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.
The purpose of this experiment was to determine the relationship between the path coefficient and seed rate for four different barley cultivars (Amal, Ibaa 265, Ibaa 99, and Buhooth 244) during the 2019-2020 winter season. The experiment was carried out using a split plot design with three replications according to a randomized complete block design (RCBD). The highest positive thru effect on grain yield was found for flag leaf area and harvest index at aseeding rate of 130 kg.h-1; the highest positive direct effect on grain yield was found for flag leaf area and plant height at aseeding rate of 160 kg.h-1; and the highest positive direct effe
A total of 20 raw milk samples were used as the fouling agent for evaluating the bacteriological effectiveness of cleaning and sanitizing of domestic milking equipment by using ozonated water at 0.5 ppm comparing to the warm water at 55! for 5 minutes respectively. The mean values of total aerobic bacteria, Coliform and E.coli that present on the plastic and stainless-steel containers after using the raw milk as fouling agent were 3.4×10-6 , 6.7x10-5 and 5.8×10-3 cfu/cm2 respectively , after cleaning the stainless steel containers by the ozonated water the mean values of total aerobic bacterial counts, Coliforms and E.coli bacteria were reduced to 1.2×10-6, 4.7×10-5 and 3.3×10-3 CFU/cm2 respectively. while after cleaning by the warm wa
... Show MoreMost available methods for unit hydrographs (SUH) derivation involve manual, subjective fitting of
a hydrograph through a few data points. The use of probability distributions for the derivation of synthetic
hydrographs had received much attention because of its similarity with unit hydrograph properties. In this
paper, the use of two flexible probability distributions is presented. For each distribution the unknown
parameters were derived in terms of the time to peak(tp), and the peak discharge(Qp). A simple Matlab
program is prepared for calculating these parameters and their validity was checked using comparison
with field data. Application to field data shows that the gamma and lognormal distributions had fit well.<
The energy requirements of corn silage harvesters and the application of precision agricultural techniques are essential for efficient and productive agricultural practices. The article aims to review previous studies on the energy requirements needed for different corn silage harvesting machines, and on the other hand, to present methods for measuring corn silage productivity directly in the field and monitoring it based on microcontrollers and artificial intelligence techniques. The process of making corn silage is done by cutting green fodder plants into small pieces, so special harvesters are used for this, called corn silage harvesters. The purpose of harvesting corn silage is to efficiently collect and store as many digestible nutrien
... Show MoreThe theatre costume with the rest of the theatre show elements constitute a system of the meaning relations that produce a visual image that helps the recipient to decipher the theatre scene, let alone the manifestation of time in its levels (past, present, future) through the design construction of the theatre elements among which is the theatre costume. In order to know the way of manifesting time through the formulation of the theatre costumes, the research question has been put as follows: how to manifest time through the design construction for the theatre costumes unit, from which the research objective is derived as follows: Revealing the possibility of the designing unit of the costumes in manifesting the levels of time wit
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