In this work, a weighted H lder function that approximates a Jacobi polynomial which solves the second order singular Sturm-Liouville equation is discussed. This is generally equivalent to the Jacobean translations and the moduli of smoothness. This paper aims to focus on improving methods of approximation and finding the upper and lower estimates for the degree of approximation in weighted H lder spaces by modifying the modulus of continuity and smoothness. Moreover, some properties for the moduli of smoothness with direct and inverse results are considered.

A new Ni(II) nanostructured chelating system (DHN) was introduced for selective optical heavy-metal ion sensing in an aqueous medium. The cooperative chelating system comprising 8-hydroxyquinoline (8-HQ) and dimethylglyoxime (DMG) has been developed for the first time in association with fibre optic sensing for selective optical heavy-metal ion sensing in an aqueous medium. The Ni(II) nanocompound fluoresces upon 578 nm excitation, showing a highly sensitive optical response with a linear calibration curve in the range 0–100 ng/mL. The regression equation of the calibration curve is y = 0.0035x + 0.9990, which indicates very good linearity, implying R2 = 0.999 with high sensitivity (calibration slope of 0.0035) and low baseline noise (bla

The current paper investigates the effect of cut-out design parameters on load-bearing capacity and buckling behaviour of steel cylindrical shell using a nonlinear finite element analysis in modelling cylinder buckling under longitudinal compressive load. The effect of four geometry design parameters: shell diameter to thickness ratio, cut-out location, orientation, and size were investigated in this study. To enhance the prediction of buckling behaviour, both geometrical and material nonlinearities were considered. An ANSYS APDL code was written and tested by verifying its validity through comparison with former buckling study. The results showed that changing the cut-out location from mid-height of the cylindrical shell towards a

A mathematical method with a new algorithm with the aid of Matlab language is proposed to compute the linear equivalence (or the recursion length) of the pseudo-random key-stream periodic sequences using Fourier transform. The proposed method enables the computation of the linear equivalence to determine the degree of the complexity of any binary or real periodic sequences produced from linear or nonlinear key-stream generators. The procedure can be used with comparatively greater computational ease and efficiency. The results of this algorithm are compared with Berlekamp-Massey (BM) method and good results are obtained where the results of the Fourier transform are more accurate than those of (BM) method for computing the linear equivalenc

Castellated columns are structural members that are created by breaking a rolled column along the center-line by flame after that rejoining the equivalent halves by welding such that for better structural strength against axial loading, the total column depth is increased by around 50 percent. The implementation of these institutional members will also contribute to significant economies of material value. The main objectives of this study are to study the enhancement of the load-carrying capacity of castellated columns with encasement of the columns by Reactive Powder Concrete (RPC) and lacing reinforcement, and serviceability of the confined castellated columns. The Castellated columns with RPC and Lacing Reinforcement improve com

The cathodic deposition of zinc from simulated chloride wastewater was used to characterize the mass transport properties of a flow-by fixed bed electrochemical reactor composed of vertical stack  of stainless steel nets, operated in batch-recycle mode. The electrochemical reactor employed potential value in such a way that the zinc reduction occurred under mass transport control. This potential was determined by hydrodynamic voltammetry using a borate/chloride solution as supporting electrolyte on stainless steel rotating disc electrode. The results indicate that mass transfer coefficient (K_m) increases with increasing of flow rate (Q) where .The electrochemical reactor proved to be efficient in removing zinc and was abl

Sheet piles are necessary with hydraulic structures as seepage cut-off to reduce the seepage. In this research, the computational work methodology was followed by building a numerical model using Geo-Studio program to check the efficiency of using concrete sheet piles as a cut-off or reducer for seepage with time if the sheet piles facing the drawdown technique. Al-Kifil regulator was chosen as a case study, an accurate model was built with a help of observed reading of the measuring devices, which was satisfactory and helped in checking the sheet piles efficiency. Through the study, three scenarios were adopted (with and without) drawdown technique, it was found that at the short time there's no effect of the drawdown technique on

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.