Let otherwise and F(x,y).be a continuous distribution function on R^2. Then there exist linear wavelet operators L_n(F,x,y)which are also distribution function and where the defining them mother wavelet is(x,y).These ...Let otherwise and F(x,y).be a continuous distribution function on R^2. Then there exist linear wavelet operators L_n(F,x,y)which are also distribution function and where the defining them mother wavelet is(x,y).These approximate F(x,y)in the supnorm.The degree of this approximation is estimated by establishing a Jackson type inequality.Furthermore we give generalizations for the case of a mother wavelet ≠,which is just any distribution function on R^2,also we extend these results in R^r,r>2.展开更多
In this paper, we extend the generalized multiresolution analysis （GMRA） to higher dimensional spaces. The GMRA is generalized from each ladder space expanded by a different scaling function with positive integer di...In this paper, we extend the generalized multiresolution analysis （GMRA） to higher dimensional spaces. The GMRA is generalized from each ladder space expanded by a different scaling function with positive integer dilation factor m ≥2. The n-d GMRA is discussed in orthogonal and bi-orthogonal cases. Then the optimal m-band wavelets are applied in processing the image datasets of the human body slices. The efficiency and superiority of the algorithm can be seen from the processing results.展开更多
Flexible skew thin plate is widely used in mechanical engineering,architectural engineering and structural engineering.High-precision analysis is very important for structural design and improvement.In this paper,the ...Flexible skew thin plate is widely used in mechanical engineering,architectural engineering and structural engineering.High-precision analysis is very important for structural design and improvement.In this paper,the multivariable wavelet finite element(MWFE)based on B-spline wavelet on the interval(BSWI)is constructed for flexible skew thin plate analysis.First,the finite element formulation is derived from multivariable generalized potential energy function.Then the generalized field variables are interpolated and calculated by BSWI.Different from the traditional wavelet finite element,the analysis precision can be improved because the generalized displacement and stress field variables are interpolated and calculated independently,the secondary calculation and the computational error are avoided.In order to verify the effectiveness of the constructed MWFE,several numerical examples are given in the end.展开更多
文摘Let otherwise and F(x,y).be a continuous distribution function on R^2. Then there exist linear wavelet operators L_n(F,x,y)which are also distribution function and where the defining them mother wavelet is(x,y).These approximate F(x,y)in the supnorm.The degree of this approximation is estimated by establishing a Jackson type inequality.Furthermore we give generalizations for the case of a mother wavelet ≠,which is just any distribution function on R^2,also we extend these results in R^r,r>2.
基金National High-Tech Research and Development Plan(2001AA231031)National Key Basic Research Plan(G1998030608)National Special R&D Plan for Olympic Games(2001BAg04B08).
文摘In this paper, we extend the generalized multiresolution analysis （GMRA） to higher dimensional spaces. The GMRA is generalized from each ladder space expanded by a different scaling function with positive integer dilation factor m ≥2. The n-d GMRA is discussed in orthogonal and bi-orthogonal cases. Then the optimal m-band wavelets are applied in processing the image datasets of the human body slices. The efficiency and superiority of the algorithm can be seen from the processing results.
基金supported by the National Natural Science Foundation of China(Grant No.51225501)the Fundamental Research Funds for the Central Universities+2 种基金the Project funded by China Postdoctoral Science Foundation(Grant No.2014M552432)the National Science and Technology Major Project of China(Grant No.2012ZX04002071)the Program for Changjiang Scholars and Innovative Research Team in University
文摘Flexible skew thin plate is widely used in mechanical engineering,architectural engineering and structural engineering.High-precision analysis is very important for structural design and improvement.In this paper,the multivariable wavelet finite element(MWFE)based on B-spline wavelet on the interval(BSWI)is constructed for flexible skew thin plate analysis.First,the finite element formulation is derived from multivariable generalized potential energy function.Then the generalized field variables are interpolated and calculated by BSWI.Different from the traditional wavelet finite element,the analysis precision can be improved because the generalized displacement and stress field variables are interpolated and calculated independently,the secondary calculation and the computational error are avoided.In order to verify the effectiveness of the constructed MWFE,several numerical examples are given in the end.
