This paper uses the density functional theory under generalised gradient approximation to analyse the stability, frontier orbitals, bond character, and static linear polarizability of H20@C80F60, which has not been is...This paper uses the density functional theory under generalised gradient approximation to analyse the stability, frontier orbitals, bond character, and static linear polarizability of H20@C80F60, which has not been isolated, as well as those of the synthesised H20@C80H60. The H20@C80F60 should be considerably stable by analysing its energy and aromaticity. The inside H and outside X will play different role in the chemical reaction involving H20@C80X60 （X = H and F）. The covalence of C H bond is in the order that the inside C H bond of H20@C80F60〉 the inside C H bond of H20@C80H60〉 the outside C-H bond of H20@C80H60, whereas the C-F bond of H20@C80F60 have both the covalent and ionic characters. The static linear polarizabilities of Cso and H20@C80X60 （X =H and F） are all isotropic.展开更多
In this paper, we prove the global existence and uniqueness of the strong and weak solutions for 2D Navier-Stokes equations on the torus $ \mathbb{T}^2 $ perturbed by a Lévy process. The existence of invariant me...In this paper, we prove the global existence and uniqueness of the strong and weak solutions for 2D Navier-Stokes equations on the torus $ \mathbb{T}^2 $ perturbed by a Lévy process. The existence of invariant measure of the solutions are proved also.展开更多
基金Project supported by the Research Starting Foundation of Hohai University (Grant No. 2084/40801130)the Natural Science Foundation of Hohai University (Grant Nos. 2008431211 and 2008430311)+2 种基金the Excellent Innovation Personal Support Plan of Hohai Universitythe Basic Scientific Research Foundation of National Centralthe Special Foundation of the Natural Natural Science (Grant No. 10947132)
文摘This paper uses the density functional theory under generalised gradient approximation to analyse the stability, frontier orbitals, bond character, and static linear polarizability of H20@C80F60, which has not been isolated, as well as those of the synthesised H20@C80H60. The H20@C80F60 should be considerably stable by analysing its energy and aromaticity. The inside H and outside X will play different role in the chemical reaction involving H20@C80X60 （X = H and F）. The covalence of C H bond is in the order that the inside C H bond of H20@C80F60〉 the inside C H bond of H20@C80H60〉 the outside C-H bond of H20@C80H60, whereas the C-F bond of H20@C80F60 have both the covalent and ionic characters. The static linear polarizabilities of Cso and H20@C80X60 （X =H and F） are all isotropic.
基金supported by National Basic Research Program of China (Grant No. 2006CB8059000)Science Fund for Creative Research Groups (Grant No.10721101)+2 种基金National Natural Science Foundation of China (GrantNos.10671197,10671168)Science Foundation of Jiangsu Province (Grant Nos.BK2006032,06-A-038,07-333)Key Lab of Random Complex Structures and Data Science,Chinese Academy of Sciences
文摘In this paper, we prove the global existence and uniqueness of the strong and weak solutions for 2D Navier-Stokes equations on the torus $ \mathbb{T}^2 $ perturbed by a Lévy process. The existence of invariant measure of the solutions are proved also.
