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.
Moment invariants have wide applications in image recognition since they were proposed.
The current research deals with practical studies that explain to the Iraqi consumer multiple instances about the phenomenon of water hammer which occur in the water pipeline operating with pressure. It concern a practical study of the characteristics of this phenomenon and economically harmful to the consumer the same time. Multiple pipe fittings are used aimed to reduce this phenomenon and its work as alternatives to the manufactured arresters that used to avoid water hammer in the sanitary installations, while the consumer did not have any knowledge as to the non-traded for many reasons, including the water pressure decreases in the networks and the use of consumer pumps to draw water directly from the network. Study found a number of
... Show MoreThe Environmental Data Acquisition Telemetry System is a versatile, flexible and economical means to accumulate data from multiple sensors at remote locations over an extended period of time; the data is normally transferred to the final destination and saved for further analysis.
This paper introduces the design and implementation of a simplified, economical and practical telemetry system to collect and transfer the environmental parameters (humidity, temperature, pressure etc.) from a remote location (Rural Area) to the processing and displaying unit.
To get a flexible and practical system, three data transfer methods (three systems) were proposed (including the design and implementation) for rural area services, the fi
... Show MoreIn the current study, haemoglobin analytes dissolved in a special buffer (KH2PO4(1M), K2HPO4(1M)) with pH of 7.4 were used to record absorption spectra measurements with a range of concentrations from (10-8 to 10-9) M and an absorption peak of 440nm using Broadband Cavity Enhanced Absorption Spectroscopy (BBCEAS) which is considered a simple, low cost, and robust setup. The principle work of this technique depends on the multiple reflections between the light source, which is represented by the Light Emitting Diode 3 W, and the detector, which is represented by the Avantes spectrophotomer. The optical cavity includes two high reflectivity ≥99% dielectric mirrors (dia
... Show MoreBased on a finite element analysis using Matlab coding, eigenvalue problem has been formulated and solved for the buckling analysis of non-prismatic columns. Different numbers of elements per column length have been used to assess the rate of convergence for the model. Then the proposed model has been used to determine the critical buckling load factor () for the idealized supported columns based on the comparison of their buckling loads with the corresponding hinge supported columns . Finally in this study the critical buckling factor () under end force (P) increases by about 3.71% with the tapered ratio increment of 10% for different end supported columns and the relationship between normalized critical load and slenderness ratio was g
... Show MoreTopology and its applications occupy the interest of many researching centers in the advanced world. From this point of view and because the near open sets play a very important role in general topology and they are now the research topics of many topologists worldwide and its sets doesn’t enter in fibrewise topology yet. Therefore, we use some of the near open sets to be model for introduce results and new spaces in fibrewise topological spaces. Also, there is a very important role of closure operators in constructing a topological spaces, so we introduce a new closure operators on the power set of vertices on graphs and conclusion theorems and new spaces from it. Furthermore, we discuss the relationships of connectedness between some ty
... Show MoreThe research deals with the structures of the contemporary travelers' buildings in particular, and which is a functional complex installations where flexibility, technical and stereotypes play an important role as well as the human values These facilities must represent physiological and psychological comfort for travelers. TThose are facilities where architectural form plays a distinguished role in reversing the specialty and identity of the building. Hence the importance of the subject has been in forced, as a result for the need to study these facilities and to determine the impact and affects by the surrounding environment, to the extent of the urban, environmental, urban, social, and psychological levels. The importance of the resea
... Show MoreThe operating characteristics of optoelectronic devices depend critically on the properties physical of the constituent materials, interesting compound has been focused on this research formed from group III and V of the periodic table. Thin film n-InSb heterjuntion were successfully fabricated on p-Si substrates by thermal evaporation technique at different annealing temperature (as prepared, 400,500,600) °C. The effect of annealing temperature on the structural, surface morphology, optical and optoelectronic properties of InSb films were investigated and studied. The crystal structure of the film was characterized by X-ray diffraction and techniques. AFM techniques inspect the surface morphology of InSb films, the study presented the val
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