The aim of this paper is to present a method for solving third order ordinary differential equations with two point boundary condition , we propose two-point osculatory interpolation to construct polynomial solution. The original problem is concerned using two-points osculatory interpolation with the fit equal numbers of derivatives at the end points of an interval [0 , 1] . Also, many examples are presented to demonstrate the applicability, accuracy and efficiency of the method by compared with conventional method .

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

The differential cross section for the Rhodium and Tantalum has been calculated by using the Cross Section Calculations (CSC) in range of energy(1keV-1MeV) . This calculations based on the programming of the Klein-Nashina and Rayleigh Equations. Atomic form factors as well as the coherent functions in Fortran90 language Machine proved very fast an accurate results and the possibility of application of such model to obtain the total coefficient for any elements or compounds.

In order to have an idea about what happens in Iraqi food establishments in relation to implement quality management system ISO 9001, this study was performed to show the actual situation of Iraqi food establishments concerning quality management system (ISO 9001:2015), reasons of implementing, factors that hinder implementing and problems faced high administration for getting establishments certification ISO 9001:2015. The study demonstrated from the questionnaire some difficulties to implement ISO 9001 for both of establishments that implemented the quality system or which in implementing of this international standard. The most important problems during implementing were business culture and costs and the most important proble

 The current paper studied the concept of right n-derivation satisfying certified conditions on semigroup ideals of near-rings and some related properties. Interesting results have been reached, the most prominent of which are the following: Let M be a 3-prime left near-ring and A_1,A_2,…,A_n are nonzero semigroup ideals of M, if d is a right n-derivation of M satisfies on of the following conditions,
d(u_1,u_2,…,(u_j,v_j ),…,u_n )=0 ∀ 〖 u〗_1 〖ϵA〗_1 ,u_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n ϵA〗_u;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=0 ∀u_1,v_1 〖ϵA〗_1,u_2,v_2 〖ϵA〗_2,…,u_j,v_j ϵ A_j,…,〖u_n,v_n ϵA〗_u ;
d((u_1,v_1 ),(u_2,v_2 ),…,(u_j,v_j ),…,(u_n,v_n ))=(u_

The present study aimed to investigate the effects of level pH and the growth phases of Coelastrella saipanensis on Chlorophyll a,b, total, and Carotene. The algae were cultured in BG11 media and grown at different pH levels. We measured chlorophyll a, b, total chlorophyll, growth phases, and carotene concentrations. The results showed that at pH 8.5, the measurements of photosynthetic pigments-chlorophyll a, Chlorophyll b, and the total chlorophyll (0.183, 0.268, and 0.433 mg L-1, respectively). The highest values of chlorophyll a (0.185 mg L-1), and b (0.339 mg L-1), and the total chlorophyll (0.492 mg L-1) were recorded in the stationary phase. In addition, the study found that at pH 8.5 and the beginning of the stationary phase,