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.
The present work reports an approach of hydrothermal growth of ZnO nanorods, which simplifies the production of low cost films with controlled morphology for H2S gas sensor application. The prepared ZnO nanorods exhibit a hexagonal wurtzite phase analyzed by the X-ray diffraction analysis. The FTIR spectra provide information that the band located between 465-570 cm-1 corresponds to the stretching bond of Zn-O, which confirms the creation of ZnO. PL spectroscopic studies showed that the doping of Ag NPs and f-MWCNT in the ZnO matrix leads to the tuning of the bandgap. The SEM analysis showed the morphology of ZnO was the nanorods. The nanocomposites Ag/ZnO and F-MWCNT/ZnO which prepared, sep
... Show MoreIn this paper the oscillation criterion was investigated for all solutions of the third-order half linear neutral differential equations. Some necessary and sufficient conditions are established for every solution of (a(t)[(x(t)±p(t)x(?(t) ) )^'' ]^? )^'+q(t) x^? (?(t) )=0, t?t_0, to be oscillatory. Examples are given to illustrate our main results.
Asthma is a chronic inflammatory disorder of the airways in which many cells and cellular elements play a role. The treatment guidelines recommend theuse of a second controller drug in addition to medium doses of inhaled corticosteroids (ICSs) rather than the use of high doses ICS alone in the treatment of moderate-severe persistent asthma. This study was conducted to compare the clinical efficacy and safety of three treatment regimens in Iraqi patients with moderate-severe persistent asthma.The study included three groups; each group included 15 patients. Patients were administered beclomethasone inhaler alone 1500-2000 μg/day, beclomethasone inhaler 750-1000 μg/day plus oral controlled release aminophylline tablets 450 mg/day or
... Show MoreThe research aims mainly to the role of the statement style costs on the basis of activity based on performance (PFABC) to reduce production cost and improve the competitive advantage of economic units and industrial under the modern business environment dominated by a lot of developments and changes rapidly, which necessitates taking them and criticize them to ensure survival and continuity. The research problem is the inability of traditional cost methods of providing useful information to the departments of units to take many administrative decisions, particularly decisions related to the product and calculating the costs of the quality of the sound and the availability of the need and the ability to replace methods capa
... Show MoreThis paper investigates the performance evaluation of two state feedback controllers, Pole Placement (PP) and Linear Quadratic Regulator (LQR). The two controllers are designed for a Mass-Spring-Damper (MSD) system found in numerous applications to stabilize the MSD system performance and minimize the position tracking error of the system output. The state space model of the MSD system is first developed. Then, two meta-heuristic optimizations, Simulated Annealing (SA) optimization and Ant Colony (AC) optimization are utilized to optimize feedback gains matrix K of the PP and the weighting matrices Q and R of the LQR to make the MSD system reach stabilization and reduce the oscillation of the response. The Matlab softwar
... Show MoreThis study investigates the impact of spatial resolution enhancement on supervised classification accuracy using Landsat 9 satellite imagery, achieved through pan-sharpening techniques leveraging Sentinel-2 data. Various methods were employed to synthesize a panchromatic (PAN) band from Sentinel-2 data, including dimension reduction algorithms and weighted averages based on correlation coefficients and standard deviation. Three pan-sharpening algorithms (Gram-Schmidt, Principal Components Analysis, Nearest Neighbour Diffusion) were employed, and their efficacy was assessed using seven fidelity criteria. Classification tasks were performed utilizing Support Vector Machine and Maximum Likelihood algorithms. Results reveal that specifi
... Show MoreIn this paper, a discretization of a three-dimensional fractional-order prey-predator model has been investigated with Holling type III functional response. All its fixed points are determined; also, their local stability is investigated. We extend the discretized system to an optimal control problem to get the optimal harvesting amount. For this, the discrete-time Pontryagin’s maximum principle is used. Finally, numerical simulation results are given to confirm the theoretical outputs as well as to solve the optimality problem.
In this paper we use Bernstein polynomials for deriving the modified Simpson's 3/8 , and the composite modified Simpson's 3/8 to solve one dimensional linear Volterra integral equations of the second kind , and we find that the solution computed by this procedure is very close to exact solution.
This study presents a practical method for solving fractional order delay variational problems. The fractional derivative is given in the Caputo sense. The suggested approach is based on the Laplace transform and the shifted Legendre polynomials by approximating the candidate function by the shifted Legendre series with unknown coefficients yet to be determined. The proposed method converts the fractional order delay variational problem into a set of (n + 1) algebraic equations, where the solution to the resultant equation provides us the unknown coefficients of the terminated series that have been utilized to approximate the solution to the considered variational problem. Illustrative examples are given to show that the recommended appro
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