There are some curved interfaces in ocean acoustic waveguides. To compute wave propagation along the range with some marching methods, a flattening of the internal interfaces and a transforming equation are needed. In...There are some curved interfaces in ocean acoustic waveguides. To compute wave propagation along the range with some marching methods, a flattening of the internal interfaces and a transforming equation are needed. In this paper a local orthogonal coordinate transform and an equation transformation are constructed to flatten interfaces and change the Helmholtz equation as a solvable form. For a waveguide with a flat top, a fiat bottom and n curved interfaces, the coefficients of the transformed Helmholtz equation are given in a closed formulation which can be thought of as an extension of the formal work related to the equation transformation with two curved internal interfaces. In the transformed horizontally stratified waveguide, the one-way reformulation based on the Dirichlet-to-Neumann （DtN） map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method to discretize the range variable and a truncated local eigenfunction expansion to approximate the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. Furthermore, the method can also be applied to wave propagation problems in acoustic waveguides associated with varied density.展开更多
Some spectral characterizations of positive operators on Hilbert lattices are presented. The application of these results can yield some equivalent relations of an irreducible positive operator. Some related results f...Some spectral characterizations of positive operators on Hilbert lattices are presented. The application of these results can yield some equivalent relations of an irreducible positive operator. Some related results for positive operators on Hilbert lattice are also obtained.展开更多
The absorption coefficient of water is an important bio-optical parameter for water optics and water color remote sensing. However, scattering correction is essential to obtain accurate absorption coefficient values i...The absorption coefficient of water is an important bio-optical parameter for water optics and water color remote sensing. However, scattering correction is essential to obtain accurate absorption coefficient values in situ using the nine-wavelength absorption and attenuation meter AC9. Establishing the correction always fails in Case 2 water when the correction assumes zero absorption in the near-infrared(NIR) region and underestimates the absorption coefficient in the red region, which affect processes such as semi-analytical remote sensing inversion. In this study, the scattering contribution was evaluated by an exponential fitting approach using AC9 measurements at seven wavelengths(412, 440, 488, 510, 532, 555, and 715 nm) and by applying scattering correction. The correction was applied to representative in situ data of moderately turbid coastal water, highly turbid coastal water, eutrophic inland water, and turbid inland water. The results suggest that the absorption levels in the red and NIR regions are significantly higher than those obtained using standard scattering error correction procedures. Knowledge of the deviation between this method and the commonly used scattering correction methods will facilitate the evaluation of the effect on satellite remote sensing of water constituents and general optical research using different scatteringcorrection methods.展开更多
A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and t...A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and the PGF errors are much reduced in the computational space. In addition, the validity of reducing the PGF errors by this covariant method in the computational and physical space over steep terrain is investigated. First, the authors implement a set of idealized experiments of increasing terrain slope to compare the PGF errors of the covariant method and those of the classic method in the computational space. The results demonstrate that the PGF errors of the covariant method are consistently much-reduced, compared to those of the classic method. More importantly, the steeper the terrain, the greater the reduction in the ratio of the PGF errors via the covariant method. Next, the authors use geometric analysis to further investigate the PGF errors in the physical space, and the results illustrates that the PGF of the covariant method equals that of the classic method in the physical space; namely, the covariant method based on the non-orthogonal a-coordinate cannot reduce the PGF errors in the physical space. However, an orthogonal method can reduce the PGF errors in the physical space. Finally, a set of idealized experiments are carried out to validate the results obtained by the geometric analysis. These results indicate that the covariant method may improve the simulation of variables relevant to pressure, in addition to pressure itself, near steep terrain.展开更多
A mixed scheme based on Wavelet Transformation (WT) is proposed for image edge detection. The scheme combines the wavelet transform and traditional Sobel and LoG (Laplacian of Gaussian) operator edge-detection algorit...A mixed scheme based on Wavelet Transformation (WT) is proposed for image edge detection. The scheme combines the wavelet transform and traditional Sobel and LoG (Laplacian of Gaussian) operator edge-detection algorithms. The precise theory analysis is given to show that the wavelet transformation has an advantage for signal processing. Simulation results show that the new scheme is better than only using the Sobel or LoG methods. Complexity analysis is also given and the conclusion is acceptable, therefore the proposed scheme is effective for edge detection.展开更多
In this paper, starting from a function analytic in a neighborhood of the unit disk and based on Bessel functions, we construct a family of generalized multivariate sinc functions, which are radial and named radial Be...In this paper, starting from a function analytic in a neighborhood of the unit disk and based on Bessel functions, we construct a family of generalized multivariate sinc functions, which are radial and named radial Bessel-sinc (RBS) functions being time-frequency atoms with nonlinear phase. We obtain a recursive formula for the RBS functions in R d with d being odd. Based on the RBS function, a corresponding sampling theorem for a class of non-bandlimited signals is established. We investigate a class of radial functions and prove that each of these functions can be extended to become a monogenic function between two parallel planes, where the monogencity is taken to be of the Clifford analysis sense.展开更多
基金the National Natural Science Foundation of China (No. 10571162)the Natural Science Foundation of Zheji-ang Province, China (No. Y605181)
文摘There are some curved interfaces in ocean acoustic waveguides. To compute wave propagation along the range with some marching methods, a flattening of the internal interfaces and a transforming equation are needed. In this paper a local orthogonal coordinate transform and an equation transformation are constructed to flatten interfaces and change the Helmholtz equation as a solvable form. For a waveguide with a flat top, a fiat bottom and n curved interfaces, the coefficients of the transformed Helmholtz equation are given in a closed formulation which can be thought of as an extension of the formal work related to the equation transformation with two curved internal interfaces. In the transformed horizontally stratified waveguide, the one-way reformulation based on the Dirichlet-to-Neumann （DtN） map is then used to reduce the boundary value problem to an initial value problem. Numerical implementation of the resulting operator Riccati equation uses a large range step method to discretize the range variable and a truncated local eigenfunction expansion to approximate the operators. This method is particularly useful for solving long range wave propagation problems in slowly varying waveguides. Furthermore, the method can also be applied to wave propagation problems in acoustic waveguides associated with varied density.
