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.
Neurogenic inflammation is pivotal in dental pulp repair, involving complex interactions between sensory nerves, immune cells, and dental pulp stem cells (DPSCs). This review aimed to identify the favorable pathways of neurogenic inflammation and neurogenic differentiation of DPSCs in the pulpal healing process. Also, to identify the techniques used to evaluate these inflammatory and differentiation processes. Both PubMed and Google Scholar databases were employed in the search strategy using keyword combinations based on MeSH terms. The search was performed for published articles in English from January 2014 to November 2024, including studies with histological and molecular findings. 29 articles only met the inclusion criteria. Neurogenic
... Show MoreIn this work, a vertical pulsating heat pipe heat exchanger (PHPHE) was designed for waste heat recovery, exchanging thermal energy between two air streams in a counterflow configuration. The heat exchanger consists of six rows, each row consists of one pulsating heat pipe (PHP), and each PHP has six turns. The working fluid used in the heat pipe was acetone with fill ratios of 50%, 60%, and 70%. The effect of evaporator inlet temperature at 40, 45, and 50°C and air velocity at 0.5, 0.7, and 0.9 m/s on the pulsating heat pipes consisting of three sections- evaporator, condenser, and adiabatic, whose dimensions were 25 x 25 x 10 cm, was studied. At the same time, the condenser temperature was maintained at 26°C. The system’s th
... Show MoreA new novel series of metalcomplexes are prepared from reactions between 2-benzoylthiobenzimidazole (L) with metal salts of Co (II) , Fe(III) and Rh (III) , while Pd(II) complex was obtained by mixing ligandsof 2-benzoylthiobenzimidazole (L) as primary ligand and bipyridine (L/ )as secondary ligand as well as palladium chloride as metal salt in an ethanoic medium. The geometry of these compounds were identified using C.H.N.microanalysis, Ultraviolet–visible, Fourier transforms infrared, magnetic susceptibility, molar conductivity and flame atomic absorption (A.A). From the dataobtained by these spectral analyses, the molecular structures for Rh and Fe complexes were proposed to be octahedral geometry. A square planar construction is propo
... Show MoreThe electrical and thermal performance of a typical single pass hybrid photovoltaic/thermal (PV/T) air collector is modeled, simulated and analyzed for two selected case studies in Iraq. An improved mathematical thermo-electrical model is derived in terms of design, operating and climatic parameters of the hybrid solar collector to evaluate its important characteristics: collector flow and heat removal factors, PV maximum power point and its temperature coefficient, and overall power and efficiency. Unlike previous PV/T thermal models, the present model is obtained with some additions and corrections in radiation and convection heat coefficients for the top loss and for the air duct with more applicable sky temperature correlation. The well
... Show MoreThin films of pure WO3 and the binary systems of TiO2:WO3,MoO3:WO3,Cr2O3:WO3, and SnO2:WO3 were prepared by pulsed laser deposition method. The single and binary compounds were sintered at 1273K for five hours. The deposition were done under vacuum of 2x10-2 Torr at various substrates like glass and single crystal silicon wafer with negative conductance at ambient temperature thickness of ≍150 nm. The structures and morphology of pure WO3
The current study investigated the stability and the extraction efficiency of emulsion liquid membrane (ELM) for Abamectin pesticide removal from aqueous solution. The stability was investigated in terms of droplet emulsion size distribution and emulsion breakage percent. The proposed ELM included a mixture of corn oil and kerosene (1:1) as a diluent, Span 80 (sorbitan monooleate) as a surfactant and hydrochloric acid (HCl) as a stripping agent without utilizing a carrier agent. Parameters such as homogenizer speed, surfactant concentration, emulsification time and internal to organic volume ratio (I/O) were evaluated. Results show that the lower droplet size of 0.9 µm and higher stable emulsion in terms of breakage percent of 1.12 % were
... Show MoreOne of the key challenges is reliable communication for Unmanned Underwater Vehicles (UUVs) since underwater environments are dynamic and challenging for signal transmission. The traditional acoustic communication systems allow long-distance communication but are limited by the low bandwidth, high latency, and doppler effect. Optical wireless, on the other hand, provides high data rates with water absorption and scattering occurring within the transmission distance, but has a short range of communication. To overcome these drawbacks, a smart hybrid optical-acoustic communication system is proposed that is a combination of Wavelength Division Multiplexing and On-Off Keying (WDM-OOK) to transmit a high-speed signal over optical and ac
... Show MoreThis research presents a response surface methodology (RSM) with I‐optimal method of DESIGN EXPERT (version 13 Stat‐Ease) for optimization and analysis of the adsorption process of the cyanide from aqueous solution by activated carbon (AC) and composite activated carbon (CuO/AC) produced by pyro carbonic acid microwave using potato peel waste as raw material. Pyrophosphate 60% (wt) was used for impregnation with an impregnation ratio 3:1, impregnation time of 4 h at 25°C, radiant power of 700 W, and activation time of 20 min. Batch experiments were conducted to determine the removal efficiency of cyanide from aqueous solution to evaluate the influences of various experimental parameters su