A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in t...A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.展开更多
The low laser induced damage threshold of the KH2PO4 crystal seriously restricts the output power of inertial confinement fusion.The micro-waviness on the KH2PO4 surface processed by single point diamond turning has a...The low laser induced damage threshold of the KH2PO4 crystal seriously restricts the output power of inertial confinement fusion.The micro-waviness on the KH2PO4 surface processed by single point diamond turning has a significant influence on the damage threshold.In this paper,the influence of micro-waviness on the damage threshold of the KH2PO4 crystal and the chief sources introducing the micro-waviness are analysed based on the combination of the Fourier modal theory and the power spectrum density method.Research results indicate that among the sub-wavinesses with different characteristic spatial frequencies there exists the most dangerous frequency which greatly reduces the damage threshold,although it may not occupy the largest proportion in the original surface.The experimental damage threshold is basically consistent with the theoretical calculation.For the processing parameters used,the leading frequency of micro-waviness which causes the damage threshold to decrease is between 350-1 μm-1 and 30-1 μm-1,especially between 90-1 μm-1 and 200-1 μm-1.Based on the classification study of the time frequencies of microwaviness,we find that the axial vibration of the spindle is the chief source introducing the micro-waviness,nearly all the leading frequencies are related to the practical spindle frequency（about 6.68 Hz,400 r/min） and a special middle frequency（between 1.029 Hz and 1.143 Hz）.展开更多
In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the f...In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ（R＋） for γ 〉 1 and the sphere function ΩεFβ（S^n-1） for someβ 〉 0 which is distinct from HI（Sn-1）.展开更多
In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unre...In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unreasonable setting of the characteristic of the system. Hereof, by means of nonstandard analysis, it is concluded that the advanced response arises from the course of Fourier analysis other than the transmission process of the signal.展开更多
文摘A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.
基金Project supported by the National Natural Science Foundation of China (Grant No. 50875066)
文摘The low laser induced damage threshold of the KH2PO4 crystal seriously restricts the output power of inertial confinement fusion.The micro-waviness on the KH2PO4 surface processed by single point diamond turning has a significant influence on the damage threshold.In this paper,the influence of micro-waviness on the damage threshold of the KH2PO4 crystal and the chief sources introducing the micro-waviness are analysed based on the combination of the Fourier modal theory and the power spectrum density method.Research results indicate that among the sub-wavinesses with different characteristic spatial frequencies there exists the most dangerous frequency which greatly reduces the damage threshold,although it may not occupy the largest proportion in the original surface.The experimental damage threshold is basically consistent with the theoretical calculation.For the processing parameters used,the leading frequency of micro-waviness which causes the damage threshold to decrease is between 350-1 μm-1 and 30-1 μm-1,especially between 90-1 μm-1 and 200-1 μm-1.Based on the classification study of the time frequencies of microwaviness,we find that the axial vibration of the spindle is the chief source introducing the micro-waviness,nearly all the leading frequencies are related to the practical spindle frequency（about 6.68 Hz,400 r/min） and a special middle frequency（between 1.029 Hz and 1.143 Hz）.
基金Supported by the National Natural Science Foundation of China(11071200,11371295)
文摘In this paper, the authors establish the LV-mapping properties for a class of singular integrals along surfaces in Rn of the form {Ф（lul）u＇ ： u ε ]t^n} as well as the related maimal operators provided that the function Ф satisfies certain oscillatory integral estimates of Van der Corput type, and the integral kernels are given by the radial function h E ε△γ（R＋） for γ 〉 1 and the sphere function ΩεFβ（S^n-1） for someβ 〉 0 which is distinct from HI（Sn-1）.
文摘In the theory of signal analysis, the existence of the advanced response, whose appearance is earlier than the input, violates the law of causation. It is believed that the presence of advanced response is due to unreasonable setting of the characteristic of the system. Hereof, by means of nonstandard analysis, it is concluded that the advanced response arises from the course of Fourier analysis other than the transmission process of the signal.
