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

Biodegradable polymers have garnered increasing attention as eco-friendly alternatives to conventional petroleum-derived plastics, which pose a global environmental challenge due to their difficult recycling and slow degradation. This study focuses on the preliminary evaluation of surface functional properties of chitosan films reinforced with TiO₂ or ZnO nanoparticles (NPs). These films were prepared at different loading ratios using the solution-casting method. Structural and morphological properties were characterized using FTIR and FESEM, while functional properties were evaluated by surface wettability, UV–Vis spectroscopy, thermogravimetric analysis and antibacterial activity testing. FTIR results showed significant changes in abs

Background: Removal of bacteria from the pulp system by instrumentation of an infected root canal, will be significantly reduced the number of bacteria, but it is well documented that instrumentation alone can-not clean and kill all bacteria found on the root canal walls. Antibacterial irrigants are needed to kill the remaining microorganisms. The aims of this study was to assess antibacterial effect of titanium tetrafluoride (TiF4) solution and brewing green tea against root canal bacteria and to compare with sodium hypochlorite and normal saline through microbiological and molecular studies. Materials and methods: Microbiological study was carried out to determine the concentration of titanium tetrafluoride and brewing green tea at which

Experiment Factorial conducted with two factor in field texture silt clay loam soil, the first factor were Two Rotavator plow which different in number of rotary blades on flanges, weight, width, made and type, the second factor were four speeds tractor 2.62, 5.10, 7.55, 9.23 km/hr to compare performance two Rotavator under depth 12 cm and knowledge slippage, distance between beat blades, practical productivity, disturbed soil volume, percentage of the soil clods which have diameter less than 5 cm under complete block design with three replications using Least Significant Design 0.05. Results showed Galucho Rotavator recorder the higher practical productivity 0>7089 ha/hr, disturbed soil volume 809.8 m3/hr, percentage of the soil clods 96.1

The experiment was conducted in Al- Mahaweel Research Station in Babel Governorate, Ministry of Agriculture during autumn season 2016-2017 to determine the role of irrigation management processes and micronutrient fertilization in growth and productivity of two varieties of wheat IPA 99 and Al-Rasheed 22 in clay loam soil classified as Typic Torriflovent. The experiment included four irrigation treatments and six fertilization treatments. The experiment was designed under randomized complete block design (RCBD) with three replications. Wheat grain IPA 99 and Al-Rasheed 22 varieties were planted in 23/11/2016 and harvested in 13/5/2017. The amount and periods of irrigation depended on sensors reading of volumetric water content was measured

In the hybrid coolingsolar systems , a solar collectoris used to convertsolar energy intoheat sourcein order to super heat therefrigerant leave thecompressor,andthisprocess helpsin the transformation ofrefrigerant state from gaseous statetothe liquid statein upper two-thirdsof thecondenserinstead of the lower two-thirdssuchas in thetraditional air-conditioning systems and this willreduce theenergyneeded torun the process ofcooling.In this research two hybrid air-conditioning system with an evacuated tube solar collector were used, therefrigerant was R22 and the capacity was 2 tons each.The tilt angle of the evacuated tube solar collector was changed and the solar collector fluid was replaced into oil instead of water.A comparison wasi

In this paper, the delay integral equations in population growth will be described,discussed , studied and transfered this model to integro-differential equation. At last,we will solve this problem by using variational approach.

    The mix promotion important to any organization in general, has been selected promotional mix tools in this research to identify the role in maximizing the Organization of sales growth business, which included the research problem several fundamental questions about the role of each promotional tool of advertising, public relations and personal selling and sales promotion direct marketing within the promotional mix in the promotion of business sales organization. The research aims to provide theoretical and field organizations surveyed about the role played by the mix promo in sales growth, and  importance of research on the identification of more than promotional tools impact on sales gr