In this paper, some intrinsic rigidity theorems are given for compact minimal submanifolds in a sphere. In particular, the pinching constant of J. Simons is improved for higher codimensions.
We obtain an inequality in Sm×R and Hm×R which is similar to DDVV conjecture.As an application,we show that a minimal submanifold in H m×R with nonnegative scalar curvature must be a surface of the type...We obtain an inequality in Sm×R and Hm×R which is similar to DDVV conjecture.As an application,we show that a minimal submanifold in H m×R with nonnegative scalar curvature must be a surface of the type γ×R,where γ is a geodesic in H m.In addition,we get a pinching theorem in Sm×R.展开更多
Let Mn be an n-dimensional compact minimal submanifolds in Sin（1）× R. We prove two pinching theorems by the Ricci curvature and the sectional curvature pinching conditions respectively. In fact, we characterize...Let Mn be an n-dimensional compact minimal submanifolds in Sin（1）× R. We prove two pinching theorems by the Ricci curvature and the sectional curvature pinching conditions respectively. In fact, we characterize the Clifford tori and Veronese submanifolds by our pinching conditions respectively.展开更多
S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length o...S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length of the second fundamental form as a function on this set. Is the image of this function a discrete set of positive numbers?展开更多
Glass fi ber reinforced gypsum(GFRG) wall panels are prefabricated panels with hollow cores, originally developed in Australia and subsequently adopted by India and China for use in buildings. This paper discusses ide...Glass fi ber reinforced gypsum(GFRG) wall panels are prefabricated panels with hollow cores, originally developed in Australia and subsequently adopted by India and China for use in buildings. This paper discusses identifi cation and calibration of a suitable hysteretic model for GFRG wall panels fi lled with reinforced concrete. As considerable pinching was observed in the experimental results, a suitable hysteretic model with pinched hysteretic rule is used to conduct a series of quasi-static as inelastic hysteretic response analyses of GFRG panels with two different widths. The calibration of the pinching model parameters was carried out to approximately match the simulated and experimental responses up to 80% of the peak load in the post peak region. Interestingly, the same values of various parameters(energy dissipation and pinching related parameters) were obtained for all fi ve test specimens.展开更多
The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displ...The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displacements plays an important role in ensuring cost-feasible or cost-effective repairs in a damaged structure after the event.An attempt is made in this study to obtain statistical estimates of constant-ductility residual displacement spectra for bilinear and pinching oscillators with 5%initial damping,directly in terms of easily available seismological,site,and model parameters.None of the available models for the bilinear and pinching oscillators are useful when design spectra for a seismic hazard at a site are not available.The statistical estimates of a residual displacement spectrum are proposed in terms of earthquake magnitude,epicentral distance,site geology parameter,and three model parameters for a given set of ductility demand and a hysteretic energy capacity coefficient in the case of bilinear and pinching models,as well as for a given set of pinching parameters for displacement and strength at the breakpoint in the case of pinching model alone.The proposed scaling model is applicable to horizontal ground motions in the western U.S.for earthquake magnitudes less than 7 or epicentral distances greater than 20 km.展开更多
基金Project supported by the National Natural Science Foundation of China.
文摘In this paper, some intrinsic rigidity theorems are given for compact minimal submanifolds in a sphere. In particular, the pinching constant of J. Simons is improved for higher codimensions.
基金supported by National Natural Science Foundation of China (Grant No.10871149)Research Fund for the Doctoral Program of Higher Education of China (Grant No. 200804860046)
文摘We obtain an inequality in Sm×R and Hm×R which is similar to DDVV conjecture.As an application,we show that a minimal submanifold in H m×R with nonnegative scalar curvature must be a surface of the type γ×R,where γ is a geodesic in H m.In addition,we get a pinching theorem in Sm×R.
基金supported by National Natural Science Foundation of China (Grant No.11271214)
文摘Let Mn be an n-dimensional compact minimal submanifolds in Sin（1）× R. We prove two pinching theorems by the Ricci curvature and the sectional curvature pinching conditions respectively. In fact, we characterize the Clifford tori and Veronese submanifolds by our pinching conditions respectively.
文摘S. S. Chern posed a problem as follows. Consider the set of all closed minimal hypersurfaces in S<sup>n+1</sup>（1） with constant scalar curvature. Take the scalar curvature and the square of the length of the second fundamental form as a function on this set. Is the image of this function a discrete set of positive numbers?
文摘Glass fi ber reinforced gypsum(GFRG) wall panels are prefabricated panels with hollow cores, originally developed in Australia and subsequently adopted by India and China for use in buildings. This paper discusses identifi cation and calibration of a suitable hysteretic model for GFRG wall panels fi lled with reinforced concrete. As considerable pinching was observed in the experimental results, a suitable hysteretic model with pinched hysteretic rule is used to conduct a series of quasi-static as inelastic hysteretic response analyses of GFRG panels with two different widths. The calibration of the pinching model parameters was carried out to approximately match the simulated and experimental responses up to 80% of the peak load in the post peak region. Interestingly, the same values of various parameters(energy dissipation and pinching related parameters) were obtained for all fi ve test specimens.
文摘The estimation of residual displacements in a structure due to an anticipated earthquake event has increasingly become an important component of performance-based earthquake engineering because controlling these displacements plays an important role in ensuring cost-feasible or cost-effective repairs in a damaged structure after the event.An attempt is made in this study to obtain statistical estimates of constant-ductility residual displacement spectra for bilinear and pinching oscillators with 5%initial damping,directly in terms of easily available seismological,site,and model parameters.None of the available models for the bilinear and pinching oscillators are useful when design spectra for a seismic hazard at a site are not available.The statistical estimates of a residual displacement spectrum are proposed in terms of earthquake magnitude,epicentral distance,site geology parameter,and three model parameters for a given set of ductility demand and a hysteretic energy capacity coefficient in the case of bilinear and pinching models,as well as for a given set of pinching parameters for displacement and strength at the breakpoint in the case of pinching model alone.The proposed scaling model is applicable to horizontal ground motions in the western U.S.for earthquake magnitudes less than 7 or epicentral distances greater than 20 km.
