Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The significance of this result is that it is unconditional which means it is proved without assuming any form of strong conjecture like the Elliott–Halberstam conjecture
At the temperature 298.15 K, some physical properties such as: refractive indices (nD), viscosities (η) and densities (ρ) were studied in four liquid-liquid mixtures: carboxylic acids (HCOOH, CH3COOH, CH3CH2COOH and CH3CH2CH2COOH) with tetrahydrofurfuryl alcohol (THFA) with the identified configuration set. These empirical data were utilized to estimate the excess molar volumes (Vm E), refractive index perversions (ΔR), viscosity deviations (ηE) and excess molar Gibbs free energy (ΔG*E). Values of Vm E, ηE , ΔG*E and ΔR were plotted versus mole fraction of tetrahydrofurfuryl alcohol. In all cases, the values of Vm E, ηE , ΔG*E and ΔR that obtained in this study were found to be negative at 298.15 K. The excess parameters
... Show MoreIt was known that every left (?,?) -derivation is a Jordan left (?,?) – derivation on ?-prime rings but the converse need not be true. In this paper we give conditions to the converse to be true.
Introduction and Aim: Diabetes mellitus patients almost always struggle with a metabolic condition known as chronic hyperglycemia. According to the World Health Organization, osteoporosis is a progressive systemic skeletal disorder that is characterized by decreasing bone mass and microstructural breakdown of bone tissue that increases susceptibility to fracture and increased risk of breaking a bone. Here, we aimed to compare the levels of CatK and total oxidative state in patients with diabetes and osteoporosis among the female Iraqi population and study the possible relationship between them. Materials and Methods: This study included 40 females with diabetes (Group G1), 40 with diabetes and osteoporosis (Group G2) and 40 normal healthy f
... Show MoreIn this paper we introduce generalized (α, β) derivation on Semirings and extend some results of Oznur Golbasi on prime Semiring. Also, we present some results of commutativity of prime Semiring with these derivation.
Software-defined networks (SDN) have a centralized control architecture that makes them a tempting target for cyber attackers. One of the major threats is distributed denial of service (DDoS) attacks. It aims to exhaust network resources to make its services unavailable to legitimate users. DDoS attack detection based on machine learning algorithms is considered one of the most used techniques in SDN security. In this paper, four machine learning techniques (Random Forest, K-nearest neighbors, Naive Bayes, and Logistic Regression) have been tested to detect DDoS attacks. Also, a mitigation technique has been used to eliminate the attack effect on SDN. RF and KNN were selected because of their high accuracy results. Three types of ne
... Show MoreThis paper investigates the concept (α, β) derivation on semiring and extend a few results of this map on prime semiring. We establish the commutativity of prime semiring and investigate when (α, β) derivation becomes zero.