Discrete Krawtchouk polynomials are widely utilized in different fields for their remarkable characteristics, specifically, the localization property. Discrete orthogonal moments are utilized as a feature descriptor for images and video frames in computer vision applications. In this paper, we present a new method for computing discrete Krawtchouk polynomial coefficients swiftly and efficiently. The presented method proposes a new initial value that does not tend to be zero as the polynomial size increases. In addition, a combination of the existing recurrence relations is presented which are in the n- and x-directions. The utilized recurrence relations are developed to reduce the computational cost. The proposed method computes app

This research paper is about thevariationin the degree of Continentality climate of the
Iraq during (40) years for a number of climate station. Using Poresof formula, it is found out
that the climate of Iraq ranges between extreme Continentality and very extreme
Continentality, and that the Continentality degree is characterized with extreme frequency
from one year to another. In certain years, the degree of climate Continentality decreases
while in other years it rises in such a way that there is no similarity in the Continental degree
from one year to another for the same station.
As for the general trend of the degree of Continentality, the last years had noticed
special variations, which are divided in to thre

In this study, a genetic algorithm (GA) is used to detect damage in curved beam model, stiffness as well as mass matrices of the curved beam elements is formulated using Hamilton's principle. Each node of the curved beam element possesses seven degrees of freedom including the warping degree of freedom. The curved beam element had been derived based on the Kang and Yoo’s thin-walled curved beam theory. The identification of damage is formulated as an optimization problem, binary and continuous genetic algorithms
(BGA, CGA) are used to detect and locate the damage using two objective functions (change in natural frequencies, Modal Assurance Criterion MAC). The results show the objective function based on change in natural frequency i

Krawtchouk polynomials (KPs) and their moments are promising techniques for applications of information theory, coding theory, and signal processing. This is due to the special capabilities of KPs in feature extraction and classification processes. The main challenge in existing KPs recurrence algorithms is that of numerical errors, which occur during the computation of the coefficients in large polynomial sizes, particularly when the KP parameter (p) values deviate away from 0.5 to 0 and 1. To this end, this paper proposes a new recurrence relation in order to compute the coefficients of KPs in high orders. In particular, this paper discusses the development of a new algorithm and presents a new mathematical model for computing the

In this paper, an approximate solution of nonlinear two points boundary variational problem is presented. Boubaker polynomials have been utilized to reduce these problems into quadratic programming problem. The convergence of this polynomial has been verified; also different numerical examples were given to show the applicability and validity of this method.

Chemical compounds, characteristics, and molecular structures are inevitably connected. Topological indices are numerical values connected with chemical molecular graphs that contribute to understanding a chemical compounds physical qualities, chemical reactivity, and biological activity. In this study, we have obtained some topological properties of the first dominating David derived (DDD) networks and computed several K-Banhatti polynomials of the first type of DDD.

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