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,

Objective(s): To assess the adequacy of mediation program on medical attendants practice toward care of kids with diabetic's ketoacidosis. Methodology: A quasi-experimental design that applied at teaching hospitals for pediatric in AL Ramadi city to establish the Effectiveness of Intervention Program on Nurses` Practices about Care of Children with Diabetic Ketoacidosis from 3th of March 2022 till 20 of March 2023. Non-probability (purposive) sample of (50), likewise was alienated into the study (experimental) group. The study group included (50) nurses non-randomly selected from AL-Ramadi Teaching Hospital.

A preliminary study has conducted in AL-Ramadi Teaching Hospital The whole number of nurse

Flexible pipes, such as GRP pipes, serve as effective underground infrastructure especially as sewer pipeline. This study is an attempt for understanding the effects of bedding types on the behavior of large diameter GRP flexible sewer pipes using three dimensional finite element approaches. Theoretical and numerical analyses were performed using both BS EN 1295-1 approach and finite element method (ABAQUS software). The effects of different parameters are studied such as, depth of backfill, bedding compaction, and backfill compaction. Due to compaction, an increase in the bedding compaction modulus (E’₁) results in a reduction of both stresses and displacements of the pipe, especially, for well compacted ba