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 event of crossing the barriers is one of the Power Games activities that have received great attention in the field of researches. Which led to ma..
The aim of the research is to know the effect of a training program based on interactive teaching strategies on achievement and creative problem solving among fourth-grade students in chemistry of the directorate of education Rusafa first, the sample was divided into two groups, one experimental and numbering (29) students and the other control group numbering (30) students. The experimental group underwent the training program in the first semester of the year (2021-2022) and the control one studied according to the usual method. Two tools were built, the first being an academic achievement test consisting of (40) multiple-choice items, and the second a test of creative problem-solving skills in a chemistry subject and consisting o
... Show MoreThe research aims to recognize the impact of the training program based on integrating future thinking skills and classroom interaction patterns for mathematics teachers and providing their students with creative solution skills. To achieve the goal of the research, the following hypothesis was formulated: There is no statistically significant difference at the level (0.05) between the mean scores of students of mathematics teachers whose teachers trained according to the proposed training program (the experimental group) and whose teachers were not trained according to the proposed training program (the control group) in Pre-post creative solution skills test. Research sample is consisted of (31) teachers and schools were distribut
... Show MoreThe objective of this study is to attempt to provide a quantitative analysis to the causes of unemployment in Iraq and its mechanisms of generation, as well as a review of the most important types of both visible and invisible unemployment, and an attempt to measure the disguised unemployment and analyze the causes. The problem of the research lies in the fact that the Iraqi Economy has been suffered for a long time although its characterized by abundant physical and natural resources, from the existence of the phenomenon of unemployment in the previous two types. Causing a lot of economic problems, represented by the great waste of resources and
... Show MoreThis paper investigates the performance evaluation of two state feedback controllers, Pole Placement (PP) and Linear Quadratic Regulator (LQR). The two controllers are designed for a Mass-Spring-Damper (MSD) system found in numerous applications to stabilize the MSD system performance and minimize the position tracking error of the system output. The state space model of the MSD system is first developed. Then, two meta-heuristic optimizations, Simulated Annealing (SA) optimization and Ant Colony (AC) optimization are utilized to optimize feedback gains matrix K of the PP and the weighting matrices Q and R of the LQR to make the MSD system reach stabilization and reduce the oscillation of the response. The Matlab softwar
... Show MoreBackground. The motor response is a fundamental ability that is evident during any physical or motor activity. However, the need for this ability varies from one sport to another and depends on the specific skills required in each sport. Objectives. This study aims to compare the average motor reaction times of the arm and leg among handball, basketball, and volleyball players aged 14 to 16 years. Methods. The sample included 30 players aged 14-16 years from the sports talent care center, evenly distributed on handball, basketball, and volleyball. Standardized tests were used to measure the speed of motor response, including the Batak Micro test for hands, which records the number of responses to light stimuli in 30 seconds, and the Saqer t
... Show MoreAlgae have been used in different applications in various fields such as the pharmaceutical industry, environmental treatments, and biotechnology. Studies show that the preparation of nanoparticles by a green synthesis method is a promising solution to many medical and environmental issues. In the current study, the green alga Stigeoclonium attenuatum (Hazen) F.S. Collins 1909 was isolated and identified from the Al-Hillah River (Governorate of Babylon) in the middle of Iraq. The green synthesis by the aqueous extract of algae was used to prepare the nanoflakes of ZnO. Nanoflakes of ZnO are characterized by X-Ray diffraction (XRD) and scanning electron microscope (SEM) with flakes shape and dimensions ranging be
... Show MoreAcrylic polymer/cement nanocomposites in dark and light colors have been developed for coating floors and swimming pools. This work aims to emphasize the effect of cement filling on the mechanical parameters, thermal stability, and wettability of acrylic polymer. The preparation was carried out using the casting method from acrylic polymer coating solution, which was added to cement nanoparticles (65 nm) with weight concentrations of (0, 1, 2, 4, and 8 wt%) to achieve high-quality specifications and good adhesion. Maximum impact strength and Hardness shore A were observed at cement ratios of 2 wt% and 4 wt%, respectively. Changing the filling ratio has a significant effect on the strain of the nanocomposites. The contact angle was i
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