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 effects of size, and temperature on the linear and nonlinear optical properties in InGaN/GaN inverse parabolic and triangular quantum wells (IPQW and ITQW) for different concentrations at the well center were theoretically investigated. The indium concentrations at the barriers were fixed to be always x_max = 0.2. The energy levels and their associated wave functions are computed within the effective mass approximation. The expressions of optical properties are obtained analytically by using the compact density-matrix approach. The linear, nonlinear, and total absorption coefficients depending on the In concentrations at the well center are investigated as a function of the incident photon energy for different

The present research has investigated the effect of microwave energy on improving the flow properties of heavy crude oil. The fragmentation of crude oil molecules was carried out with and without using 1 and 10 wt. % concentration of various types of H-donors like tetralin, cyclohexane, and naphtha.  Microwave power of 320, 385, and 540 W and radiation time 1-9 min, and temperature were studied. The kinematic viscosity and asphaltene content were measured for evaluation the improving of heavy crude oil.

   Results show that viscosity of crude oil decreased with increase H-donor concentration, a maximum percentage of viscosity reduction was10.63 % for tetralin at 6 min radiation time, while 8.67%, and 7.34% for cycl

Abstract: Consumer protection in electronic contracts is of great importance in Iraqi law, as there are detailed legislations that enhance consumer rights and provide mechanisms for compensation when necessary. In Iraq, the Consumer Protection Law of 2010 regulates these rights and ensures the availability of sufficient and clear information to consumers.

This work involves theoretical and experimental studies for seven compounds to calculate the electrons spectrum and NLO properties. The theoretical study is done by employing the Time Depending Density Functional Theory TD-DFT and B3LYP/high basis set 6-311++G (2d,2p), using Gaussian program 09. Experimental study by UV/VIS spectrophotometer device to prove the theoretical study. Theoretical and experimental results were applicable in spectrum and energy gap values, in addition to convergence theoretically the energy gap results from ΔEHOMO-LUMO and UV/VIS. spectrum. Consider the theoretical method very appropriate to compounds that absorb in vacuum UV.

The nanocompsite of alumina (Al₂O₃) produced a number of beneficial effects in alloys. There is increasing in resistance of materials to surface related failures , such as the mechanical properties , fatigue and stress corrosion cracking .The experimental results observed that the adding of reinforced  nanomaterials  type Al₂O₃  enhanced the   HB hardness, UTS, 0.2 YS and ductility of 2014 Al/Al₂O₃ nano composites . the analysis of experiments, indicated that The maximum enhancement was observed at 0.4 wt.% Al₂O₃. The ultimate improvement percentage were 15.78% HB hardness, 18.1% (UTS), 12.86% (

A friction stir spot welding (FSSW) process is an emerging solid state joining process in which the material that is being welded does not melt. In this investigation an attempt has been made to understand the effect of tool shoulder diameter on the mechanical properties of the joint. For this purpose four welding tools diameter (10,13, 16 and 19) mm at constant preheating time and plunging time were used to carry
out welding process. Effect of tool diameter on mechanical properties of welded joints was investigated using shear stress test and Microhardness of joint which welded was studied. Based on the stir welding experiments conducted in this study the results show that aluminum alloy (1200) can be welded using (FSSW) process with

The aim of this paper, study the effect of carbon nanotubes on the electrical properties of polyvinylchloride. Samples of polyvinylchloride carbon nanotubes composite prepared by using hot press technique. The weight percentages of carbon nanotubes are 0,5,10 and 20wt.%. Results showed that the D.C electrical conductivity increases with increasing of the weight percentages of carbon nanotubes. Also, the D.C electrical conductivity changed with increase temperature for different concentrations of carbon nanotubes. The activation energy of D.C electrical conductivity is decreased with increasing of carbon nanotubes concentration.