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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
Sun Sep 08 2024
Journal Name
Journal Of Ecohumanism
Academic Problems Among Iraqi University Professors: An Analytical Study
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The research aims to detect the problems of educational reality faced by university professors and identify statistically significant differences in the academic problems of university instructors. It has adopted an analytical descriptive research approach to achieve research objectives and identifies the study community with professors of public and private universities. A random sample of 250 instructors was selected for the purpose of applying the questionnaire to them, knowing the academic problems encountered in the course of their work at universities, and adopting appropriate statistical means to process and analyze the data. The research concluded with a set of results, including that all fields (infrastructure, admission of

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Publication Date
Fri Sep 24 2021
Journal Name
Proceedings Of Sixth International Congress On Information And Communication Technology
Minimizing Costs of Transportation Problems Using the Genetic Algorithm
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Publication Date
Sun Dec 02 2012
Journal Name
Baghdad Science Journal
Numerical Approach of Linear Volterra Integro-Differential Equations Using Generalized Spline Functions
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This paper is dealing with non-polynomial spline functions "generalized spline" to find the approximate solution of linear Volterra integro-differential equations of the second kind and extension of this work to solve system of linear Volterra integro-differential equations. The performance of generalized spline functions are illustrated in test examples

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
Solution of Second Kind Volterra Integral Equations Using Non-Polynomial Spline Functions
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In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

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Publication Date
Thu May 30 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Analytical approximate solutions of random integro differential equations with laplace decomposition method
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An efficient combination of Adomian Decomposition iterative technique coupled with Laplace transformation to solve non-linear Random Integro differential equation (NRIDE) is introduced in a novel way to get an accurate analytical solution. This technique is an elegant combination of theLaplace transform, and the Adomian polynomial. The suggested method will convert differential equations into iterative algebraic equations, thus reducing processing and analytical work. The technique solves the problem of calculating the Adomian polynomials. The method’s efficiency was investigated using some numerical instances, and the findings demonstrate that it is easier to use than many other numerical procedures. It has also been established that (LT

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Publication Date
Thu Sep 01 2011
Journal Name
Journal Of Economics And Administrative Sciences
A practical study of the problems of queues for vehicles in some filling stations in the city of Baghdad
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 According to the circumstances experienced by our country which led to Occurrence of many crises that are the most important crisis is gaining fuel therefore , the theory of queue ( waiting line ) had been used to solve this crisis and as the relevance of this issue indirect and essential role in daily life  .

This research aims to conduct a study of the distribution of gasoline station in (both sides AL – kharkh and AL Rusafa, for the purpose of reducing wasting time and services time through the criteria of the theory of queues and work to improve the efficiency of these stations by the other hand. we are working to reduce the cost of station and increase profits by reducing the active serv

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Publication Date
Thu Dec 30 2010
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
THE USE of DIRECT SOLAR ENERGY in ABSORPTION REFREGERATION EMPLOYING NH3 – H2O SYSTEM
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This work was conducted to study the coefficient of performance for solar absorption refrigeration by using direct solar energy using aqueous ammonia 0.45 mass fraction (ammonia – water).The experiments were carried out in solar absorption system .The system consisted of solar collector generator (0.25 m × 0.25 m × 0.04m) and condenser cooled by a water bath followed by liquid receiver and evaporator. The results showed that the maximum generator temperature was (92° - 97°) during June 2009, and the minimum evaporator temperature was (5°C - 10°C) for aqua ammonia system.. It was, also, found that the coefficient of performance, cooling ratio and amount of cooling obtainable increased with increasing maximum generator temperature

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Publication Date
Wed Sep 01 2021
Journal Name
Review Of International Geographical Education
A New Approach in Determining the Criteria of Equations for Morphometric Characteristics of River Basins - Applied Morphometric Study of The Mamaran Basin
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This study aimed at some of the criteria used to determine the form of the river basins, and exposed the need to modify some of its limitations. In which, the generalization of the elongation and roundness ratio coefficient criterion was modified, which was set in a range between (0-1). This range goes beyond determining the form of the basin, which gives it an elongated or rounded feature, and the ratio has been modified by making it more detailed and accurate in giving the basin a specific form, not only a general characteristic. So, we reached a standard for each of the basins' forms regarding the results of the elongation and circularity ratios. Thus, circular is (1-0.8), and square is (between 0.8-0.6), the blade or oval form is (0.6-0

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Publication Date
Thu Sep 01 2016
Journal Name
Revista Brasileira De Zootecnia
Effect of using insect larvae meal as a complete protein source on quality and productivity characteristics of laying hens
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Publication Date
Mon Oct 17 2016
Journal Name
Proceedings Of The Institution Of Mechanical Engineers, Part B: Journal Of Engineering Manufacture
Development and control of shaped metal deposition process using tungsten inert gas arc heat source in additive layered manufacturing
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Tungsten inert gas arc welding–based shaped metal deposition is a novel additive manufacturing technology which can be used for fabricating solid dense parts by melting a cold wire on a substrate in a layer-by-layer manner via continuous DC arc heat. The shaped metal deposition method would be an alternative way to traditional manufacturing methods, especially for complex featured and large-scale solid parts manufacturing, and it is particularly used for aerospace structural components, manufacturing, and repairing of die/molds and middle-sized dense parts. This article presents the designing, constructing, and controlling of an additive manufacturing system using tungsten inert gas plus wire–based shaped metal deposition metho

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