In this article, a new deterministic primality test for Mersenne primes is presented. It also includes a comparative study between well-known primality tests in order to identify the best test. Moreover, new modifications are suggested in order to eliminate pseudoprimes. The study covers random primes such as Mersenne primes and Proth primes. Finally, these tests are arranged from the best to the worst according to strength, speed, and effectiveness based on the results obtained through programs prepared and operated by Mathematica, and the results are presented through tables and graphs.

Abstract The dissemination of knowledge is no longer confined to schools and universities, not even books. For nearly two centuries, the media have become prominent in disseminating knowledge and culture, in its public and particularly political aspects. After the development of the media from newspapers and magazines to the visual media, their role has increased from the dissemination of abstract information and abstract knowledge towards the process of forming new knowledge through what it publishes and broadcasts from different programs such as drama, news and talk shows. The impact of the media has changed the overall community awareness. Half a century ago the media was not so powerful and widespread. The evolution of the 1990s made

Community detection is one of the most fundamental applications in understanding the structure of complicated networks. Furthermore, it is an important approach to identifying closely linked clusters of nodes that may represent underlying patterns and relationships. Networking structures are highly sensitive in social networks, requiring advanced techniques to accurately identify the structure of these communities.Most conventional algorithms for detecting communities perform inadequately with complicated networks. In addition, they miss out on accurately identifying clusters. Since single-objective optimization cannot always generate accurate and comprehensive results, as multi-objective optimization can.Therefore,we utilized two objective

Abstract

The research addresses the specification table and the extent of its use in developing achievement tests, as well as detects the obstacles to its use through a sample of (120) respondents from the faculty members in some Baghdad schools and colleges. After unpacking and processing the data statistically, the research reached several results: the study sample do not use the test map in the development of their tests, as their percentage reached (82%) and there are no statistically significant differences in the use of the specification table by the sample members according to their place of work or the number of years of experience. The results also revealed the most important reasons that prevent the use

In this research, the dynamics process of charge transfer from the sensitized  D35CPDT dye to tin(iv) oxide( ) or titanium dioxide (  ) semiconductors are carried out by using a quantum model for charge transfer. Different chemical solvents Pyridine, 2-Methoxyethanol. Ethanol, Acetonitrile, and Methanol have been used with both systems as polar media surrounded the systems. The rate for charge transfer from photo-excitation D35CPDTdye and injection into the conduction band of  or  semiconductors vary from a  to  for system and from a   to  for the system, depending on the charge transfer parameters strength coupling, free energy, potential of donor and acceptor in the system. The charge transfer rate in D35CPDT /  the syst

Liquefied petroleum gas (LPG), Natural gas (NG) and hydrogen were all used to operate spark ignition internal combustion engine Ricardo E6. A comparison of CO emissions emitted from each case, with emissions emitted from engine fueled with gasoline as a fuel is conducted.

The study was accomplished when engine operated at HUCR for gasoline n(8:1), was compared with its operation at HUCR for each fuel. Compression ratio, equivalence ratio and spark timing were studied at constant speed 1500 rpm.

CO concentrations were little at lean ratios; it appeared to be effected a little with equivalence ratio in this side, at rich side its values became higher, and it appeared to be effected by equivalence ratio highly, the results s

A theoretical study by using computer model is presented to study the energy characteristics of the vibrational – rotational levels as a function of the vibrational and rotational quantum number, respectively. The calculations were based on the basis of a multilevel model taking into account the non-equilibrium population of the rotational levels. The computational investigation has been performed to examine the vibrational-rotational characteristics of some hydrogen halides chemical laser molecules. This program takes into account the various molecules of chemical lasers such as, Hydrogen Fluoride (HF), Deuterium Fluoride (DF), Hydrogen Chloride (HCl), and Deuterium Chloride (DCl). The practical difficulties associated with this

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