The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as  increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives  a good agreement.

In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

The substantial key to initiate an explicit statistical formula for a physically specified continua is to consider a derivative expression, in order to identify the definitive configuration of the continua itself. Moreover, this statistical formula is to reflect the whole distribution of the formula of which the considered continua is the most likely to be dependent. However, a somewhat mathematically and physically tedious path to arrive at the required statistical formula is needed. The procedure in the present research is to establish, modify, and implement an optimized amalgamation between Airy stress function for elastically-deformed media and the multi-canonical joint probability density functions for multivariate distribution complet

This paper aims to validate a proposed finite element model to be adopted in predicting displacement and soil stresses of a piled-raft foundation. The proposed model adopts the solid element to simulate the raft, piles, and soil mass. An explicit integration scheme has been used to simulate nonlinear static aspects of the piled-raft foundation and to avoid the computational difficulties associated with the implicit finite element analysis.

The validation process is based on comparing the results of the proposed finite element model with those of a scaled-down experimental work achieved by other researchers. Centrifuge apparatus has been used in the experimental work to generate the required stresses to simulate t

Objective:Fluorid-containing dental alginate impression materials can exert a considerable reduction in
enamel solubility. The objective was to evaluate the effect of fluoride addition on the setting time and
compressive strength of alginate impression materials.
Methodology: 60 samples were constructed from alginate impression material (30 samples for setting
time test and 30 samples for compressive strength test).Specimens of each test divided into three
subgroup. Group A: 10 specimens of alginate were mixed with distilled water [control], Group B: 10
specimens of alginate were mixed with100-ppm fluoride and Group C:10 specimens of alginate were
mixed with 2%Naf.
Results: the result of setting time test showed t

The slurry infiltrated fiber concrete (SIFCON) is nowadays considered a special type of high fiber content concrete; it is high strength and high performance material. This paper investigates the effect of spread steel fiber into the slurry mortar on some properties of SIFCON. According to fiber distribution, two sets were used in this investigation. The first set consisted of randomly distributing fibers inside the slurry. The second set was by placing the fibers in an orderly manner inside the slurry. Crimped steel fibers with an aspect ratio of (60) were used. Two different volume fractions percentage of (7% and 9%) by volume of mold were used in both sets for this study. Also, a w/c ratio of (0.35) and superplasticiz

The refractive indices, nD densities 𝜌, and viscosities  of binary mixtures of sulfolane + n -butanol + sec- butanol + iso- butanol + tert – butanol + n-propanol and iso- propanol were measured at 298.15K. Form experimental data, excess molar volum VE , excess molar refractivity ∆nD, excess molar viscosity  E and excess molar Gibbs free energy of activation of viscous flow G *E were calculated. From n-propanol – sulfolane and iso- propanol sulfolane mixtures showed negative ∆nD, n-butanol – sulfolane, sec-butanal – sulfolane, iso-butanol – sulfolane and tert- butanol sulfolane , nD was positive over the whole mole fraction rang , while VE ,  E and G *E show a negative deviation. The

In recent decades, tremendous success has been achieved in the advancement of chemical admixtures for Portland cement concrete. Most efforts have concentrated on improving the properties of concrete and studying the factors that influence on these properties. Since the compressive strength is considered a valuable property and is invariably a vital element of the structural design, especially high early strength development which can be provide more benefits in concrete production, such as reducing construction time and labor and saving the formwork and energy. As a matter of fact, it is influenced as a most properties of concrete by several factors including water-cement ratio, cement type and curing methods employed.
Because of acce