In order to minimize the harm caused by the instability of a planing craft, a motion prediction model is essential. This paper analyzed the feasibility of using an MGM（1,N） model in grey system theory to predict pla...In order to minimize the harm caused by the instability of a planing craft, a motion prediction model is essential. This paper analyzed the feasibility of using an MGM（1,N） model in grey system theory to predict planing craft motion and carried out the numerical simulation experiment. According to the characteristics of planing craft motion, a recurrence formula was proposed of the parameter matrix of an MGMfl,N） model. Using this formula, data can be updated in real-time without increasing computational complexity significantly. The results of numerical simulation show that using an MGM（1,N） model to predict planing motion is feasible and useful for prediction. So the method proposed in this study can reflect the planing craft motion mechanism successfully, and has rational and effective functions of forecasting and analyzing trends.展开更多
The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estim...The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estimate,Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small.In the first part,the result of Li and Wan is improved.On the other hand,one of the important parameters of an error-correcting code is the dimension.In most cases,one can only get bounds for the dimension.In the second part,a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained.展开更多
Inspired by works of Masur-Minsky and Mahan Mj, we observe that the Hatcher-Thurston complex of a surface F is an interpolating complex between the pants complex and the curve complex, then we give a hierarchical stru...Inspired by works of Masur-Minsky and Mahan Mj, we observe that the Hatcher-Thurston complex of a surface F is an interpolating complex between the pants complex and the curve complex, then we give a hierarchical structure for the Hatcher-Thurston complex. By this hierarchical structure, we show a distance formula in the Hatcher-Thurston complex related to subsurfaces of positive genera. As a corollary, we show that the Hatcher-Thurston complex has one end for surface with genus at least three, the proof runs the same line as a result of Masur-Schleimer, the key tool is the distance formula.展开更多
基金Supported by the Foundation of State Key Laboratory of Autonomous Underwater Vehicle, Harbin Engineering Universitythe Fundamental Research Funds for the Central Universities (HEUCFL20101113)
文摘In order to minimize the harm caused by the instability of a planing craft, a motion prediction model is essential. This paper analyzed the feasibility of using an MGM（1,N） model in grey system theory to predict planing craft motion and carried out the numerical simulation experiment. According to the characteristics of planing craft motion, a recurrence formula was proposed of the parameter matrix of an MGMfl,N） model. Using this formula, data can be updated in real-time without increasing computational complexity significantly. The results of numerical simulation show that using an MGM（1,N） model to predict planing motion is feasible and useful for prediction. So the method proposed in this study can reflect the planing craft motion mechanism successfully, and has rational and effective functions of forecasting and analyzing trends.
基金Project supported by the National Natural Science Foundation of China (No.10990011)the Doctoral Program Foundation of Ministry of Education of China (No.20095134120001)the Sichuan Province Foundation of China (No. 09ZA087)
文摘The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estimate,Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small.In the first part,the result of Li and Wan is improved.On the other hand,one of the important parameters of an error-correcting code is the dimension.In most cases,one can only get bounds for the dimension.In the second part,a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained.
基金supported in part by RFDP 200802461001National Natural Science Foundation of China (Grant No. 10901038)
文摘Inspired by works of Masur-Minsky and Mahan Mj, we observe that the Hatcher-Thurston complex of a surface F is an interpolating complex between the pants complex and the curve complex, then we give a hierarchical structure for the Hatcher-Thurston complex. By this hierarchical structure, we show a distance formula in the Hatcher-Thurston complex related to subsurfaces of positive genera. As a corollary, we show that the Hatcher-Thurston complex has one end for surface with genus at least three, the proof runs the same line as a result of Masur-Schleimer, the key tool is the distance formula.
