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 …
The purpose of this paper is to gain a good understanding about wake region behind the car body due to the aerodynamic effect when the air flows over the road vehicle during its movement. The main goal of this study is to discuss the effect of the geometry on the wake region and the aerodynamic drag coefficient. Results will be achieved by using two different shapes, which are the fastback and the notchback. The study will be implemented by the Computational Fluid Dynamic (CFD) by using STAR-CCM+® software for the simulation. This study investigates the steady turbulent flow using k-epsilon turbulence model. The results obtained from the simulation show that the region of the air separation behind the vehicle
... Show MoreThe majority of real-world problems involve not only finding the optimal solution, but also this solution must satisfy one or more constraints. Differential evolution (DE) algorithm with constraints handling has been proposed to solve one of the most fundamental problems in cellular network design. This proposed method has been applied to solve the radio network planning (RNP) in the forthcoming 5G Long Term Evolution (5G LTE) wireless cellular network, that satisfies both deployment cost and energy savings by reducing the number of deployed micro base stations (BSs) in an area of interest. Practically, this has been implemented using constrained strategy that must guarantee good coverage for the users as well. Three differential evolution
... Show MoreThe differential protection of power transformers appears to be more difficult than any type of protection for any other part or element in a power system. Such difficulties arise from the existence of the magnetizing inrush phenomenon. Therefore, it is necessary to recognize between inrush current and the current arise from internal faults. In this paper, two approaches based on wavelet packet transform (WPT) and S-transform (ST) are applied to recognize different types of currents following in the transformer. In WPT approach, the selection of optimal mother wavelet and the optimal number of resolution is carried out using minimum description length (MDL) criteria before taking the decision for the extraction features from the WPT tree
... Show MoreThe real and imaginary part of complex dielectric constant for InAs(001) by adsorption of oxsagen atoms has been calculated, using numerical analysis method (non-linear least square fitting). As a result a mathematical model built-up and the final result show a fairly good agreement with other genuine published works.
In this study, experimental and numerical applied of heat distribution due to pulsed Nd: YAG laser surface melting. Experimental side was consists of laser parameters are, pulse duration1.3
Numerical simulations are carried out to assess the quality of the circular and square apodize apertures in observing extrasolar planets. The logarithmic scale of the normalized point spread function of these apertures showed sharp decline in the radial frequency components reaching to 10-36 and 10-34 respectively and demonstrating promising results. This decline is associated with an increase in the full width of the point spread function. A trade off must be done between this full width and the radial frequency components to overcome the problem of imaging extrasolar planets.
This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived. In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.
Porosity is important because it reflects the presence of oil reserves. Hence, the number of underground reserves and a direct influence on the essential petrophysical parameters, such as permeability and saturation, are related to connected pores. Also, the selection of perforation interval and recommended drilling additional infill wells. For the estimation two distinct methods are used to obtain the results: the first method is based on conventional equations that utilize porosity logs. In contrast, the second approach relies on statistical methods based on making matrices dependent on rock and fluid composition and solving the equations (matrices) instantaneously. In which records have entered as equations, and the matrix is sol
... Show MoreIn this paper, An application of non-additive measures for re-evaluating the degree of importance of some student failure reasons has been discussed. We apply non-additive fuzzy integral model (Sugeno, Shilkret and Choquet) integrals for some expected factors which effect student examination performance for different students' cases.