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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
Sat Aug 16 2025
Journal Name
Journal Of Oral And Dental Research
Prevalence of Orofacial Clefts: A Retrospective Crosssectional Analysis of Gynecology and Obstetrics Hospital Records in the City of Sulaimani, Kurdistan Region of Iraq
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Publication Date
Mon Oct 01 2012
Journal Name
Al–bahith Al–a'alami
Dealing of the Providers of Sport Media Content with Crises : (The Department of Media of the Ministry of Youth and Sports a Model)
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In a report by Transparency Organization in 2010, Iraq has 200 newspapers, magazines, sixty-seven radio stations and 45 satellite TV channels. The increase in these figures is measured in days or weeks and not months and years. This fact confirms the importance of studying content providers, especially youth sports content, for two reasons: the first is that young people constitute the highest percentage in Iraqi society, with all the potential involved in shaping the future aspects; the second reason is that for years sport has become an important pillar in people's lives not only in the entertainment aspect as it was seen in the past; Rather, sport has an influential presence in politi

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Publication Date
Wed Jun 27 2018
Journal Name
Iraqi Journal Of Science
Finite strain of the Tertiary rocks and their relation to tectonic deformation at Al-Tib Anticline in Missan governorate, Southeastern part of Iraq
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Publication Date
Thu Mar 01 2018
Journal Name
International Journal Of Science And Nature
EXPERIMENTAL AND THEORETICAL STUDY OF 3-BENZYL -2- MERCAPTOQUINOIZOLINE-4(3H)-ONE (BMQ) AS AN INHIBITOR OF CARBON STEEL CORROSION IN ACIDIC MEDIA
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The inhibition of 3-Benzyl -2-mercaptoquinoizoline -4 (3H)-one (BMQ) on the corrosion of carbon steel in 0.5 M HCl studied by potentionstat polarization methods at 303–333 K. Results obtained show that BMQ act as inhibitor for carbon steel in HCl solution. The inhibition efficiency increase with increase in BMQ concentration. Activation parameters and Gibbs free energy for the adsorption process using Statistical Physics calculated and discussed. Quantum chemical calculations using DFT at the B3LYP/6-31G level of theory were used to calculate some electronic properties of the molecule to verify any correlation between the inhibitive effect and molecular structure of BMQ. The quantum calculations were proceeded to get data around correlati

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Publication Date
Sat Aug 16 2025
Journal Name
Journal Of Baghdad College Of Dentistry
The effect of the addition of silanized Nano titania fillers on some physical and mechanical properties of heat cured acrylic denture base materials
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Background: Polymethyl methacrylate (PMMA) is the most commonly used material in denture fabrication. The material is far from ideal in fulfilling the mechanical requirement. The purpose of this study was to evaluate the effect of addition of 3% wt of treated (silanized) Titanium oxide Nano filler on some physical and mechanical properties of heat cured acrylic denture base material. Materials and methods: 100 specimens were constructed, 50 specimens were prepared from heat cure PMMA without additives (control) and 50 specimens were prepared from heat cure PMMA with the addition of TiO2 Nano fillers. Each group was divided into 5 sub groups according to the test performed which was mixed by probe ultra-sonication machine. Results: A highly

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Publication Date
Wed Jan 01 2020
Journal Name
Annals Of Tropical Medicine And Public Health
EFFECT OF EUCALYPTUS AND MYRTUS EXTRACTS IDENTIFICATION BY GAS CHROMATOGRAPHY-MASS SPECTROMETRY ON SOME SPECIES OF CANDIDA AS A MODEL OF MEDICAL PLANTS
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Publication Date
Tue Sep 28 2021
Journal Name
Journal Of The College Of Education For Women
An Estimated Answer of a Condition between the Interpretive Structure and Surface Structure: Al-Qurtubi’s Tafseer as a Model: عمر عقلة خليف الدعجة
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This present work is concerned with one of the syntactic issues that has been researched by many linguists, grammarians, and specialists in Islamic studies, the estimated answer to a condition. However, this topic is researched this time by examining Imam Al-Qurtbi’s opinions in interpreting related ayas from the holly Quraan in his book (Collector of Quranic Rules) or its transliteration (Al-Jami’ Li Ahkam Al-Quran). Such a step involves commenting on, tracking what Al-Qurtbi said in this regard, discussing it from the points of view of other grammarians, and judging  it accordingly, taking into account the apparent surface structures of the examples collected. To achieve this objective, the inductive analytical approach has be

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Publication Date
Sun Dec 27 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Analysis of factors affecting the desire of the customer and their impact on the market share in a competitive market National Insurance Company
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The research aims to identify the factors affecting the customer and their impact desire for market share in a competitive market National Insurance Company, where he was after the tremendous developments that have taken place in the insurance sector, crowded markets, private companies and the intensified competition among those companies on one side and public sector companies, including national insurance company on the other hand, increased attention and study in a big way the customer and the factors influencing the desire. As the national insurance company ascertains its targets once the sale of insurance documents only, but by knowing the tendencies and aspirations of current and prospective customers a way that helps to strengthen

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Publication Date
Mon Aug 01 2016
Journal Name
Iosr Journal Of Dental And Medical Sciences
Evaluating the Effect of Showing the Dental Injector to Children on Their Dental Behavior in Relation to the Vital Signs And Maternal Anxiety
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Publication Date
Sat Aug 16 2025
Journal Name
Journal Of Baghdad College Of Dentistry
Prevalence and severity of molar-incisor hypomineralisation with relation to its etiological factors among school children 7- 9 years of Al-Najaf governorate
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Background: Molar Incisor hypomineralisation (MIH) is one of the biggest challenges with great clinical interest. Currently, the etiology of MIH remains unclear. There is no previous study concerning school children aged 7 – 9 years in Al-Najaf governorate in order to estimate the prevalence and severity of molar incisor hypomineralisation and the possible associated risk factors. This study aimed to estimate the prevalence, severity and the possible associated etiological factors of molar incisor hypomineralisation and also to study the correlation between body mass index and molar incisor hypomineralisation. Material and Methods: Across sectional study conducted at Al-Najaf Governorate. A total of 600 children were enrolled those

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