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

PVA, Starch/PVA, and Starch/PVA/sugar samples of different
concentrations (10, 20, 30 and 40 % wt/wt) were prepared by casting
method. DSC analysis was carried; the results showed only one glass
transition temperature (Tg) for the samples involved, which suggest
that starch/PVA and starch/PVA/sugar blends are miscible. The
miscibility is attributed to the hydrogen bonds between PVA and
starch. This is in a good agreement with (FTIR) results. Tg and Tm
decrease with starch and sugar content compared with that for
(PVA). Systematic decrease in ultimate strength, due to starch and
sugar ratio increase, is attributed to (PVA), which has more hydroxyl
groups that made its ultimate strength higher than that for

Poly vinyl alcohol has been studied for its ability to form crystallites by using annealing method. Semicrystalline films of poly vinyl alcohol (PVA) were prepared by casting 11.5 wt. % and 13 wt. % PVA aqueous solution onto glass slides at annealing temperature range 90 -120°C and duration time 15- 60 minute. This allowed the macromolecules to form crystallites, small regions of folded and compacted chains separated by amorphous regions where single PVA chain may pass through several of these crystallites. Degree of crystallinity of PVA films (hydrogels) was determined by method of density; on the other hand the swelling behavior was conducted by the determination of water uptake, wet degree of crystallinity, gel fraction and solubilit

Scleral acrylic resin is widely used to synthesize ocular prosthesis. However, the properties of this material change over time, thus requiring the prosthesis to be refabricated. Many studies were conducted to improve these properties by reinforcing this material with nanoparticles. This study aims to evaluate the effect of silver nanoparticle powder on the mechanical properties (transverse flexural strength, impact strength, shear bond strength, surface microhardness, and surface roughness) of scleral acrylic resin used for ocular prostheses. Two concentrations were selected from the pilot study and evaluated for their effects on scleral acrylic resin properties. According to the pilot study, 0.01 and 0.02wt% AgNPs powder improved

This research aims to know the effect of the strategy of map bubbles on developing the skills of science operations among 5th grade literary students in the subject of rhetoric and application, and the design of the experimental and control groups with the pre and post-tests was used. The research sample consisted of (50) students divided into two groups, an experimental group of which reached the number of its members is (25) students and studied using the strategy of map bubbles, and a control group of its members reached (25) students and studied in the traditional (standard) method. The researchers prepared a multiple-choice achievement test with several (30) paragraphs, and its validity and consistency were extracted. Then the test was

The aim of the research is to identify the level of both organizational trust and decentralized performance of those in charge of managing local championships for the Iraqi Athletics Federation, and to identify the effect of organizational trust in decentralized performance from their point of view. The descriptive approach was based on the method of relational relations on a sample of those in charge of managing local championships for the Iraqi Federation In athletics, represented by each of (coaches, referees, members, president and members of the administrative body of the central federation, and the president of members of sub-federations) for the sports season (2020/2021) of 260 individuals, all of them were intentionally chosen by (1

This research deals with increasing the hardening and insulating the petroleum pipes against the conditions and erosion of different environments. So, basic material of epoxy has been mixed with Ceramic Nano Zirconia reinforcement material 35 nm with the percentages  (0,1,2,3,4,5) %, whereas the paint basis of broken petroleum pipes was used  to paint on it, then it was cut into dimensions (2 cm. × 2 cm.) and 0.3cm high. After the paint and percentages are completed, the samples were immersed into the paint. Then, the micro-hardness was checked according to Vickers method and thermal inspection of paint, which contained (Thermal conduction, thermal flux and Thermal diffusivity), the density of the painted samples was calculate

This 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

Surfaces 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