Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

A variety of liquid crystals comprising heterocyclics 1,3,4-oxadiazol ring [III], aminooxazol [IV]a, and aminothiazol [IV]b were synthesized through a number of steps, beginning of the reaction of 3, 3'- dimethyl - [1, 1'-biphenyl] -4, 4'- diamin, ethyl monochloroacetate and sodium acetate to synthesize diacetate compound[I]. The diester reacted with hydrazine hydrate(N2H4-H2O) to give dihydrazide compound [II], then reacted with Pyruvic acid and phosphorous oxychloride to produce diketone compound [III]. The last compound was reacted with urea and thiourea to give aminooxazol and aminothiazol respectively. The synthesized compounds actually characterized and determined the structures by melting points, FT-IR and 1H-NMR spectroscopies. By u

This paper presents a new Azo dye that was prepared from the reaction of the Benzene-1,2-diamine and 1-(2,4,6-Trihydroxy-phenyl)-ethanone, Azo dye was used to prepare a new series of complexes with general formula: [Co2(H4L) Cl2(H2O)4] and [M2(H4L)Cl4(H2O)2] (M= Cr+3, Fe+3,Rh+3 and Ru+3). The prepared materials were different measurements including to infrared, ultraviolet-visible, and mass spectrometry, as well as thermo gravimetric analysis, differential calorimetry, and elemental analysis. Conductivity, magnetic susceptibility, metal content, and chlorine content of the complexes were also assessed. The complexes prepared from the dye were used to determine their ability to inhibit free radicals by measuring their antioxidant capacity us

This research discloses the synthesis of various polyester resins, the polyesters containing homoring aromatic and others heterocyclic were synthesized by the condensation polymerization of suitable monomers (which are containing variety function groups in different structures) with phthalic anhydride. The main objective is synthesis of new polyester with keeping a reasonable electrical insulating behavior. The structural of polymer was characterized by Fourier Transform infra-red spectroscopy FTIR and HNMR. The dielectric constant (real ε' and imaginary parts ε") and AC conductivity (σAC) for all the polyester samples are studied by varying the frequency (30, 50, 70, 90, 120, 300, 500Hz and 1KHZ) at 25⁰ C. Indeed, study of the electri

A new two series of liquid crystalline Schiff bases containing thiazole moiety with different length of alkoxy spacer were synthesized, and the relation between the spacer length and the liquid crystalline behavior was investigated. The molecular structures of these compounds were performed by elemental analysis and FTIR, 1HNMR spectroscopy. The liquid crystalline properties were examined by hot stage optical polarizing microscopy (OPM) and differential scanning calorimetry (DSC). All compouns of the two series display liquid crystalline nematic mesophase. The liquid crystalline behaviour has been analyzed in terms of structural property relationship

The development of new cephalosporins with improved activity against resistant microbes, such as, MRSA (methicillin resistant Staph. aureus), P. aeruginosa, is of high potential. Chemical synthesis of two new series of thiadiazole linked to cysteine (series 1) and cephalosporins containing thiadiazole linked to cysteine through disulfide bond (series 2) were achieved. The chemical structures of the synthesized compounds were confirmed using spectral (FT-IR, ¹H-NMR) and elemental microanalysis. The incorporation of privileged chemical moieties, such as, thiadiazole, Schiff base, cysteine and sulfonamide, has been found to have great contribution to the antimicrobial activities. Compounds of series 1 (1

A series of benzohydrazide derivatives attached to coumarin moiety at position 6 and 7 have been synthesized. The reaction of coumarin derivatives (coumarin I and II) with p-nitrophenyl hydrazine yield Schiff bases (compound1a and IIa_).These Schiff bases were refluxed with benzoyl chloride to give benzohydrazide derivatives of coumarin substituted at its 6 or 7 nucleus position (Ia₁ and IIa₁).The reaction and the purity of the products were checked by thin layer chromatography (TLC). The structures of the final compounds  and  their intermediates were confirmed by their melting points, infra red spectroscopy, and elemental microanalysis(CHN).

Compounds (Ia1 and IIa1) were evaluated for&n

In this work, novel compounds of hydrazones derived from (2,4-dinitrophenyl) hydrazine were synthesized. Benzamides derivatives and sulfonamides derivatives were prepared from p-amino benzaldehyde. Then these compounds were condensed with (2,4-dinitrophenyl) hydrazine through Imine bond formation to give hydrazones compounds. The compounds were characterized using FT-IR (IR Affinity-1) spectrometer, and 1HNMR analyses. The majority of the compounds have a moderate antimicrobial activity against “Gram-positive bacteria staphylococcus Aureus, and staphylococcus epidermidis, Gram-negative bacteria Escherichia coli, and Klebsiella pneumoniae, and fungi species Candida albicans” using concentrations of 250 µg\ml.