The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The...The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The previous researches on this subject have led to the problem within the possible fifteen cases.We shall show that among the fifteen cases,the nine cases correspond to the spectral measures,and reduce the remnant six cases to the three cases.Thus,for a large class of such measures,their spectrality and non-spectrality are clear.Moreover,an explicit formula for the existent spectrum of a spectral measure is obtained.We also give a concluding remark on the remnant three cases.展开更多
We propose an efficient colocated multiple-input multiple-output radar waveform-design method based on two-step optimizations in the spatial and spectral domains. First, a minimum integrated side-lobe level strategy i...We propose an efficient colocated multiple-input multiple-output radar waveform-design method based on two-step optimizations in the spatial and spectral domains. First, a minimum integrated side-lobe level strategy is adopted to obtain the desired beam pattern with spatial nulling. By recovering the hidden convexity of the resulting fractional quadratically constrained quadratic programming non-convex problem, the global optimal solution can be achieved in polynomial time through a semi- definite relaxation followed by spectral factorization. Second, with the transmit waveforms obtained via spatial optimization, a phase changing diagonal matrix is introduced and optimized via power method-like iterations. Without influencing the shape of the optimized beam pattern, the transmit waveforms are further optimized in the spectral domain, and the desired spectral nulling is formed to avoid radar interference on the overlaid licensed radiators. Finally, the superior performance of the proposed method is demonstrated via numerical results and comparisons with other approaches to waveform design.展开更多
Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its...Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its associated twisted de Rham cohomology H＊ （M, H）. The authors show that there exists a spectral sequence {Ep/r.q, dr } derived from the filtration Fp（Ω＊ （M）） = （¤i〉p Ωi（M） of Ω＊ （M）, which converges to the twisted de Rham cohomology H＊（M, H）. It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.展开更多
In this report, we find the MBH estimated from the formalism of Wang et al. are more consistent with those from the MBH-δ, relation than those from previous single-epoch mass estimators, using a large sample of AGNs....In this report, we find the MBH estimated from the formalism of Wang et al. are more consistent with those from the MBH-δ, relation than those from previous single-epoch mass estimators, using a large sample of AGNs. Furthermore, we examine the differences between the line widths of Hβ and Mg II in detail by comparing their line profiles. The flux around the line core and that in the wing of both Hβ and Mg II show an opposite variation tendency, which indicates the BLR is multi-componential. The contribution of the wing makes the FWHM deviate from δline, and thus bias the MBH estimated from previous single-epoch mass estimators. Thus the correction on the formalism suggested by Wang et al. is crucial to MBn estimation.展开更多
A tunable modulation format converter based on spectral line-by-line pulse shaper is proposed to realize different format conversions.The pulse shaper works as a format converter by setting its frequency response equi...A tunable modulation format converter based on spectral line-by-line pulse shaper is proposed to realize different format conversions.The pulse shaper works as a format converter by setting its frequency response equivalent to the transform function between two formats.The working principles show that the format converter is suitable for different formats by adjusting its frequency response.Examples of format conversion from return to zero differential phase-shift keying(RZ-DPSK) to on-off keying(OOK) with different data packets and from return to zero(RZ) to non-return to zero(NRZ) are given.The results show that the format converter is not only suitable for different formats but also for random data packets.展开更多
基金supported by National Natural Science Foundation of China (Grant No.11171201)
文摘The present research will concentrate on the topic of Fourier analysis on fractals.It mainly deals with the problem of determining spectral self-affine measures on the typical fractals:the planar Sierpinski family.The previous researches on this subject have led to the problem within the possible fifteen cases.We shall show that among the fifteen cases,the nine cases correspond to the spectral measures,and reduce the remnant six cases to the three cases.Thus,for a large class of such measures,their spectrality and non-spectrality are clear.Moreover,an explicit formula for the existent spectrum of a spectral measure is obtained.We also give a concluding remark on the remnant three cases.
基金the National Natural Science Foundation of China （No. 61302153）
文摘We propose an efficient colocated multiple-input multiple-output radar waveform-design method based on two-step optimizations in the spatial and spectral domains. First, a minimum integrated side-lobe level strategy is adopted to obtain the desired beam pattern with spatial nulling. By recovering the hidden convexity of the resulting fractional quadratically constrained quadratic programming non-convex problem, the global optimal solution can be achieved in polynomial time through a semi- definite relaxation followed by spectral factorization. Second, with the transmit waveforms obtained via spatial optimization, a phase changing diagonal matrix is introduced and optimized via power method-like iterations. Without influencing the shape of the optimized beam pattern, the transmit waveforms are further optimized in the spectral domain, and the desired spectral nulling is formed to avoid radar interference on the overlaid licensed radiators. Finally, the superior performance of the proposed method is demonstrated via numerical results and comparisons with other approaches to waveform design.
基金supported by the National Natural Science Foundation of China(No.11171161)the Scientific Research Foundation for the Returned Overseas Chinese Scholars of the State Education Ministry(No.2012940)
文摘Let （Ω＊ （M）, d） be the de Rham cochain complex for a smooth compact closed manifolds M of dimension n. For an odd-degree closed form H, there is a twisted de Rham cochain complex （Ω＊ （M）, d ＋ H∧） and its associated twisted de Rham cohomology H＊ （M, H）. The authors show that there exists a spectral sequence {Ep/r.q, dr } derived from the filtration Fp（Ω＊ （M）） = （¤i〉p Ωi（M） of Ω＊ （M）, which converges to the twisted de Rham cohomology H＊（M, H）. It is also shown that the differentials in the spectral sequence can be given in terms of cup products and specific elements of Massey products as well, which generalizes a result of Atiyah and Segal. Some results about the indeterminacy of differentials are also given in this paper.
基金supported by the National Basic Research Program of China(Grant No.2009CB824800)the National Natural Science Foundation of China(Grant Nos.11303085,11073019,10973034,11033007,11133006 and 11103071)the Western Light Youth Project
文摘In this report, we find the MBH estimated from the formalism of Wang et al. are more consistent with those from the MBH-δ, relation than those from previous single-epoch mass estimators, using a large sample of AGNs. Furthermore, we examine the differences between the line widths of Hβ and Mg II in detail by comparing their line profiles. The flux around the line core and that in the wing of both Hβ and Mg II show an opposite variation tendency, which indicates the BLR is multi-componential. The contribution of the wing makes the FWHM deviate from δline, and thus bias the MBH estimated from previous single-epoch mass estimators. Thus the correction on the formalism suggested by Wang et al. is crucial to MBn estimation.
基金supported by the National Natural Science Foundation of China(No.61377075)New Century Excellent Talents in University(No.NCET-07-0611)
文摘A tunable modulation format converter based on spectral line-by-line pulse shaper is proposed to realize different format conversions.The pulse shaper works as a format converter by setting its frequency response equivalent to the transform function between two formats.The working principles show that the format converter is suitable for different formats by adjusting its frequency response.Examples of format conversion from return to zero differential phase-shift keying(RZ-DPSK) to on-off keying(OOK) with different data packets and from return to zero(RZ) to non-return to zero(NRZ) are given.The results show that the format converter is not only suitable for different formats but also for random data packets.
