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 new multidentate Schiff-base (E)-6,6′-((1E,1′E)-(ethane-1,2-diylbis(azan-1-yl-1-ylidene))bis(methan-1-yl-ylidene))bis(4-methyl-2-((E)(pyridine-2-ylmethylimino)methyl)phenol) H2L and its polymeric binuclear metal complexes with Cr(III), Mn(II), Fe(II), Co(II), Ni(II), Cu(II), Zn(II), Cd(II) and Hg(II) are reported. The reaction of 2,6-diformyl-4-methyl-phenol with ethylenediamine in mole ratios of 2:1 gave the precursor 3,3′-(1E,1′E)-(ethane-1,2-diylbis(azan-1-yl-1ylidene))bis(methan-1-yl-1-ylidene)bis(2-hydroxy-5-methylbenzaldehyde) W. Condensation of the precursor with 2-(amino-methyl)pyridine in mole ratios of 1:2 gave the new N6O2 multidentate Schiff-base ligand H2L. Upon complex formation, the ligand behaves as a dibasic oct

The present research was conducted to reduce the sulfur content of Iraqi heavy naphtha by adsorption using different metals oxides over Y-Zeolite. The Y-Zeolite was synthesized by a sol-gel technique. The average size of zeolite was 92.39 nm, surface area 558 m²/g, and pore volume 0.231 cm³/g. The metals of nickel, zinc, and copper were dispersed by an impregnation method to prepare Ni/HY, Zn/HY, Cu/HY, and Ni + Zn /HY catalysts for desulfurization. The adsorptive desulfurization was carried out in a batch mode at different operating conditions such as mixing time (10,15,30,60, and 600 min) and catalyst dosage (0.2,0.4,0.6,0.8,1, and 1.2 g). The most of the sulfur compounds were removed at 10 min for all catalyst ty

This article deals with the impact of including transverse ribs within the absorber tube of the concentrated linear Fresnel collector (CLFRC) system with a secondary compound parabolic collector (CPC) on thermal and flow performance coefficients. The enhancement rates of heat transfer due to varying governing parameters were compared and analyzed parametrically at Reynolds numbers in the range 5,000–13,000, employing water as the heat transfer fluid. Simulations were performed to solve the governing equations using the finite volume method (FVM) under various boundary conditions. For all Reynolds numbers, the average Nusselt number in the circular tube in the CLFRC system with ribs was found to be larger than that of the plain abs

Diazotization reaction between 1-(2,4,6-Trihydroxy-phenyl)-ethanone and diazonium salts was carried out resulting in ligand 4-(3-Acetyl-2,4,6-trihydroxy-phenylazo)-N-(5-methyl-isoxazol-3-yl)-benzenesulfonamide, this in turn reacted with the next metal ions (V4+ , Cr3+ , Mn2+ and Cu2+) forming stable complexes with unique geometries such as (Octahedral for both Cr3+ , Mn2+ and Cu2+ ,squar pyramidal for V4+). The creation of such complexes was detected by employing spectroscopic means involving ultraviolet-visible which proved the obtained geometries, fourier transfer proved the formation of azo group and and the coordination with metal ion through it. Pyrolysis (TGA & DSC) studies proved the coordination of water residues with me

The aim of this research is to study the effect of welded joint design (Butt joint and lap joint) on thejoint strength during tension and fatigue loading with different current of welding (40,50,60,70,80) ^per, and different type of wire welding. The result of this research is showed that the effect of fatigue loading on the type of joint is more than the effect of tension loading on it. And the butt joint welding is better than the lap joint welding during the fatigue loaded.The experimental results of the effect of W'elding current showed that more increasing and more decreasing the value of the heat input, during the welding was found to produce mechanical brittleness on the buttjoint welding during the static and dynamic loading. Also i

The aim of this study was to evaluate the effects of local application of bisphosphonate gel and recombinant human bone morphogenic protein 2 gel, on titanium dental implant stability and marginal bone level. Twenty-seven patients with upper and lower missing posterior tooth/teeth were included in the study with a total of 71 implants that were used for rehabilitation. The implants were randomly divided into 4 groups: 3 study groups and 1 control. Group1; local application of bisphosphonate gel, group 2; local application of recombinant human bone morphogenic protein 2 gel, group 3; local application of a mixed formula of both gels. The gel application was immediately preimplant insertion, group 4; implant insertion without application of a

The inelastic C2 form factors and the charge density distribution (CDD) for ^58,60,62Ni and ^64,66,68Zn nuclei has been investigated by employing the Skyrme-Hartree-Fock method with (Sk35-Skzs*) parametrization. The inelastic C2 form factor is calculated by using the shape of Tassie and Bohr-Mottelson models with appropriate proton and neutron effective charges to account for the core-polarization effects contribution. The comparison of the predicted theoretical values was conducted with the available measured data for C2 and CDD form factors and showed very good agreement.