A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, ...A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.展开更多
In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only f...In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal bases.Also,we have a note about a comment and a relation in the proof of Proposition 5.3 in[D.Li et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-Riesz bases,woven and P-woven g-frames.展开更多
An ultrafast framing camera with a pulse-dilation device,a microchannel plate(MCP)imager,and an electronic imaging system were reported.The camera achieved a temporal resolution of 10 ps by using a pulse-dilation devi...An ultrafast framing camera with a pulse-dilation device,a microchannel plate(MCP)imager,and an electronic imaging system were reported.The camera achieved a temporal resolution of 10 ps by using a pulse-dilation device and gated MCP imager,and a spatial resolution of 100μm by using an electronic imaging system comprising combined magnetic lenses.The spatial resolution characteristics of the camera were studied both theoretically and experimentally.The results showed that the camera with combined magnetic lenses reduced the field curvature and acquired a larger working area.A working area with a diameter of 53 mm was created by applying four magnetic lenses to the camera.Furthermore,the camera was used to detect the X-rays produced by the laser-targeting device.The diagnostic results indicated that the width of the X-ray pulse was approximately 18 ps.展开更多
文摘A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.
文摘In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal bases.Also,we have a note about a comment and a relation in the proof of Proposition 5.3 in[D.Li et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-Riesz bases,woven and P-woven g-frames.
基金National Natural Science Foundation of China(NSFC)(No.11775147)Guangdong Basic and Applied Basic Research Foundation(Nos.2019A1515110130 and 2024A1515011832)+1 种基金Shenzhen Key Laboratory of Photonics and Biophotonics(ZDSYS20210623092006020)Shenzhen Science and Technology Program(Nos.JCYJ20210324095007020,JCYJ20200109105201936 and JCYJ20230808105019039).
文摘An ultrafast framing camera with a pulse-dilation device,a microchannel plate(MCP)imager,and an electronic imaging system were reported.The camera achieved a temporal resolution of 10 ps by using a pulse-dilation device and gated MCP imager,and a spatial resolution of 100μm by using an electronic imaging system comprising combined magnetic lenses.The spatial resolution characteristics of the camera were studied both theoretically and experimentally.The results showed that the camera with combined magnetic lenses reduced the field curvature and acquired a larger working area.A working area with a diameter of 53 mm was created by applying four magnetic lenses to the camera.Furthermore,the camera was used to detect the X-rays produced by the laser-targeting device.The diagnostic results indicated that the width of the X-ray pulse was approximately 18 ps.
