Discrete Racah polynomials (DRPs) are considered essential for several applications such as approximation theory, quantum physics, and digital signal processing. However, the computation of high-order DRPs presents significant numerical and computational challenges. Even though the recent advancements in algorithms have improved numerical stability, the inherently sequential nature of these algorithms continues to be a bottleneck for large-scale implementations. This paper proposes a new multithreading-based algorithm for computing the DRP coefficients. The proposed algorithm is designed to accelerate the computation of high-order DRPs by considering the advantages of the independence of different tasks and the ability to process multiple coefficients simultaneously. The algorithm introduces distinct multithreading strategies for both zero-valued and non-zero-valued parameters, which include the zero-parameter balanced algorithm (ZPBA), the zero-parameter unbalanced algorithm (ZPUA), and the valued-parameter algorithm (VPA). The experimental results show that the proposed multithreading algorithms noticeably reduce computation time when compared to the state-of-the-art baseline algorithm. Notably, both ZPBA and VPA exhibit exceptional scalability across modern multicore architectures, delivering speedup factors exceeding 10× for large polynomial sizes. This work effectively bridges the gap between mathematical theory and high-performance computing, making the generation of large-scale DRP matrices computationally viable for advanced engineering applications.
Introduction: Carrier-based gutta-percha is an effective method of root canal obturation creating a 3-dimensional filling; however, retrieval of the plastic carrier is relatively difficult, particularly with smaller sizes. The purpose of this study was to develop composite carriers consisting of polyethylene (PE), hydroxyapatite (HA), and strontium oxide (SrO) for carrier-based root canal obturation. Methods: Composite fibers of HA, PE, and SrO were fabricated in the shape of a carrier for delivering gutta-percha (GP) using a melt-extrusion process. The fibers were characterized using infrared spectroscopy and the thermal properties determined using differential scanning calorimetry. The elastic modulus and tensile strength tests were dete
... Show MoreQuadrupole Q moments and effective charges are calculated for 9C, 11C, 17C and 19C exotic nuclei using shell model calculations. Excitations out of major shell space are taken into account through a microscopic theory which are called core-polarization effects. The simple harmonic oscillator potential is used to generate the single particle matrix elements of 9,11,17,19C. The present calculations with core-polarization effects reproduced the experimental and theoretical data very well.
بهذا البحث نقارن معاييرالمعلومات التقليدية (AIC , SIC, HQ , FPE ) مع معيارمعلومات الانحراف المحور (MDIC) المستعملة لتحديد رتبة انموذج الانحدارالذاتي (AR) للعملية التي تولد البيانات,باستعمال المحاكاة وذلك بتوليد بيانات من عدة نماذج للأنحدارالذاتي,عندما خضوع حد الخطأ للتوزيع الطبيعي بقيم مختلفة لمعلماته
... Show MorePlane cubics curves may be classified up to isomorphism or projective equivalence. In this paper, the inequivalent elliptic cubic curves which are non-singular plane cubic curves have been classified projectively over the finite field of order nineteen, and determined if they are complete or incomplete as arcs of degree three. Also, the maximum size of a complete elliptic curve that can be constructed from each incomplete elliptic curve are given.
The nonlinear refractive (NLR) index and third order susceptibility (X3) of carbon quantum dots (CQDs) have been studied using two laser wavelengths (473 and 532 nm). The z-scan technique was used to examine the nonlinearity. Results showed that all concentrations have negative NLR indices in the order of 10−10 cm2/W at two laser wavelengths. Moreover, the nonlinearity of CQDs was improved by increasing the concentration of CQDs. The highest value of third order susceptibility was found to be 3.32*10−8 (esu) for CQDs with a concentration of 70 mA at 473 nm wavelength.
We described herein the synthesized and characterized of new bent and liner core compounds containing thiazolidin-4-one ring[XI-XIII] and [XIV-XVI] respectively. These compounds synthesized by sequence reactions starting from reaction resorcinol or hydroquinone with chloracetyl chloride to yield compounds [I] and [II] ,then the later compounds reactant with 4-hydroxybenzylaldehyde to product dialdehyde compounds [III] and [IV] .The Schiff bases compounds[V-VII] and [VIII-X] synthesized from reaction the compound [III] or [IV] with different aromatic amines, while the bent and liner core mesogens containing thiazolidin-4-one ring [XI-XIII] and [XIV-XVI] synthesized from reaction Schiff bases compounds[V-VII] or [VIII-X] with thioglycolic aci
... Show MoreThe development taking place on the sports field at the general level and in the game of football at the private level, being the most popular game in the world, has reached very advanced stages. The use of modern aids and technology has contributed greatly to this development from the collective and individual aspects, as the goalkeeper is the most important position in the team, the use of devices gave objective readings about the goalkeeper’s ability in terms of skill and physical aspects, as the importance of the research lies in designing an electronic device to measure the degree of bending of the knee angle because of its great importance in developing the skill of catching and dimensions of the high ball for football goalkeepers.
... Show MoreIn this work we prepared some schiff bases by condensation urea and benzaldehyde or its derevative ( bromo benzaldehyde or hydroxy benzaldehyde ) as ( 1 : 1 ) mole ( urea : benzaldehyde or its substitution ) to prepare compounds ( A1 , B1 , C1 , D1 , E1 , F1 , G1 ) and ( 1 : 2 ) mole ( urea : benzaldehyde or its substitution ) to prepare compounds ( A2 , B2 , C2 , D2 , E1 , F2 , G2 ) . The prepared compounds identified spectroscopic by infrared spectroscopy FT-IR and Thin layer chromotography T.L.C . The force constant calculated from the wave number for the carbonyl stretching from FT-IR chart and by using the following equation K = 4?2C2?'2? The change in double bond order for carbonyl deteremined in according with some past re
... Show MoreThe research problem has crystallized and in light of these capabilities, the level of performance depends on the application of modern training methods based on actual experimentation, and those methods aim to develop the components of achievement in this competition, including the quantities of exerting the distinctive strength with speed for the arms and feet, which reflects on good skillful performance because the skill of shooting by jumping forward and high forms A major role in achieving goals during the competition that qualifies the team to win, and through the follow-up of the researcher in the field and academic field, I noticed that there is a weakness in some physical abilities, which affects performance and skill level
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