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In this paper a modified approach have been used to find the approximate solution of ordinary delay differential equations with constant delay using the collocation method based on Bernstien polynomials.

Periodontal diseases (PD) are worldwide diseases of humans either in childhood or adults. The present study aimed to find the correlation between some demographic and saliva immunological factors including the determination of saliva TLR-2, IL6, CRP, and α- amylase in patients with periodontal diseases. For this purpose, 60 patients out of which 33were males and 27 were females participated in this study from different Dental treatment Centers (Amirya Specialized Dental Center and Almaamon Specialized Dental Center ) in Baghdad/ Iraq, for the period starting from November / 2021 to February / 2022. Both age ranges for patients and control are (13-70) years, and patients’ mean ages are 34.29±15.01. Additionally, the control speci

The reinforcing effect of emphasizers can hardly be denied, hence their importance , hence the justification for writing this paper. As a particular type of adverbials , emphasizers form part of a major syntactic class. This study, thus, introduces the topic by first discussing a grammatical category characterized by being mobile and optional. The paper duly shows the scaling effect of emphasizers, their kinds and the transformational selectional rules that are operative in moving them to the right or left of the VP. It also handles their syntactic role as modifiers, their syntactic features,their occurrence or non- occurrence with negation and imperative and the position they occupy in the sentence. The paper also dwells on the agr

The impact of a simple trailing-edge plain flap on the aerodynamics of the SD7037 airfoil have been studied in this paper using computational fluid dynamics at Reynolds number of 3×105 across various low angles of attack and flap deflection angles. The computational model was evaluated by using Star CCM+ software with κ--ω SST turbulence and gamma transition model to solve Navier-Stokes equations. The accuracy of the computational model has been confirmed through comparison with experimental data, showing a high level of agreement at low angles of attack. The findings revealed that specific combinations of angles of attack and flap deflection angles could increase the lift-to-drag ratio by over 70% compared to baseline conditions, benefi

In this paper, the computational method (CM) based on the standard polynomials has been implemented to solve some nonlinear differential equations arising in engineering and applied sciences. Moreover, novel computational methods have been developed in this study by orthogonal base functions, namely Hermite, Legendre, and Bernstein polynomials. The nonlinear problem is successfully converted into a nonlinear algebraic system of equations, which are then solved by Mathematica®12. The developed computational methods (D-CMs) have been applied to solve three applications involving well-known nonlinear problems: the Darcy-Brinkman-Forchheimer equation, the Blasius equation, and the Falkner-Skan equation, and a comparison between the met

The Detour distance is one of the most common distance types used in chemistry and computer networks today. Therefore, in this paper, the detour polynomials and detour indices of vertices identified of n-graphs which are connected to themselves and separated from each other with respect to the vertices for n≥3 will be obtained. Also, polynomials detour and detour indices will be found for another graphs which have important applications in Chemistry.

The loose sand is subject to large settlement when it is exposed to high stresses. This settlement is due to the nature of the high drainage of sand, which displays foundations and constructions to a large danger. The densification of loose sandy soils is required to provide sufficient bearing capacity for the structures. Thus soil stabilization is used to avoid failure in the facilities. Traditional methods of stabilized sandy soil such as fly ash, bituminous, and cement often require an extended curing period. The use of polymers to stabilize sandy soils is more extensive nowadays because it does not require a long curing time in addition to being chemically stable. In this study, the effect of adding different percent

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