In this article, we study positive solutions to the system{Aαu（x） = Cn,αPV∫Rn（a1（x-y）（u（x）-u（y）））/（｜x-y｜n＋α）dy = f（u（x）, Bβv（x） = Cn,βPV ∫Rn（a2（x-y）（v（x）-v（y））/（｜x-y｜n＋β）dy ...In this article, we study positive solutions to the system{Aαu（x） = Cn,αPV∫Rn（a1（x-y）（u（x）-u（y）））/（｜x-y｜n＋α）dy = f（u（x）, Bβv（x） = Cn,βPV ∫Rn（a2（x-y）（v（x）-v（y））/（｜x-y｜n＋β）dy = g（u（x）,v（x））.To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.展开更多
In this paper, by using the method of moving planes, we are concerned with the symmetry and monotonicity of positive solutions for the fractional Hartree equation.
The acceleration of a high maneuvering target in signal processing is helpful to enhance the performance of the tracker and facilitate the classification of targets. At present, most of the research on acceleration es...The acceleration of a high maneuvering target in signal processing is helpful to enhance the performance of the tracker and facilitate the classification of targets. At present, most of the research on acceleration estimation is carried out in cases of a single target with time-frequency analysis methods such as fractional Fourier transform （FRFT）, Hough-ambiguity transform （HAT）, and Wigner-Vil e distribution （WVD）, which need to satisfy enough time duration and sampling theorem. Only one reference proposed a method of acceleration estimation for multiple targets based on modified polynomial phase transform （MPPT） in the lin-ear frequency modulation （LFM） continuous-wave （CW） radar. The method of acceleration estimation for multiple targets in the pulse Doppler （PD） radar has not been reported so far. Compressive sensing （CS） has the advantage of sampling at a low rate and short duration without sacrificing estimation performance. There-fore, this paper proposes a new method of acceleration estimation for multiple maneuvering targets with the unknown number based on CS with pulse Doppler signals. Simulation results validate the effectiveness of the proposed method under several conditions with different duration, measurement numbers, signal to noise ra-tios （SNR）, and regularization parameters, respectively. Simulation results also show that the performance of the proposed method is superior to that of FRFT and HAT in the condition of multiple targets.展开更多
The mismatch between echo and replica caused by underwater moving target(UMT)'s radial velocity degrades the detection performance of the matched filter(MF)for the linear frequency modulation(LFM)signal.By using t...The mismatch between echo and replica caused by underwater moving target(UMT)'s radial velocity degrades the detection performance of the matched filter(MF)for the linear frequency modulation(LFM)signal.By using the focusing property of fractional Fourier transform(FRFT)to that signal,a detection algorithm for UMT's LFM echo based on the discrete fractional Fourier transform(DFRFT)is proposed.This algorithm is less affected by the target's radial velocity compared with the other MF detection algorithm utilizing zero radial velocity replica(ZRVR),and the mathematical relation between the output peak positions of these two algorithms exists in the case of existence of target echo.The algorithm can also estimate the target distance by using this relation.The simulation and experiment show that this algorithm'sdetection performance is better than or equivalent to that of the other MF algorithm utilizing ZRVR for the LFM echo of UMT with unknown radial velocity under reverberation noise background.展开更多
In this article, we consider the fractional Laplacian equation {（-△）α/2u=k（x）f（u）,x∈Rn＋, u=0, x Rn＋, where 0 〈α 〈 2,En＋：= {x = （x1,x2,… ,xn）｜xn〉 0}. When K is strictly decreasing with respect to ...In this article, we consider the fractional Laplacian equation {（-△）α/2u=k（x）f（u）,x∈Rn＋, u=0, x Rn＋, where 0 〈α 〈 2,En＋：= {x = （x1,x2,… ,xn）｜xn〉 0}. When K is strictly decreasing with respect to ｜x＇｜, the symmetry of positive solutions is proved, where x＇ = （x1, x2,…, xn-1） ∈Rn- 1. When K is strictly increasing with respect to xn or only depend on xn, the nonexistence of positive solutions is obtained.展开更多
基金Supported by National Natural Science Foundation of China(11771354)
文摘In this article, we study positive solutions to the system{Aαu（x） = Cn,αPV∫Rn（a1（x-y）（u（x）-u（y）））/（｜x-y｜n＋α）dy = f（u（x）, Bβv（x） = Cn,βPV ∫Rn（a2（x-y）（v（x）-v（y））/（｜x-y｜n＋β）dy = g（u（x）,v（x））.To reach our aim, by using the method of moving planes, we prove a narrow region principle and a decay at infinity by the iteration method. On the basis of these results, we conclude radial symmetry and monotonicity of positive solutions for the problems involving the weighted fractional system on an unit ball and the whole space. Furthermore, non-existence of nonnegative solutions on a half space is given.
