other families of graphs.

The aim of this article is to introduce a new definition of domination number in graphs called hn-domination number denoted by . This paper presents some properties which show the concepts of connected and independent hn-domination. Furthermore, some bounds of these parameters are determined, specifically, the impact on hn-domination parameter is studied thoroughly in this paper when a graph is modified by deleting or adding a vertex or deleting an edge.

In this work the concept of semi-generalized regular topological space was introduced and studied via semi generalized open sets. Many properties and results was investigated and studied, also it was shown that the quotient space of semi-generalized regular topological space is not, in general semi-generalizedspace.

In this paper introduce some generalizations of some definitions which are, closure converge to a point, closure directed toward a set, almost ω-converges to a set, almost condensation point, a set ωH-closed relative, ω-continuous functions, weakly ω-continuous functions, ω-compact functions, ω-rigid a set, almost ω-closed functions and ω-perfect functions with several results concerning them.

Abstract. Nano-continuous mappings have a wide range of applications in pure and applied sciences. This paper aims to study and investigate new types of mappings, namely nano-para-compact, completely nano-regular, nano-para-perfect, and countably nano-para-perfect mappings in nano-topological spaces using nano-open sets. We introduce several properties and basic characterizations related to these mappings, which are essential for proving our main results. Additionally, we discuss the relationships among these types of mappings in nano-topological spaces. We also introduce the concept of nano-Ti-mapping, where i = 0, 1, 2, nano-neighborhood separated, and nano-functionally separated, along with various other definitions. We explore the relat