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.

The aim of this paper is to introduce and study the concept of SN-spaces via the notation of simply-open sets as well as to investigate their relationship to other topological spaces and give some of its properties.

In modules there is a relation between supplemented and Ï€-projective semimodules. This relation was introduced, explained and investigated by many authors. This research will firstly introduce a concept of "supplement subsemimodule" analogues to the case in modules: a subsemimodule Y of a semimodule W is said to be supplement of  a subsemimodule X if it is minimal with the property X+Y=W. A subsemimodule Y is called a supplement subsemimodule if it is a supplement of some subsemimodule of W. Then, the concept of supplemented semimodule will be defined as follows: an S-semimodule W is said to be supplemented if every subsemimodule of W is a supplemen

A Photo Dynamic Therapy (PDT) is a technique which is used with Laser to treat many of cancer
tissues. This paper deals with the relatively new therapeutic technique (PDT) with pulsed Nd:glass Laser
which was applied to human soft tissues (Ovary and Kidney tissues), and to the hard tissues (freshly
extracted human teeth), with power density of 280 watt/mm2 and exposure time 330 usec. Different
dyes (Blue, methylene, eosin, and orange) were applied to the area before irradiation to study the effect
of the pigments on the laser interaction with biological tissues. The zone of treatment (Z-necrosis) with
aid of MATLAB was determined. The relationship of zone of treatment with exposure time,
accumulated damage and fracti

In this paper by using δ-semi.open sets we introduced the concept of weakly δ-semi.normal and δ-semi.normal spaces . Many properties and results were investigated and studied. Also we present the notion of δ- semi.compact spaces and we were able to compare with it δ-semi.regular spaces

Based on the needs of the scientific community, researchers tended to find new iterative schemes or develop previous iterative schemes that would help researchers reach the fixed point with fewer steps and with stability, will be define in this paper the multi_implicit four-step iterative (MIFSI) which is development to four-step implicit fixed point iterative, to develop the aforementioned iterative scheme, we will use a finite set of projective functions ,nonexpansive function and finite set from a new functions called generalized quasi like contractive which is an amalgamation of quasi contractive function and contractive like function , by the last function and a set of sequential organized steps, we will be able to prove the existen

In this research, a new application has been developed for games by using the generalization of the separation axioms in topology, in particular regular, Sg-regular and SSg- regular spaces. The games under study consist of two players and the victory of the second player depends on the strategy and choice of the first player. Many regularity, Sg, SSg regularity theorems have been proven using this type of game, and many results and illustrative examples have been presented

This dissertation depends on study of the topological structure in graph theory as well as introduce some concerning concepts, and generalization them into new topological spaces constructed using elements of graph. Thus, it is required presenting some theorems, propositions, and corollaries that are available in resources and proof which are not available. Moreover, studying some relationships between many concepts and examining their equivalence property like locally connectedness, convexity, intervals, and compactness. In addition, introducing the concepts of weaker separation axioms in α-topological spaces than the standard once like, α-feebly Hausdorff, α-feebly regular, and α-feebly normal and studying their properties. Furthermor

The electric quadrupole moments for some nitrogen isotopes (12,14,15,16,18N) are
studied by shell model calculations with the proton-neutron formalism. Theoretical
calculations performed using the different set of effective charges due to the core
polarization effect. The effective charges in the p-shell nuclei are found to be
slightly different from those in the sd-shell nuclei. Most of the results we have
obtained are underestimated with the measured data for the isotopes considered in
this work.