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.
Friction stir spot welding (FSSW) is a relatively new welding process that may have significant advantages compared to the fusion processes as follows joining of conventionally non-fusion weldable alloys, reduced distortion and improved mechanical properties of weldable alloys joints due to the pure solidstate joining of metals. In this paper, a three-dimensional model based on finite element analysis is used to study the thermal history in the spot-welding of aluminum alloy 2024. The model take place the thermomechanical property on the process of the welded metals. The thermal history and the evolution results with numerical model at the measured point in the friction stirred spot weld have a good matching, then the prediction of the t
... Show MoreMany approaches of different complexity already exist to edge detection in
color images. Nevertheless, the question remains of how different are the results
when employing computational costly techniques instead of simple ones. This
paper presents a comparative study on two approaches to color edge detection to
reduce noise in image. The approaches are based on the Sobel operator and the
Laplace operator. Furthermore, an efficient algorithm for implementing the two
operators is presented. The operators have been applied to real images. The results
are presented in this paper. It is shown that the quality of the results increases by
using second derivative operator (Laplace operator). And noise reduced in a good
Abstrct
The administrations of Presidents Clinton and Bush Jr. have seen the emergence of neoconservatives. The neoconservative were the establishment of the Project for the New American Century (PNAC) project in 1997 during the Clinton administration. The neoconservatives, through the New Century Project, were able to make important foreign policy decisions, notably the Iraq Liberation Law, which was passed by Congress on January 26, 1998 and signed by President Clinton and became a law legitimized. Clinton became authorized to take whatever measures he saw fit to contribute to regime change in Iraq. The Bush administration has also undergone major and significant shifts in US strategy on US foreign policy. During the Bush admin
... Show MoreThe radial wave function R(r) and the radial distribution function P(r) as a function of (r), for the Hydrogen atom was calculated for several atomic state (1s,2s,2p,3s,3p,3d) The results were compared with Hydrogen like atom(He+,Li+2,Be+3).
The study showed that there are (28) plant families present in Al-Razzaza Lake. The families are (Amaranthaceae, Amaryllidaceae, Aizoaceae, Apiaceae, Apocynaceae, Asteraceae, Brassicaceae, Boraginaceae, Capparaceae, Caryophyllaceae, Cistaceae, Colchicaceae, Convolvulaceae, Cynomoriaceae, Fabaceae, Frankeniaceae, Lamiaceae, Liliaceae, Malvaceae, Orobanchaceae, Plantaginaceae, Poaceae, Polygonaceae, Ranunculaceae, Solanaceae, Tamaricaceae,Typhaceae, Zygophyllaceae). Asteraceae family is the largest number of species found in abundance in this lake, followed by the Fabaceae family.
The zeolite's textural properties have a significant effect on zeolite's effectiveness in the different industrial processes. This research aimed to study the textual properties of the NaX and FeX zeolites using the nitrogen adsorption-desorption technique at a constant low temperature. According to the International Union of Pure and Applied Chemistry, the adsorption-desorption isotherm showed that the studied materials were mixed kinds I/II isotherms and H3 type hysteresis. The Brunauer-Emmett-Teller isotherm was the best model to describe the nitrogen adsorption-desorption better than the Langmuir and Freundlich isotherms. The obtained adsorption capacity and Brunauer-Emmett-Teller surface area values for NaX were greater than FeX. Ac
... Show MoreIn this study NiO - CoO bimetallic catalysts are prepared with two Ni/Co ratios (70:30 and 80: 20) using the precipitation method of nitrate salts. The effects of Ni /Co ratio and preparation methods on the catalyst are analyzed by using different characterization techniques, i.e. atomic absorption (AA) , XRD, surface area and pore volume measurements according to the BET method . The results indicate that the best catalyst is the one containing the percentage of Ni :Co ( 70 : 30 ). Experiments indicate that the optimal conditions to prepare catalyst are stirring for three hours at a temperature of 60oC of the preparation , pH= (8-9) , calcination temperature at 400oC for two hours
... Show MoreLost circulation or losses in drilling fluid is one of the most important problems in the oil and gas industry, and it appeared at the beginning of this industry, which caused many problems during the drilling process, which may lead to closing the well and stopping the drilling process. The drilling muds are relatively expensive, especially the muds that contain oil-based mud or that contain special additives, so it is not economically beneficial to waste and lose these muds. The treatment of drilling fluid losses is also somewhat expensive as a result of the wasted time that it caused, as well as the high cost of materials used in the treatment such as heavy materials, cement, and others. The best way to deal with drilling fluid losses
... Show MoreIn data mining, classification is a form of data analysis that can be used to extract models describing important data classes. Two of the well known algorithms used in data mining classification are Backpropagation Neural Network (BNN) and Naïve Bayesian (NB). This paper investigates the performance of these two classification methods using the Car Evaluation dataset. Two models were built for both algorithms and the results were compared. Our experimental results indicated that the BNN classifier yield higher accuracy as compared to the NB classifier but it is less efficient because it is time-consuming and difficult to analyze due to its black-box implementation.