Orthogonal polynomials and their moments serve as pivotal elements across various fields. Discrete Krawtchouk polynomials (DKraPs) are considered a versatile family of orthogonal polynomials and are widely used in different fields such as probability theory, signal processing, digital communications, and image processing. Various recurrence algorithms have been proposed so far to address the challenge of numerical instability for large values of orders and signal sizes. The computation of DKraP coefficients was typically computed using sequential algorithms, which are computationally extensive for large order values and polynomial sizes. To this end, this paper introduces a computationally efficient solution that utilizes the parallel processing capabilities of modern central processing units (CPUs), namely the availability of multiple cores and multithreading. The proposed multi-threaded implementations for computing DKraP coefficients divide the computations into multiple independent tasks, which are executed concurrently by different threads distributed among the independent cores. This multi-threaded approach has been evaluated across a range of DKraP sizes and various values of polynomial parameters. The results show that the proposed method achieves a significant reduction in computation time. In addition, the proposed method has the added benefit of applying to larger polynomial sizes and a wider range of Krawtchouk polynomial parameters. Furthermore, an accurate and appropriate selection scheme of the recurrence algorithm is introduced. The proposed approach introduced in this paper makes the DKraP coefficient computation an attractive solution for a variety of applications.
Abstract: Aluminum alloys grade 6061-T6 are characterized by their excellent properties and processing characteristics which make them ideal for varieties of industrial applications under cyclic loading, aluminum alloys show less fatigue life than steel alloys of similar strength. In the current study, a nanosecond fiber laser of maximum pulse energy up to 9.9 mJ was used to apply laser shock peening process (LSP) on aluminum thin sheets to introduce residual stresses in order to enhance fatigue life under cyclic loading Box-Behnken design (BBD) based on the design of experiments (DOE) was employed in this study for experimental design data analysis, model building and optimization The effect of working parameters spot size (ω), scannin
... Show MoreThe service system has become a necessity of life in modern cities to be the most basic necessities of modern humans, they constitute a major base, which is based on the sustainability of life in the city and a standard measured through the degree of well-being and progress of civilized peoples and their interaction with the surrounding environment, making the services sector as a need not be an option, whenever the cities widened in population and space whenever provision of services and upgrading the quality and quantity more pressing, which made the subject of the services takes the biggest area of the trends and thinking of urban planners and those who in charge of drawing the cities policies. Consideri
... Show MoreAcrylic polymer/cement nanocomposites in dark and light colors have been developed for coating floors and swimming pools. This work aims to emphasize the effect of cement filling on the mechanical parameters, thermal stability, and wettability of acrylic polymer. The preparation was carried out using the casting method from acrylic polymer coating solution, which was added to cement nanoparticles (65 nm) with weight concentrations of (0, 1, 2, 4, and 8 wt%) to achieve high-quality specifications and good adhesion. Maximum impact strength and Hardness shore A were observed at cement ratios of 2 wt% and 4 wt%, respectively. Changing the filling ratio has a significant effect on the strain of the nanocomposites. The contact angle was i
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The current research aims to develop a guidance program suitable for high school students and apply it to them in order to ensure the reduction of addiction to the use of different means of communication. The researchers used the scale of addiction to the means of communication (SAS) to measure the level of addiction as well as to identify the impact of the proposed guidance program in reducing the degree of addiction to communication. It was applied to a sample of (20) female students divided equally into two groups: an experimental group of (10) female students and a control group of (10) female students from the secondary level in a school under the department of education in the education of the alma
... Show MoreThe Detour distance is one of the most common distance types used in chemistry and computer networks today. Therefore, in this paper, the detour polynomials and detour indices of vertices identified of n-graphs which are connected to themselves and separated from each other with respect to the vertices for n≥3 will be obtained. Also, polynomials detour and detour indices will be found for another graphs which have important applications in Chemistry.
The development of a reversed phase high performance liquid chromatography fluorescence method for the determination of the mycotoxins fumonisin B1 and fumonisin B2 by using silica-based monolithic column is described. The samples were first extracted using acetonitrile:water (50:50, v/v) and purified by using a C18 solid phase extraction-based clean-up column. Then, pre-column derivatization for the analyte using ortho-phthaldialdehyde in the presence of 2-mercaptoethanol was carried out. The developed method involved optimization of mobile phase composition using methanol and phosphate buffer, injection volume, temperature and flow rate. The liquid chromatographic separation was performed using a reversed phase Chromolith® RP-18e column
... Show MoreThis research came to shed light on the relationship between the requirements of (practices) high commitment management (participative decision making،information sharing، training and development،team working،rewards،selective staffing،job security ) and strategic entrepreneurship dimensions (entrepreneurial culture،entrepreneurial leadership،entrepreneurial mindset، strategic management resources ) Sought to achieve the number of goals the knowledge and applied, and tested the relationship and impact between variables in a sample size of 100 directors of personnel departments and divisions and their associates in the Iraqi contractors in Baghdad (Hamorabi، Mutassim، AL Rasheed، AL Mansour )، focused research
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