This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n + 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended approach is applicable and accurate for solving such kinds of problems.
Carbon Nanopowder was fabricated by arc discharge technique at deposition pressure of 10-5 mbar Argon gas on glass substrates. The prepared carbon nano- powder was collected from chamber and purified with nitric acid at 323K .The morphology and crystalline structure of the prepared powder was examined by X-Ray Diffraction (XRD), Atomic Force Microscope (AFM), and Scanning Electron Microscope (SEM). XRD spectrums showed that the powder exhibits amorphous structure and after purification, the powder showed hexagonal structure with a preferential orientation along(002) direction ,where AFM and SEM gave very compatible estimation on the grain size and shape of the nanopowder.
The aim of this paper is to design suitable neural network (ANN) as an alternative accurate tool to evaluate concentration of Copper in contaminated soils. First, sixteen (4x4) soil samples were harvested from a phytoremediated contaminated site located in Baghdad city in Iraq. Second, a series of measurements were performed on the soil samples. Third, design an ANN and its performance was evaluated using a test data set and then applied to estimate the concentration of Copper. The performance of the ANN technique was compared with the traditional laboratory inspecting using the training and test data sets. The results of this study show that the ANN technique trained on experimental measurements can be successfully applied to the rapid est
... Show MoreNowadays, still images are used everywhere in the digital world. The shortages of storage capacity and transmission bandwidth make efficient compression solutions essential. A revolutionary mathematics tool, wavelet transform, has already shown its power in image processing. The major topic of this paper, is improve the compresses of still images by Multiwavelet based on estimation the high Multiwavelet coefficients in high frequencies sub band by interpolation instead of sending all Multiwavelet coefficients. When comparing the proposed approach with other compression methods Good result obtained
In this research tri metal oxides were fabricated by simple chemical spray pyrolysis technique from (Sn(NO3)2.20 H2O, Zn(NO3)2.6 H2O, Cd(NO3)2.4 H2O) salts at concentration 0.1M with mixing weight ratio 50:50 were fabricated on silicon substrate n-type (111). (with & without the presence of grooves by the following diemensions (20μm width, 7.5μm depth) with thickness was about ( 0.1 ±0.05 µm) using water soluble as precursors at a substrate temperature 550 ºC±5, with spray distance (15 cm) and their gas sensing properties toward H2S gas at different concentrations (10,50,100,500 ppmv) in air were investigated at room te
... Show MoreMarkov chains are an application of stochastic models in operation research, helping the analysis and optimization of processes with random events and transitions. The method that will be deployed to obtain the transient solution to a Markov chain problem is an important part of this process. The present paper introduces a novel Ordinary Differential Equation (ODE) approach to solve the Markov chain problem. The probability distribution of a continuous-time Markov chain with an infinitesimal generator at a given time is considered, which is a resulting solution of the Chapman-Kolmogorov differential equation. This study presents a one-step second-derivative method with better accuracy in solving the first-order Initial Value Problem
... Show MoreDegenerate 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-pose
In this paper, the delay integral equations in population growth will be described,discussed , studied and transfered this model to integro-differential equation. At last,we will solve this problem by using variational approach.