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 orbital motion and longitude for some Jupiter's satellites (Amaletha, Europa, Ganymede and Callisto) were calculated from two different locations Iraq and Syria. A program was designed, the input parameters were the desired year, month, day and the longitude of the location, the output parameters results were applied in form of a file, and this file includes the longitude, orbital motion, and local time of these satellites. A specific date 1-10-2013 was taken, the results of longitude was (20-336) º and orbital motion was (92-331) º for both Iraq and Syria location with observing time (05:24:14-15:18:10) for Iraq and (04:56:33-14:50:30) for Syria. The difference in time between the two locations was constant (00:45:00), these results
... Show MoreThe Harmonic Oscillator (HO) and Gaussian (GS) wave functions within the Binary Cluster Model (BCM) were employed to investigate neutron, proton and matter densities of the ground state as well as the elastic proton form factors of one neutron 8Li and 22N halo nuclei. The long tail is a property that is clearly shown in the neutron density. The existence of a long tail in the neutron densities of 8Li and 22N indicates that these nuclei have a neutron halo structure. Moreover, the matter rms radii and the reaction cross section of these nuclei were calculated using the Glauber model.
In recent years, with the growing size and the importance of computer networks, it is very necessary to provide adequate protection for users data from snooping through the use of one of the protection techniques: encryption, firewall and intrusion detection systems etc. Intrusion detection systems is considered one of the most important components in the computer networks that deal with Network security problems. In this research, we suggested the intrusion detection and classification system through merging Fuzzy logic and Artificial Bee Colony Algorithm. Fuzzy logic has been used to build a classifier which has the ability to distinguish between the behavior of the normal user and behavior of the intruder. The artificial bee colony al
... Show MoreIn this work, chemical oxidation was used to polymerize conjugated polymer "Polypyrrole" at room temperature Graphene nanoparticles were added by in situ-polymerization to get (PPY-GN) nano. Optical and Electrical properties were studied for the nanocomposites. optical properties of the nanocomposites were studied by UV-Vis spectroscopy at wavelength range (200 -800 nm). The result showed optical absorption spectra were normally determined and the result showed that the maximum absorbance wave length at 280nm and 590nm. The optical energy gap has been evaluated by direct transition and the value has decreased from (2.1 eV for pure PPy) to (1.3 eV for 5 %wt. of GN). The optical constants such as the band tail width ΔE was evaluated, the
... Show MoreSkills learning is considered as an important factor in learning any subject as well as mathematics . Mathematical skills have a number of steps that should be learned and understood faster and with more accuracy . The practical or applied skills are type of learning which includes educational preparation and hand on skills is acquired which conducted by organized educational institutions. The sample included (120) students (males and females) first year / dept.of electrical technigues . The mathematical skills are implemented to wire up the electrical circuts. Test is implemented with questions concerned with the skills .statistical operations were conducted as well as the validity and standard deviation for the test .The results showed
... Show MoreCopper Phthalocyanine (CuPc) thin film with and without multi-walled carbon nanotubes (MWCNTs) is prepared using the solution based method and used in gas sensor and solar cell applications. The structural characteristics of the CuPc thin films showed a single peak around 7o with the preferred orientation for charge transportation. Using atomic force microscopy (AFM), morphological properties show a rough surface with some aggregates and ribbons. The optical absorption properties were determined using UV-Visible absorption spectroscopy; the optical band gap has varied after adding MWCNTs to CuPc. Electrical conductivity of CuPc:MWCNTs composite is higher than that of the pure CuPc. The CuPc thin film sensr have sh
... Show MoreThis study included prepared samples of epoxy reinforced by the novolac , aluminum , glass powder and epoxy reinforced by aluminum , glass powder and epoxy alone .They are used as reinforced materials of volum fraction amounting 40% . The mechanical properties inclouded ( tensile , compressive and wear) where the wear test inclouded different applied loads (5,10,15) . From the results showed the epoxy reinforced by aluminum and glass powder has higher compressive strength (56.91) Mpa and higher tensile strength (132.2) Mpa .But the epoxy alone has higher wear rate and the epoxy reinforced by aluminum and glass powder which have higher elasticity of modulus from the tensile test (315.7) Mpa
Ball and Plate (B&P) system is a benchmark system in the control engineering field that has been used to verify many control methods. In this paper the design of a sliding mode . controller has been investigated and verified in real-time via implementation on a real ball and plate system hardware. The mathematical model has been derived and the necessary parameters have been measured. The sliding mode controller has been designed based on the obtained mathematical model. The resulting controller has been implemented using the Arduino Mega 2560 and a ball and plate system built completely from scratch. The Arduino has been programmed by the Arduino support target for Simulink. Three test signals has been used for verification purposes
... Show MoreThe provision of safe water for people is a human right; historically, a major number of people depend on groundwater as a source of water for their needs, such as agricultural, industrial or human activities. Water resources have recently been affected by organic and/or inorganic contaminants as a result of population growth and increased anthropogenic activity, soil leaching and pollution. Water resource remediation has become a serious environmental concern, since it has a direct impact on many aspects of people’s lives. For decades, the pump-and-treat method has been considered the predominant treatment process for the remediation of contaminated groundwater with organic and inorganic contaminants. On the other side, this tech
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