In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ ...In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.展开更多
Derivatives are the foundation of mathematical calculations,however,for some functions, using the rules of finding a derivative may lead to cumbersome steps. Therefore, this paper provides a simple way using transform...Derivatives are the foundation of mathematical calculations,however,for some functions, using the rules of finding a derivative may lead to cumbersome steps. Therefore, this paper provides a simple way using transformation thought for the reciprocal function derivative.展开更多
A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for ...A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for compact supported infinitely differentiable zonal functions.Making use of the property of this sequence somehow similar to that of approxination kernels,the authors deduce that the inversion formula is true for continuous zonal functions on SL(2, R)under some condition. The classical result can be viewed as a corollary of the results here.展开更多
A cepstrum moving target detection （CEPMTD） algorithm based on cepstrum techniques is proposed for passive coherent location （PCL） radar systems. The primary cepstrum techniques are of great success in recognizing...A cepstrum moving target detection （CEPMTD） algorithm based on cepstrum techniques is proposed for passive coherent location （PCL） radar systems. The primary cepstrum techniques are of great success in recognizing the arrival times of static target echoes. To estimate the Doppler frequencies of moving targets, we divide the radar data into a large number of seg- ments, and reformat these segments into a detection matrix. Applying the cepstrum and the Fourier transform to the fast and slow time dimensions respectively, we can obtain the range information and Doppler information of the moving targets. Based on the CEPMTD outlined above, an improved CEPMTD algorithm is proposed to improve the detection performance. Theoretical analyses show that only the target＇s peak can be coherently added. The performance of the improved CEPMTD is initially vali- dated by simulations, and then by experiments. The simulation results show that the detection performance of the improved CEPMTD algorithm is 13.3 dB better than that of the CEPMTD algorithm and 6.4 dB better than that of the classical detection algorithm based on the radar cross ambiguity function （CAF）. The experiment results show that the detection performance of the improved CEPMTD algorithm is 1.63 dB better than that of the radar CAF.展开更多
基金Supported by the National Science Foundation of China(90205019)
文摘In this paper, we show that the invertible operator T, which is a bounded linear functional on a separable Hilbert space H, could factor as T = US, where U is unitary and S belongs to width-two CSL algebra algφ （φ = M∨N） when nest M or N is a countable nest, or S belongs to algφ^-1 when nests M and N are countable nests. For the factorization of nest,we obtain that T factors as T = US where S ∈ DN^-1 and U is unitary as N be a countable nest.
文摘Derivatives are the foundation of mathematical calculations,however,for some functions, using the rules of finding a derivative may lead to cumbersome steps. Therefore, this paper provides a simple way using transformation thought for the reciprocal function derivative.
文摘A constructive proof is given for the inversion formula for zonal functions on SL(2, R). A concretely constructed sequence of zonal drictions are proved to satisfy the inversion formula obtained by Harish-Chandra for compact supported infinitely differentiable zonal functions.Making use of the property of this sequence somehow similar to that of approxination kernels,the authors deduce that the inversion formula is true for continuous zonal functions on SL(2, R)under some condition. The classical result can be viewed as a corollary of the results here.
文摘A cepstrum moving target detection （CEPMTD） algorithm based on cepstrum techniques is proposed for passive coherent location （PCL） radar systems. The primary cepstrum techniques are of great success in recognizing the arrival times of static target echoes. To estimate the Doppler frequencies of moving targets, we divide the radar data into a large number of seg- ments, and reformat these segments into a detection matrix. Applying the cepstrum and the Fourier transform to the fast and slow time dimensions respectively, we can obtain the range information and Doppler information of the moving targets. Based on the CEPMTD outlined above, an improved CEPMTD algorithm is proposed to improve the detection performance. Theoretical analyses show that only the target＇s peak can be coherently added. The performance of the improved CEPMTD is initially vali- dated by simulations, and then by experiments. The simulation results show that the detection performance of the improved CEPMTD algorithm is 13.3 dB better than that of the CEPMTD algorithm and 6.4 dB better than that of the classical detection algorithm based on the radar cross ambiguity function （CAF）. The experiment results show that the detection performance of the improved CEPMTD algorithm is 1.63 dB better than that of the radar CAF.
