In the data encryption standard （DES） algorithm, there exist several bit-switching functions, including permutations, expansion, and permuted choices. They are generally presented in the form of matrixes and realize...In the data encryption standard （DES） algorithm, there exist several bit-switching functions, including permutations, expansion, and permuted choices. They are generally presented in the form of matrixes and realized by using table look-up technique in the implementation of the cryptosystem. This paper presents explicit formulas for the initial permutation IP, its inverse IP-1 , the expansion function E, and the permuted choice PC_1. It also gives the program realizations of these functions in C＋＋ applying these formulas. With the advantage of the omission of the storage space for these matrixes and the tedious inputs of tables in the implementations of DES, our experimental results shows that the explicit formulas are useful in some situations, such as wireless sensor networks where the memory capacity is limited, especially when the size of file for encrypting is not too large, preferably smaller than 256KB.展开更多
Based on the improved first order second moment method of the structural reliability, an explicit iteration algorithm is proposed, which can avoid solving structural performance function to obtain reliability index β...Based on the improved first order second moment method of the structural reliability, an explicit iteration algorithm is proposed, which can avoid solving structural performance function to obtain reliability index β and have simple calculation forms. Finally, the validity of the explicit iteration algorithm is illustrated through two examples by MATLAB programming.展开更多
In this paper, the dispersive long wave equation is studied by Lie symmetry group theory. Firstly, the Lie symmetries of this system are calculated. Secondly, one dimensional optimal systems of Lie algebra and all the...In this paper, the dispersive long wave equation is studied by Lie symmetry group theory. Firstly, the Lie symmetries of this system are calculated. Secondly, one dimensional optimal systems of Lie algebra and all the symmetry reductions are obtained. Finally, based on the power series method and the extended Tanh function method, some new explicit solutions of this system are constructed.展开更多
文摘模型预测控制(Model predictive control,MPC)具有很多优点,但用于智能汽车横摆稳定性控制时,由于其动力学模型的多约束和非线性问题,致使MPC优化算法复杂,难以实现足够短的控制周期和步长。为此,提出一种智能汽车横摆稳定性MPC的在线显式求解方法,使用泰勒展开将非线性模型预测控制(Nonlinear model predictive control,NMPC)转换为线性时变模型预测控制(Linear time-varying model predictive control,LTV-MPC)。再使用滚动调整的权重系数,将不等式约束优化转换为能直接显式求解的无约束优化,以避免多步迭代寻优、加快MPC求解速度。仿真试验结果表明,在保证相同控制效果前提下,所提出的显式解方法能使MPC的求解速度提高3~4倍,可显著提高智能汽车横摆稳定性MPC的实时性。
基金Supported by the National Natural Science Foundation of China (61272045)Natural Science Foundation of Outstanding Youth Team Project of Zhejiang Province (R1090138)Project of the State Key Laboratory of Information Security (Institute of Information Engineering, Chinese Academy of Sciences, Beijing)
文摘In the data encryption standard （DES） algorithm, there exist several bit-switching functions, including permutations, expansion, and permuted choices. They are generally presented in the form of matrixes and realized by using table look-up technique in the implementation of the cryptosystem. This paper presents explicit formulas for the initial permutation IP, its inverse IP-1 , the expansion function E, and the permuted choice PC_1. It also gives the program realizations of these functions in C＋＋ applying these formulas. With the advantage of the omission of the storage space for these matrixes and the tedious inputs of tables in the implementations of DES, our experimental results shows that the explicit formulas are useful in some situations, such as wireless sensor networks where the memory capacity is limited, especially when the size of file for encrypting is not too large, preferably smaller than 256KB.
文摘Based on the improved first order second moment method of the structural reliability, an explicit iteration algorithm is proposed, which can avoid solving structural performance function to obtain reliability index β and have simple calculation forms. Finally, the validity of the explicit iteration algorithm is illustrated through two examples by MATLAB programming.
文摘In this paper, the dispersive long wave equation is studied by Lie symmetry group theory. Firstly, the Lie symmetries of this system are calculated. Secondly, one dimensional optimal systems of Lie algebra and all the symmetry reductions are obtained. Finally, based on the power series method and the extended Tanh function method, some new explicit solutions of this system are constructed.
