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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 Jul 07 2011
Journal Name
Arabian Journal Of Geosciences
Mineralogy, geochemistry, and reserve estimation of the Euphrates limestone for Portland cement industry at Al-Najaf area, South Iraq
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Publication Date
Fri Oct 24 2025
Journal Name
Al-fatih Journal
A comparative study of resistance training on land and in the aqueousTo develop some capacity for three Al Wathba
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أن التطور العلمي الحاصل فيما يخص المجال الرياضي أرسى آفاق جديدة لمواكبة التطور الكبير في مجا ل الألعاب والفعاليات الرياضية المختلفة ,و أن تحقيق النتائج الجيدة في فعاليات العاب القوى بشكل عام والثلاثية بشكل خاص في التدريب الرياضي يتطلب إتباع الأساليب العلمية الدقيقة والموضوعية بشكل سليم ومخطط له،فضلا عنة تطبيق نظريات ومنحى جديد لمواكبة الاتجاهات الحديثة في تحقيق النتائج الجيدة للوصول إلى المستويات العالية

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Publication Date
Sun Jun 05 2016
Journal Name
Baghdad Science Journal
Development of an Eco-Friendly Method for Iron Extraction and Determination in Pharmaceuticals Using Ciprofloxacin Drug as Chelating agent
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A method is developed for the determination of iron (III) in pharmaceutical preparations by coupling cloud point extraction (CPE) and UV-Vis spectrophotometry. The method is based on the reaction of Fe(III) with excess drug ciprofloxacin (CIPRO) in dilute H2SO4, forming a hydrophobic Fe(III)- CIPRO complex which can be extracted into a non-ionic surfactant Triton X-114, and iron ions are determined spectrophotometrically at absorption maximum of 437 nm. Several variables which impact on the extraction and determination of Fe (III) are optimized in order to maximize the extraction efficiency and improve the sensitivity of the method. The interferences study is also considered to check the accuracy of the procedure. The results hav

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Publication Date
Wed Jan 01 2014
Journal Name
Scienceasia
A combined compact genetic algorithm and local search method for optimizing the ARMA(1,1) model of a likelihood estimator
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In this paper, a compact genetic algorithm (CGA) is enhanced by integrating its selection strategy with a steepest descent algorithm (SDA) as a local search method to give I-CGA-SDA. This system is an attempt to avoid the large CPU time and computational complexity of the standard genetic algorithm. Here, CGA dramatically reduces the number of bits required to store the population and has a faster convergence. Consequently, this integrated system is used to optimize the maximum likelihood function lnL(φ1, θ1) of the mixed model. Simulation results based on MSE were compared with those obtained from the SDA and showed that the hybrid genetic algorithm (HGA) and I-CGA-SDA can give a good estimator of (φ1, θ1) for the ARMA(1,1) model. Anot

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Publication Date
Mon May 29 2023
Journal Name
Rawal Medical Journal
Comparative prospective study of knee pain in medial pararpatellar and transpatellar entry for interlocking nail fixation of tibia fracture
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Objective: To compare two insertion techniques of intramedullary interlocking nails (medial parapatellar versus intrapatellar insertion) in patients with tibial fractures. Methodology: This study was performed at Al-Kindy Teaching Hospital from August 2020 until March 2022. All 32 patients with tibial fractures (29 males and 3 females) were included for tibial closed nail fixation and then followed up for 6 months. We categorized these patients into two groups; Group A (16 patients), those treated by medial parapatellar insertion of an interlocking nail, and Group B (16 patients) with transpatellar tibial nail insertion. All patients were treated by the same surgical team. Results: The range of movement in two weeks (from extension

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Publication Date
Tue Dec 01 2020
Journal Name
Environmental Nanotechnology, Monitoring & Management
Sulfonated polyindole coated magnetic zincoxysulfide ([email protected]@SPID) core/shell nanocatalyst for simultaneous photocatalytic H2 production and BPA degradation
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Photocatalyst composed of core/shell magnetic zincoxysulfide nanocomposite coated with sulfonated polyindole ([email protected]/SPID) has been prepared and used for simultaneous photocatalytic H2 production and Bisphenol A (BPA) degradation. XRD, FE-SEM, EDX, BET surface area, UV-vis DRS and VSM were used to characterize the synthesized nanocomposites. The photocatalytic performance was evaluated using batch reactor under visible light irradiation. The photocatalytic activity of [email protected]/SPID nanocomposite was revealed to exceed that of [email protected] nanocomposite due to the heterojunctions between SPID and [email protected] species. The results exhibited that the effect of BPA initial concentration was found to be effectual on the improvement

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Publication Date
Mon Apr 01 2019
Journal Name
Journal Of Educational And Psychological Researches
Analysis of the Content of the Computer Textbook for the Second Intermediate Grade According to Scientific and Moral Values
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The purpose of this research is to design a list of the scientific and moral values that should be found in the content of the computer textbook for the second intermediate grade, as well as to analyze the content of the above- mentioned book by answering the following question:

 What is the percentage of availability of scientific and moral values in the content of the computer textbook for Second Intermediate grade issued by the Iraqi Ministry of Education / the general directorate of the curriculum, for the academic year (2017-2018)? 

In order to achieve the research objectives, the descriptive method (content analysis method) was adopted. The research community has been iden

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Publication Date
Sun Dec 17 2017
Journal Name
Al-khwarizmi Engineering Journal
Experimental Study Using the Passive Solar Chimney for Evaporative Cooling With PCM and CFM as a Thermal Energy Storage
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      In this work, a test room was built in Baghdad city, with (2*1.5*1.5) m3  in dimensions, while the solar chimneys (SC) were designed with aspect ratio (ar) bigger than 12. Test room was supplied by many solar collectors; vertical single side of air pass with ar equals 25, and tilted 45o double side of air passes with ar equals 50 for each pass, both collectors consist of flat thermal energy storage box collector (TESB) that covered by transparent clear acrylic sheet, third type of collector is array of evacuated tubular collectors with thermosyphon in 45o instelled  in the bottom of TESB of vertical SC. The TESB was

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Publication Date
Wed Dec 15 2021
Journal Name
Journal Of Physics: Conference Series
Pretreated Fishbone as Low Cost-Adsorbent for Cationic Dye Adsorption from Aqueous Solutions: Equilibrium, Optimization, Kinetic and Thermodynamic Study
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The present study investigated the use of pretreated fish bone (PTFB) as a new surface, natural waste and low-cost adsorbent for the adsorption of Methyl green (MG, as model toxic basic dye) from aqueous solutions. The functional groups and surface morphology of the untreated fish bone (FB) and pretreated fish bone were characterized using Fourier transform infrared (FTIR), scanning electron microscopy (SEM) and Energy dispersive X-ray spectroscopy (EDS),respectively. The effect of operating parameters including contact time, pH, adsorbent dose, temperature, and inorganic salt was evaluated. Langmuir, Freundlich and Temkin adsorption isotherm models were studied and the results showed that the adsorption of basic dye followed Freundlich iso

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Publication Date
Wed Jun 01 2022
Journal Name
Applied Energy
Novel mathematical modeling, performance analysis, and design charts for the typical hybrid photovoltaic/phase-change material (PV/PCM) system
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