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.
In this study, silica-graphene oxide nano–composites were prepared by sol-gel technique and deposited by spray pyrolysis method on glass substrate. The effect of changing the graphene/silica ratio on the optical properties and wetting of these nano–structures has been investigated. The structural and morphological properties of the thin films have been studied by x-ray diffraction spectroscopy (XRD), field emission scanning electron microscope (FESEM), energy dispersive x-ray spectroscopy (EDS) and atomic force microscope (AFM). XRD results show that silica structures present in the synthesized films exhibit amorphous character and there is a poor arrangement in graphene plates al
Background: The main aim of the present study is to qualify and quantify voids formation of root canals obturated with GuttaCore (GC) and experimental Hydroxyapatite polyethylene (HA/PE) as new carrier-based root canal fillings by using micro computed tomography scan. Materials and methods: In the present study, eight straight single-rooted human permanent premolar teeth are selected and disinfected, then stored in distilled water. The teeth decoronated leaving a root length of 12mm each. The root canals instrumented by using crown down technique and the apical diameter of the root canal prepared to a size # 30/0.04 for achieving standardized measurements. A 5mL of 17% EDTA used to remove the smear layer followed by 5mL of 2.5% NaOCl and r
... Show MoreIn the current work, aromatic amines and alkyl halides have been converted to the corresponding azides 2a‒d and 4a-d by the reaction with sodium nitrite and sodium azide respectively for amines and sodium azide for halides. Then, dipropargyl ether derivative of D-mannose 8 has been synthesized from diacetone mannose that has been obtained by the treatment of D-mannose (5) with dry acetone in the presence of sulfuric acid. Then, aldol condensation has been used to prepare diol 7 from the mannose diacetonide 6. The reaction of compound 7 with propargyl bromide in alkaline media has been afforded dipropargyl
... Show Moreواحدة من أكثر مواد السيراميك الهيكلية الواعدة هي كربيد السيليكون(SiC) ، حيث له خصائص حرارية وكهروميكانيكية ممتازة. هذه الخصائص مفيدة ل CMC لتعزيز أداء المركب خاصة عند إضافات النانو المتكاملة. في هذا البحث, تم تصنيع مركب SiC من SiC بثلاثة تركيزات مع ZnO و Si. تم اختبار الخواص المغناطيسية لجميع المخاليط باستخدام مراقبة العينة الاهتزازية (VSM). تم تلبيد العينات الخضراء في فرن التلبيد عند 1600 درجة مئوية في بيئة النيتروجي
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