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 …
In this study the role of remote sensing and geographic information systems in the planning of some Iraqi cities, including the city of Aziziyah in Kut / Wasit Governorate, was considered. Certain appropriate models (sprawling growth patterns) have been adopted to plan this city, and tables and a future map have been prepared to arrange this city. Land uses for public services will be proposed for adopted case(Aziziyah in Kut / Wasit Governorate). This paper describes a specific application of GIS functionalities for spatial planning analysis, examines the breadth of GIS and attempts to address the analytical part’s limitations in planning studies. The study concluded, through high-resolution visuals, to the possibility of determining th
... Show MoreThe problem of rapid population growth is one of the main problems effecting countries of the world the reason for this the growth in different environment areas of life commercial, industrial, social, food and educational. Therefore, this study was conducted on the amount of potable water consumed using two models of the two satellite and aerial images of the Kadhimiya District-block 427 and Al-Shu,laa district-block 450 in Baghdad city for available years in the Secretariat of Baghdad (2005, 2011,2013,2015). Through the characteristics of geographic information systems, which revealed the spatial patterns of urban creep by determining the role and buildings to be created, which appear in the picture for the
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In this search, we examined the factorial experiments and the study of the significance of the main effects, the interaction of the factors and their simple effects by the F test (ANOVA) for analyze the data of the factorial experience. It is also known that the analysis of variance requires several assumptions to achieve them, Therefore, in case of violation of one of these conditions we conduct a transform to the data in order to match or achieve the conditions of analysis of variance, but it was noted that these transfers do not produce accurate results, so we resort to tests or non-parametric methods that work as a solution or alternative to the parametric tests , these method
... Show MoreThis paper considers approximate solution of the hyperbolic one-dimensional wave equation with nonlocal mixed boundary conditions by improved methods based on the assumption that the solution is a double power series based on orthogonal polynomials, such as Bernstein, Legendre, and Chebyshev. The solution is ultimately compared with the original method that is based on standard polynomials by calculating the absolute error to verify the validity and accuracy of the performance.
Radiation therapy plays an important role in improving breast cancer cases, in order to obtain an appropriateestimate of radiation doses number given to the patient after tumor removal; some methods of nonparametric regression werecompared. The Kernel method was used by Nadaraya-Watson estimator to find the estimation regression function forsmoothing data based on the smoothing parameter h according to the Normal scale method (NSM), Least Squared CrossValidation method (LSCV) and Golden Rate Method (GRM). These methods were compared by simulation for samples ofthree sizes, the method (NSM) proved to be the best according to average of Mean Squares Error criterion and the method(LSCV) proved to be the best according to Average of Mean Absolu
... Show MoreThe primary objective of the current paper is to suggest and implement effective computational methods (DECMs) to calculate analytic and approximate solutions to the nonlocal one-dimensional parabolic equation which is utilized to model specific real-world applications. The powerful and elegant methods that are used orthogonal basis functions to describe the solution as a double power series have been developed, namely the Bernstein, Legendre, Chebyshev, Hermite, and Bernoulli polynomials. Hence, a specified partial differential equation is reduced to a system of linear algebraic equations that can be solved by using Mathematica®12. The techniques of effective computational methods (DECMs) have been applied to solve some s
... Show MoreThis study addresses quantum computers as one of the most significant contemporary technological transformations that promise to reshape the future of global computing. It aims to clarify the conceptual foundations of quantum computing and to identify the fundamental differences between quantum and classical computers in terms of processing mechanisms, computational speed, and the ability to solve highly complex problems. The study focuses on key concepts such as the qubit, superposition, and entanglement, highlighting their role in enabling computational capabilities that exceed the limits of classical computing. It also discusses the future applications of quantum computers in areas such as cryptography, artificial intelligence, big data
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