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 the Lyapunov methods are applied. There has to find a positive definite Lyapunov function, and its derivative function has to be negative definite. A new approach had been tested in several …
Gross domestic product (GDP) is an important measure of the size of the economy's production. Economists use this term to determine the extent of decline and growth in the economies of countries. It is also used to determine the order of countries and compare them to each other. The research aims at describing and analyzing the GDP during the period from 1980 to 2015 and for the public and private sectors and then forecasting GDP in subsequent years until 2025. To achieve this goal, two methods were used: linear and nonlinear regression. The second method in the time series analysis of the Box-Jenkins models and the using of statistical package (Minitab17), (GRETLW32)) to extract the results, and then comparing the two methods, T
... Show MoreThe current study examined the effect of different sample sizes to detect the Item differential functioning (DIF). The study has used three different sizes of the samples (300, 500, 1000), as well as to test a component of twenty polytomous items, where each item has five categories. They were used Graded Response Model as a single polytomous item response theory model to estimate items and individuals’ parameters. The study has used the Mantel-Haenszel (MH) way to detect (DIF) through each case for the different samples. The results of the study showed the inverse relationship between the sample size and the number of items, which showed a differential performer.
Reservoir quality assessment is important for detecting hydrocarbon-bearing zones and guiding future enhancement strategies. This study presents a detailed petrophysical evaluation of the Mishrif Formation in the Buzurgan Oilfield, which was selected due to its strategic value through its significant remaining reserves which making it an ideal candidate for advanced evaluation techniques. This study aims for shale content, porosity, permeability, water saturation, net to gross, and lithology determination. Well log and core data were used together to establish accurate property estimations. Permeability prediction through conventional methods, like core permeability-porosity correlations, was highly dispersive due to the heterogenei
... Show MoreThe objective of this study was to investigate and compare among five different methods of contraception including combined oral contraceptive pills (COC), Depot medroxyprogesterone acetate (DMPA), copper Intrauterine contraceptive device (IUCD), vaginal spermicides and male condom used in Hawler City through estimate of their effect, relative failure rate, percentage of use, adherence and compliance and adverse effects of each contraceptive method. In order to reach to these aims, a retrospective study was conducted in Hawler City in Azadi Health Care Center over a period of 6 months from 22th November, 2010 to 15th May, 2011 during which data collection and subjects follow up for 3 months had been achieved. A conv
... Show MoreThe importance of vibrations in rotating rotors in engineering applications has been examined, as has the best approach to interpreting vibration data. The most extensively used analytical approaches for rotating shaft vibration analysis have been investigated. In this research, a detailed study was made of the Rayleigh and Dunkerley methods due to their importance in the special calculations to find the amplitude of vibrations in the rotation system. The multi-node method was used to calculate both Dunkerley's and Rayleigh's methods. An experimental platform was built to study the vibrations that occur in the rotating shafts, and the results were compared with theoretical calculations and with different distances of the bearings. It pro
... Show MoreThe current research aims to identify the effect of the learning mastery strategy using interactive learning as a therapeutic method on the achievement of secondary school students in mathematics. To achieve the research objective, the researcher selected second-grade middle school students at Al-Haybah Intermediate School for Boys and determined his research sample, which consisted of (77) students distributed into two sections: Section (A) the experimental group, with (38) students, and Section (B) the control group, with (39) students. The statistical equivalence of the two research sample groups was confirmed in the variables (intelligence test, previous achievement, and previous knowledge test). The researchers chose the par
... Show MoreThe map of permeability distribution in the reservoirs is considered one of the most essential steps of the geologic model building due to its governing the fluid flow through the reservoir which makes it the most influential parameter on the history matching than other parameters. For that, it is the most petrophysical properties that are tuned during the history matching. Unfortunately, the prediction of the relationship between static petrophysics (porosity) and dynamic petrophysics (permeability) from conventional wells logs has a sophisticated problem to solve by conventional statistical methods for heterogeneous formations. For that, this paper examines the ability and performance of the artificial intelligence method in perme
... Show More