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 numerical analysis was conducted to studying the influence of length to diameter ratio (L/D) on the behavior of the soil treated with sand columns treated with 8% sodium silicate for both floating and end bearing type by using finite element method (Plaxis 3D Foundation ) for isolated foundation of real dimensions. The analysis’s study indicate that in the floating type the best improvement ratio was achieved at (L/D=8) when using columns with a diameter of (0.5, 0.7), but when using columns with a diameter of 0.3 m, it was noticed that the bearing improvement ratio increases with increasing (L/d). While the results of the analysis for end bearing type show that the higher improvement ratio was achieved at (L/D=4) when using columns w

This study aims to evaluate and compare the cytotoxicity and biocompatibility of a modified heat-cured acrylic denture base material containing 15% phosphoric acid 2-hydroxyethyl methacrylate ester (PA2HEME) with those of nonmodified PMMA. Discs with a diameter of 12 mm and a thickness of 2 mm were prepared using a heat-cured PMMA denture base material and divided into control and experimental groups. The experimental group was modified with 15% phosphoric acid 2-hydroxyethyl methacrylate ester (PA2HEME). The modified and nonmodified materials were tested via FTIR, and the effect of modification on surface roughness was evaluated with AFM. An in vitro test was conducted to examine the cytotoxicity and biocompatibility of heat-cured acry

In this study, composite materials were prepared using unsaturated polyester resin as binder with two types of fillers (sawdust and chopped reeds). The molding method is used to prepare sheets of UPE / sawdust composite and UPE / chopped reeds composite. The mechanical properties were studied including flexural strength and Young's modulus for the samples at normal conditions (N.C). The Commercial wood, UPE and its composite samples were immersed in water for about 30 days to find the weight gain (Mt%) of water for the samples, also to find the effect of water on their flexural strength and Young's modulus. The results showed that the samples of UPE / chopped reeds composite gained highest values of flexural strength (24.

Some of the issues that have become common in our society recently after the Americans entered our country and were rubbed by some security agencies: obtaining some information from children, and the serious consequences that may lead to the lives of innocent people, became common interrogation of some security agencies and rely on their words.
There are significant cases where their testimony needs to be heard, such as their presence in some places where incidents are not witnessed by others, such as schools or being witnesses to certain crimes.
I saw the study of this case in the light of Sharia and law

Zinc sulfide (ZnS) thin films were deposited on glass substrates using pulsed laser deposition technique. The laser used is the Q-switched Nd: YAG laser with 1064nm wavelength and 1Hz pulse repetition rate and varying laser energy 700mJ-1000mJ with 25 pulse. The substrate temperature was kept constant at 100°C. The structural, morphological and optical properties of ZnS thin films were characterized with X-ray diffraction (XRD), scanning electron microscopy (SEM), atomic force microscope (AFM) and UV-VIS spectrophotometer.

The work includes synthesis and characterization of some new heterocyclic compounds, as flow: The compound (3) (5-(4-chlorophenyl) -2-hydrazinyl-1,3,4-oxadiazole was synthesized by using two methods; the first method includes the direct reaction between hydrazine hydrate 80% and 5-(4-chlorophenyl)-2- (ethylthio) 1,3,4-oxadiazole (1), the second method involves converting 5-(4-chlorophenyl)-1,3,4-oxadiazol-2-amine (2) to diazonium salt then reducing this salt to compound (3) by stannous chloride. Compound (3) was used as starting material for synthesizing several fused heterocyclic compounds. The compound 6-(4- chlorophenyl)[1,2.4] triazolo [3,4,b][1,3,4] oxadiazole-3-(2H) thione (compound 4) was synthesized from the reaction of compo