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
Abstract
The government spending in Iraq and witnessed the changes and developments, especially after 2003, which outweighed consumer spending at the expense of capital expenditure and increased support and diversity of trends towards improving pension conditions for member
... Show MoreMaintaining the quality of apricot fruits during storage is not an easy task due to the changes in their physical and chemical properties, so it is necessary to use less expensive, easy to apply, environmentally friendly, and safer preservatives to maintain the nutritional value of apricot. The damage to some fruits during storage can be a source of infection, which leads to the damage of healthy fruits more quickly, which requires building an intelligent model to detect damaged fruits. The aim of the research is to study the effect of immersing apricots in lemon juice once and sugar-water solution again on the quality properties of apricots, including sweetness, color, hardness, and water content. On the other hand, the YOLOv7 algorithm wa
... Show MoreIn this article we study the variance estimator for the normal distribution when the mean is un known depend of the cumulative function between unbiased estimator and Bays estimator for the variance of normal distribution which is used include Double Stage Shrunken estimator to obtain higher efficiency for the variance estimator of normal distribution when the mean is unknown by using small volume equal volume of two sample .
The experiment was conducted at the faculty of agriculture University of Ain Shams-Egypt, from January to March 2008, to study the effect of different levels of chromium yeast (cr-yeast) on broiler chickens on some physiological traits. A total of 450, one-day old unsexed chickens (Cobb) strain were used. The birds were randomly allocated to five treatments with 3 replicates each. The treatments were control (T1), without supplementation, T2, T3, T4 and T5 which were supplemented with 0.5, 1, 1.5 and 2 mg cr-yeast/kg diet respectively. Chromium yeast supplementation treatments caused a significant (p < 0.05) increase in plasma glucose levels, while supplemented Cr-yeast at levels of 1 (T3), 1.5 (T4), 2 (T5) mg/kg diet resulted in a signific
... Show Morethis research seeks to shed light on the study of the impact of Putinism on the Russian-Ukrainian war that broke out in early 2022, by studying the contents of the speeches of Russian President Vladimir Putin before the start of the war. This research uses the structural approach in analyzing the components of the Russian political regime. The research tools used in this research include case studies, content analysis of Russian speeches, and personal meetings of researchers and specialists in Russian affairs. It sums up a number of important conclusions, most notably are : 1) Putinism is a totalitarian regime that includes the political doctrine during the era of Russian President Vladimir Putin. 2) Duginism represents the totality of t
... Show MoreDynamic Thermal Management (DTM) emerged as a solution to address the reliability challenges with thermal hotspots and unbalanced temperatures. DTM efficiency is highly affected by the accuracy of the temperature information presented to the DTM manager. This work aims to investigate the effect of inaccuracy caused by the deep sub-micron (DSM) noise during the transmission of temperature information to the manager on DTM efficiency. A simulation framework has been developed and results show up to 38% DTM performance degradation and 18% unattended cycles in emergency temperature under DSM noise. The finding highlights the importance of further research in providing reliable on-chip data transmission in DTM application.
The optimum design is characterized by structural concrete components that can sustain loads well beyond the yielding stage. This is often accomplished by a fulfilled ductility index, which is greatly influenced by the arrangement of the shear reinforcement. The current study investigates the impact of the shear reinforcement arrangement on the structural response of the deep beams using a variety of parameters, including the type of shear reinforcement, the number of lacing bars, and the lacing arrangement pattern. It was found that lacing reinforcement, as opposed to vertical stirrups, enhanced the overall structural response of deep beams, as evidenced by test results showing increases in ultimate loads, yielding, and cracking of
... Show MoreThe optimum design is characterized by structural concrete components that can sustain loads well beyond the yielding stage. This is often accomplished by a fulfilled ductility index, which is greatly influenced by the arrangement of the shear reinforcement. The current study investigates the impact of the shear reinforcement arrangement on the structural response of the deep beams using a variety of parameters, including the type of shear reinforcement, the number of lacing bars, and the lacing arrangement pattern. It was found that lacing reinforcement, as opposed to vertical stirrups, enhanced the overall structural response of deep beams, as evidenced by test results showing increases in ultimate loads, yielding, and cracking of
... Show MoreIn order to select the optimal tracking of fast time variation of multipath fast time variation Rayleigh fading channel, this paper focuses on the recursive least-squares (RLS) and Extended recursive least-squares (E-RLS) algorithms and reaches the conclusion that E-RLS is more feasible according to the comparison output of the simulation program from tracking performance and mean square error over five fast time variation of Rayleigh fading channels and more than one time (send/receive) reach to 100 times to make sure from efficiency of these algorithms.