基金Supported by the National Natural Science Foundation of China(19771056,10571113)
文摘Some spectral characterizations of positive operators on Hilbert lattices are presented. The application of these results can yield some equivalent relations of an irreducible positive operator. Some related results for positive operators on Hilbert lattice are also obtained.
基金Supported by the National Key Research and Development Program of China(Nos.2016YFB0501502,2016YFC1400903,2016YFB0500304)the National Natural Science Foundation of China(Nos.91638201,41276184,41325004,41471308,41571361)+1 种基金the High Resolution Earth Observation Systems of National Science and Technology Major Projects(No.41-Y20A31-9003-15/17)the Director Foundation of Institute of Remote Sensing and Digital Earth,Chinese Academy of Sciences(No.Y6SJ2100CX)
文摘The absorption coefficient of water is an important bio-optical parameter for water optics and water color remote sensing. However, scattering correction is essential to obtain accurate absorption coefficient values in situ using the nine-wavelength absorption and attenuation meter AC9. Establishing the correction always fails in Case 2 water when the correction assumes zero absorption in the near-infrared(NIR) region and underestimates the absorption coefficient in the red region, which affect processes such as semi-analytical remote sensing inversion. In this study, the scattering contribution was evaluated by an exponential fitting approach using AC9 measurements at seven wavelengths(412, 440, 488, 510, 532, 555, and 715 nm) and by applying scattering correction. The correction was applied to representative in situ data of moderately turbid coastal water, highly turbid coastal water, eutrophic inland water, and turbid inland water. The results suggest that the absorption levels in the red and NIR regions are significantly higher than those obtained using standard scattering error correction procedures. Knowledge of the deviation between this method and the commonly used scattering correction methods will facilitate the evaluation of the effect on satellite remote sensing of water constituents and general optical research using different scatteringcorrection methods.
基金supported by the National Basic Research Program of China(973 Program)[grant number 2015CB954102]the National Natural Science Foundation of China[grant number41305095],[grant number 41175064]
文摘A new approach is proposed to use the covariant scalar equations of the a-coordinate （the covariant method）, in which the pressure gradient force （PGF） has only one term in each horizontal momentum equation, and the PGF errors are much reduced in the computational space. In addition, the validity of reducing the PGF errors by this covariant method in the computational and physical space over steep terrain is investigated. First, the authors implement a set of idealized experiments of increasing terrain slope to compare the PGF errors of the covariant method and those of the classic method in the computational space. The results demonstrate that the PGF errors of the covariant method are consistently much-reduced, compared to those of the classic method. More importantly, the steeper the terrain, the greater the reduction in the ratio of the PGF errors via the covariant method. Next, the authors use geometric analysis to further investigate the PGF errors in the physical space, and the results illustrates that the PGF of the covariant method equals that of the classic method in the physical space; namely, the covariant method based on the non-orthogonal a-coordinate cannot reduce the PGF errors in the physical space. However, an orthogonal method can reduce the PGF errors in the physical space. Finally, a set of idealized experiments are carried out to validate the results obtained by the geometric analysis. These results indicate that the covariant method may improve the simulation of variables relevant to pressure, in addition to pressure itself, near steep terrain.
基金Supported by the National Defence 973 project(2002HS0604,2002HS0634)
文摘A mixed scheme based on Wavelet Transformation (WT) is proposed for image edge detection. The scheme combines the wavelet transform and traditional Sobel and LoG (Laplacian of Gaussian) operator edge-detection algorithms. The precise theory analysis is given to show that the wavelet transformation has an advantage for signal processing. Simulation results show that the new scheme is better than only using the Sobel or LoG methods. Complexity analysis is also given and the conclusion is acceptable, therefore the proposed scheme is effective for edge detection.
基金National Natural Science Foundation of China (Grant Nos. 61072126 and 11126343)Natural Science Foundation of Guangdong Province (Grant No. S2011010004986)+2 种基金Guangxi Natural Science Foundation (Grant No. 2013GXNSFBA019010)University of Macao (MYRG) MYRG 116(Y1-L3)-FST13-QTMacao Science and Technology Research Fund FDCT 098/2012/A3
文摘In this paper, starting from a function analytic in a neighborhood of the unit disk and based on Bessel functions, we construct a family of generalized multivariate sinc functions, which are radial and named radial Bessel-sinc (RBS) functions being time-frequency atoms with nonlinear phase. We obtain a recursive formula for the RBS functions in R d with d being odd. Based on the RBS function, a corresponding sampling theorem for a class of non-bandlimited signals is established. We investigate a class of radial functions and prove that each of these functions can be extended to become a monogenic function between two parallel planes, where the monogencity is taken to be of the Clifford analysis sense.
