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Direct and inverse source problems for degenerate parabolic equations
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Abstract<p>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.</p>
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Publication Date
Tue Jul 01 2025
Journal Name
Ain Shams Engineering Journal
Deep neural networks for speech enhancement and speech recognition: A systematic review
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Publication Date
Sat Dec 01 2018
Journal Name
Indonesian Journal Of Electrical Engineering And Computer Science
An Energy-Aware and Load-balancing Routing scheme for Wireless Sensor Networks
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<p>Energy and memory limitations are considerable constraints of sensor nodes in wireless sensor networks (WSNs). The limited energy supplied to network nodes causes WSNs to face crucial functional limitations. Therefore, the problem of limited energy resource on sensor nodes can only be addressed by using them efficiently. In this research work, an energy-balancing routing scheme for in-network data aggregation is presented. This scheme is referred to as Energy-aware and load-Balancing Routing scheme for Data Aggregation (hereinafter referred to as EBR-DA). The EBRDA aims to provide an energy efficient multiple-hop routing to the destination on the basis of the quality of the links between the source and destination. In

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Publication Date
Wed Jan 01 2014
Journal Name
Advances In Mechanical Engineering
Experimental and Numerical Investigations of Heat Transfer Characteristics for Impinging Swirl Flow
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This paper reports experimental and computational fluid dynamics (CFD) modelling studies to investigate the effect of the swirl intensity on the heat transfer characteristics of conventional and swirl impingement air jets at a constant nozzle-to-plate distance ( L = 2 D). The experiments were performed using classical twisted tape inserts in a nozzle jet with three twist ratios ( y = 2.93, 3.91, and 4.89) and Reynolds numbers that varied from 4000 to 16000. The results indicate that the radial uniformity of Nusselt number (Nu) of swirl impingement air jets (SIJ) depended on the values of the swirl intensity and the air Reynolds number. The results also revealed that the SIJ that was fitted with an insert of y = 4.89, which correspo

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Publication Date
Sat Jul 01 2023
Journal Name
International Journal Of Intelligent Engineering And Systems
An Efficient Cryptosystem for Image Using 1D and 2D Logistic Chaotic Maps
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Publication Date
Thu Jul 02 2026
Journal Name
Journal Of Engineering
Design and Implementation of Super Elman Neural Network for SDN Robotics System
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Path planning in autonomous robotic systems (ARS) is challenging, especially in dynamic or uncertain environments. Many classical methods are computationally expensive and lack adaptability to real-world scenarios. In order to improve the overall path-planning capabilities of robots; this paper introduces a new smart robotic navigation system which uses Software Defined Network (SDN) and Multi-Spike Elman Neural Network (MS-ENN). The introduced system includes an innovative way to encode temporal information using multiple spikes which can capture much greater amounts of detail about changing environmental characteristics than conventional artificial neural networks. Additionally, it includes a spiking wave-front planner (SWP) to pr

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Publication Date
Fri May 01 2026
Journal Name
Journal Of Engineering
Crosslinked Gelatin for Sunset Yellow Dye Removal: Synthesis, Characterization, and Adsorption Performance
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Gelatin is a valuable substance that is known to have a complex 3D structure, but it has limited adsorption efficiency, which limit its application at physiological temperature. In this paper, gelatin was improved by the addition of glutaraldehyde (GTA) to enhance its ability to adsorb dye in aqueous solution. The adsorption experiments were conducted under different conditions, such as the amount of adsorbent, the concentration of the dye, and the temperature. The study found that the qe by GTA-GE (4.978 to 23.056 mg/g) and GE (4.8 to 21.333 mg/g) increased with the increase of initial dye concentrations but decreased with the amount of adsorbent. The parameters at equilibrium were at a pH of 4 and a dose of adsorbent of 100 mg in

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Publication Date
Mon Mar 01 2021
Journal Name
Iraqi Journal Of Physics
Linear and Non-Linear Optical Properties for Organic Semiconductor (CuPc) Thin Films
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Thin films of CuPc of various thicknesses (150,300 and 450) nm have been deposited using pulsed laser deposition technique at room temperature. The study showed that the spectra of the optical absorption of the thin films of the CuPc  are two bands of absorption one in the visible region at about 635 nm, referred to as Q-band, and the second in ultra-violet region where B-band is located at 330 nm. CuPc thin films were found to have direct band gap with values around (1.81 and 3.14 (eV respectively. The vibrational studies were carried out using Fourier transform infrared spectroscopy (FT-IR). Finally, From open and closed aperture Z-scan data non-linear absorption coefficient and non-linear refractive index have been calculated res

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Publication Date
Tue Jul 01 2025
Journal Name
South African Journal Of Chemical Engineering
Electrocoagulation process for cobalt removal from industrial wastewater: Optimization and kinetic study
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Publication Date
Mon May 04 2020
Journal Name
Offshore Technology Conference
Hydrate Equilibrium Model for Gas Mixtures Containing Methane, Nitrogen and Carbon Dioxide
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Abstract<p>Gas hydrate formation is considered one of the major problems facing the oil and gas industry as it poses a significant threat to the production, transportation and processing of natural gas. These solid structures can nucleate and agglomerate gradually so that a large cluster of hydrate is formed, which can clog flow lines, chokes, valves, and other production facilities. Thus, an accurate predictive model is necessary for designing natural gas production systems at safe operating conditions and mitigating the issues induced by the formation of hydrates. In this context, a thermodynamic model for gas hydrate equilibrium conditions and cage occupancies of N2 + CH4 and N2 + CO4 gas mix</p> ... Show More
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Publication Date
Wed Jan 01 2020
Journal Name
Ieee Access
Modified Elman Spike Neural Network for Identification and Control of Dynamic System
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