A facile encryption way was successfully applied to the holographic optical encryption system with high speed,multidimensionality,and high capacity,which provided a better security solution for underwater communicatio...A facile encryption way was successfully applied to the holographic optical encryption system with high speed,multidimensionality,and high capacity,which provided a better security solution for underwater communication.The reconstructed optical security system for information transmission was based on wavelengthλand focal length f that were keys to encryption and decryption.To finish the secure data transmission(λ,f)between sender and receiver,an extended Rivest-Shamir-Adleman(ERSA)algorithm for the encryption was achieved based on three-dimension quaternion function.Therein,the Pollard’s rho method was used for the evaluation and comparison of RSA and ERSA algorithms.The results demonstrate that the message encrypted by the ERSA algorithm has better security than that by RSA algorithm in the face of unpredictability and complexity of information transmission on the unsecure acoustic channel.展开更多
t Let f（z） be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af（n） be the nth normalized Fourier coefficient of f（z）. Suppose that L（sym2f, s） is the symmetric square L-functio...t Let f（z） be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af（n） be the nth normalized Fourier coefficient of f（z）. Suppose that L（sym2f, s） is the symmetric square L-function associated with f（z）, and Asym2f（n） de- notes the nth coefficient L（sym2f, s）. In this paper, it is proved that where P2 （t） is a polynomial in t of degree 2. Similarly, it is obtained that where P2（t） is a polynomial in t of degree 2.展开更多
The Fourier transform for homogeneous vector bundles over quaternion unit disk is studied, and the corresponding inversion formula and Plancherel formula are established.
Building on the pioneering work of Jean-Marie Andre and working in the laboratory he founded, the authors have developed a code called FT-1D to make Hartree-Fock electronic structure computations for stereoregular pol...Building on the pioneering work of Jean-Marie Andre and working in the laboratory he founded, the authors have developed a code called FT-1D to make Hartree-Fock electronic structure computations for stereoregular polymers using Ewald-type con- vergence acceleration methods. That code also takes full advantage of all line-group symmetries to calculate only the minimal set of two-electron integrals and to optimize the computation of the Fock matrix. The present communication reports a bench- mark study of the FT-1D code using polytetrafluoroethylene （PTFE） as a test case. Our results not only confirm the algorith- mic correctness of the code through agreement with other studies where they are applicable, but also show that the use of con- vergence acceleration enables accurate results to be obtained in situations where other widely-used codes （e.g., PLH and Crys- tal） fail. It is also found that full attention to the line-group symmetry of the PTFE polymer leads to an increase of between one and two orders of magnitude in the speed of computation. The new code can therefore be viewed as extending the range of electronic-structure computations for stereoregular polymers beyond the present scope of the successful and valuable code Crystal.展开更多
基金supported by Young Academic Leaders Program of Taiyuan Institute of Technology(No.2022XS06)Scientific Research Funding Project of Taiyuan Institute of Technology(Nos.2022LJ028,2022KJ103).
文摘A facile encryption way was successfully applied to the holographic optical encryption system with high speed,multidimensionality,and high capacity,which provided a better security solution for underwater communication.The reconstructed optical security system for information transmission was based on wavelengthλand focal length f that were keys to encryption and decryption.To finish the secure data transmission(λ,f)between sender and receiver,an extended Rivest-Shamir-Adleman(ERSA)algorithm for the encryption was achieved based on three-dimension quaternion function.Therein,the Pollard’s rho method was used for the evaluation and comparison of RSA and ERSA algorithms.The results demonstrate that the message encrypted by the ERSA algorithm has better security than that by RSA algorithm in the face of unpredictability and complexity of information transmission on the unsecure acoustic channel.
基金Project supported by the National Natural Science Foundation of China(Nos.10971119,11101249)the Shandong Provincial Natural Science Foundation of China(No.ZR2009AQ007)
文摘t Let f（z） be a holomorphic Hecke eigencuspform of weight k for the full mod- ular group. Let Af（n） be the nth normalized Fourier coefficient of f（z）. Suppose that L（sym2f, s） is the symmetric square L-function associated with f（z）, and Asym2f（n） de- notes the nth coefficient L（sym2f, s）. In this paper, it is proved that where P2 （t） is a polynomial in t of degree 2. Similarly, it is obtained that where P2（t） is a polynomial in t of degree 2.
文摘The Fourier transform for homogeneous vector bundles over quaternion unit disk is studied, and the corresponding inversion formula and Plancherel formula are established.
基金FEH was supported by U.S.National Science Foundation Grant PHY-0601758Part of this research has been funded by BELSPO(IAP P7/05 network"Functional Supramolecular Systems")+1 种基金The calculations were performed on the computing facilities of the Consortium deséquipements de Calcul Intensif(CéCI),in particular those of the Plateforme Technologique de Calcul Intensif(PTCI)installed in the University of Namur,for which we gratefully acknowledge financial support of the FNRS-FRFC(Conventions No.2.4.617.07.F and 2.5020.11)the University of Namur
文摘Building on the pioneering work of Jean-Marie Andre and working in the laboratory he founded, the authors have developed a code called FT-1D to make Hartree-Fock electronic structure computations for stereoregular polymers using Ewald-type con- vergence acceleration methods. That code also takes full advantage of all line-group symmetries to calculate only the minimal set of two-electron integrals and to optimize the computation of the Fock matrix. The present communication reports a bench- mark study of the FT-1D code using polytetrafluoroethylene （PTFE） as a test case. Our results not only confirm the algorith- mic correctness of the code through agreement with other studies where they are applicable, but also show that the use of con- vergence acceleration enables accurate results to be obtained in situations where other widely-used codes （e.g., PLH and Crys- tal） fail. It is also found that full attention to the line-group symmetry of the PTFE polymer leads to an increase of between one and two orders of magnitude in the speed of computation. The new code can therefore be viewed as extending the range of electronic-structure computations for stereoregular polymers beyond the present scope of the successful and valuable code Crystal.
