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.
Background Numerous studies indicated that workers in the health sector suffer from work stress, hassles, and mental health problems associated with COVID-19, which negatively affect the completion of their job tasks. These studies pointed out the need to search for mechanisms that enable workers to cope with job stress effectively. Objectives This study investigated psychological flow, mental immunity, and job performance levels among the mental health workforce in Saudi Arabia. It also tried to reveal the psychological flow (PF) and mental immunity (MI) predictability of job performance (JP). Method A correlational survey design was employed. The study sample consisted of 120 mental health care practitioners (therapists, psychologists, co
... Show MoreThe present paper attempts to find out the role of developmental loans in promoting strategic crops especially the basis stemming from the problem of non - defining economic feasibility study and the negative or positive revenues of developmental loans, directed to Iraqi Agricultural sector in general and Basic strategic crops in particular which resulted in the difficulty of planning and future prediction to grant loans agriculturally directed in terms of quality and quantity and the arbitrary of distributing these loans .the strategic crops have been selected as sample of population where the sample of Basic strategic crops include wheat and barley .The paper has come to several of conclusions mainly are as follows :- the increase in n
... Show MoreThis research investigates the adsorption isotherm and adsorption kinetics of nitrogen from air using packed bed of Li-LSX zeolite to get medical oxygen. Experiments were carried out to estimate the produced oxygen purity under different operating conditions: input pressure of 0.5 – 2.5 bar, feed flow rate of air of 2 – 10 L.min-1 and packing height of 9-16 cm. The adsorption isotherm was studied at the best conditions of input pressure of 2.5 bar, the height of packing 16 cm, and flow rate 6 Lmin-1 at ambient temperature, at these conditions the highest purity of oxygen by this system 73.15 vol % of outlet gas was produced. Langmuir isotherm was the best models representing the experimental data., and the m
... Show MoreThe paper presents the results of the research on the influence of the adjuvant concentration on the size of the drops produced by the spray nozzles of agricultural sprayers. For the tests, adjuvant Normaton with the composition of total nitrogen, amide nitrogen (N-NH2) and phosphorus pentoxide (P2O5) was used. The adjuvant was added to the water taken from the municipal water supply system of the city of Lublin. The tests were carried out for three concentrations, i.e. 75%, 100%, and 125% of the adjuvant concentration recommended by the manufacturer, and water without the adjuvant. The surface tension of water with adjuva
Polarization is an important property of light, which refers to the direction of electric field oscillations. Polarization modulation plays an essential role for polarization encoding quantum key distribution (QKD). Polarization is used to encode photons in the QKD systems. In this work, visible-range polarizers with optimal dimensions based on resonance grating waveguides have been numerically designed and investigated using the COMSOL Multiphysics Software. Two structures have been designed, namely a singlelayer metasurface grating (SLMG) polarizer and an interlayer metasurface grating (ILMG) polarizer. Both structures have demonstrated high extinction ratios, ~1.8·103 and 8.68·104 , and the bandwidths equal to 45 and 55 nm for th
... Show MoreIn this work, microbubble dispersed air flotation technique was applied for cadmium ions removal from wastewater aqueous solution. Experiments parameters such as pH (3, 4, 5, and 6), initial Cd(II) ions concentration (40, 80, and 120 mg/l) contact time( 2, 5, 10 , 15, and 20min), and surfactant (10, 20and 40mg/l) were studied in order to optimize the best conditions .The experimental results indicate that microbubbles were quite effective in removing cadmium ions and the anionic surfactant SDS was found to be more efficient than cationic CTAB in flotation process. 92.3% maximum removal efficiency achieved through 15min at pH 5, SDS surfactant concentration 20mg/l, flow rate250 cm3/min and at 40mg/l Cd(II) ions initial co
... Show MoreThe problem of Bi-level programming is to reduce or maximize the function of the target by having another target function within the constraints. This problem has received a great deal of attention in the programming community due to the proliferation of applications and the use of evolutionary algorithms in addressing this kind of problem. Two non-linear bi-level programming methods are used in this paper. The goal is to achieve the optimal solution through the simulation method using the Monte Carlo method using different small and large sample sizes. The research reached the Branch Bound algorithm was preferred in solving the problem of non-linear two-level programming this is because the results were better.