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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 Oct 16 2025
Journal Name
Journal Of Physical Education
Academic Achievement Level and Its Relationship with Some Fundamental Skills in Fencing for Third Year College Students
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Publication Date
Thu Oct 01 2020
Journal Name
Plant Archives
Development, validation, and pharmaceutical dosage forms application of hydrophilic interaction chromatography assay for the quantification of theophylline
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The present work establishes and validates HILIC strategies simple, accurate, exact and precise in pure form and inpharmaceutical dosage for separating and determining theophylline. These methods are developed on HILIC theophyllineseparation in columns ZIC2 and ZIC3. The eluent was prepared by mixing buffer (20% sodium acetate-40 mM, pH 5.5), 80%acetonitrile. The flow rate is 0.8 mL/min, with gradient elution and UV detection at 270 nm. In the ZIC2 and ZIC3 columns oftheophylline determining, the concentration range was 0.01-4μg.ml-1. The lower limit of detection and quantification fortheophylline were determined as 0.130, 0.190 μg.ml-1 and accuracy were 99.70%, 99.58% on ZIC2 and ZIC3, respectively. TheHILIC methods developed and validat

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Publication Date
Sat Mar 30 2024
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Optimization of Separator Size and Operating Pressure for Three-phase Separators in the West Qurna1 Oil Field
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An optimization study was conducted to determine the optimal operating pressure for the oil and gas separation vessels in the West Qurna 1 oil field. The ASPEN HYSYS software was employed as an effective tool to analyze the optimal pressure for the second and third-stage separators while maintaining a constant operating pressure for the first stage. The analysis involved 10 cases for each separation stage, revealing that the operating pressure of 3.0 Kg/cm2 and 0.7 Kg/cm2 for the second and third stages, respectively, yielded the optimum oil recovery to the flow tank. These pressure set points were selected based on serval factors including API gravity, oil formation volume factor, and gas-oil ratio from the flow tank.    To impro

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Publication Date
Sun Dec 01 2013
Journal Name
Baghdad Science Journal
The Ecology and geographical distribution for the species of the genus Salvia L. of labiatae in Iraq
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The study included general survey of some districts of Iraq in order to determinate new distribution areas for 33 species of the genus salvia L. ,new collections obtained , new locations for many species recorded. Observed specimens in most Iraqi herbaria were studies and identified. ,the flowering period were also studied

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Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
Study the Relationship between Beta Decay Stability of Nuclide and its Shape for Some even-even Isobars
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The aim of this work is to learn the relationship of the stability of (β) emitter isobars with their shape for some isobaric elements with even mass number (A=152 - 162). To reach this goal firstly the most stable isobar have been determined by plotting mass parabola (plotting the binding energy (B.E) as a function of the atomic number (Z)) for each isobaric family. Then three-dimensional representation graphics for each nucleus in these isobaric families have been plotted to illustrate the deformation in the shape of a nucleus. These three-dimensional representation graphics prepared by calculating the values of semi-axis minor (a), major (b) and (c) ellipsoid axis’s. Our results show that the shape of nuclides which is represented the

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Publication Date
Mon Apr 20 2020
Journal Name
Neuroquantology
The Role of Water Absorption on Thermal Conductivity and Mechanical Properties for (Recycling HDPE-Coal Ash) Composite
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Publication Date
Sun Dec 03 2017
Journal Name
Baghdad Science Journal
Synthesis New Liquid Selective Electrodes of Ciprofloxacin Hydrochloride for Determination Ciprofloxacin in Pure form and Pharmaceuticals Preparation.
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New membrane electrodes for determination of ciprofloxacin hydrochloride were prepared depending on ciprofloxacin hydrochloride - phosphotungstic acid (CFH-PT) as an active material and these electrodes were made with three plasticizers: Di-octylphenylphosphonate(DOPH), Di-butyl phosphate (DBP)Tri-n-butyl phosphate(TBP), in PVC matrix. One of the ciprofloxacin electrodes was gave Nernstian slope equal to 57.21 mV/ decade for DOPH membrane with concentration range from 1.5×10-5 to1.0×10-1 M, and detection limit equal to 1.5×10-6 M .Lifetime was 93 days. Non- Nernstian responses equal to 39.40 and 30.70 mV/ decade for membranes DBP, TBP, respectively. These electrodes were gave concentration range from 1.0× 10-5 to 1.0×10-2 and from 4.0

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Publication Date
Wed Mar 04 2020
Journal Name
International Journal Of Psychosocial Rehabilitation
The Effect of Using Fit Light Exercise in Some Physiological Indicators and Smash Shot for Badminton’s Players
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The reason for applying the project is for the development of some physiological variables and skill performance using a device for the first time applied in Iraq to a sample of badminton players, and this device has a patent on 7/2/2019. An experimental method is used for a sample of (12) players from (Al-Orthodoxy club). The experimental group is applied the proposal technique, while, the control group is instructed by the coach.The results of the research attribute to the role of the proposal exercises of fit light technology, thus, this technology has increased the attention and focusing of the sample and some physiological variables and smash shot skill. It has been concluded that the exercises using fit light technology is helped to i

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Publication Date
Tue Dec 01 2015
Journal Name
Journal Of Engineering
Calibration and verification of the hydraulic model for Blue Nile river from Roseires dam to Khartoum city
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This research represents a practical attempt applied to calibrate and verify a hydraulic model for the Blue Nile River. The calibration procedures are performed using the observed data for a previous period and comparing them with the calibration results while verification requirements are achieved with the application of the observed data for another future period and comparing them with the verification results. The study objective covered a relationship of the river terrain with the distance between the assumed points of the dam failures along the river length. The computed model values and the observed data should conform to the theoretical analysis and the overall verification performance of the model by comparing it with anothe

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Publication Date
Wed Aug 01 2012
Journal Name
International Journal Of Geographical Information Science
Assessing similarity matching for possible integration of feature classifications of geospatial data from official and informal sources
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