We study the existence,uniqueness and Hlder regularity of the solution to a stochastic semilinear equation arising from 1-dimensional integro-differential scalar conservation laws.The equation is driven by double-para...We study the existence,uniqueness and Hlder regularity of the solution to a stochastic semilinear equation arising from 1-dimensional integro-differential scalar conservation laws.The equation is driven by double-parameter fractional noises.In addition,the existence and moment estimate are also obtained for the density of the law of such a solution.展开更多
In order to listen to brain activity as a piece of music, we proposed a scale-free brainwave music （SFBM） technology, which translates the scalp EEG into music notes according to the power law of both EEG and music....In order to listen to brain activity as a piece of music, we proposed a scale-free brainwave music （SFBM） technology, which translates the scalp EEG into music notes according to the power law of both EEG and music. In this paper, the methodology was further extended to chorus music of two channels from the two hemispheres. Firstly, EEG data from two channels symmetrically located on the left and fight hemispheres are translated into MIDI sequences by SFBM, respectively, where the EEG parameters modulate the pitch, duration and volume of each music note. Then, the two sequences are fiitered into a chorus of the Chinese pentatonic scale or the Western major scale. The resulted Chinese and Western music at different sleep stages illustrate distinct differences in harmony, and the music with Chinese pentatonic scale sounds more harmonious.展开更多
基金supported by Mathematical Tianyuan Foundation of China(Grant No.11226198)Priority Academic Program Development of Jiangsu Higher Education Institutions+1 种基金National Natural Science Foundation of China(Grant No.11171062)Innovation Program of Shanghai Municipal Education Commission(Grant No.12ZZ063)
文摘We study the existence,uniqueness and Hlder regularity of the solution to a stochastic semilinear equation arising from 1-dimensional integro-differential scalar conservation laws.The equation is driven by double-parameter fractional noises.In addition,the existence and moment estimate are also obtained for the density of the law of such a solution.
基金The Fundamental Research Funds for the Central Universities
文摘In order to listen to brain activity as a piece of music, we proposed a scale-free brainwave music （SFBM） technology, which translates the scalp EEG into music notes according to the power law of both EEG and music. In this paper, the methodology was further extended to chorus music of two channels from the two hemispheres. Firstly, EEG data from two channels symmetrically located on the left and fight hemispheres are translated into MIDI sequences by SFBM, respectively, where the EEG parameters modulate the pitch, duration and volume of each music note. Then, the two sequences are fiitered into a chorus of the Chinese pentatonic scale or the Western major scale. The resulted Chinese and Western music at different sleep stages illustrate distinct differences in harmony, and the music with Chinese pentatonic scale sounds more harmonious.
