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

In this work, the precursor [2-(1,5-dimethyl-3-oxo-2-phenyl-2,3-dihydro-1H-pyrazol-4-ylimino)acetic acid] was synthesised from 4-aminoantipyrine and glyoxylic acid, this precursor has been used in the synthesis of new multidentate ligand [2-((E)-3-(2-hydroxyphenylimino)-1,5-dimethyl-2-phenyl-2,3-dihydro-1H-pyrazol-4-ylimino)acetic acid][H2L] type (N2O2). The ligand was refluxed in ethanol with metal ions [VO(II), Mn(II), Co(II) and Ni(II)] salts to give complexes of general molecular formula:[M(H2L)2(X)(Y)].B, where: M=VO(II), X=0, Y=OSO3-2, B=2H2O; M=Mn(II),Co(II) ,X=Cl, Y=Cl, B=0; M=Ni(II), X=H2O, Y=Cl, B=Cl. These complexes were characterised by atomic absorpition(A.A), F.T-I.R., (U.V-Vis)spectroscopies (1H,13C NMR for ligand only), alon

          The use of silicon carbide is increasing significantly in the fields of research and technology. Topological indices enable data gathering on algebraic graphs and provide a mathematical framework for analyzing the chemical structural characteristics. In this paper, well-known degree-based topological indices are used to analyze the chemical structures of silicon carbides. To evaluate the features of various chemical or non-chemical networks, a variety of topological indices are defined. In this paper, a new concept related to the degree of the graph called "bi-distance" is introduced, which is used to calculate all the additive as well as multiplicative degree-based indices for the isomer of silicon carbide, Si₂

A field experiment was conducted during winter season of 2021 at a research station of college of agricultural engineering sciences, university of Baghdad to determine the response of active fertility percentage and seed yield and its components of faba bean (Vicia faba L. cv. Aguadulce) to distance between plants and spraying of nano and traditional boron. A Randomized Complete Block Design according to split-plots arrangement was used at three replicates. The main plots were three distances between plants (25, 35 and 45 cm), while the sub plots including spraying of distilled water only (control treatment), spraying of boron at a 100 mg L-1 and spraying of nano boron at two concentrations (10 and 15 mg L-1). The results showed that the 25

Background: The healing period for bone–implant contact takes 3–6 months or even longer. Application of Escherichia coli-derived recombinant human bone morphogenetic protein-2 (ErhBMP-2) to implant surfaces has been of great interest on osseointegration due to its osteoinductive potential. The objective of this study was to evaluate the effect of ErhBMP-2 on implant stability. Materials and methods: A total of 48 dental implants were inserted in 15 patients. Twenty four implants coated with 0.5 mg/ml ErhBMP-2 (study group). The other 24 implants were uncoated (control group). Each patient was received at least two dental implants at the same session. Both groups were followed with repeated implant stability measurements by me

Reduce the required time for measuring the permeability of clayey soils by using new manufactured cell

The analytic solution for the unsteady flow of generalized Oldroyd- B fluid on oscillating rectangular duct is studied. In the absence of the frequency of oscillations, we obtain the problem for the flow of generalized Oldroyd- B fluid in a duct of rectangular cross- section moving parallel to its length. The problem is solved by applying the double finite Fourier sine and discrete Laplace transforms. The solutions for the generalized Maxwell fluids and the ordinary Maxwell fluid appear as limiting cases of the solutions obtained here. Finally, the effect of material parameters on the velocity profile spotlighted by means of the graphical illustrations

The surface finish of the machining part is the mostly important characteristics of products quality and its indispensable customers’ requirement. Taguchi robust parameters designs for optimizing for surface finish in turning of 7025 AL-Alloy using carbide cutting tool has been utilized in this paper. Three machining variables namely; the machining speeds (1600, 1900, and 2200) rpm, depth of cut (0.25, 0.50, 0.75) mm and the feed rates (0.12, 0.18, 0.24) mm/min utilized in the experiments. The other variables were considered as constants. The mean surface finish was utilized as a measuring of surface quality. The results clarified that increasing the speeds reduce the surface roughness, while it rises with increasing the depths and fee