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.
Ensuring reliable data transmission in Network on Chip (NoC) is one of the most challenging tasks, especially in noisy environments. As crosstalk, interference, and radiation were increased with manufacturers' increasing tendency to reduce the area, increase the frequencies, and reduce the voltages. So many Error Control Codes (ECC) were proposed with different error detection and correction capacities and various degrees of complexity. Code with Crosstalk Avoidance and Error Correction (CCAEC) for network-on-chip interconnects uses simple parity check bits as the main technique to get high error correction capacity. Per this work, this coding scheme corrects up to 12 random errors, representing a high correction capac
... Show MoreIn parallel with the shell model using the harmonic oscillator's single-particle wave functions, the Hartree-Fock approximation was also used to calculate the neutron skin thickness, the mirror charge radii, and the differences in proton radii for 13O-13B and 13N-13C mirror nuclei. The calculations were done for both mirror nuclei in the psdpn model space. Depending on the type of potential used, the calculated values of skin thickness are affected. The symmetry energy and the symmetry energy's slope at nuclear saturation density were also determined, and the ratio of the density to the saturation density of nuclear matter and the symmetry energy has a nearly linear correlation. The mirror ener
... Show MoreThe aim of this research is to measure the effect of Adey- Shire model in the achievement and critical thinking of first intermediate female students in mathematics. The researcher adopted the experimental method with a post-test, the research of sample consists of (60) female students, divided into two groups with (30) students in the experimental group, that studied with Adey- Shire model, and (30) students in the control group who studied in the usual way. The two groups are equivalent in many variables. The researcher makes two tests of multiple choices, the first one is an achievement test consists (30) items and another test was for a critical thinking test with (25) items. The statistical analysis make to both tests is made with s
... Show MoreThe present study is carried out to identify the algae in the groundwater of the three areas of Tikrit city, including (the center of Tikrit , the region of AL-Jazira , Awainat village) by nine wells, a depths ranged between 9 meter at well 8 and 110 meter at wells 3 and 5 . And examined the environmental characteristics of physical, chemical and biological factors during the study period from September 2009 to June 2010. It is obtained that wells in the study area is lower alkalinity, average it ranged (6.448-7.418). It was noted that the values of the dissolved oxygen are few and almost non-existent in some cases it ranged between (6.5-6.3)mg/l , analysis of biological oxygen demand refers to wells water (clean- very clean) average
... Show MoreThe Research aims to investigate into reality in terms of planning and scheduling management process for sake the implementation and maintenance of irrigation and drainage projects in the Republic of Iraq, with an indication of the most important obstacles that impede the planning and scheduling management process for these projects and ways of addressing them and minimizing their effects. For the purpose of achieving the goal of the research, a sci
... Show MoreThe current research discusses the topic of the formal data within the methodological framework through defining the research problem, limits and objectives and defining the most important terms mentioned in this research. The theoretical framework in the first section addressed (the concept of the Bauhaus school, the philosophy of the Bauhaus school and the logical bases of this school). The second section dealt with (the most important elements and structural bases of the Bauhaus school) which are considered the most important formal data of this school and their implications on the fabrics and costumes design. The research came up with the most important indicators resulting from the theoretical framework.
Chapter three defined the
In this work, the calculation of matter density distributions, elastic charge form factors and size radii for halo 11Be, 19C and 11Li nuclei are calculated. Each nuclide under study are divided into two parts; one for core part and the second for halo part. The core part are studied using harmonic-oscillator radial wave functions, while the halo part are studied using the radial wave functions of Woods-Saxon potential. A very good agreement are obtained with experimental data for matter density distributions and available size radii. Besides, the quadrupole moment for 11Li are generated.