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

Epithelial mesenchymal transition (EMT) is a process comprising cellular and molecular events which result in cells shifting from an epithelial to a mesenchymal phenotype. Periodontitis is a destructive chronic disease of the periodontium initiated in response to a dysbiotic microbiome, and dominated by Gram-negative bacteria in the subgingival niches accompanied by an aberrant immune response in susceptible subjects. Both EMT and periodontitis share common risk factors and drivers, including Gram-negative bacteria, excess inflammatory cytokine production, smoking, oxidative stress and diabetes mellitus. In addition, periodontitis is characterized by down-regulation of key epithelial markers such as E-cadherin together with up-regulation of

A polycrystalline CdSe thin films doped with (5wt%) of Cu was fabricated using vacuum evaporation technique in the substrate temperature range(Ts=RT-250)oC on glass substrates of the thickness(0.8?m). The structure of these films are determined by X-ray diffraction (XRD). The X-ray diffraction studies shows that the structure is polycrystalline with hexagonal structure, and there are strong peaks at the direction (200) at (Ts=RT-150) oC, while at higher substrate temperature(Ts=150-250) oC the structure is single crystal. The optical properties as a function of Ts were studied. The absorption, transmission, and reflection has been studied, The optical energy gap (Eg)increases with increase of substrate temperature from (1.65

The histological structure of integument in Mastacembelus mastacembelus have been investigated from skin fragments cut from nine regions at body surface. The results revealed that the integument of the fish investigated comprises three principal layers- the epidermis, the dermis (corium) and the subcutis-All the three principal layers may further be divided into secondary layers according to the function performed by their cells. The epidermis may further divided into three layers- the outermost epithelial coverage, the middle layer and the basal layer (stratum germinatiuum)-The dermis consists of a relatively thin upper layer of loose vascular connective tissue called the stratum laxum and a thick lower compact layer- the stratum compactu

The aim of the present study was to investigate the histological structure of the tongue in Mongoose (Herpestes javanicus) and its related to the feeding pattern. Five adult animals were used in this study . The tongues were dissected and fixed in 10% formalin, then prepared by following stages (dehydration, clearing, and embedding).The serial section(5µ) were stained with(H&E) and some special stains.The histological examination showed that the tongue consists of three tunicae (mucosa, submucosa and musclaris) and the lining epithelium of the filiform papillae is composed of keratinized stratified squamous epithelial tissue. The cylindrical papillae are covered with a highly keratinized stratified squamous epithelial tissue, whereas the k

The structure is considered in its scientific formula one of the concepts which complete the architectural image that seeks to take out an effective and attractive structure in contemporary architectural production, especially that the structure -in general- represents strength in addition to delight and functional benefits according to Vitruvius trinity. So, the role of structure depends on making its aesthetical properties able to give efficiency within architectural product. That has come through adoption of intellectual mechanism of structural means and details –as a whole or parts- and focused on structure with the recipient's needs, aesthetical, and sensory purposes in addition to its fundamental role of stabilit