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

 Some metal ions (Mn+2, Co+2, Ni+2, Cu+2,Zn+2 and Cd+2) complexes of quodridentats Schiff base derived from (2-hydroxy benzaldehyde and 4,4'-methylenedianiline as primary ligand and 3-picoline (3-pic) secondary ligand  have been synthesized and characterized on the basis of their  1H ,13C-NMR, FT-IR, UV-Vis spectroscopy, conductivity measurements, elemental analysis, and magnetic moments, metal to ligands ratio in all complexes has been found to be (1:1:2) (M:Schiff base:3-pic), Schiff base behaves as neutral tetra dentate ligand with (N2,O2) system from the results obtained, the following general formula has suggested for the prepared complexes [M+2(2-mbd)(3-pic)2] and octahedral stereochemistry, Where M+2 = (Mn , Co , Ni

In this rescrch,new mixed ligand Schiff base complexes of Mn(II),Co(II),Ni(II),Cu(II), Cd(II), and Hg(II) are formulated from the Schiff base( L)resulting from  o-phathalaldehyde(o-PA) with p-nitroaniline(p-NA)as a primary ligand and anthranilic acid as a subordinate ligand. Diagnosis of prepared Ligand and its complexes is done by spectral methods mass spectrometer;1H -NMR for ligand Schiff base FTIR, UV-Vis, molar conductance, elemental microanalyses, atomic absoption and magnetic susceptibility. The analytical studies for the all new complexes have shown octahedral geometries. The study of organicperformance  of ligand Schiff base and its complexes show various activity agansit four type of bactria two gram (+) and two gram (-) .

A new series of transition metal complexes of Cu(II), Ni(II), Co(II) and Fe(III) have been synthesized from the Schiff base (L1) and (L2) derived from Semicarbazide hydro chloride and 4-chlorobenzaldehyde or 4-bromobenzaldehyde. The structural features have been arrived from their elemental analyses, magnetic susceptibility, molar conductivity, IR, UV-Vis. and 1H NMR spectral studies. The data show that the complexes have composition of [M(L)2](NO3)2 and [Fe(L)2 (NO3)2](NO3) where the M=Co(II),Ni(II) and Cu(II) ;L=L1and L2 type. The magnetic susceptibility and UV-Vis spectral data of the complexes suggest a square planer geometry for Co(II) and Cu(II) but Fe(III) octahedral geometry and Ni(II) tetrahedral geometry around the central metal i

       Synthesis and preliminary biological evaluation of imidazo (2, 1-b) Thiazole derivatives is reported. Under Mannich conditions, a series of new imidazo (2, 1-b) Thiazole derivatives were synthesized. Starting from the reaction of 2- amino thiazole with 4- bromo phenyl bromide to produce 5-(4-bromo phenyl) imidazo (2, 1-b) thiazoles, following by introduce the substituted aminomethyl at position 6-by reacting with different aromatic amines under Mannich conditions to afford 6-secondary amine-5-(4-bromo phenyl) imidazo (2,1-b) thiazole in high yields.

FT-IR, 1H NMR, and 13C NMR techniques were used to characterize the synthesized derivatives. In addition, all compounds were tested for their antioxidant activity, and thr

The New Schiff base ligand 4,4'-[(1,1'-Biphenyl)-4,4'-diyl,bis-(azo)-bis-[2-Salicylidene thiosemicarbazide](HL)(BASTSC)and its complexes with Co(II), Ni(II), and Cu(II) were prepared and characterized by elemental analysis, electronic, FTIR, magnetic susceptibility measurements. The analytical and spectral data showed, the stiochiometry of the complexes to be 1:1 (metal: ligand). FTIR spectral data showed that the ligand behaves as dibasic hexadentate molecule with (N, S, O) donor sequence towards metal ions. The octahedral geometry for Co(II), Ni(II), and Cu(II) complexes and non electrolyte behavior was suggested according to the analysis data.

Simple, economic and sensitive mathematical spectrophotometric methods were developed for the estimation 4-aminoantipyrine in presence of its acidic product. The estimation of binary mixture 4-aminoantipyrine and its acidic product was achieved by first derivative and second derivative spectrophotometric methods by applying zero-crossing at (valley 255.9nm and 234.5nm) for 4-aminoantipyrine and (peak 243.3 nm and 227.3nm) for acidic product. The value of coefficient of determination for the liner graphs were not less than 0.996 and the recovery percentage were found to be in the range from 96.555 to 102.160. Normal ratio spectrophotometric method 0DD was used 50 mg/l acidic product as a divisor and then measured at 299.9 nm with correlat

    Simple, economic and sensitive mathematical spectrophotometric methods were developed for the estimation 4-aminoantipyrine in presence of its acidic product. The estimation of binary mixture 4-aminoantipyrine and its acidic product was achieved by first derivative and second derivative spectrophotometric methods by applying zero-crossing at (valley 255.9nm and 234.5nm) for 4-aminoantipyrine and (peak 243.3 nm and 227.3nm) for acidic product. The value of  coefficient of determination  for the liner  graphs were  not less than 0.996 and the recovery percentage were found to be in the range from 96.555 to 102.160. Normal ratio spectrophotometric method 0DD was used 50 mg/l acidic product as a divisor

Calcium-Montmorillonite (bentonite) [Ca-MMT] has been prepared via cation exchange reaction using benzalkonium chloride [quaternary ammonium] as a surfactant to produce organoclay which is used to prepare polymer composites. Functionalization of this filler surface is very important factor for achieving good interaction between filler and polymer matrix. Basal spacing and functional groups identification of this organoclay were characterized using X-Ray Diffraction (XRD) and Fourier Transform Infrared (FTIR) spectroscopy respectively.  The (XRD) results showed that the basal spacing of the treated clay (organoclay) with the benzalkonium chloride increased to 15.17213 ⁰A, this represents an increment of about 77.9% in the

Some coordination complexes of Co(??), Ni(??), Cu(??), Cd(??) and Hg(??) are reacted in ethanol with Schiff base ligand derived from of 2,4,6- trihydroxybenzophenone and 3-aminophenol using microwave irradiation and then reacted with metal salts in ethanol as a solvent in 1:2 ratio (metal: ligand). The ligand [H4L] is characterized by FTIR, UV-Vis, C.H.N, 1H-NMR,13C-NMR, and mass spectra. The metal complexes are characterized by atomic absorption, infrared spectra, electronic spectra, molar conductance, (C.H.N for Ni(??) complex) and magnetic moment measurements. These measurements indicate that the ligand coordinates with metal (??) ion in a tridentate manner through the nitrogen and oxygen atoms of the ligand, octahedral structures