For Riemann problem in n(n ≥ 3) dimensional(n-D) conservation laws, dimension of equations can be only reduced one dimension by applying self-similar approach, so transformed equations are at least two dimensional (2...For Riemann problem in n(n ≥ 3) dimensional(n-D) conservation laws, dimension of equations can be only reduced one dimension by applying self-similar approach, so transformed equations are at least two dimensional (2D) equations which are also very hard although some pioneer works have been done in references [1-3].展开更多
Surface electromyogram （EMG） signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers＇ right forearm flexor respectively in the process of forearm su...Surface electromyogram （EMG） signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers＇ right forearm flexor respectively in the process of forearm supination （FS） and forearm pronation （FP）.After the raw action surface EMG （ASEMG） signal was decomposed into several sub-signals with wavelet packet transform （WPT）,five fractal dimensions were respectively calculated from the raw signal and four sub-signals by the method based on fuzzy self-similarity.The results show that calculated from the sub-signal in the band 0 to 125 Hz,the fractal dimensions of FS ASEMG signals and FP ASEMG signals distributed in two different regions,and its error rate based on Bayes decision was no more than 2.26%.Therefore,the fractal dimension is an appropriate feature by which an FS ASEMG signal is distinguished from an FP ASEMG signal.展开更多
For any Pisot number β it is known that the set F（β） ={t ： limn→∞‖tβn‖ = 0} is countable, where ‖α‖ is the distance between a real number a and the set of integers. In this paper it is proved that every m...For any Pisot number β it is known that the set F（β） ={t ： limn→∞‖tβn‖ = 0} is countable, where ‖α‖ is the distance between a real number a and the set of integers. In this paper it is proved that every member in this set is of the form cβn, where n is a nonnegative integer and e is determined by a linear system of equations. Furthermore, for some self-similar measures μ associated with β, the limit at infinity of the Fourier transforms limn→μ（tβn）≠0 if and only if t is in a certain subset of F（β）. This generalizes a similar result of Huang and Strichartz.展开更多
The authors construct self-similar solutions for an N-dimensional transport equation,where the velocity is given by the Riezs transform.These solutions imply nonuniqueness of weak solution.In addition,self-similar sol...The authors construct self-similar solutions for an N-dimensional transport equation,where the velocity is given by the Riezs transform.These solutions imply nonuniqueness of weak solution.In addition,self-similar solution for a one-dimensional conservative equation involving the Hilbert transform is obtained.展开更多
基金Supported by the National Natural Science Foundation of China(No. 10001023), Huo Yingdong Fellowship(81004), Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, Natural Science Foundation of Guangdong(No. 000804) and Natural Science Foundation of Guangdong Education Bureau(No. 200030).
文摘For Riemann problem in n(n ≥ 3) dimensional(n-D) conservation laws, dimension of equations can be only reduced one dimension by applying self-similar approach, so transformed equations are at least two dimensional (2D) equations which are also very hard although some pioneer works have been done in references [1-3].
基金The National Natural Science Foundation of China(No.60171006)the National Basic Research Programof China (973 Pro-gram) (No.2005CB724303).
文摘Surface electromyogram （EMG） signals were identified by fractal dimension.Two patterns of surface EMG signals were acquired from 30 healthy volunteers＇ right forearm flexor respectively in the process of forearm supination （FS） and forearm pronation （FP）.After the raw action surface EMG （ASEMG） signal was decomposed into several sub-signals with wavelet packet transform （WPT）,five fractal dimensions were respectively calculated from the raw signal and four sub-signals by the method based on fuzzy self-similarity.The results show that calculated from the sub-signal in the band 0 to 125 Hz,the fractal dimensions of FS ASEMG signals and FP ASEMG signals distributed in two different regions,and its error rate based on Bayes decision was no more than 2.26%.Therefore,the fractal dimension is an appropriate feature by which an FS ASEMG signal is distinguished from an FP ASEMG signal.
文摘For any Pisot number β it is known that the set F（β） ={t ： limn→∞‖tβn‖ = 0} is countable, where ‖α‖ is the distance between a real number a and the set of integers. In this paper it is proved that every member in this set is of the form cβn, where n is a nonnegative integer and e is determined by a linear system of equations. Furthermore, for some self-similar measures μ associated with β, the limit at infinity of the Fourier transforms limn→μ（tβn）≠0 if and only if t is in a certain subset of F（β）. This generalizes a similar result of Huang and Strichartz.
基金Project supported by the MCINN (Spain) (No.MTM2008-03754)the ERC (No.StG-203138CDSIF)
文摘The authors construct self-similar solutions for an N-dimensional transport equation,where the velocity is given by the Riezs transform.These solutions imply nonuniqueness of weak solution.In addition,self-similar solution for a one-dimensional conservative equation involving the Hilbert transform is obtained.
