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 parall

Experts have given much attention on the use of waste in asphalt paving because of its significance from a sustainability perspective. This paper evaluated the performance properties of asphalt concrete mixes modified with Crumb Rubber (CR) as a partial replacement for two grade sizes of fine aggregate (2.36, and 0.3 mm) at six replacement rates: 0%, 2%, 4%, 6%, 8%, and 10% by weight. Asphalt concrete mixes were prepared at their Optimum Asphalt Content (OAC) and then tested for their engineering properties. Marshall properties, fatigue, rutting, ideal CT index test, Scanning Electron Microscopy (SEM), and Energy-Dispersive X-ray (EDX) spectroscopy were deployed to examine the crystalline structure and elemental composition of the C

     Optimal control methods are used to get an optimal policy for harvesting renewable resources. In particular, we investigate a discretization fractional-order biological model, as well as its behavior through its fixed points, is analyzed. We also employ the maximal Pontryagin principle to obtain the optimal solutions. Finally, numerical results confirm our theoretical outcomes.

The current research includes the adsorption of Rhodmine-B Dye on the surface of Citrus Leaves using the technique of UV. Vis spectrophotometer to determine data of quantitative adsorption at various contact time, ionic strength, PH and temperature conditions. As a function of temperatures 25,35,45,55 ⁰C, the dsorption phenomenon was examined, and the results showed that Rhodamine-B adsorption Citrus leaves rose with increasing temperatures on the surface (endothermic process). Using various NaCl solution concentrations, the effect of ionic strength on adsorption has also been studied. Increasing the importance of ionic strength has been shown to improve the amount of adsorption of Rhodamine-B on citrus leaves at constant temp

       In this paper, investigations were carried out on the effects of simultaneous partial substitution of Tl at the Hg site on the physical properties of an Hg_1-xTl_xBa₂Ca₂Cu₃O_8+δ cuprate superconductor with x= 0, 0.1, 0.2, 0.3 and 0.4. Two steps of the solid state reaction method were used to prepare samples in capsule. The results showed that the optimum sintering temperature was equal to 850 ^ᵒC and the sintering time was equal to 20 h for the prepared samples.  

    The best conditions for constitution and stabilization of the high T_c phase-1223 were obtained by investigating the e

Let A ⊆ V(H) of any graph H, every node w of H be labeled using a set of numbers; , where d(w,v) denotes the distance between node w and the node v in H, known as its open A-distance pattern. A graph H is known as the open distance-pattern uniform (odpu)-graph, if there is a nonempty subset A ⊆V(H) together with  is the same for all . Here  is known as the open distance pattern uniform (odpu-) labeling of the graph H and A is known as an odpu-set of H. The minimum cardinality of vertices in any odpu-set of H, if it exists, will be known as the odpu-number of the graph H. This article gives a characterization of maximal outerplanar-odpu graphs. Also, it establishes that the possible odpu-number of an odpu-maximal outerplanar graph i

Each educational system aims at having an effective way of

teaching that leads to an effective learing.This needs preparing good inputs in their standard qualifications and good effective ways in the phae of processes during which reliable and valid methods and technjqucs of teaching are used.

Instructional techniques have gained, lately, an increasing and

great attention of educationists because of their many techniques arc Frcinet's  which they can be applied in our cducutional institution (schools, institutes and colleges),after giving a brief profile of Frcint

and  his educa      tiona! ideas and  his innovations in the field of

instructional techniques.<

Objectives: The study aims to assess the school refusal behavior of first class pupils at primary schools and identifying the relationship between the school refusal behavior and some of socio-demographic characteristics for the pupils.

Methodology:  A descriptive-analytic study was initiated from November 1^st, 2012 to April 1^st, 2013. A random sample of 411 students is selected from a probability stratified sample of 17 primary schools for both sexes in 4 sectors in Baghdad Al-Rasafa and Al-Karkh districts which are selected randomly from first class of primary school. A Self administrative questionnaire (Parents' Version) which constructed by the rese