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:
This research seeks to test the influence of intellectual capital as an explanatory variable and its components (human capital, structural capital, relational capital) and sustainable competitive performance as a responsive variable and its components (reducing service delivery cycle time, rapid response to market demand, increasing customer satisfaction, providing better Quality of service, increasing market share)” through a field study, and here the research problem was diagnosed in an attempt to answer the following question: Is there awareness among the senior management within the private colle
... Show MoreDifferent parameters of double pipe helical coil were investigation experimentally. Four coils were used; three with a curvature ratio (0.037, 0.031, and 0.028) and 11mm diameter of the inner tube while the fourth with 0.033 curvature ratio and 13 mm diameter of the inner tube. The hot water flow in the inner tube whereas the cold water flows in the annulus. The inlet temperatures of hot and cold water are 50 0C and 18 0C respectively. The inner mass flow rate ranges from 0.0167 to 0.0583 kg/s. The results show the Nusselt number increase with increase curvature ratio. The Nusselt number of the coil with 0.037 curvature ratio increases by approximately 12.3 % as compare with 0.028 curvature ratio. The results also r
... Show MoreThe present study investigated the impact of fuel kind on the emitted emissions at the idling period. Three types of available fuels in Iraq were tested. The tests conducted on ordinary gasoline with an octane number of 82, premium gasoline with an octane number of 92, and M20 (consist of 20% methanol and 80% regular gasoline). The 2 liters Mercedes-Benz engine was used in the experiments.
The results showed that engine operation at idle speed emits high levels of CO, CO2, HC, NOx and noise. The produced emission levels depend highly on fuel type. The premium gasoline (ON=92) represents the lower emissions level except for noise at all idling speed. Adding methanol to ordinary gasoline (ON=82) showed high levels of emi
... Show MoreThe study of Stress- Strain relation for novolac reinforced by qujurate plant was carried out before and after the immersing in boiled water at 100C0 . It was found that the compression strength and surface hardness decreased when the composites immersed in boiled water for long times.
The traction property is one of the important mechanical properties, especially the rotary parts which are subjected to constant and variable loads There are many methods used to improve this property, and the shoot peening by metal balls is considered the most critical one. the study focuses on this characteristic of steel CK35 used in many engineering applications as the rotating shafts and railway This study shows that the fatigue strength is improved by14% after shoot peening with metal balls. The study includs the rehabilitation of damaged samples as a result of fatigue corrosion. The standard solution adopted was 36% MgCl2 with a 30 days immersion period. These samples has been improved by 6% after it decreased by18% d
... Show MorePartial shading is one of the problems that affects the power production and the efficiency of photovoltaic module. A series of experimental work have been done of partial shading of monocrystalline PV module; 50W, Isc: 3.1A, Voc: 22V with 36 cells in series is achieved. Non-linear power output responses of the module are observed by applying various cases of partial shading (vertical and horizontal shading of solar cells in the module). Shading a single cell (corner cell) has the greatest impact on output energy. Horizontal shading or vertical shading reduced the power from 41W to 18W at constant solar radiation 1000W/m2 and steady state condition. Vertical blocking a column
... Show MoreThis paper is concerned with Double Stage Shrinkage Bayesian (DSSB) Estimator for lowering the mean squared error of classical estimator ˆ q for the scale parameter (q) of an exponential distribution in a region (R) around available prior knowledge (q0) about the actual value (q) as initial estimate as well as to reduce the cost of experimentations. In situation where the experimentations are time consuming or very costly, a Double Stage procedure can be used to reduce the expected sample size needed to obtain the estimator. This estimator is shown to have smaller mean squared error for certain choice of the shrinkage weight factor y( ) and for acceptance region R. Expression for
... Show MoreThis work describes the weathering effects (UV-Irradiation, and Rain) on the thermal conductivity of PS, PMMA, PS/PMMA blend for packaging application. The samples were prepared by cast method at different ratios (10, 30, 50, 70, and 90 %wt). It was seen that the thermal conductivity of PMMA (0.145 W/m.K), and for PS(0.095 W/m.K), which increases by PS ratio increase up to 50% PS/PMMA blend then decreased that was attributed to increase in miscibility of the blend involved. By UV-weathering, it was seen that thermal conductivity for PMMA increased with UV-weathering up to (30hr) then decreased, that was attributed to rigidity and defect formation, respectively. For 30%PS/PMMA, there results showed unsystematic decrease in thermal conduct
... Show MoreThere are many applied Economic studies that have found positive nexus between financial development and poverty reduction in developing countries. Iraq has witnessed an increasing rate of poverty during the period 1980-2010 due to many internal and external factors such as wars, economic sanctions, inflation, a high rate of unemployment, and political and security instability. Therefore, the investigation about the solutions to reduce poverty becomes very necessary, and enhancing the financial development in Iraq is one of these options. This is due to that the financial development could reduce the poverty rates through two channels: the first is direct via the offering of the loans and other financial facilities to the poor, a
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