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.
This investigation pertains to the evaluation of water quality in SAWA Lake, located in the Al-Muthanna province of Southern Iraq, from 1977 to 2020. Understanding the water quality and assessments of this Lake is of great importance. The Lake is home to small, transparent, blind fish measuring approximately 10 cm and is often referred to as the "wonderful" or "strange" Lake due to its many unique features. The study focuses on several elements to represent water quality, including total dissolved solids (TDS), electrical conductivity (EC), pH, and temperature (T), which were measured directly in the field. Additionally, scientific concepts such as K+, Ca2+, Cl-, HCO
Abstract This study investigated the treatment of textile wastewater contaminated with Acid Black 210 dye (AB210) using zinc oxide nanoparticles (ZnO NPs) through adsorption and photocatalytic techniques. ZnO NPs were synthesized using a green synthesis process involving eucalyptus leaves as reducing and capping agents. The synthesized ZnO NPs were characterized using UV-Vis spectroscopy, SEM, EDAX, XRD, BET, Zeta potential, and FTIR techniques. The BET analysis revealed a specific surface area and total pore volume of 26.318 m2/g. SEM images confirmed the crystalline and spherical nature of the particles, with a particle size of 73.4 nm. A photoreactor was designed to facilitate the photo-degradation process. The study investigated the inf
... Show MoreThe aim of this work is to learn the relationship of the stability of (β) emitter isobars with their shape for some isobaric elements with even mass number (A=152 - 162). To reach this goal firstly the most stable isobar have been determined by plotting mass parabola (plotting the binding energy (B.E) as a function of the atomic number (Z)) for each isobaric family. Then three-dimensional representation graphics for each nucleus in these isobaric families have been plotted to illustrate the deformation in the shape of a nucleus. These three-dimensional representation graphics prepared by calculating the values of semi-axis minor (a), major (b) and (c) ellipsoid axis’s. Our results show that the shape of nuclides which is represented the
... Show MoreThis study aims to develop a thermosensitive mucoadhesive periodontal in situ gel of secnidazole for local release of drug for treatment of periodontitis, in order to increase the drug residence time and to increase patient compliance while lowering the side effects of the drug.
Cold method was used to prepare 30 formulas of secnidazole periodontal in situ gel, using different concentrations of thermosensitive polymers (poloxamer407 alone or in combination with poloxamer 188) and methyl cellulose (MC ) or hydroxypropyl methylcellulose (HPMC K4M )in different concentrations used as mucoadhesive polymer and the resultant formulations were subjected to several tests such as gelation temperature GT, appearance and pH value. The fo
... Show MoreThe purpose of this study is to investigate the research on artificial intelligence algorithms in football, specifically in relation to player performance prediction and injury prevention. To accomplish this goal, scholarly resources including Google Scholar, ResearchGate, Springer, and Scopus were used to provide a systematic examination of research done during the last ten years (2015–2025). Through a systematic procedure that included data collection, study selection based on predetermined criteria, categorisation based on AI applications in football, and assessment of major research problems, trends, and prospects, almost fifty papers were found and analysed. Summarising AI applications in football for performance and injury p
... Show MoreThis research studies the comparison of deep neural network models and performance evaluation to predict the gold prices of time series, where the gold prices contain high fluctuations and non-linear patterns that are difficult to capture using traditional models, which makes predicting them a significant challenge. Therefore, the focus was on using deep learning models represented by (LSTM), (Bi-LSTM), (GRU) and (Bi-GRU). The results showed the superiority of the (Bi-GRU) model according to comparison criteria (MSE), (RMSE), (MAE), and (R∧2) compared to other models because it was able to understand the time patterns better by processing the data in both directions and provided superior performance, which indicates its effectiveness, eff
... Show More