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 work presents the use of laser diode in the fiber distributed data interface FDDI networks. FDDI uses optical fiber as a transmission media. This solves the problems resulted from the EMI, and noise. In addition it increases the security of transmission. A network with a ring topology consists of three computers was designed and implemented. The timed token protocol was used to achieve and control the process of communication over the ring. Nonreturn to zero inversion (NRZI) modulation was carried out as a part of the physical (PHY) sublayer. The optical system consists of a laser diode with wavelength of 820 nm and 2.5 mW maximum output power as a source, optical fiber as a channel, and positive intrinsic negative (PIN) photodiode
... Show MoreThis article aims to determine the time-dependent heat coefficient together with the temperature solution for a type of semi-linear time-fractional inverse source problem by applying a method based on the finite difference scheme and Tikhonov regularization. An unconditionally stable implicit finite difference scheme is used as a direct (forward) solver. While by the MATLAB routine lsqnonlin from the optimization toolbox, the inverse problem is reformulated as nonlinear least square minimization and solved efficiently. Since the problem is generally incorrect or ill-posed that means any error inclusion in the input data will produce a large error in the output data. Therefore, the Tikhonov regularization technique is applie
... Show MoreIn this paper solar radiation was studied over a region of Baghdad (Latitude 33.3o and longitude 44.4o). The two parts of global solar radiation: diffuse and direct solar radiation were estimated depending on the clearance index of measured data (Average Monthly mean global solar radiation). Metrological data of measured (average monthly mean diffuse and direct solar radiation) were used to comparison the results and show the agreement between them. Results are determined by applying Liu and Jordan two models (1960). Excel 2007program is used in calculation, graphics and comparison the results.
Foreign direct investment has seen increasing interest worldwide, especially in developing economies. However, statistics have shown that Yemen received fluctuating FDI inflows during the period under study. Against this background, this research seeks to determine the relationship and impact of interest rates on FDI flows. The study also found other determinants that greatly affected FDI inflows in Yemen for the period 1990-2018. Study data collected from the World Bank and International Monetary Fund databases. It also ensured that the time series were made balanced and interconnected, and then the Auto Regressive Distributed Lag method used in the analysis. The results showed that the interest rates and
... Show MoreThis work discusses the beginning of fractional calculus and how the Sumudu and Elzaki transforms are applied to fractional derivatives. This approach combines a double Sumudu-Elzaki transform strategy to discover analytic solutions to space-time fractional partial differential equations in Mittag-Leffler functions subject to initial and boundary conditions. Where this method gets closer and closer to the correct answer, and the technique's efficacy is demonstrated using numerical examples performed with Matlab R2015a.
In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.
The research aims to find approximate solutions for two dimensions Fredholm linear integral equation. Using the two-variables of the Bernstein polynomials we find a solution to the approximate linear integral equation of the type two dimensions. Two examples have been discussed in detail.
The aim of this study is to propose reliable equations to estimate the in-situ concrete compressive strength from the non-destructive test. Three equations were proposed: the first equation considers the number of rebound hummer only, the second equation consider the ultrasonic pulse velocity only, and the third equation combines the number of rebound hummer and the ultrasonic pulse velocity. The proposed equations were derived from non-linear regression analysis and they were calibrated with the test results of 372 concrete specimens compiled from the literature. The performance of the proposed equations was tested by comparing their strength estimations with those of related existing equations from literature. Comparis
... Show MoreThe aim of this study to identify the effect of using two strategies for active learning ( Jigsaw Strategy & Problems Solving) in learning some balanced beam's skills in artistic gymnastics for women , as well as to identify the best of the three methods (jigsaw strategy , problems solving and the traditional method) in learning some skills balance beam , the research has used the experimental methodology, and the subject included the students of the college of Physical Education and Sports Sciences / University of Baghdad / third grade and by the lot was selected (10) students for each group of groups Search three and The statistical package for social sciences (SPSS) was used means, the standard deviation and the (T.test), the one way a n
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