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

The hydrodynamics of a co-current down flow bubble column has been investigated with air – water system. A Perspex bubble column of 5cm in diameter and 1.5m height is used as a test contactor using nozzles of 7, 8 and 9 mm diameter for air-water distributing. The column is provided with three electro-resistivity needle probes for bubble detection.
Experimental work is carried out with air flow rates from 0.09 to 0.45 m3/hr and liquid flow rates from 0.65 to 1.1m3/hr in order to study the effects of superficial gas velocity, nozzle diameter and liquid flow rate on the characteristics of hydrodynamic interactions viz. gas hold up, bubble diameter and bubble velocity by using two technical methods, direct height measurements for air-wa

Background: Fertility plays great role in animal reproduction since high quality semen improves sheep industry reproduction. The current worldwide data revealed the closely related of CNP to reproductive function of rams. Aims: Evaluation the effect of CNP on cooled sperms using the traditional and molecular assays. Methods: Totally, 20 testicular samples were collected, processed to obtain the semen samples and divided into two parts; one treated with the suitable dose of CNP and the otherserved as a control. Sperm samples of both groups were cooled for 3 days and tested at 0 0h, 24h, 48h and 72h. Results: The findings revealed that the suitable dose of CNP-treated sperms was 0.0110-13. Values individual motility, live sperm

Each school of Islamic jurisprudence has principles and rules upon which the diligent work in these schools is based. This is due to the view of sanctification of these rulings, as they are divine rulings. Therefore, the goal is to reach a ruling that represents the intent of the legislator as much as possible.
Hence, these schools of thought established rules for issuing fatwas with the intention of restricting the performance of a fatwa to the hands of those who are qualified for it and have met its conditions, so they gave priority to the most knowledgeable person over others to perform the fatwa. In the Hanafi school of thought, for example, the saying of Imam Abu Hanifa (may God have mercy on him) is given precedence over others,

Enhancing fatigue resistance in asphalt binders and mixtures is crucial for prolonging pavement lifespan and improving road performance. Recent advancements in nanotechnology have introduced various nanomaterials such as alumina (NA), carbon nanotubes (CNTs), and silica (NS) as potential asphalt modifiers. These materials possess unique properties that address challenges related to asphalt fatigue. However, their effectiveness depends on proper dispersion and mixing techniques. This review examines the mixing methods used for each nanomaterial to ensure uniform distribution within the asphalt matrix and maximize performance benefits. Recent research findings are synthesized to elucidate how these nanomaterials and their mixing proce

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 performance, carcass quality and enzyme activity through 35 days of experimental periods. 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 and T2, T3, T4 and T5 which were supplemented with 0.5, 1, 1.5 and 2 mg Cr-yeast /kg diet, respectively. Live body weight and weight gain were significantly (p<0.05) higher when Cr-yeast were supplemented at 1 (T3), 1.5 (T4) and 2 (T5) mg/kg diet. Fe

This study included collecting of 150 specimens of the Iraqi Bird Bulbule Pycnonotus lecuotis mesoptamiae (Pycnotidae , Passeriformes), from the 1st of November 2004 to 30th of October 2005 in the city of Baghdad and its suburbs, in concern of identifying the internal parasite of the digestive tract of these birds and studying the diseases resulted from the infection. The study showed that the bird Bulbule is Parasitized by Four types of Cestodes ,two of them are recorded in this kind of bird in Iraq for the first time ,Paradicranotinae anormalis and Haploparaxis sp. , and the other two are Raillietina tetragona and Allohymenolepsis sp. ,and by two types of Pin Worm(Trematode) that are identified for the first time in the Bird Bulb