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

New complexes of Al(III) such as [Al (Ura) (Phen) (OH2) Cl ] Cl. 2H2O, [Al(Ura)2(OA)(OH2)Cl].H2O and [Al(Ura)3Cl3]H2O type, where (Ura)=Uracil, (Phen)= 1,10-Phenanthroline monohydrate and (OA)= Oxalic acid dihydrate, were prepared. The elemental microanalysis, FT.IR, electronic spectra, and magnetic susceptibility as well as the conductivity measurements are characterized. For isolated three complexes for six coordinated of Al(III) are proposed with molecular formulas that depend on the nature of (Ura), (Phen) and (OA) present. The suggested molecular structure into all complexes for aluminum ion is octahedral geometries .The antibacterial efficacy was examined from metal salt (AlCl3), ligands and metal complexes into the pathogenic bacteri

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

In this study, an easy, low-cost, green, and environmentally
friendlier reagents have been used to prepare CdS QDs, in chemical
reaction method by mixed different ratio of CdO and sulfur in
paraffin liquid as solvent and oleic acid as the reacting media in
different concentration to get the optimum condition of the reaction
to formation CdS QDs. The results give an indication that the
behavior is at small concentration of 4ml of the oleic acid is best
concentration which give CdS QDs of small about to 9.23 nm with
nano fiber configuration.

Synthesis and study liquid crystalline properties of new compounds with terminal groups of amides ([III]a-c,[IV]a-c and [VI]n), alkoxy series[V]n or ester with azo linkage ([IX]a-c and[X]a-c) containing thaizole ring. These series were synthesized by many steps starting from 4- hydroxyacetophenone or 4-aminoacetophenone. The synthesized compounds were characterized using melting points, FTIR, C.H.N.S analysis and for some of them 1H NMR spectroscopy. The liquid crystalline properties were studied by hot stage polarizing microscopy and differential scanning calorimetry DSC. All compounds of series [III]a-c,[IV]a-c and compounds [V]n showed enantiotropic liquid crystal. While the series [VI]n showed nematic mesomorphism except [VI]8 did not s

In the current endeavor, a new Schiff base of 14,15,34,35-tetrahydro-11H,31H-4,8-diaza-1,3(3,4)-ditriazola-2,6(1,4)-dibenzenacyclooctaphane-4,7-dien-15,35-dithione was synthesized. The new symmetrical Schiff base (Q) was employed as a ligand to produce new complexes comprising Co(II), Ni(II), Cu(II), Pd(II), and Pt(II) metal-ions at a ratio of 2:1 (Metal:ligand). There have been new ligands and their complexes validated by (FTIR), (UV-visible), 1H-NMR, 13C-NMR, CHNS, and FAA spectroscopy, Thermogravimetric analysis (TG), Molar conductivity, and Magnetic susceptibility. The photostabilization technique to enhance the polymer was also used. The ligand Q and its complexes were mixed in 0.5% w/w of polyvinyl chloride in tetrahydrofuran