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.
Simple and sensitive kinetic methods are developed for the determination of Paracetamol in pure form and in pharmaceutical preparations. The methods are based on direct reaction (oxidative-coupling reaction) of Paracetamol with o-cresol in the presence of sodium periodate in alkaline medium, to form an intense blue-water-soluble dye that is stable at room temperature, and was followed spectrophotometriclly at λmax= 612 nm. The reaction was studied kinetically by Initial rate and fixed time (at 25 minutes) methods, and the optimization of conditions were fixed. The calibration graphs for drug determination were linear in the concentration ranges (1-7 μg.ml-1) for the initial rate and (1-10 μg.ml-1) for the fixed time methods at 25 min.
... Show MoreDiacerein (DCN) is a semi-synthetic anthraquinone derivative of Rhein that is indicated for the management of osteoarthritis. Diacerein exhibits poor dissolution in the GIT fluids and suffers from low bioavailability upon oral administration in addition to the laxative effect of Rhein metabolites. The aim of the present study was to develop novasomal vesicles with optimized entrapment efficiency and size to serve as a carrier for transdermal delivery of diacerein. Novasomal vesicles were prepared by thin film hydration method thin film hydration. The prepared vesicles were optimized utilizing different surfactant to cholesterol molar ration, sonication type, different sonication times and varying fatty acid level. The prepared vesicles were
... Show MoreAbstract Background: Timely diagnosis of periodontal disease is crucial for restoring healthy periodontal tissue and improving patients’ prognosis. There is a growing interest in using salivary biomarkers as a noninvasive screening tool for periodontal disease. This study aimed to investigate the diagnostic efficacy of two salivary biomarkers, lactate dehydrogenase (LDH) and total protein, for periodontal disease by assessing their sensitivity in relation to clinical periodontal parameters. Furthermore, the study aimed to explore the impact of systemic disease, age, and sex on the accuracy of these biomarkers in the diagnosis of periodontal health. Materials and methods: A total of 145 participants were categorized into three groups based
... Show MorePreserving the Past and Building the Future: A Sustainable Urban Plan for Mosul, Iraq
The petroleum industry, which is one of the pillars of the national economy, has the potential to generate vast wealth and employment possibilities. The transportation of petroleum products is complicated and changeable because of the hazards caused by the corrosion consequences. Hazardous chemical leaks caused by natural disasters may harm the environment, resulting in significant economic losses. It significantly threatens the aim for sustainable development. When a result, determining the likelihood of leakage and the potential for environmental harm, it becomes a top priority for decision-makers as they develop maintenance plans. This study aims to provide an in-depth understanding of the risks associated with oil and gas pipeli
... Show More