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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
Mon Mar 07 2022
Journal Name
Journal Of Educational And Psychological Researches
Math Word Problems in Mathematics Books for the First Three Grads of the Basic Stage in Palestine (An analytical and Evaluative Study)
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This study aimed at revealing the degree of availability of standards of word problems in mathematics books for the first three grades of the basic stage in Palestine. For this purpose, the researcher prepared an analysis tool and a list of criteria consisting of two areas: linguistic formulation and mathematical content. Every area had seven items. The results of the study showed that the third-grade mathematics book has the highest degree of availability of the standards with 85.75%, and then came the second-grade mathematics book with 83.12%. Finally, the first-grade mathematics book came with 80.13%. In the light of the previous results, the researcher recommended to develop the language of word problems, to take into account their i

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Publication Date
Mon May 04 2009
Journal Name
Journal Of Al-nahrain University
Solution of two-dimensional fractional order volterra integro-differential equations
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In this paper, our aim is to study variational formulation and solutions of 2-dimensional integrodifferential equations of fractional order. We will give a summery of representation to the variational formulation of linear nonhomogenous 2-dimensional Volterra integro-differential equations of the second kind with fractional order. An example will be discussed and solved by using the MathCAD software package when it is needed.

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Publication Date
Sat Jul 20 2024
Journal Name
Journal Of Interdisciplinary Mathematics
Elzaki transform decomposition approach to solve Riccati matrix differential equations
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Elzaki Transform Adomian decomposition technique (ETADM), which an elegant combine, has been employed in this work to solve non-linear Riccati matrix differential equations. Solutions are presented to demonstrate the relevance of the current approach. With the use of figures, the results of the proposed strategy are displayed and evaluated. It is demonstrated that the suggested approach is effective, dependable, and simple to apply to a range of related scientific and technical problems.

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Publication Date
Sat Jul 01 2000
Journal Name
Bulletin Of The Iraq Natural History Museum (p-issn: 1017-8678 , E-issn: 2311-9799)
UTTILIZATION OF LIPIDS AS SOURCE OF ENERGY DURING HIBERNATION OF RANA RIDIBUNDA PALLAS, 1771
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The aim of this study is to calculate the ene expenditure from fatty substance contents of the
frog. Rana ridibunda during its hibernation. It was found that, almost, all frogs enter
hibernation during the last week of December and emerge from hibernation during the first
week of March. Hence, January and February are considered the hibernation period.
December is the pre-hibernation period and March is the post-hibernation period. The
reduction in percent of body lipid during the hibernation period was 4.8% in males and 7.7%
in females. The reduction in percent of lipid of fat bodies during the hibernation period was
2.758% in males and 0.733% in females.
The calorific value of R. ridibunda lipid amounted to 1233

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Publication Date
Sun Jan 01 2017
Journal Name
Ieee/acm Transactions On Audio, Speech, And Language Processing
Underdetermined Convolutive Source Separation Using GEM-MU With Variational Approximated Optimum Model Order NMF2D
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Publication Date
Wed Jul 31 2019
Journal Name
Journal Of Engineering
Evaluation of the Accuracy of Digital Elevation Model Produced from Different Open Source Data
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This study aims to estimate the accuracy of digital elevation models (DEM) which are created with exploitation of open source Google Earth data and comparing with the widely available DEM datasets, Shuttle Radar Topography Mission (SRTM), version 3, and Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model (ASTER GDEM), version 2. The GPS technique is used in this study to produce digital elevation raster with a high level of accuracy, as reference raster, compared to the DEM datasets. Baghdad University, Al Jadriya campus, is selected as a study area. Besides, 151 reference points were created within the study area to evaluate the results based on the values of RMS.Furthermore, th

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Publication Date
Mon Jan 28 2019
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
The Role of Economic Reform in attracting Direct Foreign Investment in EYGPT
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  Developing countries have depended since long time on the developed countries to increase the levels of development and improving rates of growth direction to the  best way where taking this dependence many shapes influenced by the evolution  form of international relations and this dependence shows how the great deficiencies in sources of local financing, which called  developing countries to increase their reliance on external funding sources, represented in the form of grants, subsidies, loans and foreign investment, pursuing States in that the application of economic reform policies in pursuit of faster economic growth and restructure its economy and achieve economic stability. In the early eighties of the last

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Publication Date
Fri Jan 29 2016
Journal Name
Al- Mustansiriyah J. Sci.
The Approximate Solution of Newell Whitehead Segel and Fisher Equations Using The Adomian Decomposition Method
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In the present work, we use the Adomian Decomposition method to find the approximate solution for some cases of the Newell whitehead segel nonlinear differential equation which was solved previously with exact solution by the Homotopy perturbation and the Iteration methods, then we compared the results.

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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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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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