Many of the elementary transformations of determinants which are used in their evaluation and in the solution of linear equations may by expressed in the notation of matrices. In this paper, some new interesting formulas of special matrices are introduced and proved that the determinants of these special matrices have the values zero. All formulation has been coded in MATLAB 7.

Phenoxathiin was prepared by the reaction of diphenyl ether with sulfur in the presence of anhydrous aluminum chloride. This work comprised the synthesis of new phenoxathiin derivatives containing heterocyclic moieties. These heterocyclic compounds were synthesized in three groups. The first group was made up of 2-(oxoalken-1-yl) phenoxathiin derivatives (3a-3j) obtained from the reaction of 2-acetylphenoxathiin with different aromatic aldehyde in the presence of sodium hydroxide. The other two groups involved compounds produced from the reaction of (3a-3j) with hydrazine hydrate in acetic acid to get 2-(1-acetyl pyrazolin-3-yl) phenoxathiin derivatives (4a-4j), and phenyl hydrazine in the presence of piperidine to afford 2-(1-phenyl pyrazo

Several new derivatives of 1, 2, 4-triazoles linked to phthalimide moiety were synthesized through following multisteps. The first step involved preparation of 2, 2-diphthalimidyl ethanoic acid [2] via reaction of two moles of phthalimide with dichloroacetic acid. Treatment of the resulted imide with ethanol in the second step afforded 2, 2-diphthalimidyl ester [3] which inturn was introduced in reaction with hydrazine hydrate in the third step, producing the corresponding hydrazide derivative [4]. The synthesized hydazide was introduced in different synthetic paths including treatment with carbon disulfide in alkaline solution then with hydrazine hydrate to afford the new 1, 2, 4-triazole [10]. Reaction of compound [10] with different alde

Condensation of 1,2- dibromo ethane with para hydroxy benzoic acid gave 1,2-Ethane-bis- 4-oxybenzoic [1]. This Compound was converted with the thionyl chloride to give 1,2-Ethane-bis- 4-oxybenzoyl chloride [2]. Reaction of compound [2] with thiosemicarbizades gave 1,2-Ethanebis[4-oxybenzoyl-thiosemicarbazide] [3] and opteined 1,2-Ethane-bis[3-mercapto-5-phenoxy- 1,2,4-triazole] [4] from treatment compound [3] with NaOH (4%) .The new compounds 1,2- Ethane-bis[3-(substituted thioacyl)-4-(substituted acyl)-5 phenoxy-1,2,4-triazole] [5a-d] and 1,2- Ethane-bis[3-(substituted alkylthio)-5 phenoxy-1,2,4-trizole] [5e-f] derived from compound [4] were synthesized and characterized by physical and spectral data. All the compounds [4], [5a-d] and [5e-

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

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

Using the Neural network as a type of associative memory will be introduced in this paper through the problem of mobile position estimation where mobile estimate its location depending on the signal strength reach to it from several around base stations where the neural network can be implemented inside the mobile. Traditional methods of time of arrival (TOA) and received signal strength (RSS) are used and compared with two analytical methods, optimal positioning method and average positioning method. The data that are used for training are ideal since they can be obtained based on geometry of CDMA cell topology. The test of the two methods TOA and RSS take many cases through a nonlinear path that MS can move through tha

Using the Neural network as a type of associative memory will be introduced in this paper through the problem of mobile position estimation where mobile estimate its location depending on the signal strength reach to it from several around base stations where the neural network can be implemented inside the mobile. Traditional methods of time of arrival (TOA) and received signal strength (RSS) are used and compared with two analytical methods, optimal positioning method and average positioning method. The data that are used for training are ideal since they can be obtained based on geometry of CDMA cell topology. The test of the two methods TOA and RSS take many cases through a nonlinear path that MS can move through that region. The result