The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the h...The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.展开更多
We propose a simple gradation representation method using a binary-weighted computer-generated hologram（CGH） to be displayed on a high-speed spatial light modulator that can be controlled by the pulse-width modulati...We propose a simple gradation representation method using a binary-weighted computer-generated hologram（CGH） to be displayed on a high-speed spatial light modulator that can be controlled by the pulse-width modulation technique. The proposed method uses multiple bit planes comprising binary-weighted CGHs with various pulse widths. The object points of a three-dimensional（3D） object are assigned to multiple bit planes according to their gray levels. The bit planes are sequentially displayed in a time-division-multiplexed manner.Consequently, the proposed method realizes a gradation representation of a reconstructed 3D object.展开更多
基金The Natural Science Foundation of Jiangsu Province(No.BK2012736)the Natural Science Foundation of Chuzhou University(No.2010kj006Z)
文摘The linear operations of the equivalent classes of crossed modules of Lie color algebras are studied. The set of the equivalent classes of crossed modules is proved to be a vector space, which is isomorphic with the homogeneous components of degree zero of the third cohomology group of Lie color algebras. As an application of this theory, the crossed modules of Witt type Lie color algebras is described, and the result is proved that there is only one equivalent class of the crossed modules of Witt type Lie color algebras when the abelian group Г is equal to Г＋. Finally, for a Witt type Lie color algebra, the classification of its crossed modules is obtained by the isomorphism between the third cohomology group and the crossed modules.
基金supported by the Japan Society for the Promotion of Science through a Grantin-Aid for Scientific Research(C)15K00153+1 种基金a Grant-in-Aid for Scientific Research(A)25240015
文摘We propose a simple gradation representation method using a binary-weighted computer-generated hologram（CGH） to be displayed on a high-speed spatial light modulator that can be controlled by the pulse-width modulation technique. The proposed method uses multiple bit planes comprising binary-weighted CGHs with various pulse widths. The object points of a three-dimensional（3D） object are assigned to multiple bit planes according to their gray levels. The bit planes are sequentially displayed in a time-division-multiplexed manner.Consequently, the proposed method realizes a gradation representation of a reconstructed 3D object.
