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 family Chalcididae (Order: Hymenoptera) is known as one of the large chalcidoid wasps with some distinct morphological characters. The first occurrence of two parasitoid species belonging to this family was reported in the Al-Husayniya district Karbala Province, Iraq; which are: Brachymeria podagrica (Fabricius, 1787) and Chalcis myrifex (Sulzer, 1776). Both species were collected by using the sweeping net from orchards during July 2020.

The majority of Iraqi translator-student have problems at two main levels: the conceptual level and the productive level. From different perspectives, such problems are either related to ‘language’ or to ‘cognition’. This binary view is an indication to the implicit and interchangeable relationship between language and cognition. The relationship between cognition language and translator starts with the first language and its effect on the Iraqi translators. Identifying the effect is the aim of the present study. It is hypothesized that Iraqi students are negatively influenced by the problems and weaknesses of first language schema. This reflects the major claim and later concludes that first language instruction in the Iraq

Objectives: Assessment of glycodelin (GD) as a marker for unruptured ectopic pregnancy (EP) in the first trimester of pregnancy. Materials and Methods: This case-control study was conducted during June 2016 to May 2017 in the Obstetrics and Gynecological Department of Baghdad University at Baghdad teaching hospital/medical city complex. In this study, 100 pregnant women in their first trimester of pregnancy were included after clinical and ultrasonic findings. Results: Based on the results, GD levels in EP were significantly lower than those with normal intrauterine pregnancy (1.58 ± 1.18 vs. 30.1 ± 11.9). In addition, using receiver operator curve analysis, the cut-off GD level of 9.5 and less had acceptable validity results (100

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.

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.

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect