Dispersion relation matrices, with the screened Coulomb interaction between a charged dust particle and all other particles taken into account, are derived for waves in body centred cubic （bcc） and face centred cub...Dispersion relation matrices, with the screened Coulomb interaction between a charged dust particle and all other particles taken into account, are derived for waves in body centred cubic （bcc） and face centred cubic （fcc） lattices in three-dimensional strongly coupled complex plasma crystals separately. The matrices are then calculated in characteristic directions to obtain the longitudinal and transverse eigenmodes. The longitudinal and transverse waves for these cases are discussed separately.展开更多
The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techn...The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techniques. However, the application of this extended procedure is often hampered by its complexity in computation and by lack of some appropriate theory. In this paper, by use of the empirical processes we established a large sample theory for the robust PP estimators of the principal components and dispersion matrix.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant Nos 40731056, 10778613 and 10575018)the National Basic Research Program of China (Grant No 2008CB787103)
文摘Dispersion relation matrices, with the screened Coulomb interaction between a charged dust particle and all other particles taken into account, are derived for waves in body centred cubic （bcc） and face centred cubic （fcc） lattices in three-dimensional strongly coupled complex plasma crystals separately. The matrices are then calculated in characteristic directions to obtain the longitudinal and transverse eigenmodes. The longitudinal and transverse waves for these cases are discussed separately.
基金The researcb was partially supported by the National Natural Science Foundation of China under Grant No.19631040.
文摘The principal component analysis （PCA） is one of the most celebrated methods in analysing multivariate data. An effort of extending PCA is projection pursuit （PP）, a more general class of dimension-reduction techniques. However, the application of this extended procedure is often hampered by its complexity in computation and by lack of some appropriate theory. In this paper, by use of the empirical processes we established a large sample theory for the robust PP estimators of the principal components and dispersion matrix.
