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.
Manganese dioxide rotating cylinder electrode prepared by anodic deposition on a graphite substrate using MnSO4 solution in the presence of 0.918 M of H2SO4. The influence of different operational parameters (MnSO4 concentration, current density, time, and rotation speed) on the structure, and morphology of MnO2 deposit film was examined widely. The structure and crystal size determined by X-ray diffraction (XRD), the morphology examined by scanning electron microscopy (SEM) and atomic force microscopy (AFM) techniques. The γ-MnO2 obtained as the main product of the deposition process. It found that the four parameters have a significant influence on the structure, morphology, and roughness of the prepared MnO2 deposit. The crystal size in
... Show MoreA step to net-zero of carbon dioxide losses in the microalgae cultivation process was targeted in the current study. This research was carried out by using pre-dissolved inorganic carbon (DIC) as a source of carbon with two doses of twenty-five and fifty millilitres.
The relationship between government revenues and the fiscal balance represents a central pillar in the analysis of fiscal sustainability. However, its modeling faces a fundamental challenge in the form of structural uncertainty, which is not captured by point estimates in traditional models such as ARDL, as these models assume structural stability that is inconsistent with the nature of rentier economies. The current study aims to develop a fuzzy framework by constructing a Fuzzy Autoregressive Distributed Lag (FARDL) model. This is achieved through integrating the Autoregressive Distributed Lag (ARDL) approach with fuzzy logic theory, thereby enabling the incorporation of uncertainty into the inherent structure of the economic rela
... Show MoreIn this paper, thin films of undoped and nickel oxide (NiO) doped titanium dioxide (TiO2) were prepared using the chemical spray pyrolysis deposition (CSP) technique, with different concentrations of nickel oxide (NiO) in the range (3-9) wt%. The morphological, structural, electrical, and sensing properties of a gas of the prepared thin films were examined. XRD measurements showed that TiO2 films have a polycrystalline structure. AFM analysis showed that these films have a regular structure both before and after doping . The roughness of these films decreased after adding impurities but then the opposite of that took place. The electrical and gas sensing properties of titanium dioxide was also affected after dopin
... Show MoreThe integration of Artificial Intelligence with Big Data Analytics is one of the most groundbreaking developments that could change the face of educational sustainability in higher education.. Using AI and Big Data technologies not only makes the educational process more efficient but also changes the way people learn and thus opens the door for educators and institutions to make decisions based on the data. The document imparts the manner that the use of AI and the digital revolution can remove student requirements, execute the efficiency of the curriculum, and acquire the balance of educational resources through a majority of instances and the latest developments in that field. Furthermore, the paper, along with the issues of morality wit
... Show MoreLet G be a graph with p vertices and q edges and be an injective function, where k is a positive integer. If the induced edge labeling defined by for each is a bijection, then the labeling f is called an odd Fibonacci edge irregular labeling of G. A graph which admits an odd Fibonacci edge irregular labeling is called an odd Fibonacci edge irregular graph. The odd Fibonacci edge irregularity strength ofes(G) is the minimum k for which G admits an odd Fibonacci edge irregular labeling. In this paper, the odd Fibonacci edge irregularity strength for some subdivision graphs and graphs obtained from vertex identification is determined.
Aerial manipulation of objects has a number of advantages as it is not limited by the morphology of the terrain. One of the main problems of the aerial payload process is the lack of real-time prediction of the interaction between the gripper of the aerial robot and the payload. This paper introduces a digital twin (DT) approach based on impedance control of the aerial payload transmission process. The impedance control technique is implemented to develop the target impedance based on emerging the mass of the payload and the model of the gripper fingers. Tracking the position of the interactional point between the fingers of gripper and payload, inside the impedance control, is achieved using model predictive control (MPD) approach.
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