Let （M^n, g） be an n-dimensional complete noncompact Riemannian manifold with harmonic curvature and positive Sobolev constant. In this paper, by employing an elliptic estimation method, we show that （M^n, g） is a...Let （M^n, g） be an n-dimensional complete noncompact Riemannian manifold with harmonic curvature and positive Sobolev constant. In this paper, by employing an elliptic estimation method, we show that （M^n, g） is a space form if it has sufficiently small Ln/2-norms of trace-free curvature tensor and nonnegative scalar curvature. Moreover, we get a gap theorem for （M^n, g） with positive scalar curvature.展开更多
Electron cyclotron emission imaging（ECEI） can provide measurements of 2D electron temperature fluctuation with high temporal and spatial resolution in magnetic fusion plasma devices. Two ECEI systems located in diff...Electron cyclotron emission imaging（ECEI） can provide measurements of 2D electron temperature fluctuation with high temporal and spatial resolution in magnetic fusion plasma devices. Two ECEI systems located in different toroidal ports with 67.5 degree separation have been implemented on J-TEXT to study the 3D structure of magnetohydrodynamic（MHD） instabilities. Each system consists of 12（vertical） × 16（horizontal） = 192 channels and the image of the 2nd harmonic X-mode electron cyclotron emission can be captured continuously in the core plasma region. The field curvature adjustment lens concept is developed to control the imaging plane for receiving optics of the ECEI systems. Field curvature of the image can be controlled to match the emission layer. Consequently, a quasi-3D image of the MHD instability in the core of the plasma has been achieved.展开更多
基金Acknowledgements The author would like to express his sincere thanks to the referees for valuable remarks. This work was supported in part by the National Natural Science Foundation of China （Grant No. 11071225）, the Natural Science Foundation of Anhui Provincial Education Department （Grant No. KJ2012A228）, and Project-2010JPKC07.
文摘Let （M^n, g） be an n-dimensional complete noncompact Riemannian manifold with harmonic curvature and positive Sobolev constant. In this paper, by employing an elliptic estimation method, we show that （M^n, g） is a space form if it has sufficiently small Ln/2-norms of trace-free curvature tensor and nonnegative scalar curvature. Moreover, we get a gap theorem for （M^n, g） with positive scalar curvature.
基金supported by the National Magnetic Confinement Fusion Science Program of China under Grant Nos.2013GB106002 and 2014GB109002National Natural Science Foundation of China under Grant Nos.10990210 and 11275200
文摘Electron cyclotron emission imaging（ECEI） can provide measurements of 2D electron temperature fluctuation with high temporal and spatial resolution in magnetic fusion plasma devices. Two ECEI systems located in different toroidal ports with 67.5 degree separation have been implemented on J-TEXT to study the 3D structure of magnetohydrodynamic（MHD） instabilities. Each system consists of 12（vertical） × 16（horizontal） = 192 channels and the image of the 2nd harmonic X-mode electron cyclotron emission can be captured continuously in the core plasma region. The field curvature adjustment lens concept is developed to control the imaging plane for receiving optics of the ECEI systems. Field curvature of the image can be controlled to match the emission layer. Consequently, a quasi-3D image of the MHD instability in the core of the plasma has been achieved.
