In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test. Moreover, new modifications are suggested in order to eliminate pseudoprimes. The study covers random primes such as Mersenne primes and Proth primes. Finally, these tests are arranged from the best to the worst according to strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematica, and the results are presented through tables and graphs.

Multi-carrier direct sequence code division multiple access (MC-DS-CDMA) has emerged recently as a promising candidate for the next generation broadband mobile networks. Multipath fading channels have a severe effect on the performance of wireless communication systems even those systems that exhibit efficient bandwidth, like orthogonal frequency division multiplexing (OFDM) and MC-DS-CDMA; there is always a need for developments in the realisation of these systems as well as efficient channel estimation and equalisation methods to enable these systems to reach their maximum performance. A novel MC-DS-CDMA transceiver based on the Radon-based OFDM, which was recently proposed as a new technique in the realisation of OFDM systems, will be us

Gelatin-grafted N- proflavine acryl amide was synthesized through two steps; firstly the Gelatin was grafted with acrylic acid free radically using Ammonium per-sulfate at 60℃, Then it was modified to its corresponding acyl chloride derivation, second step included the substitution with amino group of proflavine, in this research Gelatin was used as a natural nontoxic, water soluble polymer as a drug carrier. The prepared pro drug polymer was characterized by FTIR and 1H-NMR spectroscopies, Controlled drug release was studied in different pH values at 37℃. Many advantages were obtained comparing with other known methods.

characteristic tissues and cells, exerting their pharmacological aspects and alleviating a lot of diseased processes. Accordingly, this research is about introducing some isatins to be nucleophilically attacked at C3 forming products of azomethine ylide functionality. These iminium compounds were made by allowing certain isatins to be reacted with the secondary amino acid, proline, at acetic acid and methanol medium and then collected after purification to be identified with total Leukocyte count (TLC) and melting point. The structural characterization was performed by fourier-transform infrared spectroscopy (FTIR), proton nuclear magnetic resonance (1H-NMR), and community health nursing (CHN) analysis. The microbiological evaluatio

Copper (I) complex containing folic acid ligand was prepared and characterized on the basis of metal analyses, UV-VIS, FTIR spectroscopies and magnetic susceptibility. The density functional theory (DFT) as molecular modeling calculations was used to determine the donor atoms of folic acid ligand which appear clearly at oxygen atoms binding to hydrogen. Detection of donation sights is supported by theoretical parameters such as geometry, mulliken population, mulliken charge and HOMO-LUMO gap obtained by DFT calculations.

Complexes of Lanthanide ione Ln(III) =La(III) , Ce(III),Pr(III) and Nd(III) withligands of nicotinamide (na) and Benzimidazole (BIMD) have been prepared withgeneral formula [M(na)3(BIMD)3](NO3) where :M = Ln(III) = La(III) , Ce(III) , Gd(III) , Nd(III) .Na = nicotinamide = C7H6N2OBIMD = Benzimidazole = C7H6N2All compounds have been characterized by spectroscopic methods [FT-IR , UV-VIS ,AAS] , microanalysis (C.H.N) Along with conductivity measurements , solubility ,melting point , theroitical measurment by using chem office 3D prog .Model (2000) .Frome the above data the proposed moleculer structure for all complexes with its ionsis octahydral geometries

Five membered heterocyclics derivatives were synthesized in this work by three routes. The first route includes the synthesis of N-benzoic acid 1,2,3,-triazole derivatives (3),(4) by diazotation of methyl-2-amino benzoate and treating the resulted salt (1) with sodium azide and ethyl acetoacetate or acetyl acetone, respectively. In the second route, derivatives of pyrazole (8) pyrazolin-5-one (9), (10) were prepared by the reaction of the salt (1) with some active methylene compounds to give the corresponding hydrazones derivatives (5-7) which then they were treated with hydrazine hydrate. The third route afforded the synthesis of three derivatives (12), (15a), (15b) of thiazolidinone by two different methods. AII compounds were confirmed b

New 2-amino thiazole ,oxodiazole, sulphonilamide and diazin derivatives of N-(α-chloro aceto)-3-(tolyl imino)-5-bromo-2-oxo-indole(2) have been synthesized .The preparation process started by the reaction of 5-bromo isatin with  P-toluidine in the presence of glacial acetic acid and dimethylformamide(DMF) as a solvent to give  3-(tolyl imino)5-bromo-1H-indole-2-one.(1), Compound (1) with sodium hydride  in dimethylformamide(DMF) at 0C0 gave a suspension of the sodium salt of Schiff base derivative and subsequent reaction with monochloroacetylchloride obtained  the intermediate compound(2).Compound(2) was  reacted with different reagents  in four routes.The first route involved direct reaction with substituted  2-aminobenzothiazole u