In this work, we study several features of the non-zero divisor graphs (ℵZD- graph) for the ring Zn of integer modulo n. For instance, the clique number, radius, girth, domination number, and the local clustering coefficient are determined. Furthermore, we present an algorithm that calculates the clique number and draws the non-zero divisor for the ring Zn.

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

High-resolution imaging of celestial bodies, especially the sun, is essential for understanding dynamic phenomena and surface details. However, the Earth's atmospheric turbulence distorts the incoming light wavefront, which poses a challenge for accurate solar imaging. Solar granulation, the formation of granules and intergranular lanes on the sun's surface, is important for studying solar activity. This paper investigates the impact of atmospheric turbulence-induced wavefront distortions on solar granule imaging and evaluates, both visually and statistically, the effectiveness of Zonal Adaptive Optics (AO) systems in correcting these distortions. Utilizing cellular automata for granulation modelling and Zonal AO correction methods,

Abstract We have been studied and analysis the electronic current at the interfaces of Au/PTCDA system according to simple quantum mode for the electronics transition rate due to postulate quantum theory. Calculation of electronic current were performed at interface of Au/PTCDA as well as for investigation the feature of electronic density at this devices. The transition of electronic current study under assume the electronic state of Au and PTCDA were continuum and the states of electrons must be closed to energy level for Au at Fermi state, and the potential at interface feature depended on structure of Au and PTCDA material. The electronic transition current feature was dependent on the driving force energy that results of absorption ene

This research aims at investigating pupils’ ability in using discourse markers which are identified in the English textbooks of secondary schools. Four texts are chosen from third intermediate class. The four texts are short stories of different topics.                                                  

        This research hypothesizes that there are no statistical significant differences among Iraqi intermediate pupils’ ability in using textual

Biometrics represent the most practical method for swiftly and reliably verifying and identifying individuals based on their unique biological traits. This study addresses the increasing demand for dependable biometric identification systems by introducing an efficient approach to automatically recognize ear patterns using Convolutional Neural Networks (CNNs). Despite the widespread adoption of facial recognition technologies, the distinct features and consistency inherent in ear patterns provide a compelling alternative for biometric applications. Employing CNNs in our research automates the identification process, enhancing accuracy and adaptability across various ear shapes and orientations. The ear, being visible and easily captured in

Reservoir study has been developed in order to get a full interesting of the Nahr Umr formation in Ratawi oil field. Oil in place has been calculated for Nahr Umr which was 2981.37 MM BBL. Several runs have been performed to get matching between measured and calculated of oil production data and well test pressure. In order to get the optimum performance of Nahr Umr many strategies have been proposed in this study where vertical and horizontal wells were involved in addition to different production rates. The reservoir was first assumed to be developed with vertical wells only using production rate of (80000–125000) STB/day. The reservoir is also proposed to produce using horizontal wells besides vertical wells with production rat

Frustrated Total Internal Reflection FTIR phenomenon is manifested employing Newton‟s rings setup generated via a coherent light beam of a laser diode ( . All concentric bright and dark rings, except the central bright spot, were noticed to recede (disappear) when the incident angle exceeded the critical angle of 41o.
It was also shown that the current setup has proven its applicability for other tests and can give convenient results that conform with theory. Neither the concept nor the design is beyond what can be realized in an undergraduate laboratory. However, technical improvements in mounting the prism - lens may be advisable. As an extension of the experiments, the effect can be studied using hollow prism filled with liquids