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

Bulk polycrystalline samples have been prepared by the two-step solid state reaction process. It has been observed that as grown Tl2-xHgxSr2Ca2Cu3O10+δ (with x = 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1) corresponds to the 2223 phase. It has been found that Tc varies with Hg content .The optimum Tc is about 120K for the composition Tl1.6Hg0.4Sr2Ca2Cu3O10+δ.The microstructure for Tl1.6Hg0.4Sr2Ca2Cu3O10+δ observed to be most dense and this phase exhibits the highest stability.

Many condensed polymers [A1-A7] were prepared via reaction of (Ethylenediaminetetraacetic acid = EDTA), with different prepared imide-diamines by modification [ modification of amino acids and antibiotics (B1- B7)] Imide-diamines were prepared by chlorination of L-amino acids such as [ L-Histidine, L-Alanine, L-Valine, L-Glycine and L-Aspargine ] or selected antibiotics such as [Cephallixine monohydrate and Amoxilline ] with thionyl chloride at 0°C, then reacted with ammonia to obtain imidediamines [B1-B7] . The physical properties of all prepared condensed polymers [A1-A7], new prepared diamines [B1-B7] were studied and characterized by FT -IR spectroscope to certify the structural formulas. The thermal analysis (TGA, DTA) were studied, a

BACKGROUND: Sacral nerve stimulation (SNS) approved for use in North America since 1997 despite the fact that the concept of using SNS to treat patients with voiding dysfunction discussed first almost 50 years ago. AIM: The objectives of the study were to assess the effectiveness of SNS the short and long term for patients with overactive bladder (OAB) dysfunction and its relation to age, gender, and causes. PATIENTS AND METHODS: This is a clinical prospective study that involved 50 cases (32 females and 18 males) with OAB. It was carried out at Ibn Sina Hospital, and the neurosciences hospital in Baghdad/Iraq from April 2015 to April 2018. All the patients were assessed preoperatively and certain inclusion criteria were

The study of biopolymers and their derivative materials had received a considerable degree of attention from researchers in the preparation of novel material. Biopolymers and their derivatives have a wide range of applications as a result of their bio-compatibility, bio-degradability and non-toxicity. In this paper, chitosan reacted with different aldehydes(2,4 –dichloro- benzaldehyde or 2-methyl benzaldehyde), different ketones (4-bromoacetophenone or 3-aminoacetophenone) to produce chitosan schiff base (1-4) . Chitosan schiff base (1-4) reacted with glutaric acid or adipic acid in acidic media in distilled water according to the steps of Fischer and Speier to produce compounds (5-12)

Based on the streamer growth model, the streamer discharge propagation was simulated in aid of finite element technique. That was done within two non- mixed dielectric liquids (Normal-Hexane and Acetone) located between two electrodes in pin - plane configuration. The output results show that, the path of the streamer was affected by the interface between the two liquids; the streamer path crosses this interface under some conditions such as the permittivity of the liquids and the distance between this interface and the tip of the pin. Under other conditions, the streamer path grows along the interface. The results were assisted by the development of the potential and the electric field distributions with the growth of the streamer propa

Taking into account the significance of food chains in the environment, it demonstrates the interdependence of all living things and has economic implications for people. Hunting cooperation, fear, and intraspecific competition are all included in a food chain model that has been developed and researched. The study tries to comprehend how these elements affect the behavior of species along the food chain. We first examined the suggested model's solution properties before calculating every potential equilibrium point and examining the stability and bifurcation nearby. We have identified the factors that guarantee the global stability of the positive equilibrium point using the geometric approach. Additionally, the circumstances that would gu

This article investigates the development of the following material properties of concrete with time: compressive strength, tensile strength, modulus of elasticity, and fracture energy. These properties were determined at seven different hydration ages (18 h, 30 h, 48 h, 72 h, 7 days, 14 days, 28 days) for four pure cement concrete mixes totaling 336 specimens tested throughout the study. Experimental data obtained were used to assess the relationship of the above properties with the concrete compressive strength and how these relationships are affected with age. Further, this study investigates prediction models available in literature and recommendations are made for models that are found suitable for application to early age conc

In this paper, photometric analysis of two short period group of the eclipsing binaries (RS CVn); RT And and BH Vir is presented. New physical and geometric parameters were obtained by performing two computer modeling. The first model is software package PHOEBE based on the Wilson–Devinney method, and the second is Binary Maker 3 (BM3).Our results are in good agreement with those obtained using the same modeling.