In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg g...In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with dimension 2n+1,ΩHn is an open set and Δ~ _Hu denotes the approximate derivative of the absolute continuous part Da_Hu with respect to D_Hu.In addition,a Lusin type approximation theorem for a SBV_H function is proved.展开更多
Based on remote sensing data, field investigation and trench measurement along the piedmont fault (Wujumengkou Dongfengcun) of Mt. Serteng, the vertical displacement rate has been found to be 0 88～1 83mm/a since the ...Based on remote sensing data, field investigation and trench measurement along the piedmont fault (Wujumengkou Dongfengcun) of Mt. Serteng, the vertical displacement rate has been found to be 0 88～1 83mm/a since the late period of late Pleistocene and 0 89mm/a since the middle period of Holocene. Using the progressive constraining method,five paleoearthquake events have been distinguished from two large trenches since Holocene. They occurred 9000±1300a B.P., 6500±500a B.P., 5770a B.P., 4200±300a B.P. and 3250±250a B.P., respectively. From the late period of late Pleistocene to the beginning of Holocene, some paleoearthquake events may have been missed due to a variety of reasons. All of the paleoearthquake events displayed clustering characteristics to a certain extent. The first cluster was occurred around 8900a B.P., the second cluster occurred between 5700～6500a B.P. and the last cluster was occurred in 3250～4200 a B.P. The interval between the first cluster and the second cluster was about 2400a while that between the second cluster and the third cluster was only 1570a. No earthquake events have cut the ground surface along this active fault segment since 3250a B.P. The lapse time is more than the recurrence interval between two paleoearthquake clusters. Therefore, there is a potential risk for a recurring earthquake along this active fault segment.展开更多
In this paper we aim to show a compactness theorem for SBVH(Ω) of special functions u with bounded variation and with ↓△H^c u=0 in the Heisenberg group H^n.
In this paper, the BMO spaces for the Heisenberg group targets are studied. Some properties of the BMO spaces and the John-Nirenberg estimates are obtained.
文摘In this paper lower semicontinuity of the functional I(u)=∫_Ωf(x,u,Δ~ _Hu)dx is investigated for f being a Carathéodory function defined on Hn×R×R^2n and for u∈SBV_H(Ω),where Hn is the Heisenberg group with dimension 2n+1,ΩHn is an open set and Δ~ _Hu denotes the approximate derivative of the absolute continuous part Da_Hu with respect to D_Hu.In addition,a Lusin type approximation theorem for a SBV_H function is proved.
文摘Based on remote sensing data, field investigation and trench measurement along the piedmont fault (Wujumengkou Dongfengcun) of Mt. Serteng, the vertical displacement rate has been found to be 0 88～1 83mm/a since the late period of late Pleistocene and 0 89mm/a since the middle period of Holocene. Using the progressive constraining method,five paleoearthquake events have been distinguished from two large trenches since Holocene. They occurred 9000±1300a B.P., 6500±500a B.P., 5770a B.P., 4200±300a B.P. and 3250±250a B.P., respectively. From the late period of late Pleistocene to the beginning of Holocene, some paleoearthquake events may have been missed due to a variety of reasons. All of the paleoearthquake events displayed clustering characteristics to a certain extent. The first cluster was occurred around 8900a B.P., the second cluster occurred between 5700～6500a B.P. and the last cluster was occurred in 3250～4200 a B.P. The interval between the first cluster and the second cluster was about 2400a while that between the second cluster and the third cluster was only 1570a. No earthquake events have cut the ground surface along this active fault segment since 3250a B.P. The lapse time is more than the recurrence interval between two paleoearthquake clusters. Therefore, there is a potential risk for a recurring earthquake along this active fault segment.
文摘In this paper we aim to show a compactness theorem for SBVH(Ω) of special functions u with bounded variation and with ↓△H^c u=0 in the Heisenberg group H^n.
文摘In this paper, the BMO spaces for the Heisenberg group targets are studied. Some properties of the BMO spaces and the John-Nirenberg estimates are obtained.
