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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
Fri Feb 08 2019
Journal Name
Iraqi Journal Of Laser
Design and Simulation of Optical Element Use in Solid State Blue Laser Source
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Solid state blue laser source is a solid state laser include generation of IR laser light 1064 nm and companied with other wavelength 810 nm that invented from other active medium (Tm:ZBLAN) and non-linear crystal (CLBO) are used to generate fourth harmonic of the resultant wavelength 1874 nm that is blue laser light of 460nm. Several optical component have been designed by multilayer dielectric structure and anti reflection coating analysis. By using MATLAB soft ware, the simulation done and used the following non linear material (ZrO2, HfO2, MgO, SiO, Ta2O5 CaF2) and other linear material (ZnO, MgF2, GaAs, AlAs, BaF2, LiF, TiO2) as coating material. The result showed that as more quarter wave layers are added to the structure, the refl

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Publication Date
Thu Oct 21 2021
Journal Name
Iraqi Journal Of Agricultural Sciences
SYNTHESIS, CHARACTERIZATION AND CYCLAZATION OF PYRAN USING Ag2O NANOPARTICLE FROM NATURAL SOURCE “GINGER”
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This study was aimed to synthesis Ag2O nanoparticles (N.P.s) utilizing the Ginger plant (Zingiber officinale) extract. As catalysts for pyran derivatives formation employing a three-component coupling reaction among aromatic and aliphatic aldehydes, malononitrile, and dimedone. The nanoparticles exhibit robust catalytic activity with high productivity. Results revealed that Ag2O NPs improved various vital features, like higher yields, reaction time, simple chemical separation, catalytic economic efficiency, and quick process. This study aimed to cyclize heterocyclic compounds to provide new hetero compounds applying nano-oxides obtained from natural (unmanufactured) sources and used in several medical, pharmaceutical, and industrial

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Publication Date
Fri Jan 01 2016
Journal Name
Al-mustansiriyah Journal Of Science
Calculate optical parameters of ions beam from plasma source
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Publication Date
Mon May 11 2020
Journal Name
Baghdad Science Journal
Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients: eventually positive solutions and differential inequalities
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In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

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Publication Date
Tue Dec 01 2020
Journal Name
Baghdad Science Journal
Novel use of XRF in the adsorption processes for the direct analysis of cadmium and silver in absorbent Na-alginate beads
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         The Na-alginate bead is commonly used in biotechnology fields such as adsorption due to ion exchange between Ca and Na with elements. Scanning electron microscopy (SEM-EDX) has proven to be a comparative method in the detections of these adsorbed elements, but the un-flat forming area of beads that can introduce impossible of the detection of element adsorbed. In contrast, X-ray fluorescence (XRF) documents analysis of elements, direct examination, which may analysis the adsorbents of elements. Here, this Study evaluated the possibility by using XRF for the direct analysis for examples of Cd and Ag in a bench stand. This Study compared this to commonly use

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Publication Date
Mon Apr 11 2022
Journal Name
Iraqi Journal Of Science
International Journal on Technical and Physical Problems of Engineering
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International Journal on Technical and Physical Problems of Engineering

Publication Date
Fri Sep 30 2022
Journal Name
Journal Of Economics And Administrative Sciences
Choosing the best method for estimating the survival function of inverse Gompertz distribution by using Integral mean squares error (IMSE)
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In this research , we study the inverse Gompertz distribution (IG) and estimate the  survival function of the distribution , and the survival function was evaluated using three methods (the Maximum likelihood, least squares, and percentiles estimators) and choosing the best method estimation ,as it was found that the best method for estimating the survival function is the squares-least method because it has the lowest IMSE and for all sample sizes

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Publication Date
Fri Sep 30 2022
Journal Name
Journal Of Economics And Administrative Sciences
Choosing the best method for estimating the survival function of inverse Gompertz distribution by using Integral mean squares error (IMSE)
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In this research , we study the inverse Gompertz distribution (IG) and estimate the  survival function of the distribution , and the survival function was evaluated using three methods (the Maximum likelihood, least squares, and percentiles estimators) and choosing the best method estimation ,as it was found that the best method for estimating the survival function is the squares-least method because it has the lowest IMSE and for all sample sizes

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Publication Date
Sat Dec 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
The importance of direct foreign investment on development of Iraqi oil industry for the period (2003-3010)
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Oil industry played a major role in delineating the course and type o development in both imported and exported Arabic countries alike where its revenues has perform an essential role in forming programs and plans of development on both national and international level in addition to anticipation of future consuming.

Iraq, as an oil producer country with a revenues –based economy depends on oil in building its economy totally including its infrastructure having a the greatest conformed reservoir which make the government budget depends largely on oil revenues where its strategic importance lies in funding all aspects of expenders as it is considered the prime source of foreign currency.  The chall

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Publication Date
Tue Feb 10 2026
Journal Name
F1000research
Simultaneous Numerical Determination of Two Time-dependent Coefficients in Second Order Parabolic Equation With Nonlocal Initial and Boundary Conditions
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Background This study establishes a mathematically consistent and computational framework for the simultaneous identification of two time-dependent coefficients in a one-dimensional second-order parabolic partial differential equation. The considered problem is governed by nonlocal initial, boundary, and integral overdetermination conditions. Methods The direct problem is solved using the Crank-Nicolson finite difference method (FDM), which ensures unconditional stability and second-order accuracy in both spatial and temporal discretizations. The corresponding inverse problem is reformulated as a nonlinear regularized least-squares optimization problem and efficiently solved used the MATLAB subroutine

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