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

Synthesis three organic inhibitors for carbon steel corrosion: 2-(propylthio)-1H-benzo[d]imidazole (PTBI), 2-(allylthio)- 1H-benzo[d]imidazole (ATBI) and 2-(prop-2-ynylthio)-1H-benzo[d]imidazole (YTBI) were prepared from reaction of 2-mercapto benzimidazole with different alkyl halide. The melting point and TLC were used to confirm the purity of the inhibitors as well as using the [FTIR, 1H-NMR and 13C-NMR] for the identify structures. The synthesized inhibitors were examined by potentiostatic polarization measurement as corrosion inhibitors of carbon steel in acidic media [1M H2SO4 ].The polarization measurement results showed that the mixed type inhibitors. In addition, the efficiency of inhibitors (YTBI) were studied at different con

         Allopurinol derivative were prepared by reacting the (1-chloroacetyl)-2-Hydropyrazolo{3,4-d}pyrimidine-4-oneiwith 5- methoxy- 2-aminoibenzothiazoleiunder certain conditions to obtain new compound  ( N- (2-aminoacetyl (5-methoxy) benzothiazole -2yl) (A₄), Reaction of 5-(P-dimethyl amine benzene)-2-amino-1,3,4- oxadiazole in the presence of potassium carbonate anhydrous to yield new  compound (N-(2- aminoacetyl-5-(P-dimethyl amine benzene )-1,3,4-oxadiazoles-2-yl)(A₃₀) and Azo compound (N-(5-(Azo-2-hydroxy-5-amino benzene)-1,3-Diazol-2yl)Allopurinol(A₄₆). The structure of prepared compounds were confirmed by (FT-IR)

Chromene is considered a fused pyran ring with a benzene ring, which is found in many plants and is part of many important compounds such as anthocyanidins, anthocyanins, catechins, and flavanones. These compounds are included under the headings "flavonoids" and "isoflavonoids." These compounds are well known as bioactive molecules with wide medicinal uses. According to these pharmacokinetic characteristics, many researchers are giving more attention to this type of compound and its derivatives. Many chromene derivatives have been synthesized to study their biological effects for the treatment of many diseases. Furthermore, the researcher displayed wide interest in finding new methods for synthesizing chromene derivatives. These met

Many previous investigations have found quercetin to be a powerful antioxidant and antitumor flavonoid, but its poor bioavailability has limited its use. This current study investigated the effects of two newly synthesized Quercetin Schiff bases containing 2-amino thiadiazole-5-thiol (Q1), and its benzyl derivatives (Q2) on MCF-7 human breast cancer cells. Cell viability and apoptosis were assessed to determine the toxic effects of Q1 and Q2. Cytotoxicity valuation showed that both compounds inhibited MCF-7 cell growth, and lactate dehydrogenase (LDH) activity increased in a dose-dependent aspect compared to the control group. Comet assay results observed that Q1 and Q2 induce more serious DNA damage than the control (untreated cell

A numerical simulation is made on the thermal lensing effect in an laser diode end-pumped Nd:YAG laser rod. Based on finite element method (FEM), the laser rod temperature distribution is calculated and the focal length is deduced for a Gaussian and super-Gaussian pump beam profiles.

At the pump power of 20W, the highest temperature located at the center of end-pumped face was 345K, and the thermal lens focal length was 81.4mm along the x-z axis. 

The results indicate that the thermal lensing effect sensitively depend on the pump power, waist radius of the pump beam and the pump distribution in a laser rod geometry.

Background: Change in palatal vault shape and Reinforcement of high impact acrylic denture base resin may in turn affect the dimensional accuracy of acrylic resin and affecting the fitness of the denture.This study evaluated tostudy the effect of fiber reinforcement for high-impact acrylic resin denture base with different palatal vault shapes on adaptation or gap space between the denture base and the stone cast and compare with non-fiber reinforcement and effect of palatal vault shapes on adaptation of non-reinforced and fiber reinforced high impact denture base acrylic resin Material and method: Three different palatal vault shapes were prepared on standard casts using CNC (computer numerical control) machine. 60 samples of heat polymeri

Streamlined peristaltic transport patterns, bifurcations of equilibrium points, and effects of an inclined magnetic field and channel are shown in this study. The incompressible fluid has been the subject of the model's investigation. The Reynolds values for evanescence and an infinite wavelength are used to constrain the flow while it is being studied in a slanted channel with a slanted magnetic field. The topologies over their domestic and cosmopolitan bifurcations are investigated for the outcomes, and notion of the dynamical system are employed. The Mathematica software is used to solve the nonlinear autonomous system. The flow is found to have three different flow distributions namely augmented, trapping and backward flow. Outc

In the present study, magnet silica-coated Ag2WO4/Ag2S nanocomposites (FOSOAWAS) were fabricated via a multistep method to address the drawbacks related to single photocatalysts (pure Ag2WO4 and pure Ag2S) and to clarify the significant influence of semiconductor heterojunction on the enhancement of visible-light-driven organic degradation. Different techniques were performed to investigate the elemental composition, morphology, magnetic and photoelectrochemical properties of the fabricated FOSOAWAS photocatalyst. The FOSOAWAS photocatalyst (1 g/L) exhibited excellent photodegradation efficiency (99.5%) against Congo red dye (CR = 20 ppm) after 140 min of visible-light illumination. This result confirmed the ability of the heterojunction be