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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
Thu Dec 21 2023
Journal Name
Mathematical Modelling Of Engineering Problems
A Numerical Investigation into Wheel-Track Profile Optimization for Minimizing Stress and Mitigating Hunting Phenomena
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Publication Date
Sat Aug 01 2026
Journal Name
Chemical Engineering Research And Design
Waste-derived silica and alumina as sustainable additives for enhanced water-based drilling mud formulations
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The escalating generation of industrial waste alongside the growing demand for high-performance, environmentally sustainable drilling fluids presents critical challenges to the oil and gas sector. Conventional drilling fluid additives are predominantly synthesized from virgin materials, contributing to resource depletion and environmental burden. Objectives: This study pioneers a circular economy approach by synthesizing silica nanoparticles (SiO2NPS) and alumina nanoparticles (Al2O3NPs) entirely from locally sourced industrial waste — bentonite clay and aluminum scrap, respectively — and evaluating their performance as functional additives in water-based drilling fluids (WBDFs). Novelty: To the best of our knowledge, this represents th

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Publication Date
Fri Mar 01 2024
Journal Name
Journal Of Energy Storage
Accelerated charging dynamics in shell-and-multi-tube latent heat storage systems for building applications
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Publication Date
Mon May 01 2023
Journal Name
International Journal Of Emerging Technologies In Learning
The Effect of Cognitive Modeling in Mathematics Achievement and Creative Intelligence for High School Students
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Publication Date
Fri Jun 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
Dumping and Its Challenges in Extent of World Trade Organization "Models for selected Agricultural Goods"
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The subject of dumping is considering today one of the subjects in which form an obstruction arise in front of the cycle of growth for some countries , such as the study of dumping is capturing a large attention by the competent because either a big  role and effect in growing the economies of nations then the subject of dumping became a field turn around its sides many measures and laws … and may be done resorting to by many states of the world to anti-dumping as approach of determent weapon delimit  the impact of dumping and gives the national agriculture sector the opportunity for rising and growing so this section of international economics is capturing a special importance and represent in same time an important

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Publication Date
Fri Mar 01 2019
Journal Name
Iraqi Journal Of Physics
Synthesized pure cobalt oxide nanostructure and doped with yttrium by hydrothermal method for photodetector applications
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In this study, pure Co3O4 nano structure and doping with 4 %, and
6 % of Yttrium is successfully synthesized by hydrothermal method.
The XRD examination, optical, electrical and photo sensing
properties have been studied for pure and doped Co3O4 thin films.
The X-ray diffraction (XRD) analysis shows that all films are
polycrystalline in nature, having cubic structure.
The optical properties indication that the optical energy gap follows
allowed direct electronic transition calculated using Tauc equation
and it increases for doped Co3O4. The photo sensing properties of
thin films are studied as a function of time at different wavelengths to
find the sensitivity for these lights.
High photo sensitivity dope

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Publication Date
Fri May 15 2026
Journal Name
Network
Toward Efficient Virtual Cell-Based Topology Management and Adaptive Routing for Underwater Wireless Sensor Networks
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Underwater Wireless Sensor Networks (UWSNs) play a vital role in ocean monitoring and exploration. However, harsh underwater conditions and frequent topology changes caused by node and sink mobility pose significant challenges for reliable routing. Conventional routing protocols that depend on global route reconstruction and static paths generate excessive control overhead and degrade performance in large-scale underwater environments. In this paper, we propose an energy-efficient virtual cell-based mobile-sink adaptive routing (VC-MAR) protocol for UWSNs. The sensing field is logically partitioned into a three-dimensional grid of virtual cells, where a cell-gateway is elected in each cell to construct a low-overhead routing backbon

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Publication Date
Fri May 01 2026
Journal Name
Journal Of Engineering
Electronic Circuit Design and Modeling of Biodegradable Mxene-Based Wireless Biosensor for Deep Wound Monitoring
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One of the most significant challenges of medical care is the infection of postoperative wounds, and conventional visual examination often fails to detect it early. This research proposes the design of an innovative, passive wireless telemetry system for non-intrusive monitoring of the wound-healing process.  The system integrates a biocompatible resonance circuit (LC) with a high-sensitivity piezoresistive sensor based on MXene (Ti3C2Tx). It operates within the standard industrial and medical (ISM) band at 13.56 MHz.The detection mechanism in the system is based on the principle of "impedance modulation" (Impedance Modulation), which arises from changes in the sensor's resistance under physiological tissue pressure. The system was

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Publication Date
Mon Apr 01 2019
Journal Name
Materials Science In Semiconductor Processing
Synthesis and annealing process of ultra-large SnS nanosheets for FTO/SnS/CdS/Pt photocathode
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SnS has been widely used in photoelectric devices due to its special band gap of 1.2-1.5 eV. Here, we reported on the fabrication of SnS nanosheets and the effect of synthesis condition together with heat treatment on its physical properties. The obtained band gap of the SnS nanosheets is in the rage of 1.37-1.41 eV. It was found that the photo-current density of a thin film comprised of SnS nanosheets could be enhanced significantly by annealing treatment. The maximum photo-current density of the stack structure of FTO/SnS/CdS/Pt was high as 389.5 mu A cm(-2), rendering its potential application in high efficiency solar hydrogen production.

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Publication Date
Sat Jul 01 2017
Journal Name
Journal Of Construction Engineering And Management
Identification, Quantification, and Classification of Potential Safety Risk for Sustainable Construction in the United States
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