Analysis on the Formation Reason of A Rare Big Hailstone Weather in Nantong City

By using the ground and high-altitude observation data,NCEP 6 h reanalysis data and CINRAD/SA radar observation data,the circulation situation,the atmospheric stability degree and the radar echo characteristics of a strong convection weather which occurred in Nantong area of Jiangsu Province on June 14 in 2009 were analyzed.The results showed that the hailstone happened in the large scale background of coastal trough rear which was established by the northeast low vortex.The warm air in the middle-low layer was covered with the cold air in 500 hPa,which provided the favorable condition for the occurrence of strong convection weather which included the hailstone,the thunderstorm,the strong wind and so on.Seen from the analysis on the radar echo,the windstorm which induced this strong convective weather had the characteristics of super monomer windstorm.In the northwest and the southeast,there were 2 obvious outflow boundaries and the overhanging structure characteristics.The strong vertical shear and the suitable frozen layer height in the middle-low layer of troposphere were also favorable to fall the hailstone.

On complete convergence in Marcinkiewicz-Zygmund type SLLN for random variables

We consider a generalization of Baum-Katz theorem for random variables satisfying some cover conditions.Consequently,we get the results for many dependent structures,such as END,ϱ^(*)mixing,ϱ^(-)mixing andφ-mixing,etc.

THE VOLUME AND TOPOLOGY OF A COMPLETE RIEMANNIAN MANIFOLD

It is conjectured that the manifold with nonnegative Ricci curvature and weaked bounded geometry is of finite topological type, if The paper partially solves this conjecture. In the same time, the paper also discusses the volume growth of a manifold with asymptotically nonnegative Ricci curvature.

Single-Doppler Radar Observations of a High Precipitation Supercell Accompanying the 12 April 2003 Severe Squall Line in Fujian Province

In this study,single Doppler radar data were used to examine the structure and evolution of a high precipitation（HP） supercell embedded in a cold front near Jianyang,Fujian Province on 12 April 2003.The synoptic environment was characterized by high humidity at low levels,moderate CAPE（convective available potential energy;1601 J kg^（-1））,moderate wind shear（22 m s^（-1） in 0-5 km）,and veering of the horizontal winds with height,similar to those HP supercells previously observed in midlatitudes.In addition,the calculated bulk Richardson number was only 16,suggesting favorable environmental conditions for supercell development. The documented storm was located at the leading edge of a squall line.It was initiated from a single cell at 0732 UTC.It evolved into a bow shape gradually,and then split into two separate storms along the storm motion direction through the apex of the bow echo.The left-moving storm dissipated rapidly, but the right-moving storm strengthened and evolved into an HP supercell,lasting for more than 1 h.The radar reflectivity of the HP supercell during its mature stage showed a typical low-level hook echo at the front flank of the storm with its maximum reflectivity beyond 70 dBZ.Above the hook echo,an elevated maximum reflectivity core accompanied by a bounded weak-echo region（BWER） and a down-shear echo overhanging aloft were clearly identified.The elevated BWER,marked by 40-50-dBZ reflectivity values,was surrounded by values of 60-70 dBZ.A well-defined mesocyclone lasted about 1 h and was collocated with the low-level WER and middle-level BWER.The radar-estimated time-height profiles of mesocyclone rotational velocity and diameter indicated that this mesocyclone formed initially at middle level,then deepened and strengthened rapidly with the vertical depth deeper than 8 km and rotational velocity stronger than 24 m s^（-1） at the mature stage,and later decayed rapidly.The GBVTD（ground-based velocity track display）-derived primary circulation showed that the maximum tangential wind of the mesocyclone appeared at middle level （3-5 km） with a value of about 20 m s^（-1）.The mean radial wind field was characterized with a low-level inflow below 4 km,and accompanied by stronger updraft near the mesocyclone center.Between 4 and 7 km.the tangential wind profile resembled a Rankine combined vortex with the radius of maximum wind （RMW） at 3 km.and there was outflow/inflow inside/outside of the RMW.Correspondingly,the vertical velocity indicated a stronger updraft at the RMW and a weak downdraft inside the RMW.Above 7 km,the outflow strengthened and extended outside the RMW. In summary,the reflectivity structures of the storm and the accompanying mesocyclone were similar to those midlatitude HP supercells proposed in Miller＇s paper in 1994.However,the evolution of the HP supercell,including its three stages：ordinary storm,bow echo,and storm splitting,was quite different from those documented before.

Two New Lipschitz Type Spaces and Their Characterizations

In this paper,we first introduce the weak Lipschitz spaces WLip_(q,α),1<q<∞,0<α<1 which are the analog of weak Lebesgue spaces L^(q,∞)in the setting of Lipschitz space.We obtain the equivalence between the norm ||·||_(Lipα)and ||·||_(()WLip_(q,α)).As an application,we show that the commutator M_(β)~b is bounded from L~p to L^(q,∞) for some p ∈(1,∞) and 1/p-1/q=(α+β)/n if and only if b is in Lip_(α).We also introduce the weak central bounded mean oscillation space WCBMO_(q,α) and give a characterization of WCBMO_(q,α) via the boundedness of the commutators of Hardy type operators.