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

This paper propose the semi - analytic technique using two point osculatory interpolation to construct polynomial solution for solving some well-known classes of Lane-Emden type equations which are linear ordinary differential equations, and disusse the behavior of the solution in the neighborhood of the singular points along with its numerical approximation. Many examples are presented to demonstrate the applicability and efficiency of the methods. Finally , we discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems.

In this article, the notions  are introduced by using soft ideal and soft semi-open sets, which are - - - -closed sets " -closed" where many of the properties of these sets are clarified. Some games by using soft- -semi, soft separation axioms: like ( ₀   ( ₀  Using many figures and proposition to study the relationships among these kinds of games with some examples are explained.

The significance of the work is to introduce the new class of open sets, which is said Ǥ- -open set with some of properties. Then clarify how to calculate the boundary area for these sets using the upper and lower approximation and obtain the best accuracy.

In this contribution new oxazepine compounds containing azo group were preppared. In the firststep,4-(dimethylamino)-3-((4-methoxy phenyl) diazenyl) benzaldehyde [Z] was synthesised by using 4-methoxyaniline. The second step was the condensation reaction between aldehyde group of the azo compound [Z] and
different primary aromatic amines [4-hydroxyaniline, 4-chloroaniline and 4-amino- N-(pyrimidin-2-yl) benzenesulfonamide] to yield new azo Schiff bases compounds [A1-A3] respectively. In the final step, oxazepine compounds [B1-B3] and [B4-B6] were prepared from reaction imines compounds [A1-A3] with maleic anhydride and phathalic anhydride in dry benzene respectively. All these derivatives were c

In this paper we deal with the problem of ciphering and useful from group isomorphism for construct public key cipher system, Where construction 1-EL- Gamal Algorithm. 2- key- exchange Algorithm

Background: Obesity and dental caries are multifactorial diseases related to poor eating habits and show a close relationship with the sociodemographic characteristics of individuals presenting these diseases. This research aimed to investigate the severity of dental caries among group of obese boys aged 12 year in relation to salivary interleukin-6 (IL-6) and C-reactive protein (CRP) of unstimulated whole saliva in comparison with normal weighted boys of the same age. Materials and Methods: The study group included 40 obese boys, with an age of 12 year. The control group included 40 normal weighted boys of the same age. The total sample involved for nutritional status assessment using Body Mass Index specific for age and gender according t