In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-...In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.展开更多
The present work introduces a system for recognizing static signs in Mexican Sign Language (MSL) using Jacobi-Fourier Moments (JFMs) and Artificial Neural Networks (ANN). The original color images of static signs are ...The present work introduces a system for recognizing static signs in Mexican Sign Language (MSL) using Jacobi-Fourier Moments (JFMs) and Artificial Neural Networks (ANN). The original color images of static signs are cropped, segmented and converted to grayscale. Then to reduce computational costs 64 JFMs were calculated to represent each image. The JFMs are sorted to select a subset that improves recognition according to a metric proposed by us based on a ratio between dispersion measures. Using WEKA software to test a Multilayer-Perceptron with this subset of JFMs reached 95% of recognition rate.展开更多
Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional p...Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional power spectra（FrFT moment） of the linear chirp signal.This method can adaptively determine the optimum FrFT order by maximizing the second-order central FrFT moment.This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably.This improves the mean square error minimization beamformer by reducing effectively the signal-noise cross terms due to the finite data length de-correlation operation.Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.展开更多
The pth moment Lyapunov exponent of a two-codimension bifurcation systern excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtai...The pth moment Lyapunov exponent of a two-codimension bifurcation systern excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtained. In order to evaluate the asymptotic expansion of the moment Lyapunov exponent, via a perturbation method, a ralevant eigenvalue problem is obtained. The eigenvalue problem is then solved by a Fourier cosine series expansion, and an infinite matrix is thus obtained, whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent. Finally, the convergence of procedure is numerically illustrated, and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed.展开更多
Line broadening in a diffraction intensity profile of powdered crystalline materials due to stacking fault has been characterized in terms of the zeroth, first, second, third, and fourth moments and the fourth cumulan...Line broadening in a diffraction intensity profile of powdered crystalline materials due to stacking fault has been characterized in terms of the zeroth, first, second, third, and fourth moments and the fourth cumulant. Calculations have been derived showing that the first moment causes a shift in the peak position of the profile while the third moment affects its shape. The intensity expression has been derived on the basis of usual Cartesian coordinates and also of polar coordinates indicated by the probability of the fault and the reciprocal lattice parameter as the two axes. The expressions for the fourth cumulant have also been so derived. Here we have used three different approaches to determine methods for calculating the fourth cumulant due to stacking faults. The three forms of the equations derived here are for different coordinate systems, but will arrive at the same answers.展开更多
文摘In this paper, we consider the reconstruction of the wave field in a bounded domain. By choosing a special family of functions, the Cauchy problem can be transformed into a Fourier moment problem. This problem is ill-posed. We propose a regularization method for obtaining an approximate solution to the wave field on the unspecified boundary. We also give the convergence analysis and error estimate of the numerical algorithm. Finally, we present some numerical examples to show the effectiveness of this method.
文摘The present work introduces a system for recognizing static signs in Mexican Sign Language (MSL) using Jacobi-Fourier Moments (JFMs) and Artificial Neural Networks (ANN). The original color images of static signs are cropped, segmented and converted to grayscale. Then to reduce computational costs 64 JFMs were calculated to represent each image. The JFMs are sorted to select a subset that improves recognition according to a metric proposed by us based on a ratio between dispersion measures. Using WEKA software to test a Multilayer-Perceptron with this subset of JFMs reached 95% of recognition rate.
基金supported by the National Natural Science Foundation of China (606720846060203760736006)
文摘Traditionally,beamforming using fractional Fourier transform（FrFT） involves a trial-and-error based FrFT order selection which is impractical.A new numerical order selection scheme is presented based on fractional power spectra（FrFT moment） of the linear chirp signal.This method can adaptively determine the optimum FrFT order by maximizing the second-order central FrFT moment.This makes the desired chirp signal substantially concentrated whereas the noise is rejected considerably.This improves the mean square error minimization beamformer by reducing effectively the signal-noise cross terms due to the finite data length de-correlation operation.Simulation results show that the new method works well under a wide range of signal to noise ratio and signal to interference ratio.
基金supported by the National Natural Science Foundation of China(Nos.11072107,91016022,and 11232007)
文摘The pth moment Lyapunov exponent of a two-codimension bifurcation systern excited parametrically by a real noise is investigated. By a linear stochastic transformation, the differential operator of the system is obtained. In order to evaluate the asymptotic expansion of the moment Lyapunov exponent, via a perturbation method, a ralevant eigenvalue problem is obtained. The eigenvalue problem is then solved by a Fourier cosine series expansion, and an infinite matrix is thus obtained, whose leading eigenvalue is the second-order of the asymptotic expansion of the moment Lyapunov exponent. Finally, the convergence of procedure is numerically illustrated, and the effects of the system and the noise parameters on the moment Lyapunov exponent are discussed.
文摘Line broadening in a diffraction intensity profile of powdered crystalline materials due to stacking fault has been characterized in terms of the zeroth, first, second, third, and fourth moments and the fourth cumulant. Calculations have been derived showing that the first moment causes a shift in the peak position of the profile while the third moment affects its shape. The intensity expression has been derived on the basis of usual Cartesian coordinates and also of polar coordinates indicated by the probability of the fault and the reciprocal lattice parameter as the two axes. The expressions for the fourth cumulant have also been so derived. Here we have used three different approaches to determine methods for calculating the fourth cumulant due to stacking faults. The three forms of the equations derived here are for different coordinate systems, but will arrive at the same answers.
