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
To observe the effect of media of the internal pressure on the equivalent stress distribution in the tube, an experimental study is done by constructing a testing rig to apply the hydraulic pressure and three dies are manufactured with different bulging configurations (square, cosine, and conical). In the other part, ANSYS APDL is generated to analyze the bulging process with hydraulic and rubber (natural and industrial) media. It was found that when the media is a rubber, the stress is decreased about 9.068% in case of cosine die and 5.4439% in case of conical die and 2.8544% in case of square die. So, it can be concluded that the internal pressure in the rubber media is much better than in hydraulic media. Also, the force needed for fo
... Show MoreThe 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 MoreSurfaces quality is one of the most specified customer requirements for machine parts. The major indication of surfaces quality on machined parts is surface roughness. The research aim is to study the cutting conditions and their effects on the surface roughness. This paper utilizes regression models to predict surface roughness over the machining time for variety of cutting conditions in turning. In the experimental part for turning, different types of materials (Aluminum alloy, Copper alloy, and Gray cast iron) were considered with different cutting speed ( ) and feed rate ( ). A mathematical Model depending on statistical-mathematical method between surface roughness (Rz ) and cutting condition ( , ) were derived, for the three materials
... Show MoreThis search aim to measure Hardness for Epoxy resin and for unsaturated Polyester resin as base materials for composite Hybrid and the materials used is Hybrid fiber Carbon-Kevlar. The Hand Lay-up method was used to manufacture plates of Epoxy resin (EP) and unsaturated Polyester EP,UPE backed by Hybrid fiber (Carbon-Kevlar) and with small volume fraction 5,10 and 15 for every there are Layer of fibers (1,2 and 3). The hardness test was count for material EP, UPE resin and there composites and that we notice that the Hardness (HB) decreased with increase of temperatures.
There 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
... 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 MoreThe research aimed at designing teaching program using jigsaw in learning spiking in volleyball as well as identifying the effect of these exercises on learning spring in volleyball. The researchers used the experimental method on (25) students as experimental group and (27) students as controlling group and (15) students as pilot study group. The researchers conducted spiking tests then the data was collected and treated using proper statistical operations to conclude that the strategy have a positive effect in experimental group. Finally, the researchers recommended using the strategy in making similar studies on other subjects and skills.
Partial 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
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