Recognition of \text {PSL}(2,p) by order and some information on its character degrees where p is a prime

Let \(G\) be a finite group and \(\text {cd}(G)\) be the set of irreducible character degrees of \(G\) . In this paper we prove that if \(p\) is a prime number, then the simple group \(\text {PSL}(2,p)\) is uniquely determined by its order and some information about its character degrees. In fact we prove that if \(G\) is a finite group such that (i) \(|G|=|\text {PSL}(2,p)|\) , (ii) \(p\in \text {cd}(G)\) , (iii) \(\text {cd}(G)\) has an even integer, and (iv) there does not exist any element \(a\in \text {cd}(G)\) such that \(2p\mid a\) , then \(G\cong \text {PSL}(2,p)\) . As a consequence of our result we get that \(\text {PSL}(2,p)\) is uniquely determined by its order and the largest and the second largest character degrees.     

Experimental and thermodynamic modelling of systems containing water and ethylene glycol: Application to flow assurance and gas processing

Accurate knowledge of hydrate phase equilibrium in the presence of inhibitors is crucial to avoid gas hydrate formation problems and to design/optimize production, transportation and processing facilities. In this communication, we report new experimental dissociation data for various systems consisting of methane/water/ethylene glycol and natural gas/water/ethylene glycol. A statistical thermodynamic approach, with the Cubic-Plus-Association equation of state, is employed to model the phase equilibria. The hydrate-forming conditions are modelled by the solid solution theory of van der Waals and Platteeuw. The thermodynamic model was used to predict the hydrate dissociation conditions of methane and natural gases in the presence of distilled water or ethylene glycol aqueous solutions. Predictions of the developed model are validated against independent experimental data and the data generated in this work. A good agreement between predictions and experimental data is observed, supporting the reliability of the developed model.