In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi

The new, standard molecular biologic system for duplicating DNA enzymatically devoid of employing a living organism, like E. coli or yeast, represents polymerases chain reaction (PCR). This technology allows an exponential intensification of a minor quantity of DNA molecule several times. Analysis can be straightforward with more DNA available. A thermal heat cycler performs a polymerization chain reaction that involves repeated cycles of heating and cooling the reactant tubes at the desired temperature for each reaction step. A heated deck is positioned on the upper reaction tube to avoid evaporating the reaction mixture (normally volumes range from 15 to 100 l per tube), or an oil layer can be placed on a reaction mixture su

Cerebellum is the most important and critical part of the central nervous system, cerebellum is very sensitive to the abnormal changes during the embryological development in its histological structure, the exposure to any infection during embryogenesis produce abnormalities in the cerebellum and behavioral of offspring. In this study we tried to study the ontogenesis of the cerebellum in the embryos of the albino rats and detection the effect of the AgNPs on the ontogenesis of the rat cerebellum after exposure of AgNPs during pregnancy. we used 60 female pregnant rats divided in to three group, each contain 20 female, (G1) treated with 2mg/kg /day suspension of silver nanoparticles (Ag NPs) (G2) treated with 20mg/kg/day AgNPs from first da

Poly [2-methoxy-5-(2-ethylhexyloxy)-1, 4-phenylenevinyl] (MEH-PPV) thin films were created in this study using both spin coating and drop casting processes. MEH-PPV thin films generated by Ferric Chloride (FeCl3) doping (0.03, 0.06, 0.09, and 0.12 wt%) were studied for some physical features using Fourier-Transform Infrared Spectroscopy (FTIR), Field Emission Scanning Electron Microscopy (FE-SEM), and Energy Dispersive X-ray Spectroscopy (EDX). An FTIR test showed that there was no chemical reaction that occurred between Ferric Chloride (FeCl3) and MEH-PPV, but rather a physical one, that is, an organic material composite occurred. As for FE-SEM, the pure sample MEH-PPV formed uniformly, but when FeCl3 was added by weight, we have differ

The characterization of ZnO and ZnO:In thin films were confirmed by spray pyrolysis technique. The films were deposited onto glass substrate at a temperature of 450°C. Optical absorption measurements were also studied by UV-VIS technique in the wavelength range 300-900 nm which was used to calculate the optical constants. The changes in dispersion and Urbach parameters were investigated as a function of In content. The optical energy gap was decreased and the wide band tails were increased in width from 616 to 844 eV as the In content increased from 0wt.% to 3wt.%. The single–oscillator parameters were determined also the change in dispersion was investigated before and after doping.

Nano crystalline copper sulphide (Cu2S) thin films pure and 3% Bi doped were deposited on glass substrate by thermal evaporation technique of thickness 400±20 nm under a vacuum of ~ 2 × 10− 5 mbar to study the influence of annealing temperatures ( as-deposited, and 573) K on structural, surface morphology and optical properties of (Cu2S and Cu2S:3%Bi). (XRD) X-ray diffraction analysis showed (Cu2S and Cu2S:3%Bi) films before and after annealing are polycrystalline and hexagonal structure. AFM measurement approves that (Cu2S and Cu2S:3%Bi) films were Nano crystalline with grain size of (105.05-158.12) nm. The optical properties exhibits good optical absorption for Cu2S:3%Bi films. Decreased of optical band gap from 2.25 to 2 eV after dop

Sliding Mode Controller (SMC) is a simple method and powerful technique to design a robust controller for nonlinear systems. It is an effective tool with acceptable performance. The major drawback is a classical Sliding Mode controller suffers from the chattering phenomenon which causes undesirable zigzag motion along the sliding surface. To overcome the snag of this classical approach, many methods were proposed and implemented. In this work, a Fuzzy controller was added to classical Sliding Mode controller in order to reduce the impact chattering problem. The new structure is called Sliding Mode Fuzzy controller (SMFC) which will also improve the properties and performance of the classical Sliding Mode control

Copper (Cu) is an essential trace element for the efficient functioning of living organisms. Cu can enter the body in different ways, and when it surpasses the range of biological tolerance, it can have negative consequences. The use of different nanoparticles, especially metal oxide nanoparticles, is increasingly being expanded in the fields of industry and biomedical materials. However, the impact of these nanoparticles on human health is still not completely elucidated. This comparative study was conducted to evaluate the impacts of copper oxide nanoparticles (CuO NPs) and copper sulphate (CuSO4 0.5 (H2O)) on infertility and reproductive function in male albino mice BALB/c. Body weight, the weight of male reproductive organs, mal

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  This study is concerned with the estimation of constant  and time-varying parameters in non-linear ordinary differential equations, which do not have analytical solutions. The estimation is done in a multi-stage method where constant and time-varying parameters are estimated in a straight sequential way from several stages. In the first stage, the model of the differential equations is converted to a regression model that includes the state variables with their derivatives and then the estimation of the state variables and their derivatives in a penalized splines method and compensating the estimations in the regression model. In the second stage, the pseudo- least squares method was used to es

The paper is concerned with the state and proof of the existence theorem of a unique solution (state vector) of couple nonlinear hyperbolic equations (CNLHEQS) via the Galerkin method (GM) with the Aubin theorem. When the continuous classical boundary control vector (CCBCV) is known, the theorem of existence a CCBOCV with equality and inequality state vector constraints (EIESVC) is stated and proved, the existence theorem of a unique solution of the adjoint couple equations (ADCEQS) associated with the state equations is studied. The Frcéhet derivative derivation of the "Hamiltonian" is obtained. Finally the necessary theorem (necessary conditions "NCs") and the sufficient theorem (sufficient conditions" SCs") for optimality of the stat