In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the methods has been presented. In addition, the maximum error remainder () has been computed to demonstrate the accuracy of the proposed methods. The results persuasively prove that CM and D-CMs are reliable and accurate in obtaining the approximate solutions to the problems, with obvious superiority in accuracy for D-CMs than for CM.
The Dagum Regression Model, introduced to address limitations in traditional econometric models, provides enhanced flexibility for analyzing data characterized by heavy tails and asymmetry, which is common in income and wealth distributions. This paper develops and applies the Dagum model, demonstrating its advantages over other distributions such as the Log-Normal and Gamma distributions. The model's parameters are estimated using Maximum Likelihood Estimation (MLE) and the Method of Moments (MoM). A simulation study evaluates both methods' performance across various sample sizes, showing that MoM tends to offer more robust and precise estimates, particularly in small samples. These findings provide valuable insights into the ana
... Show MoreThis paper proposes improving the structure of the neural controller based on the identification model for nonlinear systems. The goal of this work is to employ the structure of the Modified Elman Neural Network (MENN) model into the NARMA-L2 structure instead of Multi-Layer Perceptron (MLP) model in order to construct a new hybrid neural structure that can be used as an identifier model and a nonlinear controller for the SISO linear or nonlinear systems. Two learning algorithms are used to adjust the parameters weight of the hybrid neural structure with its serial-parallel configuration; the first one is supervised learning algorithm based Back Propagation Algorithm (BPA) and the second one is an intelligent algorithm n
... Show MoreIn this work, the switching nonlinear dynamics of a Fabry-Perot etalon are studied. The method used to complete the solution of the differential equations for the nonlinear medium. The Debye relaxation equations solved numerically to predict the behavior of the cavity for modulated input power. The response of the cavity filled with materials of different response time is depicted. For a material with a response time equal to = 50 ns, the cavity switches after about (100 ns). Notice that there is always a finite time delay before the cavity switches. The switch up time is much longer than the cavity build-up time of the corresponding linear cavity which was found to be of the order of a few round-trip ti
... Show MoreThis paper aims to study the second-order geometric nonlinearity effects of P-Delta on the dynamic response of tall reinforced concrete buildings due to a wide range of earthquake ground motion forces, including minor earthquake up to moderate and strong earthquakes. The frequency domain dynamic analysis procedure was used for response assessment. Reinforced concrete building models with different heights up to 50 stories were analyzed. The finite element software ETABS (version 16.0.3) was used to analyze reinforced concrete building models.
The study reveals that the percentage increase in buildings' sway and drift due to P-Delta effects are nearly constant for specific building height irrespective of the seism
... Show MoreWe propose two simple, rapid, and convenient spectrophotometric methods which are described for the determination of cephalexin in bulk and its pharmaceutical preparations. They are based on the measurement of the flame atomic emission of potassium ion (in the first method) and colorimetric determination of the green colored solution at 610 nm formed after the reaction of cephalexin with potassium permanganate as an oxidant agent (in the second method) in basic medium. The working conditions of the methods are investigated and optimized. Beer's law plot shows a good correlation in the concentration range of 5-40?g ml-1. The detection limits are 2.573,2.814 ?g ml-1 for the flame emission photometric method and 1.844,2.016 ?g ml-1 for colo
... Show MoreChromatographic and spectrophotometric methods for the estimation of mebendazole in
pharmaceutical products were developed. The flow injection method was based on the oxidation of
mebendazole by a known excess of sodium hypochlorite at pH=9.5. The excess sodium hypochlorite is then
reacted with chloranilic acid (CAA) to bleach out its color. The absorbance of the excess CAA was recorded
at 530 nm. The method is fast, simple, selective, and sensitive. The chromatographic method was carried out
on a Varian C18 column. The mobile phase was a mixture of acetonitrile (ACN), methanol (MeOH), water
and triethylamine (TEA), (56% ACN, 20% MeOH, 23.5% H2O, 0.5% TEA, v/v), adjusted to pH = 3.0 with
1.0 M hy
Based on nonlinear self- diffraction technique, the nonlinear optical properties of thin slice of matter can be obtained. Here, nonlinear characterization of nano-fluids consist of hybrid Single Wall Carbon Nanotubes and Silver Nanoparticles (SWCNTs/Ag-NPs) dispersed in acetone at volume fraction of 6x10-6, 9x10-6, 18x10-6 have been investigated experimentally. Therefore, CW DPSS laser at 473 nm focused into a quartz cuvette contains the previous nano-fluid was utilized. The number of diffraction ring patterns (N) has been counted using Charge - Coupled- Device (CCD) camera and Pc with a certain software, in order to find the maximum change of refractive index ( of fluids. Our result show that the fraction volume of 18x10-6 is more nonli
... Show MoreWith the increasing use of antibiotics around the world, the study and appreciation of antibiotics has become essential. An antibiotic formulation may include one or added active ingredients depending on the type and method of manufacturing the antibiotic. Antibiotics can only combat diseases of bacterial origin. As for viral diseases such as the common cold and influenza, antibiotics will not be able to combat them. The objective of this review is to digest the literature related to estimation of antibiotics and to show the methods that have been used in the estimation of the antibiotics (amoxicillin, ampicillin, cephalothin, carbenicillin, and cefotaxime) in medicinal preparations and a biological fluid for example blood
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