In this paper we used Hosoya polynomial ofgroupgraphs Z_1,...,Z₂₆ after representing each group as  graph and using Dihedral group to"encrypt the plain texts with the immersion property which provided Hosoya polynomial to immerse the cipher text in another"cipher text to become very"difficult to solve.

   The aim of this paper is to introduce and study new class of fuzzy function called fuzzy semi pre homeomorphism in a fuzzy topological space by utilizing fuzzy semi pre-open sets. Therefore, some of their characterization has been proved; In addition to that we define, study and develop corresponding to new class of fuzzy semi pre homeomorphism in fuzzy topological spaces using this new class of functions.

A theoretical study including the effects of the fusion characteristics parameters on the fundamental fusion rate for the BEC state in D-D fusion reaction is deal with varieties physical parameters such as the fuels density, fuel temperature and the astrophysics S-factor are processed to bring an approximately a comparable results to agree with the others previously studies.

         Let  be any group with identity element (e) . A subgroup intersection graph of  a subset  is the Graph with V ( ) =  - e and two separate peaks c and d contiguous for c and d if and only if      , Where  is a Periodic subset of resulting from  . We find some topological indicators in this paper and Multi-border (Hosoya and Schultz) of   , where    ,  is aprime number.

This work includes synthesis of new six membered heterocyclic rings with effective amino group using the reaction of benzylideneacetophenone (chalcone) (1) with thiourea or urea in alcoholic basic medium to form: 1,3-thiazen-2-amine (2), and 1,3-oxazin-2-amine (8) respectively. The diazotization reaction was carried out with sodium nitrite in presence of hydrochloric acid to form diazonium salts which suffered coupling reaction with naphthols and phenols in the presence of sodium hydroxide to form colored azo dyes (4-7, and 10-13). o-methylation reaction of compounds (7) and (10) yielded : 1,3-thiazin -2-yl-diazenyl (14), and 1,3-oxazin-2-yl-diazenyl (15) respectively.The new compounds were characterized using vario

In this paper, a new analytical method is introduced to find the general solution of linear partial differential equations. In this method, each Laplace transform (LT) and Sumudu transform (ST) is used independently along with canonical coordinates. The strength of this method is that it is easy to implement and does not require initial conditions.

This search reports the synthesis of some new series of Schiff base compounds for trimetheprim derivatives which known high been known as a medicinal effectiveness. Trimetheprim was condensed with several substituted aldehydes compounds.(4-dimethyl amine benzaldehyde , propanal , salicaldehyde, 2.4 dimethoxy benzaldehyde and 4- methyl benzaldehyde) to obtain Schiff base products(1a-5a) and several substituted ketones compound (4-aminoacetophenone,4-chloroacetophenone, isobutyleketone, acetylacetone and acetophenone) to obtain Schiff base products(6b-10b) in ethanol in the presence of concentrated sulphuric acid as a catalyst to yield the Schiff base. The structure of synthesized compounds has been established on the basis of their Chemical

Circular data (circular sightings) are periodic data and are measured on the unit's circle by radian or grades. They are fundamentally different from those linear data compatible with the mathematical representation of the usual linear regression model due to their cyclical nature. Circular data originate in a wide variety of fields of scientific, medical, economic and social life. One of the most important statistical methods that represents this data, and there are several methods of estimating angular regression, including teachers and non-educationalists, so the letter included the use of three models of angular regression, two of which are teaching models and one of which is a model of educators. ) (DM) (MLE) and circular shrinkage mod

Chloroacetamide derivatives (2a-g) have been prepared through reaction of chloroacetyl chloride(1) (which prepared by the reaction of chloroacetic acid with thionyl chloride) with primary aromatic amines and sulfa compounds to afford compounds (2a-g) which then reacted with p-hydroxy benzaldehyde via Williamson reaction to obtaine the new compounds 2-(4-formyl phenoxy)-N-aryl acetamide (3a-g). Finally , compounds (3a-g) will be use as a good synthon to prepare the Schiff bases represented by compounds 2-(4-aryliminophenoxy)-N-arylacetamide (4a-g). through , reaction with some primary aromatic amine. All the prepared compounds were investigated by the available physical and spectroscopic methods.