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
Excess molar volumes of five ternary mixtures of 2- methoxy ethanol(1) +butyl acetate(2)+benzene(3), +toluene(3), +chlorobenzene(3), +bromobenzene(3), and +nitrobenzene(3) have been measured at 303.15K. The excess molar volume exhibited positive deviation over the entire range of composition in the systems 2-methoxy ethanol(1)+ butyl acetate(2)+ benzene(3),+toluene(3) and sigmoid behavior in the case of the remaining systems. Flory's statistical theory have been extended to predict the excess molar volumes of the five ternary mixtures at 303.15 k over a wide range of composition . An excellent agreement has been found between the experimental and theoretical excess molar volumes , both in magnitude and sign .
Refractive indices (nD), viscosities (η) and densities (r) were deliberated for the binary mixtures created by dipropyl amine with 1-octanol, 1-heptanol, 1-hexanol, 1-pentanol and tert-pentyl alcohol at temperature 298.15 K over the perfect installation extent. The function of Redlich-Kister were used to calculate and renovated of the refractive index deviations (∆nD), viscosity deviations (ηE), excess molar Gibbs free energy (∆G*E) and excess molar volumes(Vm E). The standard errors and coefficients were respected by this function. The values of ∆nD, ηE, Vm E and ∆G*E were plotted against mole fraction of dipropyl amine. In all cases the obtained ηE, ∆G*E, Vm E and ∆nD values were negative at 298.15K. Effect of carbon atoms
... Show MoreRefractive indices (nD), viscosities (η) and densities (ρ) were deliberated for the binary mixtures created by dipropyl amine with 1-octanol, 1-heptanol, 1-hexanol, 1-pentanol and tert-pentyl alcohol at temperature 298.15 K over the perfect installation extent. The function of Redlich-Kister were used to calculate and renovated of the refractive index deviations (∆nD), viscosity deviations (ηE), excess molar Gibbs free energy (∆G*E) and excess molar volumes (VmE) The standard errors and coefficients were respected by this function. The values of ∆nD, ηE, VmE and ∆G*E were plotted against mole fraction of dipropyl amine. In all cases the obtained ηE, ∆G*E, VmE and ∆nD values were negative at 298.15K. Effect of carbo
... Show MoreA non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.
Cox regression model have been used to estimate proportion hazard model for patients with hepatitis disease recorded in Gastrointestinal and Hepatic diseases Hospital in Iraq for (2002 -2005). Data consists of (age, gender, survival time terminal stat). A Kaplan-Meier method has been applied to estimate survival function and hazerd function.
Intrusion detection systems (IDS) are useful tools that help security administrators in the developing task to secure the network and alert in any possible harmful event. IDS can be classified either as misuse or anomaly, depending on the detection methodology. Where Misuse IDS can recognize the known attack based on their signatures, the main disadvantage of these systems is that they cannot detect new attacks. At the same time, the anomaly IDS depends on normal behaviour, where the main advantage of this system is its ability to discover new attacks. On the other hand, the main drawback of anomaly IDS is high false alarm rate results. Therefore, a hybrid IDS is a combination of misuse and anomaly and acts as a solution to overcome the dis
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