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

Calcium carbonate is predominantly present in aqueous systems, which is
commonly used in industrial processes. It has inverse solubility characteristics
resulting in the deposition of scale on heat transfer surface. This paper focuses on
developing methods for inhibition of calcium carbonate scale formation in cooling
tower and air cooler system where scaling can cause serious problems, ZnCl 2 and ZnI
2 has been investigated as scale inhibitor on AISI 316 and 304. ZnCl 2 were more
effective than ZnI 2 in both systems, and AISI 316 show more receptivity to the
chlorides salt compared to AISI 304. The inhibitors were more effective in cooling
tower than air cooler system. AISI 316 show more constant inhibition effic

This study is unique in this field. It represents a mix of three branches of technology: photometry, spectroscopy, and image processing. The work treats the image by treating each pixel in the image based on its color, where the color means a specific wavelength on the RGB line; therefore, any image will have many wavelengths from all its pixels. The results of the study are specific and identify the elements on the nucleus’s surface of a comet, not only the details but also their mapping on the nucleus. The work considered 12 elements in two comets (Temple 1 and 67P/Churyumoy-Gerasimenko). The elements have strong emission lines in the visible range, which were recognized by our MATLAB program in the treatment of the image. The percen

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 importance of specifying proper aggregate grading for achieving satisfactory performance in pavement applications has long been recognized. To improve the specifications for superior performance, there is a need to understand how differences in aggregate gradations within the acceptable limits may affect unbound aggregate base behavior. The effects of gradation on strength, modulus, and deformation characteristics of high-quality crushed rock base materials are described here. Two crushed rock types commonly used in constructing heavy-duty granular base layers in the State of Victoria, Australia, with three different gradations each were used in this study. The gradations used represent the lower, medium, and upper gradation li