In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superi...In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superior to those of approximation by polynomial operators and by expansions of classical orthogonal series.展开更多
In this paper the asymptotic behavior of Gibbs function for a class of M-band wavelet expansions is given. In particular, the Daubechies’ wavelets are included in this class.
It is well known that the Walsh-Fourier expansion of a function from the-block space (?)([0,1)), 1< q≤∞, converges pointwise a. e. We prove that the same result is true for the expansion of a function from (?) in...It is well known that the Walsh-Fourier expansion of a function from the-block space (?)([0,1)), 1< q≤∞, converges pointwise a. e. We prove that the same result is true for the expansion of a function from (?) in certain periodized smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1<p<∞. converges in norm and pointwise almost everywhere.展开更多
In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield...In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reprodueing identities （not necessary coming from a frame）.展开更多
The optimal attitude control problem of spacecraft during its solar arrays stretching process is discussed in the present paper. By using the theory of wavelet analysis in control algorithm, the discrete orthonormal w...The optimal attitude control problem of spacecraft during its solar arrays stretching process is discussed in the present paper. By using the theory of wavelet analysis in control algorithm, the discrete orthonormal wavelet function is introduced into: the optimal control problem, the method of wavelet expansion is substituted for the classical Fourier basic function. An optimal control algorithm based on wavelet analysis is proposed. The effectiveness of the wavelet expansion approach is shown by numerical simulation.展开更多
We consider expansions of the type arising from Wilson bases. We characterize such expansions for L^2（R）. As an application, we see that such an expansion must be orthonormal, in contrast to the case of wavelet expa...We consider expansions of the type arising from Wilson bases. We characterize such expansions for L^2（R）. As an application, we see that such an expansion must be orthonormal, in contrast to the case of wavelet expansions generated by translations and dilation.展开更多
Acoustic scattering cross sections of smart furtive obstacles are studied and discussed.A smart furtive obstacle is an obstacle that,when hit by an incoming field,avoids detection through the use of a pressure current...Acoustic scattering cross sections of smart furtive obstacles are studied and discussed.A smart furtive obstacle is an obstacle that,when hit by an incoming field,avoids detection through the use of a pressure current acting on its boundary.A highly parallelizable algorithm for computing the acoustic scattering cross section of smart obstacles is developed.As a case study,this algorithm is applied to the(acoustic)scattering cross section of a"smart"(furtive)simplified version of the NASA space shuttle when hit by incoming time-harmonic plane waves,the wavelengths of which are small compared to the characteristic dimensions of the shuttle.The solution to this numerically challenging scattering problem requires the solution of systems of linear equations with many unknowns and equations.Due to the sparsity of these systems of equations,they can be stored and solved using affordable computing resources.A cross section analysis of the simplified NASA space shuttle highlights three findings:i)the smart furtive obstacle reduces the magnitude of its cross section compared to the cross section of a corresponding"passive"obstacle;ii)several wave propagation directions fail to satisfactorily respond to the smart strategy of the obstacle;iii)satisfactory furtive effects along all directions may only be obtained by using a pressure current of considerable magnitude.Numerical experiments and virtual reality applications can be found at the website:http://www.ceri.uniroma1.it/ceri/zirilli/w7.展开更多
基金This work is supported by the Natural Science Foundation of Zhejiang,PR China.
文摘In this paper we estimate the degree of approximation of wavelet expansions. Our result shows that the degree has the exponential decay for function f(x)∈L2 continuous in a finite interval (a, b) which is much superior to those of approximation by polynomial operators and by expansions of classical orthogonal series.
基金The authors are partially supported by the Chinese National Natural Science Foundation(19571972)the Key Project Foundation(69735020)the Zhejiang Provincial Science Foundation of China(196083)
文摘In this paper the asymptotic behavior of Gibbs function for a class of M-band wavelet expansions is given. In particular, the Daubechies’ wavelets are included in this class.
文摘It is well known that the Walsh-Fourier expansion of a function from the-block space (?)([0,1)), 1< q≤∞, converges pointwise a. e. We prove that the same result is true for the expansion of a function from (?) in certain periodized smooth periodic non-stationary wavelet packets bases based on the Haar filters. We also consider wavelet packets based on the Shannon filters and show that the expansion of Lp-functions, 1<p<∞. converges in norm and pointwise almost everywhere.
基金This work is partially financed by NSC under 87-2115-M277-001.
文摘In this paper, we give necessary and sufficient conditions for two families of Gabor functions of a certain type to yield a reproducing identity on L^2（R^n）. As applications, we characterize when such families yield orthonormal or bi-orthogonal expansions. We also obtain a generalization of the Balian-Low theorem for general reprodueing identities （not necessary coming from a frame）.
基金the National Natural Science Foundation of China.
文摘The optimal attitude control problem of spacecraft during its solar arrays stretching process is discussed in the present paper. By using the theory of wavelet analysis in control algorithm, the discrete orthonormal wavelet function is introduced into: the optimal control problem, the method of wavelet expansion is substituted for the classical Fourier basic function. An optimal control algorithm based on wavelet analysis is proposed. The effectiveness of the wavelet expansion approach is shown by numerical simulation.
基金Supported by National Natural Science Foundation of China(Grant Nos.10671062,11071065 and 11171306)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20094306110004)Hu’nan Provincial Natural Science Foundation of China(Grant No.06JJ5012)
文摘In this paper, a new result on pointwise convergence of wavelets of generalized Shannon type is proved, which improves a theorem established by Zayed.
文摘We consider expansions of the type arising from Wilson bases. We characterize such expansions for L^2（R）. As an application, we see that such an expansion must be orthonormal, in contrast to the case of wavelet expansions generated by translations and dilation.
基金the DEISA Consortium(www.deisa.eu),co-funded through the EU FP6 project RI-031513 and the FP7 project RI-222919,for support within the DEISA Extreme Computing Initiative.
文摘Acoustic scattering cross sections of smart furtive obstacles are studied and discussed.A smart furtive obstacle is an obstacle that,when hit by an incoming field,avoids detection through the use of a pressure current acting on its boundary.A highly parallelizable algorithm for computing the acoustic scattering cross section of smart obstacles is developed.As a case study,this algorithm is applied to the(acoustic)scattering cross section of a"smart"(furtive)simplified version of the NASA space shuttle when hit by incoming time-harmonic plane waves,the wavelengths of which are small compared to the characteristic dimensions of the shuttle.The solution to this numerically challenging scattering problem requires the solution of systems of linear equations with many unknowns and equations.Due to the sparsity of these systems of equations,they can be stored and solved using affordable computing resources.A cross section analysis of the simplified NASA space shuttle highlights three findings:i)the smart furtive obstacle reduces the magnitude of its cross section compared to the cross section of a corresponding"passive"obstacle;ii)several wave propagation directions fail to satisfactorily respond to the smart strategy of the obstacle;iii)satisfactory furtive effects along all directions may only be obtained by using a pressure current of considerable magnitude.Numerical experiments and virtual reality applications can be found at the website:http://www.ceri.uniroma1.it/ceri/zirilli/w7.
