Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,ea...Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.展开更多
based on optimal design on the core element of the sensor,a wireless and passive surface acoustic wave（SAW）temperature sensor integrated with ID Tag was presented.A reflective delay line,which consists of a transduc...based on optimal design on the core element of the sensor,a wireless and passive surface acoustic wave（SAW）temperature sensor integrated with ID Tag was presented.A reflective delay line,which consists of a transducer and eight reflectors on YZ LiNbO3 substrate.Was fabricated as the sensor element,in which,three reflectors were used for temperature sensing,and the other five were for the ID Tag using phase encoding.Single phase unidirectional transducers（SPUDTs）and shorted grating were used to structure the sAW device,leading to excellent signal to noise ratio（SNR）.The performance of the SAW device was simulated by the coupling of modes（COM）prior to fabrication.Using the network analyzer,the response in time domain of the fabricated 434 MHz SAW sensor was characterized,the measured S11 agrees well with the simulated one,sharp reflection peaks,high signal/noise,and low spurious noise between the reflection peaks were observed.Using the radar system based on FSCW as the reader unit.the developed SAW temperature sensors were evaluated wirelessly.Excellent1 inearity and good resolution of士1℃ were observed.展开更多
基金Supported partially by National Key Research and Development Project(2020YFA0712300)。
文摘Spin group and screw algebra,as extensions of quaternions and vector algebra,respectively,have important applications in geometry,physics and engineering.In threedimensional projective geometry,when acting on lines,each projective transformation can be decomposed into at most three harmonic projective reflections with respect to projective lines,or equivalently,each projective spinor can be decomposed into at most three orthogonal Minkowski bispinors,each inducing a harmonic projective line reflection.In this paper,we establish the corresponding result for three-dimensional affine geometry:with each affine transformation is found a minimal decomposition into general affine reflections,where the number of general affine reflections is at most three;equivalently,each affine spinor can be decomposed into at most three affine Minkowski bispinors,each inducing a general affine line reflection.
基金supported by the National Nature Science Foundation of China(11074268,10834010)
文摘based on optimal design on the core element of the sensor,a wireless and passive surface acoustic wave（SAW）temperature sensor integrated with ID Tag was presented.A reflective delay line,which consists of a transducer and eight reflectors on YZ LiNbO3 substrate.Was fabricated as the sensor element,in which,three reflectors were used for temperature sensing,and the other five were for the ID Tag using phase encoding.Single phase unidirectional transducers（SPUDTs）and shorted grating were used to structure the sAW device,leading to excellent signal to noise ratio（SNR）.The performance of the SAW device was simulated by the coupling of modes（COM）prior to fabrication.Using the network analyzer,the response in time domain of the fabricated 434 MHz SAW sensor was characterized,the measured S11 agrees well with the simulated one,sharp reflection peaks,high signal/noise,and low spurious noise between the reflection peaks were observed.Using the radar system based on FSCW as the reader unit.the developed SAW temperature sensors were evaluated wirelessly.Excellent1 inearity and good resolution of士1℃ were observed.
