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
The impact of applying the K-W-L self-scheduling technique on first-year intermediate students' learning of basic volleyball skills, Ayad Ali Hussein*, Israa Fouad Salih
في هذا البحث نحاول تسليط الضوء على إحدى طرائق تقدير المعلمات الهيكلية لنماذج المعادلات الآنية الخطية والتي تزودنا بتقديرات متسقة تختلف أحيانا عن تلك التي نحصل عليها من أساليب الطرائق التقليدية الأخرى وفق الصيغة العامة لمقدرات K-CLASS. وهذه الطريقة تعرف بطريقة الإمكان الأعظم محدودة المعلومات" LIML" أو طريقة نسبة التباين الصغرى" LVR" والتي تمثل حسب الصيغة (14.2) الوجه الآخر لطريقة الLIML والتي تشتهر في تقدير معلمات معادل
... Show MoreLet R be a commutative ring with identity, and W be a unital (left) R-module. In this paper we introduce and study the concept of a quasi-small prime modules as generalization of small prime modules.
Recently, microalgae have become a promising source in the production of biofuel. However, the cost of production is still the main obstacle to develop of this type of source. Although there are many extensive studies on the requirements provided for the cultivation of the microalgae, the study of the process, via the variables that affect the cultivation of microalgae, being still one of the important tasks to improve the production of biofuel. The present article is a serious attempt to investigate of use commercial fertilizer NPK (20:20:20+TE N: P: K) as considered a cheap nutrient medium in growth Chlorella vulgaris by comparison with traditional nutrient (Chu.10 medium). In addition, the current study addresses effect of di
... Show MoreRecently, microalgae have become a promising source in the production of biofuel. However, the cost of production is still the main obstacle to develop of this type of source. Although there are many extensive studies on the requirements provided for the cultivation of the microalgae, the study of the process, via the variables that affect the cultivation of microalgae, being still one of the important tasks to improve the production of biofuel. The present article is a serious attempt to investigate of use commercial fertilizer NPK (20:20:20+TE N: P: K) as considered a cheap nutrient medium in growth Chlorella vulgaris by comparison with traditional nutrient (Chu.10 medium). In addition, the current study addresses effect of different spar
... Show MoreA fast moving infrared excess source (G2) which is widely interpreted as a core-less gas and dust cloud approaches Sagittarius A* (Sgr A*) on a presumably elliptical orbit. VLT
In this work, we construct the projectively distinct (k, n)-arcs in PG (3, 4) over Galois field GF (4), where k 5, and we found that the complete (k, n)-arcs, where 3 n 21, moreover we prove geometrically that the maximum complete (k, n)-arc in PG (3, 4) is (85, 21)-arc. A (k, n)-arcs is a set of k points no n+ 1 of which are collinear. A (k, n)-arcs is complete if it is not contained in a (k+ 1, n)-arcs
Viscosities (η) and densities (ρ) of atenolol and propranolol hydrochloride in water and in concentrations (0.05 M) and (0.1 M) aqueous solution of threonine have been used to reform different important thermodynamic parameters like apparent molal volumes fv partial molal volumes at infinite dilution fvo , transfer volume fvo (tr), the slop Sv , Gibbs free energy of activation for viscous flow of solution ΔG*1,2 and the B-coefficient have been calculated using Jones-Dole equation. These thermodynamic parameters have been predicted in terms of solute-solute and solute-solvent interaction.
Apparent molar volume, V?, and viscosity B-coefficient of nicotinc acid in water and in aqueous NaCl solutions have been determined from density and viscosity measurements at (293.15, 298.15, 303.15 and 308.15) K. The experimental density data were evaluated by Masson equation, and the derived, apparent molar volume at infinite dilution, Vo?, and the slope Sv, were interpreted in term of solute-solvent and solute- solute interactions. Transfer apparent molar volumes at infinite dilution of nicotinic acid from water to NaCl solutions at various temperatures have been calculated.The viscosity data have been analyzed using Jones-Dole equation, and the derived parameters, Jones-Dolecoefficient, B,and Falkenhagen coefficient,A, have been also in
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