In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz ...In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.展开更多
A pneumatic launcher is theoretically investigated to study its natural transverse vibration in water. Considering the mass effect of the sealing cover, the launcher is simplified as a uniform cantilever beam with a t...A pneumatic launcher is theoretically investigated to study its natural transverse vibration in water. Considering the mass effect of the sealing cover, the launcher is simplified as a uniform cantilever beam with a top point mass. By introducing the boundary and continuity conditions into the motion equation, the natural frequency equation and the mode shape function are derived. An iterative calculation method for added mass is also presented using the velocity potential function to account for the mass effect of the fluid on the launcher. The first 2 order natural frequencies and mode shapes are discussed in external flow fields and both external and internal flow fields. The results show good agreement with both natural frequencies and mode shapes between the theoretical analysis and the FEM studies. Also, the added mass is found to decrease with the increase of the mode shape orders of the launcher. And because of the larger added mass in both the external and internal flow fields than that in only the external flow field, the corresponding natural frequencies of the former are relatively smaller.展开更多
Advances in quantum computers threaten to break public key cryptosystems such as RSA, ECC, and EIGamal on the hardness of factoring or taking a discrete logarithm, while no quantum algorithms are found to solve certai...Advances in quantum computers threaten to break public key cryptosystems such as RSA, ECC, and EIGamal on the hardness of factoring or taking a discrete logarithm, while no quantum algorithms are found to solve certain mathematical problems on non-commutative algebraic structures until now. In this background, Majid Khan et al.proposed two novel public-key encryption schemes based on large abelian subgroup of general linear group over a residue ring. In this paper we show that the two schemes are not secure. We present that they are vulnerable to a structural attack and that, it only requires polynomial time complexity to retrieve the message from associated public keys respectively. Then we conduct a detailed analysis on attack methods and show corresponding algorithmic description and efficiency analysis respectively. After that, we propose an improvement assisted to enhance Majid Khan's scheme. In addition, we discuss possible lines of future work.展开更多
文摘In this paper,we study real symmetric Toeplitz matrices commutable with tridiagonal matrices, present more detailed results than those in [1], and extend them to nonsymmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.
基金Foundation item： Supported by the National Natural Science Foundation of China （51379083） and the Specialized Research Fund for the Doctoral Program of Hiher Education （20120142110051）.
文摘A pneumatic launcher is theoretically investigated to study its natural transverse vibration in water. Considering the mass effect of the sealing cover, the launcher is simplified as a uniform cantilever beam with a top point mass. By introducing the boundary and continuity conditions into the motion equation, the natural frequency equation and the mode shape function are derived. An iterative calculation method for added mass is also presented using the velocity potential function to account for the mass effect of the fluid on the launcher. The first 2 order natural frequencies and mode shapes are discussed in external flow fields and both external and internal flow fields. The results show good agreement with both natural frequencies and mode shapes between the theoretical analysis and the FEM studies. Also, the added mass is found to decrease with the increase of the mode shape orders of the launcher. And because of the larger added mass in both the external and internal flow fields than that in only the external flow field, the corresponding natural frequencies of the former are relatively smaller.
基金supported in part by the National Natural Science Foundation of China(Grant Nos.61303212,61170080,61202386)the State Key Program of National Natural Science of China(Grant Nos.61332019,U1135004)+2 种基金the Major Research Plan of the National Natural Science Foundation of China(Grant No.91018008)Major State Basic Research Development Program of China(973 Program)(No.2014CB340600)the Hubei Natural Science Foundation of China(Grant Nos.2011CDB453,2014CFB440)
文摘Advances in quantum computers threaten to break public key cryptosystems such as RSA, ECC, and EIGamal on the hardness of factoring or taking a discrete logarithm, while no quantum algorithms are found to solve certain mathematical problems on non-commutative algebraic structures until now. In this background, Majid Khan et al.proposed two novel public-key encryption schemes based on large abelian subgroup of general linear group over a residue ring. In this paper we show that the two schemes are not secure. We present that they are vulnerable to a structural attack and that, it only requires polynomial time complexity to retrieve the message from associated public keys respectively. Then we conduct a detailed analysis on attack methods and show corresponding algorithmic description and efficiency analysis respectively. After that, we propose an improvement assisted to enhance Majid Khan's scheme. In addition, we discuss possible lines of future work.
