Several theorems on the finiteness of energy for quasi- harmonic spheres are proved, some counter- examples which state thatthe energy of quasi- harmonic sphere may be infinite are given.The results support some con...Several theorems on the finiteness of energy for quasi- harmonic spheres are proved, some counter- examples which state thatthe energy of quasi- harmonic sphere may be infinite are given.The results support some conditions of a question posed by Lin Fanghua and Wang Changyou.展开更多
§ 1. IntroductionIn [1], R. Schoen and S. T. Yan used harmonic map to study the topology of a non-compact complete stable hypersurface in a manifold of non-negative curvature. Essentially the method is to prove f...§ 1. IntroductionIn [1], R. Schoen and S. T. Yan used harmonic map to study the topology of a non-compact complete stable hypersurface in a manifold of non-negative curvature. Essentially the method is to prove first the nonexistence of some kind of nonconstant harmonic map and then to draw the relative conclusions concerning the topology. Such nonexistence theorems have been obtained in [3] and [4] in cases where the concerned manifolds are compact. The aim of this paper is to study the non-compact complete case. Our main results can be stated as follows.展开更多
Observations collected in the Badan Jaran desert hinterland and edge during 19-23 August 2009 and in the Jinta Oasis during 12-16 June 2005 are used to assess three methods for calculating the heat storage of the5-20-...Observations collected in the Badan Jaran desert hinterland and edge during 19-23 August 2009 and in the Jinta Oasis during 12-16 June 2005 are used to assess three methods for calculating the heat storage of the5-20-cm soil layer.The methods evaluated include the harmonic method,the conduction-convection method,and the temperature integral method.Soil heat storage calculated using the harmonic method provides the closest match with measured values.The conduction-convection method underestimates nighttime soil heat storage.The temperature integral method best captures fluctuations in soil heat storage on sub-diurnal timescales,but overestimates the amplitude and peak values of the diurnal cycle.The relative performance of each method varies with the underlying land surface.The land surface energy balance is evaluated using observations of soil heat flux at 5-cm depth and estimates of ground heat flux adjusted to account for soil heat storage.The energy balance closure rate increases and energy balance is improved when the ground heat flux is adjusted to account for soil heat storage.The results achieved using the harmonic and temperature integral methods are superior to those achieved using the conduction-convection method.展开更多
文摘Several theorems on the finiteness of energy for quasi- harmonic spheres are proved, some counter- examples which state thatthe energy of quasi- harmonic sphere may be infinite are given.The results support some conditions of a question posed by Lin Fanghua and Wang Changyou.
基金Projects Supported by the Science Fund of the Chinese Academy of Sciences.
文摘§ 1. IntroductionIn [1], R. Schoen and S. T. Yan used harmonic map to study the topology of a non-compact complete stable hypersurface in a manifold of non-negative curvature. Essentially the method is to prove first the nonexistence of some kind of nonconstant harmonic map and then to draw the relative conclusions concerning the topology. Such nonexistence theorems have been obtained in [3] and [4] in cases where the concerned manifolds are compact. The aim of this paper is to study the non-compact complete case. Our main results can be stated as follows.
基金Supported by the National Science and Technology Support Program of China(2012BAH29B03)National(Key) Basic Research and Development(973)Program of China(2009CB421402)
文摘Observations collected in the Badan Jaran desert hinterland and edge during 19-23 August 2009 and in the Jinta Oasis during 12-16 June 2005 are used to assess three methods for calculating the heat storage of the5-20-cm soil layer.The methods evaluated include the harmonic method,the conduction-convection method,and the temperature integral method.Soil heat storage calculated using the harmonic method provides the closest match with measured values.The conduction-convection method underestimates nighttime soil heat storage.The temperature integral method best captures fluctuations in soil heat storage on sub-diurnal timescales,but overestimates the amplitude and peak values of the diurnal cycle.The relative performance of each method varies with the underlying land surface.The land surface energy balance is evaluated using observations of soil heat flux at 5-cm depth and estimates of ground heat flux adjusted to account for soil heat storage.The energy balance closure rate increases and energy balance is improved when the ground heat flux is adjusted to account for soil heat storage.The results achieved using the harmonic and temperature integral methods are superior to those achieved using the conduction-convection method.
