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 the present work the clathrate hydrate dissociation enthalpies of refrigerant R134a+ water system, and R134a + water + salt system were determined. The heat of dissociation of three types of aqueous salts solutions of NaCl, KBr and NaF at three concentrations (0.09, 0.17and 0.26) mol·kg⁻¹ for each salt type, were enthalpy measured. The Clapeyron equation was used tocalculate heat of dissociation of experimental data for binary and ternary system.In order to find the effect of compressibility factor on heat dissociation enthalpy, the study was conducted by using equation of state proposed by Peng and Robinson Stryjek-Vera (PRSV). The obtained results of dissociation enthalpy for binary system were (143.8) kJ.mol^-1

The present work aimed to study the efficiency of nanofiltration (NF) and reverseosmosis (RO) process for water recovery from electroplating wastewater and study the factors affecting the performance of two membrane processes. Nanofiltration and reverse osmosismembranes are made from polyamide as spiral wound module. The inorganic materials ZnCl 2 CuCl2 .2H2O, NiCl.2.6H2O and CrCl3.6H2O were used as feed solutions. The operating parametersstudied were: operating time, feed concentrations for heavy metal ions, operating pressure, feed flow rate, feed temperature and feed pH. The experimental results showed, the permeateconcentration increased and water flux decreased with increase in time from 0 to 70 min. Thepermeate concentrations incre

  In the present work, We study the structural and optical properties of (ZnO), which are prepared by thermal evaporation technique, where deposit (Zn) on glass substrates at different thicknesses (150,250,350)nm, deposited on glass substrate at R.T. with rate (5 nm sec-1). And then we make oxidation for (Zn) films at temperature (500) and using the air for one hour, and last annealing samples at temperature (400,500) for one hour. The investigation of (XRD) indicates that the (ZnO) films are polycrystalline type of hexagonal with a preferred orientation along (002) to all samples and analysis reveals that the intensity of this orientation increases with the increase of the thickness and annealing temperature.   &nbsp

The electric quadrupole moments for some scandium isotopes (41, 43, 44, 45, 46, 47Sc) have been calculated using the shell model in the proton-neutron formalism. Excitations out of major shell model space were taken into account through a microscopic theory which is called core polarization effectives. The set of effective charges adopted in the theoretical calculations emerging about the core polarization effect. NushellX@MSU code was used to calculate one body density matrix (OBDM). The simple harmonic oscillator potential has been used to generate the single particle matrix elements. Our theoretical calculations for the quadrupole moments used the two types of effective interactions to obtain the best interaction compared with the exp

Background: Bone augmentation techniques are commonly employed in medical fields. This biomaterial system must be readily available, easily applicable by minimally-invasive technique and able to release an osteoinductive growth factor. Such a system will be able to engineer new bone formation locally at the site of injection. Hyaluronic acid has osteogenic potential that can be exploited not only for repairing bone defects but also for providing transplantable bone for the reconstruction of a variety of bone defects. The aims of this study were to evaluate the effects of Hyaluronic acid gel on bone healing by immunohistochemical estimation of transforming growth factor -beta 3 in experimental and control groups. Materials and methods: Thirt

The aim of this work is to learn the relationship of the stability of (β) emitter isobars with their shape for some isobaric elements with even mass number (A=152 - 162). To reach this goal firstly the most stable isobar have been determined by plotting mass parabola (plotting the binding energy (B.E) as a function of the atomic number (Z)) for each isobaric family. Then three-dimensional representation graphics for each nucleus in these isobaric families have been plotted to illustrate the deformation in the shape of a nucleus. These three-dimensional representation graphics prepared by calculating the values of semi-axis minor (a), major (b) and (c) ellipsoid axis’s. Our results show that the shape of nuclides which is represented the

The present work aimed to study the efficiency of nanofiltration (NF) and reverse osmosis (RO) process for water recovery from electroplating wastewater and study the factors affecting the performance of two membrane processes. Nanofiltration and reverse osmosis membranes are made from polyamide as spiral wound module. The inorganic materials ZnCl2, CuCl2.2H2O, NiCl2.6H2O and CrCl3.6H2O were used as feed solutions. The operating parameters studied were: operating time, feed concentrations for heavy metal ions, operating pressure, feed flow rate, feed temperature and feed pH. The experimental results showed, the permeate concentration increased and water flux decreased with increase in time from 0 to 70 min. The permeate concentrations incre

Iraqi oil crudes have some of the physical and chemical characteristics that distinguish it from other types of oil crudes in the world. Some of these features such us molecular composition, rheological, viscosity and emulsions are studied carefully by researchers. In this work, a comparative study of the linear and the non-linear optical properties for typical heavy and light crude oils of Iraqi origin was studied utilizing Z-scan technique. The He -Ne laser of wavelength 632.8 nm had been used for this purpose. These samples were collected from Basra and Kut oil fields. The values of the non-linear refractive index (n₂), non-linear absorption coefficient (β), and third-order electrical susceptibility (χ³) were e