The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz（x） of this particular triangular array of ...The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz（x） of this particular triangular array of i.i,d, random variables Z1,n, Z2 n,...,Zn,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if Fj,…… Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that Gz（x） does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases.展开更多
Molecular dynamics simulation with an all-atom force field has been carded out on the two binary sys- tems of [bmim][PF6]-CO2 and [bmim][NO3]-CO2 to study the transport properties, volume expansion and micro- structur...Molecular dynamics simulation with an all-atom force field has been carded out on the two binary sys- tems of [bmim][PF6]-CO2 and [bmim][NO3]-CO2 to study the transport properties, volume expansion and micro- structures. It was found that addition of CO2 in the liquid phase can greatly decrease the viscosity of ionic liquids （ILs） and increase their diffusion coefficient obviously. Furthermore, the volume expansion of ionic liquids was found to increase with the increase of the mole fraction of CO2 in the liquid phase but less than 35% for the two simulated systems, which had a significant difference with CO2 expanded organic solvents. The main reason was that there were some void spaces inter and intra the molecules of ionic liquids. Finally, site to site radial distribution functions and corresponding number integrals were investigated and it was found that the change of microstructures of ILs bv addition CO2 had a great influence on the orooerties of ILs.展开更多
基金Project partially supported by the National Natural Science Foundation of Switzerland
文摘The sequences {Zi,n, 1≤i≤n}, n≥1 are multi-nomial distribution among i.i.d, random variables {X1,i, i≥1}, {X2,i, i≥1 } {Xm,i, i≥1 }. The extreme value distribution Gz（x） of this particular triangular array of i.i,d, random variables Z1,n, Z2 n,...,Zn,n is discussed. A new type of not max-stable extreme value distributions which are Fréchet mixture, Gumbel mixture and Weibull mixture has been found if Fj,…… Fm belong to the same MDA. Whether mixtures of different types of extreme value distributions exist or not and the more general case are discussed in this paper. We found that Gz（x） does not exist as mixture forms of the different types of extreme value distributions after we investigated all cases.
基金Supported by the National Natural Science Foundation of China(20976026,20976028)the Natural Science Foundation of Liaoning Province(20102030,20031072)
文摘Molecular dynamics simulation with an all-atom force field has been carded out on the two binary sys- tems of [bmim][PF6]-CO2 and [bmim][NO3]-CO2 to study the transport properties, volume expansion and micro- structures. It was found that addition of CO2 in the liquid phase can greatly decrease the viscosity of ionic liquids （ILs） and increase their diffusion coefficient obviously. Furthermore, the volume expansion of ionic liquids was found to increase with the increase of the mole fraction of CO2 in the liquid phase but less than 35% for the two simulated systems, which had a significant difference with CO2 expanded organic solvents. The main reason was that there were some void spaces inter and intra the molecules of ionic liquids. Finally, site to site radial distribution functions and corresponding number integrals were investigated and it was found that the change of microstructures of ILs bv addition CO2 had a great influence on the orooerties of ILs.
