In this paper we introduce new class of open sets called weak N-open sets and we study the relation between N-open sets , weak N-open sets and some other open sets. We prove several results about them. 

   The purpose of this paper is to study   new  types of open sets in bitopological spaces.    We shall introduce the concepts of  L- pre-open and L-semi-p-open sets

By use the notions pre-g-closedness and pre-g-openness we have generalized a class of separation axioms in topological spaces. In particular, we presented in this paper new types of regulαrities, which we named ρg­regulαrity and Sρg­regulαrity. Many results and properties of both types have been investigated and have illustrated by examples.

Ruthenium-Ruthenium and Ruthenium–ligand interactions in the triruthenium "[Ru₃(μ-H)(μ₃-κ²-Hamphox-N,N)(CO)₉]" cluster are studied at DFT level of theory. The topological indices are evaluated in term of QTAIM (quantum theory of atoms in molecule). The computed topological parameters are in agreement with related transition metal complexes documented in the research papers. The QTAIM analysis of the bridged core part, i.e., Ru₃H, analysis shows that there is no bond path and bond critical point (chemical bonding) between Ru(2) and Ru(3). Nevertheless, a non-negligible delocalization index for this non-bonding interaction is calculated

 The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals of near-rings and some related properties. Interesting results have been reached, the most prominent of which are the following: Let M be a 3-prime left near-ring and A_1,A_2,…,A_n are nonzero semigroup ideals of M, if d is a right n-derivation of M satisfies on of the following conditions,
d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=0 ∀u_1,v_1 〖ϵA〗_1,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u ;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=(u_

  In this paper, we introduce a new class of sets, namely , s*g--open sets and we show that the family of all s*g--open subsets of a topological space ) ,X(  from a topology on X which is finer than  . Also , we study the characterizations and basic properties of s*g-open sets and s*g--closed sets . Moreover, we use these sets to define and study a new class of functions, namely , s*g-  -continuous functions and s*g-  -irresolute functions in topological spaces . Some properties of these functions have been studied .

This paper performance for preparation and identification of six new complexes of a number of transition metals Cr (lII), Mn (I1), Fe (l), Co (II), Ni (I1), Cu (Il) with: N - (3,4,5-Trimethoxy phenyl-N - benzoyl Thiourea (TMPBT) as a bidentet ligand. The prepared complexes have been characterized, identified on the basis of elemental analysis (C.H.N), atomic absorption, molar conductivity, molar-ratio ,pH effect study, I. Rand UV spectra studies. The complexes have the structural formula ML₂X₃ for Cr (III), Fe (III), and ML₂X₂ for Mn (II), Ni (II), and MLX₂ for Co (Il) , Cu (Il).

     The objective of this paper is to show modern class of open sets which is an -open. Some functions via this concept were studied and the relationships such as continuous function strongly -continuous function -irresolute function -continuous function.

The m-consecutive-k-out-of-n: F linear and circular system consists of n sequentially connected components; the components are ordered on a line or a circle; it fails if there are at least m non-overlapping runs of consecutive-k failed components. This paper proposes the reliability and failure probability functions for both linearly and circularly m-consecutive-k-out-of-n: F systems. More precisely, the failure states of the system components are separated into two collections (the working and the failure collections); where each one is defined as a collection of finite mutual disjoint classes of the system states. Illustrative example is provided.

The topic of the research tagged (narrative structure and its impact on building open and closed endings in the fictional film) is summarized by studying the mechanism of employing closed and open endings in the fictional film. novelist, then the need for it, as well as the objectives of the research and clarifying its limits as well as its importance. Then moving to the theoretical framework, which included three topics, where the first topic was entitled (the cinematic construction of the film narrative), either the second topic (the structure of complexity and narrative solutions), or the third topic dealt with the subject (the structure of the end and its relationship to the construction of the narrative). After completing the theore