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.
The main function of a power system is to supply the customer load demands as economically as possible. Risk criterion is the probability of not meeting the load. This paper presents a methodology to assess probabilistic risk criteria of Al-Qudus plant before and after expansion; as this plant consists of ten generating units presently and the Ministry Of Electricity (MOE) is intending to compact four units to it in order to improve the performance of Iraqi power system especially at Baghdad region. The assessment is calculated by a program using Matlab programming language; version 7.6. Results show that the planned risk is (0.003095) that is (35 times) less than that in the present plant risk; (0.1091); which represents respectable imp
... Show MoreHeat pipes and two‐phase thermosyphon systems are passive heat transfer systems that employ a two‐phase cycle of a working fluid within a completely sealed system. Consequently, heat exchangers based on heat pipes have low thermal resistance and high effective thermal conductivity, which can reach up to the order of (105 W/(m K)). In energy recovery systems where the two streams should be unmixed, such as airconditioning systems of biological laboratories and operating rooms in hospitals, heat pipe heat exchangers (HPHEs) are recommended. In this study, an experimental and theoretical study was carried out on the thermal performance of an air‐to‐air HPHE filled with two refrigerants as working fluids, R22 and R407c. The heat pipe he
... Show MoreThis research was one of the terms that used by Al-Bazzar in his musnad and this term was (Al-azza) who launched on some ways and hadiths and I collected those narration, and I have graduated and studied it to access to the meaning which Al-Bazzar want that from this description. In the introduction of the research, I have mention the importance of the subject and the reasons for his selection and also my plan, a preface where I mentioned the definition of Al-Bazzar and his musnad, then in the first section I defined Al-azza linguistically and idiomatically , the second section I studied the hadiths that Al-Bazzar described them with azza ,and then I conclude it with my results that I have reach
... Show MoreIn this work the interaction of plasma jet with water and hydrogen peroxide liquids used for assisted teeth bleaching by plasma jet had been study. A homemade plasma jet system was used. The plasma jet supply by 15 W electrical power generated by high voltage power supply of 9.6 kV peak to peak and frequency of 33 kHz .this power supply generate high electric field on electrodes that would be enough to ionize the argon gas. Some important agents were study such as the effect of the Ar gas flow rates on the length of the plasma jet, the influence of plasma jet on some properties of water and two hydrogen peroxide concentrations 25 % and 30 % like pH, conductivity and liquid temperature for different exposure time. The liquids temperature
... Show MoreThe current work is focused on the rock typing and flow unit classification for reservoir characterization in carbonate reservoir, a Yamama Reservoir in south of Iraq (Ratawi Field) has been selected, and the study is depending on the logs and cores data from five wells which penetrate Yamama formation. Yamama Reservoir was divided into twenty flow units and rock types, depending on the Microfacies and Electrofacies Character, the well logs pattern, Porosity–Water saturation relationship, flow zone indicator (FZI) method, capillary pressure analysis, and Porosity–Permeability relationship (R35) and cluster analysis method. Four rock types and groups have been identified in the Yamama formation de
Liquid membrane electrodes for the determination iron(III) were constructed based on chloramphenicol sodium succinate and iron(III) CPSS-Fe(III) as ion pair complex, with four plasticizers Di-butyl phosphate (DBP); Di-butyl phthalate (DBPH); Di-octyl phthalate (DOP); Tri-butyl phosphate (TBP); in PVC matrix . These electrodes give Nernstian and sub-Nernstian slopes (19.79, 24.60, 16.01 and 13.82mV/decade) and linear ranges from (1x10-5-1x10-2 M, 1x10-5-1x10-2 M, 1x10-6-1x10-2 M and 1x10-5-1x10-2 M) respectively. The best electrode was based on DBP plasticizer which gave a slope 19.79 mV/decade, correlation coefficient 0.9999, detection limit of 9×10-6 M, lifetime 37 day displayed good stability and reproducibility and used to determine
... Show MoreThe effect of the magnetic abrasive finishing (MAF) method on the temperature rise (TR), and material removal rate (MRR) has been investigated in this paper. Sixteen runs were to determine the optimum temperature in the contact area (between the abrasive powder and surface of workpiece) and the MRR according to Taguchi orthogonal array (OA). Four variable technological parameters (cutting speed, finishing time, working gap, and the current in the inductor) with four levels for each parameter were used, the matrix is known as a L16 (44) OA. The signal to noise ratio (S/N) ratio and analysis of the variance (ANOVA) were utilized to analyze the results using (MINITAB17) to find the optimum condition and identify the significant p
... Show MoreBackground: Currently there are four general approaches to correct refractive errors: refractive corneal surgery, crystalline lens surgery and implantation of an intraocular lens in anterior or posterior chamber. Aim: To evaluate the predictability, safety and stability of toric phakic implantable collamer lens implantation to correct moderate to high myopic astigmatism. Methods: Sixty eyes of 40 patients underwent implantation of a toric implantable collamer lens (V4c design) in the Eye Specialty Private Hospital, Baghdad, Iraq were studied. The mean spherical refraction was -11.32±3.17 diopter (D) with a range of -6.00 to -18.00 D and a mean cylinder of -2.61±1.16 with range of -1.00 to -5.50 D. The outcome measures that evaluat
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