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

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Heterogeneous organic compounds play an important role in our daily life as they contribute in many medical and industrial fields and are in continuous development as a result of the preparation of new derivatives with different properties. From this premise, the goal of this work appears, which is preparation of (four, five, six, and seven) membered ring systems derived from furfural, by its reaction with different aromatic aldehydes, and record their antioxidant activity by using free radical scavenging method of DPPH radicals. The new ring systems are synthesized by reacting the prepared Schiff-bases with different ring closure agents (chloroacetyl chloride, mercaptoaceticacid, anthranilic acid, and phthalic anhydride), the prep

Abstract As a part of our ongoing project on the design and synthesis of new 4-thiazolidinone derivatives with antimicrobial activity, four new 4-thiazolidinone derivatives carrying bromo, nitro, methyl, and chloro groups on the benzene ring were synthesized by starting with the 7-amino-4-methylcoumarin moiety, linking coumarin with various phenyl isothiocynate to form the thiourea group, and then cyclizing the derivatives, characterized by IR and 1HNMR, and assayed in vitro for their antimicrobial activity against Gram positive and Gram negative bacteria and fungi. Overall, 2-(4-methyl-2-oxo-2H-chromen-3-yl)-3-(4-nitrophenyl) thiazolidin-4-one to be the most powerful individuals in the series. Based on the observed data, it can be sta

Background: Contact between implant material and bones must be strong and fast creation, to fulfill these properties appropriate surface modifications must apply on used implants. In this contribution; double surface modifications are applied on Ti-6Al-4V alloy to accelerate osseointegration. Materials and methods: Anodic process is utilized to create titania nanotubes (TNTs) on the screws made from Ti-6Al-4V alloy. These implants were coated with nano ZrO2 particles. Second modification was annealing anodized screws at 8000C, and implanted in tibiae of nine adult New Zealand white rabbits. Results: Physical and histological consequences of two surface modifications on Ti-6Al-4V alloy screws were studied. Scanning electron microscope (SEM)

Bacterial infections pose an ongoing challenge due to resistance developed by infectious bacteria. So much research targeting designing new antibacterials is published annually. Our goal is to synthesize compounds that have given antibacterial activity according to molecular docking against the chosen target protein and that have acceptable ADMET properties that can be synthesized and used in the future. New 2-(5-methoxy-1-(4-chlorobenzene)-2-methyl-1H-indol-3-yl)acetohydrazide derivatives’ antibacterial efficacy against two common strains of Gram-negative and Gram-positive microorganisms has been developed, produced, and investigated. Sophisticated, modern analytical methods, including ATR-FTIR and 1H NMR spectroscopy, were used