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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 Dec 02 2012
Journal Name
دراسات عربية في التربية وعلم النفس
The effectiveness of environmental enrichment activities in the achievement of chemistry and environmental awareness for fifth-grade science students
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Publication Date
Wed Jan 01 2025
Journal Name
Special Topics &amp; Reviews In Porous Media: An International Journal
EXPERIMENTAL AND NUMERICAL INVESTIGATION OF A DOUBLE PASS SOLAR AIR HEATER PROVIDED WITH POROUS ABSORBER PLATE FOR DRYING APPLICATIONS
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This investigation integrates experimental and numerical approaches to study a novel solar air heater aimed at achieving an efficient design for a solar collector suitable for drying applications under the meteorological conditions of Iraq. The importance of this investigation stems from the lack of optimal exploitation of solar energy reaching the solar collector, primarily attributable to elevated thermal losses despite numerous designs employed in such solar systems. Consequently, enhancing the thermal performance of solar collectors, particularly those employed in crop drying applications, stands as a crucial focal point for researchers within this domain. Two identical double-pass solar air heaters were designed and constructed for

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Publication Date
Sun Mar 12 2023
Journal Name
Egyptian Journal Of Chemistry
Studying the Molecular Interactions for Potash Alum with Distilled Water and Aqueous Solution of Ethylene Glycol at Different Temperatures.
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Publication Date
Wed Aug 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Measurement of Government Debt Indicators and the most Its important Effects in Iraq for The period of 1990 – 2013
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Indicators of government debt is of extreme importanse in economic activity through knowledge of the economic impact of government debt, if the phenomenon is accepted or prepared to dangerous stage by stage, and there fore it can Through these indicators to measure the degree of indebtedness in relation to the economic activity of the Government on the one hand, the governments  ability to repay  the other hand.

      Due to this it inferred that the degree of indebtedness in Iraq  specificratio has exceed 60% during the period 1990 – 2002 ntejh lack of political and economic stability of the government, which led to the governments  inability to repay the ma

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Publication Date
Wed Nov 21 2018
Journal Name
International Journal Of Control, Automation And Systems
Design and Stability Analysis of a Fractional Order State Feedback Controller for Trajectory Tracking of a Differential Drive Robot
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Publication Date
Wed Mar 01 2023
Journal Name
Journal Of Applied Spectroscopy
Spectrophotometric Method for the Determination of Naphazoline Nitrate in Bulk and Pharmaceutical Preparations by Using 1,2-Naphthoquinone-4-Sulfonate
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A simple, accurate, and cost-efficient UV-Visible spectrophotometric method has been developed for the determination of naphazoline nitrate (NPZ) in pure and pharmaceutical formulations. The suggested method was based on the nucleophilic substitution reaction of NPZ with 1,2-naphthoquinone-4-sulfonate sodium salt in alkaline medium at 80°C to form an orange/red-colored product of maximum absorption (λmax) at 483 nm. The stoichiometry of the reaction was determined via Job's method and limiting logarithmic method, and the mechanism of the reaction was postulated. Under the optimal conditions of the reaction, Beerʼs law was obeyed within the concentration range 0.5–50 μg/mL, the molar absorptivity value (ε) was 5766.5 L × mol–1 × c

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Publication Date
Mon Feb 06 2023
Journal Name
Journal Of The College Of Basic Education
Synthesis and Characterization of some biologically active transition metal complexes for a ligand derived from dimedone with mixed ligands.
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The aim of the work is synthesis and characterization of bidentate ligand [3-(3-acetylphenylamino)-5,5-dimethylcyclohex-3-enone][HL], from the reaction of dimedone with 3-amino acetophenone to produce the ligand [HL], the reaction was carried out in dry benzene as a solvent under reflux. The prepared ligand [HL] was characterized by FT-IR, UV-Vis spectroscopy, 'H, 8C-NMR spectra, Mass spectra, (C.H.N) and melting point. The mixed ligand complexes were prepared from ligand [HL] was used as a primary ligand while 8-hydroxy quinoline [HQ] was used as a secondary ligand with metal ion M(IT).Where M(IT) = (Mn ,Co ,Ni ,Cu ,Zn ,Cd and Pd) at reflux ,using ethanol as a solvent, KOH as a

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Publication Date
Fri Mar 01 2019
Journal Name
Studia Ubb Chemia,
EXCESS AND DEVIATIONS PROPERTIES FOR THE BINARY SOLVENT MIXTURES OF TETRAHYDROFURFURYL ALCOHOL WITH SOME AROMATIC HYDROCARBONS AT 298.15 K.
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In this work, excess properties (eg excess molar volume (VE), excess viscosity (ȠE), excess Gibbs free energy of activation of viscos flow (ΔG* E) and molar refraction changes (ΔnD) of binary solvent mixtures of tetrahydrofurfuryl alcohol (THFA) with aromatic hydrocarbons (benzene, toluene and p-xylene) have been calculated. This was achieved by determining the physical properties including density ρ, viscosity Ƞ and refraction index nD of liquid mixtures at 298.15 K. Results of the excess parameters and deviation functions for the binary solvent mixtures at 298.15 K have been discussed by molecular interactions that occur in these mixtures. Generally, parameters showed negative values and have been found to fit well to Redlich-Kister

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Publication Date
Sun Dec 01 2013
Journal Name
Journal Of Engineering
Application of Water Quality Index and Water Suitability for Drinking of the Euphrates River within Al-Anbar Province, Iraq.
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In this study water quality was indicated in terms of Water Quality Index that was determined through summarizing multiple parameters of water test results. This index offers a useful representation of the overall quality of water for public or any intended use as well as indicating pollution, which are useful in water quality management and decision making. The application of Water Quality Index (WQI) with ten physicochemical water quality parameters was performed to evaluate the quality of Euphrates River water for drinking usage. This was done by subjecting the water samples collected from seven stations within Al-Anbar province during the period 2004-2010 to comprehensive physicochemical analysis. The ten physicochemical parame

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Publication Date
Mon Jan 01 2024
Journal Name
Jordanian Journal Of Computers And Information Technology
BEYOND WORDS: HARNESSING SPEECH SOUND FOR SPEAKER AGE AND GENDER DETECTION USING 1D CNN ARCHITECTURE WITH SELF-ATTENTION MECHANISM
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Beyond the immediate content of speech, the voice can provide rich information about a speaker's demographics, including age and gender. Estimating a speaker's age and gender offers a wide range of applications, spanning from voice forensic analysis to personalized advertising, healthcare monitoring, and human-computer interaction. However, pinpointing precise age remains intricate due to age ambiguity. Specifically, utterances from individuals at adjacent ages are frequently indistinguishable. Addressing this, we propose a novel, end-to-end approach that deploys Mozilla's Common Voice dataset to transform raw audio into high-quality feature representations using Wav2Vec2.0 embeddings. These are then channeled into our self-attentio

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