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

The objective of this investigation was to study the effects of a mixture of three arbuscular mycorrhizae (Glomus etunicatum, G. leptotichum and Rhizophagus intraradices) on the development of fusarium wilt disease in tomato plants in the presence and absence of organic matter (peatmoss). Results indicated an increase in mycorrhizal root dry weight especially in the presence of the organic matter, on the other hand this parameter was significantly decreased when Fusarium oxysporum f. sp. Lycopersiciwas added simultaneously with the mycorrhiza, Moreover, mycorrhiza and organic matter significantly reduced the damping off seedling disease, disease severity and rate of infection of tomato leaves and roots caused by the pathogenic fungus, These

    A new Schiff base complex was prepeard and characterized: Chloro –Oxo (bis(Ohydroxy benzaldehyde) O-phenylene di imination ) Vanadium (V) with general  formula (VOLCL). Complex was studied by using Three different organics Organic The photo chemistry of this  solvent with different polarity . These solvents were ( Acetone,pyridinest chloro form) . It was found that the chelate Vanadium (V) complex decomposed photochemically in these solvents during . In the tra oxidation –reduction reaction leading to free radical derived in the ligand of shiff base â„“ .Vanadium IV chelate complex . It was also found that the quantum yield of photo decomposition (Ñ„d) and Activity ratio did  not de

This study describe the effect of temperature on the optical
properties of nickel(ii) phthalocyanine tetrasulfonic acid tetrasodium
salt (NiPcTs) organic thin films which are prepared by spin coating
on indium tin oxide (ITO-glass). The optical absorption spectra of
these thin films are measured. Present studies reveal that the optical
band gap energies of NiPcTs thin films are dependent on the
annealing temperatures. The optical band gap decreases with increase
in annealing temperature, then increased when the temperature rising
to 473K. To enhance the results of Uv-Vis measurements and get
more accurate values of optical energy gaps; the Photoluminescence
spectra of as-deposited and annealed NiPcTs thin fi

In this work, the effects of solvent properties on the characteristics of absorption and fluorescence for two laser dyes was studied. Dyes used in this work include Coumarin 5400 and DCM, while the solvents include ethanol, methanol, acetone, propanol and chloroform. Coumarin 5400 dye shows sharp fluorescence peaks in the green band of visible region while the DCM dye shows relatively wide band within 590-630 nm. Therefore, the selection of any dye for random gain medium applications should be performed after determining the most appropriate solvent as the optimum fluorescence characteristics are obtained.

In the present work, leaching process studiedusing organic acids (acetic acid and lactic acid) to extract phosphate from the Iraqi Akashat phosphate ore by separation of calcareous materials (mainly calcite). This approach characterized by energy conservation, environmental enhancement by recovery of calcite as calcium sulfate (gypsum), keeping the physical and chemical properties of apatite. Samples were analyzed using X-ray diffraction and FTIR spectrophotometer. From the obtained experimental data it was found that using the two organic acids yields closed purity values of the produced apatite at the optimum conditions, while at different acid concentrations, it was found that the efficiency of acetic acid is higher at the low acid co