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.
Electronic remote identification (ER-ID) is a new radio frequency (RF) technology that is initiated by the Federal Aviation Authorities (FAA). For security reasons, traffic control, and so on, ER-ID has been applied for drones by the FAA to enable them to transmit their unique identification and location so that unauthorized drones can be identified. The current limitation of the existing ER-ID algorithms is that the application is limited to the Wi-Fi and Bluetooth wireless controllers, which results in a maximum range of 10–20 m for Bluetooth and 50–100 m for Wi-Fi. In this study, a mathematical computing technique based on finite state automaton (FSA) is introduced to expand the range of the ER-ID RF system and reduce the ene
... Show MoreStuck pipe is a prevalent and costly issue in drilling operations, with the potential to cost the petroleum industry billions of dollars annually. To reduce the likelihood of this issue, efforts have been made to identify the causes of stuck pipes. The main mechanisms that cause stuck pipes include drill cutting of the formation, inappropriate hole-cleaning, wellbore instability, and differential sticking forces, particularly in highly deviated wellbores. The significant consequences of a stuck pipe include an increase in well costs and Non-Productive Time (NPT), and in the worst-case scenario, the loss of a wellbore section and down-hole equipment, or the need to sidetrack, plug, or abandon the well. This paper provides a comprehensive
... Show MoreHard-grade asphalt binders like AC20-30 typically exhibit excessive stiffness, reduced penetration, and compromised workability, necessitating modification before use in paving applications. This study evaluates the efficacy of regular polyalphaolefin (PAO), a synthetic olefin-based lubricant, as a performance-enhancing modifying agent for such binders. AC20-30 was blended with PAO at dosages ranging from 2 wt.% to 10 wt.%, and the modified binders were characterized via penetration, ductility, softening point, and rotational viscosity measurements, alongside advanced rheological and chemical-morphological analyses. Incorporating PAO in AC20-30 asphalt progressively reduced the binder stiffness and enhanced its flexibility, with all modifie
... Show MoreIn this paper, we will illustrate a gamma regression model assuming that the dependent variable (Y) is a gamma distribution and that it's mean ( ) is related through a linear predictor with link function which is identity link function g(μ) = μ. It also contains the shape parameter which is not constant and depends on the linear predictor and with link function which is the log link and we will estimate the parameters of gamma regression by using two estimation methods which are The Maximum Likelihood and the Bayesian and a comparison between these methods by using the standard comparison of average squares of error (MSE), where the two methods were applied to real da
... Show MoreIn order to promote sustainable steel-concrete composite structures, special shear connectors that can facilitate deconstruction are needed. A lockbolt demountable shear connector (LB-DSC), including a grout-filled steel tube embedded in the concrete slab and fastened to a geometrically compatible partial-thread bolt, which is bolted on the steel section's top flange of a composite beam, was proposed. The main drawback of previous similar demountable bolts is the sudden slip of the bolt inside its hole. This bolt has a locked conical seat lug that is secured inside a predrilled compatible counter-sunk hole in the steel section's flange to provide a non-slip bolt-flange connection. Deconstruction is achieved by demounting the tube from the t
... Show MoreIn the current worldwide health crisis produced by coronavirus disease (COVID-19), researchers and medical specialists began looking for new ways to tackle the epidemic. According to recent studies, Machine Learning (ML) has been effectively deployed in the health sector. Medical imaging sources (radiography and computed tomography) have aided in the development of artificial intelligence(AI) strategies to tackle the coronavirus outbreak. As a result, a classical machine learning approach for coronavirus detection from Computerized Tomography (CT) images was developed. In this study, the convolutional neural network (CNN) model for feature extraction and support vector machine (SVM) for the classification of axial
... Show MoreIn this paper, the deterministic and the stochastic models are proposed to study the interaction of the Coronavirus (COVID-19) with host cells inside the human body. In the deterministic model, the value of the basic reproduction number determines the persistence or extinction of the COVID-19. If , one infected cell will transmit the virus to less than one cell, as a result, the person carrying the Coronavirus will get rid of the disease .If the infected cell will be able to infect all cells that contain ACE receptors. The stochastic model proves that if are sufficiently large then maybe give us ultimate disease extinction although , and this facts also proved by computer simulation.