We consider the boundedness of the n-dimension oscillatory hyper- Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. T...We consider the boundedness of the n-dimension oscillatory hyper- Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. The main theorems significantly improve some known results.展开更多
Consider the oscillatory hyper-Hilbert transform Hn,α,βf（x）=∫0^1 f（x-Г（t））e^it-βt^-1-α dt along the curve P（t） = （tp1, tP2,..., tpn）, where β 〉 α ≥ 0 and 0 〈 p1 〈 p2 〈 ... 〈 Pn. We prove that ...Consider the oscillatory hyper-Hilbert transform Hn,α,βf（x）=∫0^1 f（x-Г（t））e^it-βt^-1-α dt along the curve P（t） = （tp1, tP2,..., tpn）, where β 〉 α ≥ 0 and 0 〈 p1 〈 p2 〈 ... 〈 Pn. We prove that H n,α,β is bounded on L2 if and only if β ≥ （n ＋ 1）α. Our work extends and improves some known results.展开更多
The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of th...The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.展开更多
This paper is concerned with the oscillatory properties of the third-order nonlinear delay dynamic equations of the form??on time scales , where ?is a quotient of odd positive integers. Applying the inequality techniq...This paper is concerned with the oscillatory properties of the third-order nonlinear delay dynamic equations of the form??on time scales , where ?is a quotient of odd positive integers. Applying the inequality technique we present two new sufficient conditions which ensure that every solution of equations is oscillatory or converges to zero. The results obtained improve and complement some known results in the literature.展开更多
This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is m...This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is modeled as a signal that can be sparsely denoted by high Q-factor TQWT;similarly, the transient component is modeled as a piecewise smooth signal that can be sparsely denoted using low Q-factor TQWT. Since the low and high Q-factor TQWT has low coherence, the morphological component analysis (MCA) can effectively decompose the signal into oscillatory and transient components. The corresponding optimization problem of MCA is resolved by the split augmented Lagrangian shrinkage algorithm (SALSA). The applications of the proposed method to speech, electroencephalo-graph (EEG), and electrocardiograph (ECG) signals are included.展开更多
Due to the sensitivity of the frequency measurement of power system transient oscillatory signal with respect to noise signal, a new measurement method based on Wavelet Transform and Windowed Fourier Transform is prop...Due to the sensitivity of the frequency measurement of power system transient oscillatory signal with respect to noise signal, a new measurement method based on Wavelet Transform and Windowed Fourier Transform is proposed. An analysis using LabVIEW on oscillatory signal containing various noise components is carried on and it is shown that the proposed method can detect the oscillatory frequency more accurately and quickly.展开更多
Purpose: To analyse the parameters of frequency domain and time domain of the OPs in branch retinal vein occlusion (BRVO) and central retinal vein occlusion (CRVO). Methods : OPs from 9 eyes of BRVO, 9 eyes of CRVO an...Purpose: To analyse the parameters of frequency domain and time domain of the OPs in branch retinal vein occlusion (BRVO) and central retinal vein occlusion (CRVO). Methods : OPs from 9 eyes of BRVO, 9 eyes of CRVO and 40 normal control eyes were tested . The frequency spectra of the OPs were derived through Fast Fourier Transform (FFT) . The mean frequency spectra, the total power, the maximum magnitude, the maximum power and the dominant frequency in frequency domain of the OPs from the eyes of BRVO, CRVO and the normal control group were compared with each other. The OPs waveforms were reconstructed with the OPs frequency spectra data by counter-FFT. In time domain, the latencies, the amplitudes and the sum of the amplitudes of the four wavelets of OPs were measured and compared in the above subjects.Results: There were no statistically significant differences in the magnitudes of frequency spectra, the total power, the maximum magnitude and the maximum power in the frequency range from 110 to 250展开更多
基金Acknowledgements The authors are thankful to the referees for their careful reading and useful comments. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11501516, 11471288） and the Natural Science Foundation of Zhejiang Province （No. LQ15A010003）.
文摘We consider the boundedness of the n-dimension oscillatory hyper- Hilbert transform along homogeneous curves on the α-modulation spaces, including the inhomogeneous Besov spaces and the classical modulation spaces. The main theorems significantly improve some known results.
文摘Consider the oscillatory hyper-Hilbert transform Hn,α,βf（x）=∫0^1 f（x-Г（t））e^it-βt^-1-α dt along the curve P（t） = （tp1, tP2,..., tpn）, where β 〉 α ≥ 0 and 0 〈 p1 〈 p2 〈 ... 〈 Pn. We prove that H n,α,β is bounded on L2 if and only if β ≥ （n ＋ 1）α. Our work extends and improves some known results.
文摘The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.
文摘This paper is concerned with the oscillatory properties of the third-order nonlinear delay dynamic equations of the form??on time scales , where ?is a quotient of odd positive integers. Applying the inequality technique we present two new sufficient conditions which ensure that every solution of equations is oscillatory or converges to zero. The results obtained improve and complement some known results in the literature.
文摘This paper describes a method for decomposing a signal into the sum of an oscillatory component and a transient component. The process uses the tunable Q-factor wavelet transform (TQWT): The oscillatory component is modeled as a signal that can be sparsely denoted by high Q-factor TQWT;similarly, the transient component is modeled as a piecewise smooth signal that can be sparsely denoted using low Q-factor TQWT. Since the low and high Q-factor TQWT has low coherence, the morphological component analysis (MCA) can effectively decompose the signal into oscillatory and transient components. The corresponding optimization problem of MCA is resolved by the split augmented Lagrangian shrinkage algorithm (SALSA). The applications of the proposed method to speech, electroencephalo-graph (EEG), and electrocardiograph (ECG) signals are included.
文摘Due to the sensitivity of the frequency measurement of power system transient oscillatory signal with respect to noise signal, a new measurement method based on Wavelet Transform and Windowed Fourier Transform is proposed. An analysis using LabVIEW on oscillatory signal containing various noise components is carried on and it is shown that the proposed method can detect the oscillatory frequency more accurately and quickly.
文摘Purpose: To analyse the parameters of frequency domain and time domain of the OPs in branch retinal vein occlusion (BRVO) and central retinal vein occlusion (CRVO). Methods : OPs from 9 eyes of BRVO, 9 eyes of CRVO and 40 normal control eyes were tested . The frequency spectra of the OPs were derived through Fast Fourier Transform (FFT) . The mean frequency spectra, the total power, the maximum magnitude, the maximum power and the dominant frequency in frequency domain of the OPs from the eyes of BRVO, CRVO and the normal control group were compared with each other. The OPs waveforms were reconstructed with the OPs frequency spectra data by counter-FFT. In time domain, the latencies, the amplitudes and the sum of the amplitudes of the four wavelets of OPs were measured and compared in the above subjects.Results: There were no statistically significant differences in the magnitudes of frequency spectra, the total power, the maximum magnitude and the maximum power in the frequency range from 110 to 250
