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.
In this paper, the problem of resource allocation at Al-Raji Company for soft drinks and juices was studied. The company produces several types of tasks to produce juices and soft drinks, which need machines to accomplish these tasks, as it has 6 machines that want to allocate to 4 different tasks to accomplish these tasks. The machines assigned to each task are subject to failure, as these machines are repaired to participate again in the production process. From past records of the company, the probability of failure machines at each task was calculated depending on company data information. Also, the time required for each machine to complete each task was recorded. The aim of this paper is to determine the minimum expected ti
... Show MoreAir pollution refers to the release of pollutants into the air that are detrimental to human health and the planet as a whole.In this research, the air pollutants concentration measurements such as Total Suspended Particles(TSP), Carbon Monoxides(CO),Carbon Dioxide (CO2) and meteorological parameters including temperature (T), relative humidity (RH) and wind speed & direction were conducted in Baghdad city by several stations measuring numbered (22) stations located in different regions, and were classified into (industrial, commercial and residential) stations. Using Arc-GIS program ( spatial Analyses), different maps have been prepared for the distribution of different pollutant
We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed (LSD) to estimate the parameters an
... Show MoreFrom a group of 60 patients with dentoalveolar infections among which 10 were diabetic and 10 non-diabetic were elected as test group as well as 10 normal subjects as control group. Six Staphylococcus aureus and Streptococcus anginousus were diagnosed in the first and second group of the patients the immune status of the patients and control subject were tested by pathogen specific antibody titre, neotrophil NBT reduction phagocytosis and leukocyte inhibition LIF. Diabetic patients with dentoalveolar infection shows decreased specific antibody titers, subnormal neutrophil NBT phagocytic % as well as non significant LIF % in comparison non diabetic reveal high specific antibody titers against , high neutrophil NBT% and significant LIF% re
... Show MoreThe nucleon momentum distributions (NMD) for the ground state and elastic electron scattering form factors have been calculated in the framework of the coherent fluctuation model and expressed in terms of the weight function (fluctuation function). The weight function has been related to the nucleon density distributions of nuclei and determined from theory and experiment. The nucleon density distributions (NDD) is derived from a simple method based on the use of the single particle wave functions of the harmonic oscillator potential and the occupation numbers of the states. The feature of long-tail behavior at high momentum region of the NMD has been obtained using both the theoretical and experimental weight functions. The observed ele
... Show MoreThe ejector refrigeration system is a desirable choice to reduce energy consumption. A Computational Fluid Dynamics CFD simulation using the ANSYS package was performed to investigate the flow inside the ejector and determine the performance of a small-scale steam ejector. The experimental results showed that at the nozzle throat diameter of 2.6 mm and the evaporator temperature of 10oC, increasing boiler temperature from 110oC to 140oC decreases the entrainment ratio by 66.25%. At the boiler temperature of 120oC, increasing the evaporator temperature from 7.5 to 15 oC increases the entrainment ratio by 65.57%. While at the boiler temperature of 120oC and
... Show MoreObjective: To assess the clinical learning environment and clinical training for students' in maternal and child
health nursing.
Methodology: A descriptive study was conducted on non probability sample (purposive) of (175) students' in
Nursing College/ University of Baghdad for the period of June 19th to July 18th 2013. A questionnaire was used as a
tool of data collection to fulfill with objective of the study and consisted of three parts, including demographic,
clinical learning environment and clinical training for students' in maternal and child health nursing. Descriptive
statistical analyses were used to analyze the data.
Results: The results of the study revealed that the 65.1% of student at age which ranged b
The need for wireless sensing technology has rapidly increased recently, specifically the usage of electromagnetic waves which becoming more required as a source of information. Silicon carbide (SiC) Nano particles has been used in this study, the material under test (MUT) was exposed directly to a microwave field to examine the electromagnetic behavior. The permittivity and permeability were investigated with different filler materials to approach best and optimal electromagnetic absorbing characteristics to assist engineers to monitor structure-based composite for defects evaluation that may occur during operation conditions or through manufacturing process. XRD, FESEM and both complex permittivity and permeability were measured f
... Show MoreThe ground state proton, neutron and matter densities of exotic 11Be and 15C nuclei are studied by means of the TFSM and BCM. In TFSM, the calculations are based on using different model spaces for the core and the valence (halo) neutron. Besides single particle harmonic oscillator wave functions are employed with two different size parameters Bc and Bv. In BCM, the halo nucleus is considered as a composite projectile consisting of core and valence clusters bounded in a state of relative motion. The internal densities of the clusters are described by single particle Gaussian wave functions.
Elastic electron scattering proton f
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