We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the un...We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the unit speed. The models, without or with immigration, are constructed as measure-valued processes by pathwise unique solutions of stochastic equations driven by time-space Poisson random measures. In the subcritical branching case, we give a sufficient condition for the ergodicity of the process with immigration. Two large number laws and a central limit theorem of the occupation times are proved.展开更多
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
基金supported by the National Key R&D Program of China(2020YFA0712901).
文摘We study age-structured branching models with reproduction law depending on the remaining lifetime of the parent. The lifespan of an individual is determined at its birth and its remaining lifetime decreases at the unit speed. The models, without or with immigration, are constructed as measure-valued processes by pathwise unique solutions of stochastic equations driven by time-space Poisson random measures. In the subcritical branching case, we give a sufficient condition for the ergodicity of the process with immigration. Two large number laws and a central limit theorem of the occupation times are proved.
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.
