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

Background: The desire for an attractive appearing fixed orthodontic appliance fueled the use of ceramic brackets and clear accessories. Elastics are one of the most versatile materials available to orthodontists so studying their effect on the esthetic appearance is important. This an in vivo study, conducted to evaluate the effect of exposing stretched clear elastomeric ligatures to the oral environment from four different companies (OrthoTechnology, Morelli, Ortho Organizer, and Ormco). Materials and Methods: A total of 240 elastomeric modules were examined, 60 modules from each brand. Each of the 60 patients enrolled in the study, received 4 elastomeric modules on the 4 lower incisors, one from each brand. The specimens were placed on t

Background: The Initial (primary) stability is one of the factors that play an important role in the success of the dental implants. The purpose of this study was to evaluate the initial stability of dental implant with horizontal plate by using five analytical tests: insertion torque, removal torque, resonance frequency analysis, push-in test and pull-out test. Materials and methods: Two different lengths of dental implants (5mm and 10mm) were tested in this study; each dental implant was 4mm in diameter with a square threads shape of 1mm pitch and 0.5mm depth. The crestal area was 4.2mm diameter contained a right angle margin circumferential ring while the apical area was tapered with two self-tapping grooves. In this study, the initial s

Abstract: -
The concept of joint integration of important concepts in macroeconomic application, the idea of ​​cointegration is due to the Granger (1981), and he explained it in detail in Granger and Engle in Econometrica (1987). The introduction of the joint analysis of integration in econometrics in the mid-eighties of the last century, is one of the most important developments in the experimental method for modeling, and the advantage is simply the account and use it only needs to familiarize them selves with ordinary least squares.

Cointegration seen relations equilibrium time series in the long run, even if it contained all the sequences on t

Static Synchronous Series Compensator (SSSC) is a well known device for effectively regulating the active power flow in a power system. In this paper, the SSSC linearized power flow equations are incorporated into Newton-Raphson algorithm in a MATLAB written program to investigate the control of active poweer flow and the transient stability of a five bus and a thirty bus IEEE test systems, during abnormal conduction (three phase fault near buses). A comparison of the results obtained for the base case without SSSC and with it to investigate the effectiveness of the device on both of the active power flow and the transient stability.

Solar energy usage in Iraq is facing many issues; one of those is the accumulation “of the dust on the surface of the solar module which” would highly lower its efficiency. The present work study the effect of dust accumulation” on installing fixed solar modules with different inclined angles 15^o, 33^o, 45^o, 60^o. Evaluation of the solar modules performance under different circumstance conditions such as rain, wind and humidity are considered in study of dust effect on solar module performance. The results show that the lowest output average efficiencies of solar modules occurs at 15^o horizontally inclined angle are 7.4% , 6.7% , 8.0% , 8.1%, and 8.4% for the cor

Many countries are very important in their interest not only in diversifying foreign reserves, but in determining and planning their volume in accordance with the goals set, namely facing potential external shocks, as the research aims to determine the extent of the strength of foreign reserves in the possession of the Central Bank in relation to every influential variable in the Iraqi economy. , in order to determine the minimum level of reserves that requires reconsideration of the exchange rate, as the research adopted the inductive analytical method in analyzing real (Quantitative data) for the research variables in the years of study, as the research adopted a set of analytical indicators approved by the International Moneta

The research aims to measure the impact of positive and negative fiscal policy shocks on monetary stability in Iraq, which represents monetary stability as an indicator of real and price stability. Fiscal policy shocks are quantitative changes in public spending and public revenue affecting the output and price cycle, and fiscal policy despite the accompanying time gaps, but it remains a policy Influential and has a significant degree of impact on economic growth and development in developing countries. The fiscal policy represents a numerical translation of the economic and social objectives planned in the state's general budget tool consistent with the GDP cycle. The economic and social goals stem from the core of the functions and the ma