Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potenti...Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.展开更多
As one of the most promising materials for two-dimensional transition metal chalcogenides(2D TMDs),molybdenum diselenide(MoSe_(2))has great potential in photodetectors due to its excellent properties like tunable band...As one of the most promising materials for two-dimensional transition metal chalcogenides(2D TMDs),molybdenum diselenide(MoSe_(2))has great potential in photodetectors due to its excellent properties like tunable bandgap,high carrier mobility,and excellent air stability.Although 2D MoSe_(2)-based photodetectors have been reported to exhibit admired performance,the large-area 2D MoSe_(2)layers are difficult to be achieved via conventional synthesis methods,which severely impedes its future applications.Here,we present the controllable growth of large-area 2D MoSe_(2)layers over 3.5-inch with excellent homogeneity by a simple post-selenization route.Further,a high-quality n-MoSe_(2)/p-Si van der Waals(vdW)heterojunction device is in-situ fabricated by directly growing 2D n-MoSe_(2)layers on the patterned p-Si substrate,which shows a self-driven broadband photoresponse ranging from ultraviolet to mid-wave infrared with an impressive responsivity of 720.5 mA·W^(−1),a high specific detectivity of 10^(13) Jones,and a fast response time to follow nanosecond pulsed optical signal.In addition,thanks to the inch-level 2D MoSe_(2)layers,a 4×4 integrated heterojunction device array is achieved,which has demonstrated good uniformity and satisfying imaging capability.The large-area 2D MoSe_(2)layer and its heterojunction device array have great promise for high-performance photodetection and imaging applications in integrated optoelectronic systems.展开更多
The development of pressure sensor arrays capable of distinguishing the shape and texture details of objects is of considerable interest in the emerging fields of smart robots,prostheses,human-machine interfaces,and a...The development of pressure sensor arrays capable of distinguishing the shape and texture details of objects is of considerable interest in the emerging fields of smart robots,prostheses,human-machine interfaces,and artificial intelligence(AI).Here we report an integrated pressure sensor array,by combining solution-processed two-dimensional(2D)MoS2 van der Waals(vdW)thin film transistor(TFT)active matrix and conductive micropyramidal pressure-sensitive rubber(PSR)electrodes made of polydimethylsiloxane/carbon nanotube composites,to achieve spatially revolved pressure mapping with excellent contrast and low power consumption.We demonstrate a 10×10 active matrix by using the 2D MoS2 vdW-TFTs with high on-off ratio>10^(6),minimal hysteresis,and excellent device-to-device uniformity.The combination of the vdW-TFT active matrix with the highly uniform micropyramidal PSR electrodes creates an integrated pressure sensing array for spatially resolved pressure mapping.This study demonstrates that the solution-processed 2D vdW-TFTs offer a solution for active-matrix control of pressure sensor arrays,and could be extended for other active-matrix arrays of electronic or optoelectronic devices.展开更多
基金Supported by National Natural Science Foundation of China(10471048)Research Foundation of Hubei Education Committee(B20092809)Research Foundation of Xianning University(Bk0714)
文摘Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.
基金This work was financially supported by the National Key R&D Program of China(No.2022YFB2803900)the National Natural Science Foundation of China(Nos.U2004165,U22A20138,and 11974016)+1 种基金the Natural Science Foundation of Henan Province,China(No.202300410376)Key Research and Development Program(social development)of Jiangsu Province(No.BE2021667).
文摘As one of the most promising materials for two-dimensional transition metal chalcogenides(2D TMDs),molybdenum diselenide(MoSe_(2))has great potential in photodetectors due to its excellent properties like tunable bandgap,high carrier mobility,and excellent air stability.Although 2D MoSe_(2)-based photodetectors have been reported to exhibit admired performance,the large-area 2D MoSe_(2)layers are difficult to be achieved via conventional synthesis methods,which severely impedes its future applications.Here,we present the controllable growth of large-area 2D MoSe_(2)layers over 3.5-inch with excellent homogeneity by a simple post-selenization route.Further,a high-quality n-MoSe_(2)/p-Si van der Waals(vdW)heterojunction device is in-situ fabricated by directly growing 2D n-MoSe_(2)layers on the patterned p-Si substrate,which shows a self-driven broadband photoresponse ranging from ultraviolet to mid-wave infrared with an impressive responsivity of 720.5 mA·W^(−1),a high specific detectivity of 10^(13) Jones,and a fast response time to follow nanosecond pulsed optical signal.In addition,thanks to the inch-level 2D MoSe_(2)layers,a 4×4 integrated heterojunction device array is achieved,which has demonstrated good uniformity and satisfying imaging capability.The large-area 2D MoSe_(2)layer and its heterojunction device array have great promise for high-performance photodetection and imaging applications in integrated optoelectronic systems.
基金Y.H.acknowledges the financial support from the Office of Naval Research through award N00014-18-1-2491.X.F.D.acknowledged the support from the US Department of Energy,Office of Basic Energy Sciences,Division of Materials Science and Engineering through award DE-SC0018828(material preparation).
文摘The development of pressure sensor arrays capable of distinguishing the shape and texture details of objects is of considerable interest in the emerging fields of smart robots,prostheses,human-machine interfaces,and artificial intelligence(AI).Here we report an integrated pressure sensor array,by combining solution-processed two-dimensional(2D)MoS2 van der Waals(vdW)thin film transistor(TFT)active matrix and conductive micropyramidal pressure-sensitive rubber(PSR)electrodes made of polydimethylsiloxane/carbon nanotube composites,to achieve spatially revolved pressure mapping with excellent contrast and low power consumption.We demonstrate a 10×10 active matrix by using the 2D MoS2 vdW-TFTs with high on-off ratio>10^(6),minimal hysteresis,and excellent device-to-device uniformity.The combination of the vdW-TFT active matrix with the highly uniform micropyramidal PSR electrodes creates an integrated pressure sensing array for spatially resolved pressure mapping.This study demonstrates that the solution-processed 2D vdW-TFTs offer a solution for active-matrix control of pressure sensor arrays,and could be extended for other active-matrix arrays of electronic or optoelectronic devices.
