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.
Generally, statistical methods are used in various fields of science, especially in the research field, in which Statistical analysis is carried out by adopting several techniques, according to the nature of the study and its objectives. One of these techniques is building statistical models, which is done through regression models. This technique is considered one of the most important statistical methods for studying the relationship between a dependent variable, also called (the response variable) and the other variables, called covariate variables. This research describes the estimation of the partial linear regression model, as well as the estimation of the “missing at random” values (MAR). Regarding the
... Show MoreTheoretical spectroscopic study of Beryllium Oxide has been carried out, Boltzmann distribution of P, Q and R branches in the range of (0<J<13) at temperature 4200K for (0-0) band for electronic transitions B1Σ+-A1Π and B1Σ-X1Σ. The Boltzmann distribution of these branches has a maximum values at equal J approximately while the values of relative population are different. For the B1Σ+- X1Σ+ transition the branch's lines extend towards lower wavenumber. This is because (Bv'-Bv") value is negative, i.e Bv'< Bv" For B1Σ+-A1Π
... Show MoreThe study focused on the treatment of real oilfield produced water from the East Baghdad field affiliated to the Midland Oil Company (Iraq) using an oil skimming process followed by a coagulation/flocculation process for zero liquid discharge system applications. Belt type oil skimmer was utilized for evaluating the process efficiency with various operating conditions such as temperature (17-40 °C) and time (0.5-2.5 hr.). Polyaluminum chloride (PAC) coagulant and polyacrylamide (PAM) flocculant was used to investigate the performance of the coagulation/flocculation process with PAC dosage (5-90 ppm) and pH (5-10) as operating conditions. In the skimming process, the oil content, COD, turbidity, and TSS decreased with an increase in tempera
... Show MoreThe present paper attempts to find out the role of developmental loans in promoting strategic crops especially the basis stemming from the problem of non - defining economic feasibility study and the negative or positive revenues of developmental loans, directed to Iraqi Agricultural sector in general and Basic strategic crops in particular which resulted in the difficulty of planning and future prediction to grant loans agriculturally directed in terms of quality and quantity and the arbitrary of distributing these loans .the strategic crops have been selected as sample of population where the sample of Basic strategic crops include wheat and barley .The paper has come to several of conclusions mainly are as follows :- the increase in n
... Show MoreThe research aims to show the role or extent of the impact of financing in its various forms on the municipal performance before and after the financial deficit through relying on the analytical research methodology of the research community represented by the Directorate General of Municipalities and the Directorate of Maysan municipalities as a sample of research (13) municipal institutions for a period of (8) years, Considering the completion of the final accounts of these years, which provides the necessary data for the study, in addition to the variation in the quality and amounts of grants allocated to municipal institutions during these years, which gives a clearer and more comprehensive picture of the reality of allocatio
... Show MoreLasmiditan (LAS) was formulated as a nanoemulsion based in situ gel (NEIG)with the aim of improving its oral bioavailability via application intranasally. The solubility of LAS in oils, emulsifiers, and co-emulsifiers was determined to identify nanoemulsion (NE)components. Phase diagrams were constructed to identify the area of nanoemulsification. LAS NE was formulated using the spontaneous nanoemulsification method. Four NEs (F19, F24, F31, and F34) containing 7-15 % oleic acid (OA) as an oily phase, 40-55% labrasol (LR), and transcutol (TC) as emulsifier mixture at (1:1), (2:1), (3:1), and (1:2) ratio with 30-53 % (w/w) aqueous phase, having suitable optical transparency of 95–98%, globule size of 104-140 nm and polydisper
... Show MorePlatinum nanoparticles (PtNPs) exhibit promising biomedical properties, but concerns about biocompatibility and synthesis-related toxicity remain. This study aimed to develop eco-friendly PtNPs using aqueous broccoli extract as a natural reducing and stabilizing agent, and to assess their multifunctional biomedical potential. PtNPs were synthesized through sonochemical reduction of K₂PtCl₆ in broccoli extract, followed by purification and comprehensive physicochemical characterization. UV–Vis confirmed nanoparticle formation at 253 nm, while XRD and FTIR analyses verified the crystalline FCC structure and phytochemical capping. TEM revealed mainly spherical PtNPs with an average core size of 14.83 ± 7.67 nm. Conversely, DLS showe
... Show MoreObjective: This study aims to examine how implementing Extensible Business Reporting Language (XBRL) enhances the efficiency and quality of environmental audits and sustainability reporting in eco-friendly universities. Aligned with Sustainable Development Goal 12 (Responsible Consumption and Production), the study emphasizes promoting transparency and precision in sustainability reporting to encourage responsible management of resources within academic institutions. Theoretical Framework: The importance of our study is evident in the importance of accurate and transparent reports in the development of environmental performance with theories of sustainable reporting and environmental auditing. One of the most important digital
... Show MoreThe present study deals with the effect of teaching speaking Strategies (SS) on EFL Iraqi College students. The use of speaking strategies not only solves learners’ communication problems, but also enhances the learner’s interaction in target language, and improves their oral proficiency .The aim of the study is to find out the effect of teaching SS used by EFL College students .The learner of the first stage is population of the study at the Department of English, College of Education /Ibn-Rushd .The sample consists of (60) students distributed on experimental group(A) as well as control group(B) each group contains (30) students . In order to achieve the aim of the study, questionnaire has been constructed to be taught on the experime
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