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 research aims to verify the presence of correlation between the financial cycle and the economic cycle in the Iraqi economy. During the research period, the Iraqi economy witnessed a crisis cycle due to the permanent deviations in the state budget and the occurrence of sustainable deficits during the period of the economic blockade with the coincidence of an inflationary economic cycle due to the cheap money policy and the occurrence of Negative supply shocks due to the blockade and the madly high general level of prices, in addition to the weak financial planning of the state budget during the post-economic blockade and the entry of the economy into a stagnant economic cycle due to security and political instability, low levels of priv
... Show MoreA theoretical study on corrosion inhibitors was done by quantum calculations includes semi-empirical PM3 and Density Functional Theory (DFT) methods based on B3LYP/6311++G (2d,2P). Benzimidazole derivative (oxo(4- ((phenylcarbamothioyl) carbamoyl)phenyl) ammonio) oxonium (4NBP) and thiourea derivative 2-((4- bromobenzyl)thio) -1H-benzo[d] imidazole (2SB) were used as corrosion inhibitors and an essential quantum chemical parameters correlated with inhibition efficiency, EHOMO (highest occupied molecular orbital energy) and ELUMO (lowest molecular orbital energy). Other parameters are also studied like energy gap [ΔE (HOMO-LUMO)], electron affinity (EA), hardness (Δ), dipole moment (μ), softness (S), ionization potential (IE), absolut
... Show MoreIn this research prepared two composite materials , the first prepared from unsaturated polyester resin (UP) , which is a matrix , and aluminum oxide (Al2O3) , and the second prepared from unsaturated polyester resin and aluminum oxide and copper oxide (CuO) , the two composites materials (Alone and Hybrid) of percentage weight (5,10,15)% . All samples were prepared by hand layup process, and study the electrical and thermal conductivity. The results showed decrease electrical conductivity from (10 - 2.39) ×10-15 for (Up+ Al2O3) and from (10 - 2.06)×10-15 for (Up+ Al2O3+ CuO) .But increase thermal conductivity from( 0.17 - 0.505) for (Up+ Al2O3) and from (0.17 - 0.489) for (Up+ Al2O3+ CuO).
This work aims to enhance acoustic and thermal insulation properties for polymeric composite by adding nanoclay and rock wool as reinforcement materials with different rations. A polymer blend of (epoxy+ polyester) as matrix materials was used. The Hand lay-up technique was used to manufacture the castings. Epoxy and polyester were mixed at different weight ratios involving (50:50, 60:40, 70:30, 80:20, and 90:10) wt. % of (epoxy: polyester) wt. % respectively. Impact tests for optimum sample (OMR), caustic and thermal insulation tests were performed. Nano clay (Kaolinite) with ratios ( 5 and 7.5% ) wt.% , also hybrid reinforcement materials involving (Kaolite 5 & 7.5 % wt.% + 10% volume fraction of rockwool ) were added as reinforcem
... Show Moreوفقأ للدراسات السابقة تم تحضير ليكاند آزو جديد (ن-(3-اسيتايل-2-هيدروكسي-5-مثيل-فنيل)ن-(4-كاربوكسي-سايكلوهكسيل مثيل)-ملح الدايازونيوم) وبعد التحقق من الصيغة المقترحة وفق نتائج التحاليل وبعد استخدام الليكاند لتحضير سلسلة ن المعقدات باستخدام نسب مولية متساوية (1:1) من الليكاند وتفاعلها مع كل من املاح المنغنيز والكوبلت والنيكل والنحاس والخارصين وبعد التحقق وفق تقنيات التحاليل الطيفية والتشخيصية(الاشعة فوق البنف
... Show MoreNanomaterials, including nanoparticles such as iron oxide nanoparticles, have received great attention from researchers due to their unique properties and applications. There are several diverse methods, including chemical, physical, and green biological methods, to prepare iron oxide nanoparticles. The green method was chosen because it is safer, purer, and less toxic compared to other methods. Therefore, the green method is a promising and environmentally friendly method in the near future. The aqueous extract of Iraqi orange leaves was used to prepare nano iron oxide, it was examined structurally and spectrally by several techniques (X-ray diffraction- XRD, Fourier transform infrared - FT-IR, field emission scanning electron micr
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This research aims at examining the expected gap between the fact of planning and controlling process of production at the State Company for Electric Industries and implementation of material requirements planning system in fuzzy environment. Developing solutions to bridge the gap is required to provide specific mechanisms subject to the logic of fuzzy rules that will keep pace with demand for increased accuracy and reduced waiting times depending on demand forecast, investment in inventory to reduce costs to a minimum.
The proposed solutions for overcoming the research problem has required some questions reflecting the problem with its multiple dimensions, which ar
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