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Direct and inverse source problems for degenerate parabolic equations
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Abstract<p>Degenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-posed identification of a space-dependent source from a time-integral observation of the weighted main dependent variable. For both, this inverse source problem as well as its corresponding direct formulation, we rigorously investigate the question of well-posedness. We also give examples of inverse problems for which sufficient conditions guaranteeing the unique solvability are fulfilled, and present the results of numerical simulations. It is hoped that the analysis initiated in this study will open up new avenues for research in the field of direct and inverse problems for degenerate parabolic equations with applications.</p>
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Publication Date
Thu Mar 12 2020
Journal Name
Al-khwarizmi Engineering Journal
Inverse Kinematics Analysis and Simulation of a 5 DOF Robotic Arm using MATLAB
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Kinematics is the mechanics branch which dealswith the movement of the bodies without taking the force into account. In robots, the forward kinematics and inverse kinematics are important in determining the position and orientation of the end-effector to perform multi-tasks. This paper presented the inverse kinematics analysis for a 5 DOF robotic arm using the robotics toolbox of MATLAB and the Denavit-Hartenberg (D-H) parameters were used to represent the links and joints of the robotic arm. A geometric approach was used in the inverse kinematics solution to determine the joints angles of the robotic arm and the path of the robotic arm was divided into successive lines to accomplish the required tasks of the robotic arm.Therefore, this

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Publication Date
Tue Sep 08 2020
Journal Name
Baghdad Science Journal
Convergence Analysis for the Homotopy Perturbation Method for a Linear System of Mixed Volterra-Fredholm Integral Equations
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           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

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Publication Date
Sun Dec 07 2014
Journal Name
Baghdad Science Journal
Convergence of the Generalized Homotopy Perturbation Method for Solving Fractional Order Integro-Differential Equations
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In this paper,the homtopy perturbation method (HPM) was applied to obtain the approximate solutions of the fractional order integro-differential equations . The fractional order derivatives and fractional order integral are described in the Caputo and Riemann-Liouville sense respectively. We can easily obtain the solution from convergent the infinite series of HPM . A theorem for convergence and error estimates of the HPM for solving fractional order integro-differential equations was given. Moreover, numerical results show that our theoretical analysis are accurate and the HPM can be considered as a powerful method for solving fractional order integro-diffrential equations.

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Publication Date
Sun Sep 07 2014
Journal Name
Baghdad Science Journal
Deriving the Composite Simpson Rule by Using Bernstein Polynomials for Solving Volterra Integral Equations
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In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.

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Publication Date
Thu Aug 31 2023
Journal Name
Journal Of Kufa For Mathematics And Computer
Four Points Block Method with Second Derivative for Solving First Order Ordinary Differential Equations
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Publication Date
Mon Mar 03 2014
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Apparent Viscosity Direct from Marsh Funnel Test
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Accurate and simple techniques for measurement of fluid rheological properties are important for field operations in the oil industry. Marsh Funnels are popular qualitycontrol tools used in the field for drilling fluids and they offer a simple, practical alternative to viscosity measurement. In the normal measurements, a single point (drainage time) is used to determine an average viscosity; little additional information is extracted regarding the non-Newtonian behavior of the fluid. Here, a new model is developed and used to determine the rheological properties of drilling muds and other non-Newtonian fluids using data of fluid density and drainage time collected from a Marsh Funnel as a function of viscosity. The funnel results for viscos

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Publication Date
Sun Mar 30 2014
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Apparent Viscosity Direct from Marsh Funnel Test
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Accurate and simple techniques for measurement of fluid rheological properties are important for field operations in the oil industry. Marsh Funnels are popular quality-control tools used in the field for drilling fluids and they offer a simple, practical alternative to viscosity measurement. In the normal measurements, a single point (drainage time) is used to determine an average viscosity; little additional information is extracted regarding the non-Newtonian behavior of the fluid.
Here, a new model is developed and used to determine the rheological properties of drilling muds and other non-Newtonian fluids using data of fluid density and drainage time collected from a Marsh Funnel as a function of viscosity. The funnel results for

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Publication Date
Tue Jul 01 2014
Journal Name
Political Sciences Journal
Foreign direct investment in Iraq and its role in economic development
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الاستثمار الاجنبي المباشر في العراق ودوره في تحقيق التنمية الاقتصادية

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Publication Date
Mon Apr 14 2014
Journal Name
Elsevier Procedia Economics And Finance
Economic Growth and Foreign Direct Investment Inflows: The Case of Qatar
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Recently, Qatar, a well-known oil production country, has been convinced as a successful case in attracting foreign direct investment (FDI) as a smaller economy. This paper aims to investigate how FDI inflows affect Qatar’s business cycles. Time series data was selected from 1990 to 2010 as available. The VAR Impulse Responses and the Granger Causality test were mainly employed by using Eviews. The derived result shows that the FDI inflows and the economic growth in Qatar interact with each other in a relatively long term.

Publication Date
Wed Jan 01 2014
Journal Name
Siam Journal On Control And Optimization
A Duality Approach for Solving Control-Constrained Linear-Quadratic Optimal Control Problems
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