The wavelets have many applications in engineering and the sciences, especially mathematics. Recently, in 2021, the wavelet Boubaker (WB) polynomials were used for the first time to study their properties and applications in detail. They were also utilized for solving the Lane-Emden equation. The aim of this paper is to show the truncated Wavelet Boubaker polynomials for solving variation problems. In this research, the direct method using wavelets Boubaker was presented for solving variational problems. The method reduces the problem into a set of linear algebraic equations. The fundamental idea of this method for solving variation problems is to convert the problem of a function into one that involves a finite number of variables. Different numerical examples were given to demonstrate the applicability and validity of this method using the Matlab program. Also, the results of this technique were compared with the exact solution, and graphs were added to these examples to test the convergence of Wavelet Boubaker polynomials using this method.
In this paper flotation method experiments were performed to investigate the removal of lead and zinc. Various parameters such as pH, air flow rate, collector concentrations, collector type and initial metal concentrations were tested in a bubble column of 6 cm inside diameter. High recoveries of the two metals have been obtained by applying the foam flotation process, and at relatively short time 45 minutes . The results show that the best removal of lead about 95% was achieved at pH value of 8 and the best removal of zinc about 93% was achieved
at pH value of 10 by using 100 mg/l of Sodium dodecylsulfate (SDS) as a collector and 1% ethanol as a frother. The results show that the removal efficiency increased with increasing initial m
In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional partial differential equation with parameter. The algorithm for the numerical solution of this equation is based on implicit and an explicit difference method. Finally, numerical example is provided to illustrate that the numerical method for solving this equation is an effective solution method.
In high-dimensional semiparametric regression, balancing accuracy and interpretability often requires combining dimension reduction with variable selection. This study intro- duces two novel methods for dimension reduction in additive partial linear models: (i) minimum average variance estimation (MAVE) combined with the adaptive least abso- lute shrinkage and selection operator (MAVE-ALASSO) and (ii) MAVE with smoothly clipped absolute deviation (MAVE-SCAD). These methods leverage the flexibility of MAVE for sufficient dimension reduction while incorporating adaptive penalties to en- sure sparse and interpretable models. The performance of both methods is evaluated through simulations using the mean squared error and variable selection cri
... Show MoreHistidine was determined via measurement of total luminescence (i:e creation of chemiluminescence and insitu irradiation of released light to an acceptor fluorophore molecule to initiate fluorescence from fluorescien molecule in flat – spiral micro cell designed for this measurement . A detailed description of robust linear equation for the range of 0.002 – 0.05 mol.L-1 for a sample size of 70 µL with a correlation coefficient of 0.9879 and a coefficient of determination of 97.59% while for a quadratic model of the same concentration range was 0.9881 correlation coefficient and 97.63% coefficient of determination. Analysis of variance was conducted for both kinds of models . It indicated that their was no significa
... Show MoreThe study investigated the behaviour of asphalt concrete mixes for aggregate gradations, according to the Iraqi specification using the Bailey method designed by an Excel spreadsheet. In mixing aggregates with varying gradations (coarse and fine aggregate), The Bailey method is a systematic methodology that offers aggregate interlocking as the backbone of the framework and a controlled gradation to complete the blends. Six types of gradation are used according to the bailey method considered in this study. Two-course prepared Asphalt Concrete Wearing and Asphalt Concrete binder, the Nominal Maximum Aggregate Sizes (NMAS) of the mixtures are 19 and 12.5 mm, respectively. The total number of specimens was 240 for both layers (15 samp
... Show MoreCeftriaxone sodium were one of the widely antibacterial drugs used. Azo dye derivatization of diazonium salt that formed via the reaction between ceftriaxone with hydrochloric acid and sodium nitrite was developed for the on-research drug analysis then coupling with each one 2,5-dimethylphenol (2,5-DMP) and 4-tertbutylphenol (4-TBP) respectively in the alkaline media. The developed diazonium coupling methods include an optimization study. The results show a limit of detection and limit of quantification 0.482, 0.284 µg/mL, and 1.607, 0.945 µg/mL using 2,5-DMP and 4-TBP reagents respectively. Moreover, the recovery % obtained was 100.89%, and 103.37% at linear concentration range 3.0 – 50, and 10 – 30 µg/mL, with mo
... Show MoreThe objective of an Optimal Power Flow (OPF) algorithm is to find steady state operation point which minimizes generation cost, loss etc. while maintaining an acceptable system performance in terms of limits on generators real and reactive powers, line flow limits etc. The OPF solution includes an objective function. A common objective function concerns the active power generation cost. A Linear programming method is proposed to solve the OPF problem. The Linear Programming (LP) approach transforms the nonlinear optimization problem into an iterative algorithm that in each iteration solves a linear optimization problem resulting from linearization both the objective function and constrains. A computer program, written in MATLAB environme
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