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 bandwidth requirements of telecommunication network users increased rapidly during the last decades. Optical access technologies must provide the bandwidth demand for each user. The passive optical access networks (PONs) support a maximum data rate of 100 Gbps by using the Orthogonal Frequency Division Multiplexing (OFDM) technique in the optical access network. In this paper, the optical broadband access networks with many techniques from Time Division Multiplexing Passive Optical Networks (TDM PON) to Orthogonal Frequency Division Multiplex Passive Optical Networks (OFDM PON) are presented. The architectures, advantages, disadvantages, and main parameters of these optical access networks are discussed and reported which have many ad

The survey and checklist of invasive species of the insects in some different localities of Iraq are revised; 24 invasive species were documented until December 2018 during the current investigations. The species distributions, common names and synonyms are given.

The current investigation included all of exotic species in Iraq, which are not collected during this study.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fifth order with delay by using the Lyapunov-Krasovskii functional approach, we obtain some conditions of instability of solution of such equation.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

Various visual media are becoming an increasingly important and active instrument of communication. This fact has led some political parties and leading personalities in Iraq to make use of them as an accepted forum for the discussion of public affairs usually in a manner that conforms to their declared policy. They have to draw as much popular support as they could for the causes which they fight for. As a result, a state of great confusion has been created from the contradictory statements made by the contending parties and gave left grave consequences on all types of the audience receiving them. The problem of the study can be summarized in one major question: What is the opinions of the audience as regards the statements made by the