A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyva...A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyvalues of the shuffled image according to the changed chaotic values of the same position between the above nonlinearchaotic sequence and the sorted chaotic sequence.The experimental results demonstrate that the image encryptionscheme based on a shuffling map shows advantages of large key space and high-level security.Compared with someencryption algorithms,the suggested encryption scheme is more secure.展开更多
In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arb...In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.展开更多
Ramanujan sums （RS） and their Fourier transforms have attracted more and more attention in signal processing in recent years. Due to their non-periodic and non-uniform spectrum, RS are widely used in low-frequency n...Ramanujan sums （RS） and their Fourier transforms have attracted more and more attention in signal processing in recent years. Due to their non-periodic and non-uniform spectrum, RS are widely used in low-frequency noise processing, Doppler spectrum estimation and time-frequency analysis. However, the traditional method for calculating RS values is rather complex since it requires two numbers＇ factorization in two arithmetic functions. For a length-n vector, its Ramanujan-Fourier transform usually involves a series of RS values which will occupy O（n2） memory units. Thus, in this paper an approach based on prime-composition is proposed to reduce the complexity of RS calculation to O（n）. Meanwhile, the complexity of Ramanujan-Fourier transform can be further reduced from O（n2） to O（n In（In（n））） .展开更多
基金Supported by Research Fond for the Doctoral of Higher Education of China,the Hunan Natural Science Foundation under Grant No.05JJ30121the Scientific Research Fund of Hunan Provincial Education Department under Grant No.08B011Educational Research Fund of Hunan Provincial Education Department under Grant No.09C013
文摘A new image encryption approach is proposed.First,a sort transformation based on nonlinear chaoticalgorithm is used to shuffle the positions of image pixels.Then the states of hyper-chaos are used to change the greyvalues of the shuffled image according to the changed chaotic values of the same position between the above nonlinearchaotic sequence and the sorted chaotic sequence.The experimental results demonstrate that the image encryptionscheme based on a shuffling map shows advantages of large key space and high-level security.Compared with someencryption algorithms,the suggested encryption scheme is more secure.
基金This work was supported by the National Basic Research Program of China （No.2013CB922200）, the National Natural Science Foundation of China （No.21222308, No.21103187, and No.21133006）, the Chinese Academy of Sciences, and the Key Research Program of the Chinese Academy of Sciences.
文摘In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.
基金Supported by the National Natural Science Foundation of China(No.61071070)
文摘Ramanujan sums （RS） and their Fourier transforms have attracted more and more attention in signal processing in recent years. Due to their non-periodic and non-uniform spectrum, RS are widely used in low-frequency noise processing, Doppler spectrum estimation and time-frequency analysis. However, the traditional method for calculating RS values is rather complex since it requires two numbers＇ factorization in two arithmetic functions. For a length-n vector, its Ramanujan-Fourier transform usually involves a series of RS values which will occupy O（n2） memory units. Thus, in this paper an approach based on prime-composition is proposed to reduce the complexity of RS calculation to O（n）. Meanwhile, the complexity of Ramanujan-Fourier transform can be further reduced from O（n2） to O（n In（In（n））） .