基金supported by NSFC(11761082)Yunnan Province,Young Academic and Technical Leaders Program(2015HB028)
文摘In this paper, by using the method of moving planes, we are concerned with the symmetry and monotonicity of positive solutions for the fractional Hartree equation.
基金supported by the National Natural Science Foundation of China(6110216561102167)
文摘The acceleration of a high maneuvering target in signal processing is helpful to enhance the performance of the tracker and facilitate the classification of targets. At present, most of the research on acceleration estimation is carried out in cases of a single target with time-frequency analysis methods such as fractional Fourier transform （FRFT）, Hough-ambiguity transform （HAT）, and Wigner-Vil e distribution （WVD）, which need to satisfy enough time duration and sampling theorem. Only one reference proposed a method of acceleration estimation for multiple targets based on modified polynomial phase transform （MPPT） in the lin-ear frequency modulation （LFM） continuous-wave （CW） radar. The method of acceleration estimation for multiple targets in the pulse Doppler （PD） radar has not been reported so far. Compressive sensing （CS） has the advantage of sampling at a low rate and short duration without sacrificing estimation performance. There-fore, this paper proposes a new method of acceleration estimation for multiple maneuvering targets with the unknown number based on CS with pulse Doppler signals. Simulation results validate the effectiveness of the proposed method under several conditions with different duration, measurement numbers, signal to noise ra-tios （SNR）, and regularization parameters, respectively. Simulation results also show that the performance of the proposed method is superior to that of FRFT and HAT in the condition of multiple targets.
基金Sponsored by National Nature Science Foundation of China(60472101)
文摘The mismatch between echo and replica caused by underwater moving target(UMT)'s radial velocity degrades the detection performance of the matched filter(MF)for the linear frequency modulation(LFM)signal.By using the focusing property of fractional Fourier transform(FRFT)to that signal,a detection algorithm for UMT's LFM echo based on the discrete fractional Fourier transform(DFRFT)is proposed.This algorithm is less affected by the target's radial velocity compared with the other MF detection algorithm utilizing zero radial velocity replica(ZRVR),and the mathematical relation between the output peak positions of these two algorithms exists in the case of existence of target echo.The algorithm can also estimate the target distance by using this relation.The simulation and experiment show that this algorithm'sdetection performance is better than or equivalent to that of the other MF algorithm utilizing ZRVR for the LFM echo of UMT with unknown radial velocity under reverberation noise background.
基金supported by the Fundamental Research Founds for the Central Universities(3102015ZY069)the Natural Science Basic Research Plan in Shaanxi Province of China(2016M1008)
文摘In this article, we consider the fractional Laplacian equation {（-△）α/2u=k（x）f（u）,x∈Rn＋, u=0, x Rn＋, where 0 〈α 〈 2,En＋：= {x = （x1,x2,… ,xn）｜xn〉 0}. When K is strictly decreasing with respect to ｜x＇｜, the symmetry of positive solutions is proved, where x＇ = （x1, x2,…, xn-1） ∈Rn- 1. When K is strictly increasing with respect to xn or only depend on xn, the nonexistence of positive solutions is obtained.
