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.
This research work aims to the determination of molybdenum (VI) ion via the formation of peroxy molybdenum compounds which has red-brown colour with absorbance wave length at 455nm for the system of ammonia solution-hydrogen peroxide-molybdenum (VI) using a completely newly developed microphotometer based on the ON-Line measurement. Variation of responses expressed in millivolt. A correlation coefficient of 0.9925 for the range of 2.5-150 ?g.ml-1 with percentage linearity of 98.50%. A detection limit of 0.25 ?g.ml-1 was obtained. All physical and chemical variable were optimized interferences of cation and anion were studied classical method of measurement were done and compared well with newly on-line measurements. Application for the use
... Show MoreThis work describes, selenium (Se) films were deposited on clean glass substrates by dc planar magnetron sputtering technique.The dependence of sputtering deposition rate of Se film deposited on pressure and DC power has been studied. The optimum argon pressure has range (4x10-1 -8x10-2 )mbar. The optical properties such as absorption coefficient (α) was determined using the absorbance and transmission measurement from UnicoUV-2102 PC spectrophotometer, at normal incidence of light in the wavelength range of 200-850 nm. And also we calculated optical constants(refractive index (n), dielectric constant (εi,r), and Extinction coefficient (κ) for selenium films.
The tax system, like any other system, as a set of elements and parts that complement each other and are interrelated and interact to achieve specific goals, and is a natural reflection of the economic, social and political conditions prevailing in society, and therefore the objectives of tax policy formulated in line with the objectives of economic policy in general, which means that any change in economic policy clearly affects fiscal policy measures and fiscal policy in particular.
The problem of searching for the impact of foreign direct investment in the Iraqi tax system was focused on the study the of foreign direct investment and therole played in developing and improving the economic reality and its implicatio
... Show MoreThe purpose of the current research is to identify the most important problems that primary school students suffer from inside and outside the classroom from the point of view of their teachers. A sample of (100) male and female teachers was chosen from the Rusafa\ second Directorate for the academic year (2018-2019). The research tool was prepared after reviewing literature related to the issue of problems and difficulties facing students or students in the school stage and even at university. The researcher reached several results that were discussed in the fourth chapter, with a set of conclusions based on the results of the research, and come up with several recommendations and suggestions.
The aim of this paper is to shed the light on the concepts of agency theory by measuring one of the problems that arise from it, which is represented by earnings management (EM) practices. The research problem is demonstrated by the failure of some Iraqi banks and their subsequent placement under the supervision of the Central Bank of Iraq, which was attributed, in part, to the inadequacy of the agency model in protecting stakeholders in shareholding institutions, as well as EM, pushed professional institutions to adopt the corporate governance model as a method to regulate the problem of accounting information asymmetry between the parties to the agency. We are using the Beneish M-score model and the financial analysis equations in
... Show MoreIn this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems.
In this paper, we study the growth of solutions of the second order linear complex differential equations insuring that any nontrivial solutions are of infinite order. It is assumed that the coefficients satisfy the extremal condition for Yang’s inequality and the extremal condition for Denjoy’s conjecture. The other condition is that one of the coefficients itself is a solution of the differential equation .
The techniques of fractional calculus are applied successfully in many branches of science and engineering, one of the techniques is the Elzaki Adomian decomposition method (EADM), which researchers did not study with the fractional derivative of Caputo Fabrizio. This work aims to study the Elzaki Adomian decomposition method (EADM) to solve fractional differential equations with the Caputo-Fabrizio derivative. We presented the algorithm of this method with the CF operator and discussed its convergence by using the method of the Cauchy series then, the method has applied to solve Burger, heat-like, and, couped Burger equations with the Caputo -Fabrizio operator. To conclude the method was convergent and effective for solving this type of
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