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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 23 2026
Journal Name
Egyptian Journal Of Aquatic Biology And Fisheries
Evaluation of the Yellow Mealworm (Tenebrio molitor) Meal as an Alternative Protein Source for Common Carp (Cyprinus carpio) Fingerlings
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This study evaluated yellow mealworm (Tenebrio molitor) larvae meal as an alternative animal-protein ingredient in diets for common carp (Cyprinus carpio) fingerlings. Two diets were compared for 60 days: a conventional fish-meal diet (T1; 32.09% crude protein) and a diet in which the animal-protein component was replaced weight-for-weight with T. molitor meal (T2; 23.88% crude protein). Each treatment was tested in duplicate tanks containing 28 fingerlings per tank, and growth was assessed over three consecutive 20-day phases. The initial mean body weight was 3.21 g. Weight gain differed significantly between treatments (p < 0.05), with the highest total value recorded in T2 (4.87 ± 0.47 g). The T2 diet produced a significantly higher fee

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
An approximate solution for solving linear system of integral equation with application on "Stiff" problems
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An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly

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Publication Date
Mon Oct 01 2012
Journal Name
Computers &amp; Mathematics With Applications
Boundary element formulations for the numerical solution of two-dimensional diffusion problems with variable coefficients
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Publication Date
Wed Aug 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Proposed Measure for Effect Size in Mediation Analysis with Solution to Some Mediation Process Problems
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In this paper, the effect size measures was discussed, which are useful in many estimation processes for direct effect and its relation with indirect and total effects. In addition, an algorithm to calculate the suggested measure of effect size was suggested that represent the ratio of direct effect to the effect of the estimated parameter using the Regression equation of the dependent variable on the mediator variable without using the independent variable in the model. Where this an algorithm clear the possibility to use this regression equation in Mediation Analysis, where usually used the Mediator and independent variable together when the dependent variable regresses on them. Also this an algorithm to show how effect of the

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Publication Date
Sun Dec 01 2019
Journal Name
2019 First International Conference Of Computer And Applied Sciences (cas)
A Comparison for Some of the estimation methods of the Parallel Stress-Strength model In the case of Inverse Rayleigh Distribution
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Publication Date
Fri Jul 10 2026
Journal Name
Mathematical And Computational Applications
A Regularized Numerical Solution to an Inverse Coefficient Problem for the Forced Vibrations of a Cantilever Beam Equation Under Nonlocal Conditions
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This study tackles a fourth-order inverse problem involving a cantilever beam with nonlocal conditions to simultaneously calculate the beam’s displacement and an unknown time-dependent coefficient. A finite difference approach is suggested to discretize the hyperbolic fourth-order equation. A stability analysis for the proposed scheme is also provided. The indirect problem is the minimization of the misfit function. The goal of the minimization algorithm is to reduce the gap between the measured (noisy) data and the numerical computed solution provided by the model. To achieve stable results, Tikhonov’s regularization technique is employed, and two numerical test examples are shown to illustrate the suggested scheme's reliabilit

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Catalyzed and Promoted Direct Reaction of Ethyl Chloride with Silicon Using Stirred-Bed Reactor
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In this paper a stirred-bed performed of the copper catalyzed synthesis of ethylchlorosilanes from silicon and ethyl chloride was described. A Si-catalyst mixture prepared by reaction of CuCl and Si was employed. The compositions of products were mainly ethyltrichlorosilane, diethyldichlorosilane, and ethyldichlorosilane and mainly depended on the extent of Cu in the mixture and the reaction temperature. A promoting effect on the extent of adsorption was observed on the addition of certain additives. The kinetic data revealed the direct depended of the reaction rate on C2H5Cl pressure.

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Publication Date
Thu Mar 30 2017
Journal Name
Iraqi Journal Of Pharmaceutical Sciences ( P-issn 1683 - 3597 E-issn 2521 - 3512)
Determination of Cefalexin by Direct (UV- Vis) Spectrophotometer and Indirect(Flame Atomic Absorption) Technique
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         A new method for the determination of the drug cefalexin in some Pharmaceuticals using (UV-Vis) and  indirect Flame Atomic Absorption Spectrophotometer (FAAS) , Fe III should forms a chelating complex with cefalexin (CEX –Fe III) at pH (1-8) and the best pH for the formation of (CEX –Fe III) chelating complex was (2) .The complex extracted with Methanol  and  Dimethy-Sulphoxide .The mole-ratio method has been used to determine the structure of chelate (CEX - Fe III) and found to be 2:1 LM ( Ligand : Metal.) .

Keywords : Cefalexin , chelating complex.

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Publication Date
Fri Nov 01 2019
Journal Name
Journal Of Engineering
A Comparison Study of Brine Desalination using Direct Contact and Air Gap Membrane Distillation
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Membrane distillation (MD) is a hopeful desalination technique for brine (salty) water. In this research, Direct Contact Membrane Distillation (DCMD) and  Air Gap Membrane Distillation (AGMD) will be used. The sample used is from Shat Al –Arab water (TDS=2430 mg/l). A polyvinylidene fluoride (PVDF) flat sheet membrane was used as a flat sheet form with a plate and frame cell. Several parameters were studied, such as; operation time, feed temperature, permeate temperature, feed flow rate. The results showed that with time, the flux decreases because of the accumulated fouling and scaling on the membrane surface. Feed temperature and feed flow rate had a positive effect on the permeate flux, while permeate temperatu

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Publication Date
Sun Mar 01 2015
Journal Name
Baghdad Science Journal
Removal of Direct 50 Dyes from Aqueous Solution Using Natural Clay and Organoclay Adsorbents
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In this study, hexadecyltrimethylammonium bromide (HDMAB) - bentonite was synthesized by placing alkylammonium cation onto bentonite. Adsorption of textile dye such as direct Yellow 50 on natural bentonite and HDMAB -bentonite was investigated. The effects of pH, contact time,dosage clay and temperature were investigated experimentally .The Langmuir and Freundlish isotherms equations were applied to the data and values of parameters of these isotherm equations were evaluated. The study indicated that using 0.2 g of HDMAB (hexadecyltrimethylammonium bromide) lead to increase the percentage removal(R%) from 78% for pure bentonite to 99 %. The optimum pH value for the adsorption experiments was found to be pH=3 and therefore all the experim

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