The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for app...The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.展开更多
Based on the data of the cases of severe convection weather such as hail,thunderstorm(thunderstorm gale)and short-time heavy precipitation in recent 10 years,the spatial and temporal distribution characteristics of di...Based on the data of the cases of severe convection weather such as hail,thunderstorm(thunderstorm gale)and short-time heavy precipitation in recent 10 years,the spatial and temporal distribution characteristics of different types of severe convection weather were analyzed.The results show that the frequency of severe convection weather tended to increase,of which short-time heavy precipitation and thunderstorm weather rose,and hail and thunderstorm gale weather decreased.Severe convection weather began to extend in late spring and early autumn.Typical cases were selected to analyze the evolution mechanism,and the conceptual models of severe convective weather caused by cold advection forcing,warm advection forcing and baroclinic frontogenesis were obtained.The key predictors for the potential prediction of severe convection weather were proposed,such as CAPE(convective available potential energy)for hail weather,UH index(maximum ascending helicity)for thunderstorm gale and PWV(precipitable water vapor)for short-time heavy precipitation.ERA5 data were used to get the forecast threshold of the key factor of classified severe convection weather,and it was verified that the threshold was available.Meanwhile,the causes of the error of failure cases were analyzed.For instance,the larger deviation of CAPE was caused by the 2 m deviation of temperature.Supplementary correction method and threshold were given to provide a reference for the objective forecast and early warning of severe convection weather.展开更多
文摘The goal of this paper is to confirm that the unitary group U(H) on an infinite dimensional complex Hilbert space is a topological group in its strong topology, and to emphasize the importance of this property for applications in topology. In addition, it is shown that U(H) in its strong topology is metrizable and contractible if H is separable. As an application Hilbert bundles are classified by homotopy.
基金Supported by the Open-end Funds of Key Laboratory for Disaster Prevention and Mitigation of Qinghai Province(QFZ-2021-Z04)。
文摘Based on the data of the cases of severe convection weather such as hail,thunderstorm(thunderstorm gale)and short-time heavy precipitation in recent 10 years,the spatial and temporal distribution characteristics of different types of severe convection weather were analyzed.The results show that the frequency of severe convection weather tended to increase,of which short-time heavy precipitation and thunderstorm weather rose,and hail and thunderstorm gale weather decreased.Severe convection weather began to extend in late spring and early autumn.Typical cases were selected to analyze the evolution mechanism,and the conceptual models of severe convective weather caused by cold advection forcing,warm advection forcing and baroclinic frontogenesis were obtained.The key predictors for the potential prediction of severe convection weather were proposed,such as CAPE(convective available potential energy)for hail weather,UH index(maximum ascending helicity)for thunderstorm gale and PWV(precipitable water vapor)for short-time heavy precipitation.ERA5 data were used to get the forecast threshold of the key factor of classified severe convection weather,and it was verified that the threshold was available.Meanwhile,the causes of the error of failure cases were analyzed.For instance,the larger deviation of CAPE was caused by the 2 m deviation of temperature.Supplementary correction method and threshold were given to provide a reference for the objective forecast and early warning of severe convection weather.
