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 sig

Background: This in vitro study was carried out to evaluate the effects of various veneering dentin ceramic thicknesses and repeated firings on the color of lithium disilicate glass-ceramic (IPS e.max Press) and zirconium-oxide (IPS ZirCAD) all-ceramic systems, measured by clinical spectrophotometers (Easyshade Advance 4.0) . Materials and methods: The 72specimens cube-shaped have the dimension of about 11 mm in width, 14 mm in length, 1mm in thickness, these cores divided into 3 groups according to the type of material each group have (24)core specimens. Each group had been divided into three sub-groups (each having 8 specimens) according to veneering with dentin ceramic thicknesses: as 0.5, 1, or 2 mm (n=8). IPS e.max press and ZirCAD c

Two field experiments were conducted during the spring season 2020 in Karbala governorate to study the effect of irrigation systems, irrigation intervals, biofertilizers and polymers on some characteristics of vegetative growth and potato production. The results showed that there were significant differences in the values of the average plant height due to the effect of the double interference between the irrigation system and the improvers, The height of potato plant under any irrigation system was superior when adding conditioners compared to the control treatment, as it reached 48.56, 58.00 and 64.33cm when adding polymer, biofertilizer, and polymers+ biofertilizers, respectively compared with the control treatment of 44.64cm in the surf

Technology developed at very rapid paces in the last decade of the twentieth century and what followed, especially communication technology, as the World Wide Web appeared in the mid-nineties of the last century, Facebook in 2004 and 2006, the mobile phone, 1993, 1994, and social networking sites. The other. These technological developments have had an impact on societies, whether among individuals in one country or among different peoples. The citizen in any part of the world has become a journalist who practices the work of a specialized or professional journalist, even if he does not know how to read and write, or has a low level of education, as he can now transmit events from wherever he is to the world, through his personal page, or v

Biodiesel production from microalgae depends on the biomass and lipid production. Both biomass and lipid accumulation is controlled by several factors. The effect of various culture media (BG11, BBM, and Urea), nutrients stress [nitrogen (N), phosphorous (P), magnesium (Mg) and carbonate (CO₃)] and gamma (γ) radiation on the growth and lipid accumulation of   Dictyochloropsis splendida were investigated. The highest biomass and lipid yield of D. splendida were achieved on BG11 medium. Cultivation of D. splendida in a medium containing 3000 mg L⁻¹ N, or 160 mg L⁻¹ P, or 113 mg L⁻¹ Mg, or 20 mg L^-1 CO_3, led to enhanced growth rate. While u

Greywater is a possible water source that can be improved for meeting the quality required for irrigation. Treatment of greywater can range from uncomplicated coarse filtration to advanced biological treatment. This article presents a simple design of a small scale greywater treatment plant, which is a series of physical and natural processes including screening, aeration, sedimentation, and filtration using granular activated carbon filter and differentiates its performance with sand filter. The performance of these units with the dual filter media of (activated carbon with sand) in treatment of greywater from Iraqi house in Baghdad city during 2019 and that collected from several points including washbasins, kitchen si