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

This research includes synthesis of new heterocyclic derivatives of N-benzyl-5-bromoisatin. New 1, 2, 4-triazole, oxazoline and thiazoline derivatives of [N-benzyl-5-bromo-3-(Ethyliminoacetate)-indole-2-one] (2) have been synthesized. The preparation process started by the reaction of 5-bromoisatin with sodium hydride in dimethylformamide (DMF) at 0°C, gave suspension of sodium salt of 5-bromoisatin and subsequent reaction with benzylchloride to give N-benzyl-5-bromoisatin (1). Compound (1) reacted with ethylglycinate (Schiff base) obtained the intermediate compound (2) which reacted with different reagents in two ways. The first way, compound (2) reacted with (hydrazine hydrate, semicarbazide, phenylsemicarbazide and thiosemicarbazide)

ABSTRACT : A new ligand [ 2- (3-acetylthioureido)-3-phenylpropanoic acid (APA) is synthesized by reaction of acetyl isothiocyanate with phenylalanine (1:1). It is characterized by micro elemental analysis (C.H.N.S.), FT-IR, (UV-Vis) and 1H and 13CNMR spectra. Some metals ions complexes of this ligand were prepared and characterized by FT-IR, UV-Visible spectra, conductivity measurements, magnetic susceptibility and atomic absorption. From results obtained, the following formula [M(APA)2] where M2+ = Mn, Co, Ni, Cu, Zn, Cd and Hg, the proposed molecular structure for these complexes as tetrahedral geometry, except copper complex is has square planer geometry.

This study outlines the synthesis of substituted 1,2,4-triazole derivatives through the cyclization reaction of thiourea derivatives. The process begins with the reaction of different halides with KSCN to produce isothiocyanate derivatives. then followed by a reaction with isonicotinic acid hydrazide to yield thioureas (1-6), with a yield rate of (72-88%). Then, compounds (1-6) were treated with alkaline medium 4 N (NaOH) to produced 1,2,4-triazole derivatives (7-12) with a yield (51-69%).The structure of the prepared compounds was characterized using FTIR,1HNMR and 13CNMR spectroscopy. Some of the synthesized compounds were tested for antimicrobial activity when, compound 9 showed strong activity against gram positive bacteria (Sta

New Fourteen compounds were synthesized in four steps. The first step included synthesis of 2-biphenyl fused ring of imidazo(1,2- a)pyrimidine from the reaction of 2-aminopyrimidine and biphenyl phenacyl bromide . The second step was introduced aldehyde group from the reaction of 2-biphenyl fused rings of imidazo(1,2-a)pyrimidine with POCl3 in presence of DMF and CHCl3. 3-Carbaladehyde derivatives of fused imidazo/pyrimidine was reacted with different aromatic amines to afford new Schiff bases. These new 3- imines derivatives was reduced by using sodiumborohydride to yield another new 3-aminomethyl-2-biphenyl imidazo (1,2-a)pyrimidine derivatives in moderate yield .Some new prepared compounds were identified by melting point, FT- IR , 13C-

In this study, synthesised new ligand: potassium 2,2'-(quinoxaline-2,3- diyl)bis(1-phenylhydrazinecarbodithioate) (L). The ligand synthesised by reacting N1,N2-dip-tolyloxalamide as the starting material with CS2 and KOH to add the CS2 group and then with phenylendiammine to achieve (L). The ligand used in the synthesis of complexes with (CoII, NiII and CdII). The new ligand and its complexes characterised by FT-IR, UV-Vis, 1H, 13C-NMR, Mass spectroscopy, and elemental analysis, in addition to the above techniques were using magnetic moment, atomic absorption, chloride content, and melting point to describe the metal complexes.

New schiff bases series (VIII) a-e and 1,3-thiazolidin-4-one derivatives (IX) a-e containing the 1,2,4-triazole and 1,3,4-thiazazole rings were synthesized and screening their biological activities. These compounds were identified via Fourier transform infrared (FT-IR) spectra, some via Proton nuclear magnetic resonance (1H-NMR) and mass spectra. The biological results indicated that all of these compounds did not reveal antibacterial effectiveness against (Escherichia coli and Klebsiella species) (G-). Some of these compounds showed moderate antibacterial activity against (Staphylococcus aureus, and Staphylococcus epidermidis) (G+), and all compounds exhibited moderate activity against Candida albicans.

A series of Schiff bases linked to phthalimidyl phenyl sulfonate moiety have been synthesized via multistep synthesis. The first step involved reaction of phthalic anhydride with aniline producing N-phenyl phthalamic acid which was subsequently dehydrated to the corresponding N-phenyl phthalimide via treatment with acetic anhydride and anhydrous sodium acetate. The synthesized imide was treated with chlorosulfonic acid in the third step producing 4-(N-phthalimidyl) phenyl sulfonyl chloride which was introduced in reaction with 4-hydroxy acetophenone in the fourth step producing 4-[4-(N-phthalimidyl) phenyl sulfonate] acetophenone and this in turn was introduced successfully in condensation reaction with various aromatic primary amines affor