IN this note the infinite-dimensional Lie superalgebras of Cartan type X(m,n)(X=W,S,H or K)over field F of prime characteristic are constructed.Then the second class of finite-dimensional Lie superalgebras of Cartan t...IN this note the infinite-dimensional Lie superalgebras of Cartan type X(m,n)(X=W,S,H or K)over field F of prime characteristic are constructed.Then the second class of finite-dimensional Lie superalgebras of Cartan type over F is defined.Their simplicity and re-strictability are discussed.Finally a conjecture about classification of the展开更多
Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the...An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the structures of such zero-sets which imply inparticular,the unique decomposition of an algebraic differential variety into its irreduciblecomponents.These formulas will find applications in various directions including mechanicaltheorem-proving of differential geometries.展开更多
We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresp...We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are constructed and expressed by the inner and outer operators. This expression combined geometrics of different dimensions and metric relations. We present the structure of the framework, data structure design, and the data storage, editing and updating mechanisms of the proposed 3D GIS data model. 3D GIS geometric and topological analyses are performed by CGA metric, geometric and topological operators using an object-oriented approach. Demonstrations with 3D residence district data suggest that our 3D data model expresses effectively geometric objects in different dimensions, which supports computation of both geometric and topological relations. The clear and effective expression and computation structure has the potential to support complex 3D GIS analysis, and spatio-temporal analysis.展开更多
In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary tr...In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.展开更多
A Kalman filter used in strapdown AHRS (Attitude Heading Reference System) based on micro machined inertial sensors is introduced. The composition and principle of the system are described. The attitude algorithm and ...A Kalman filter used in strapdown AHRS (Attitude Heading Reference System) based on micro machined inertial sensors is introduced. The composition and principle of the system are described. The attitude algorithm and error model of the system are derived based on the quaternion formulation. The real time quaternion based Kalman filter is designed. Simulation results show that accuracy of the system is better than 0.04 degree without disturbance of lateral acceleration and reduced to 0.44 degree with l...展开更多
Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz ...Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili.展开更多
文摘IN this note the infinite-dimensional Lie superalgebras of Cartan type X(m,n)(X=W,S,H or K)over field F of prime characteristic are constructed.Then the second class of finite-dimensional Lie superalgebras of Cartan type over F is defined.Their simplicity and re-strictability are discussed.Finally a conjecture about classification of the
文摘Let F be a field and char F = p > 3. In this paper the derivation algebras of Lie superalgebras W and S of Cartan-type over F are determined by the calculating method.
文摘An algebraic differential variety is defined as the zero-set of a differentialpolynomial set,and algebraic differential geometry is devoted to the study of such varieties.We give various decomposition formulas for the structures of such zero-sets which imply inparticular,the unique decomposition of an algebraic differential variety into its irreduciblecomponents.These formulas will find applications in various directions including mechanicaltheorem-proving of differential geometries.
基金supported by National High Technology R & D Program of China (Grant No. 2009AA12Z205)Key Project of National Natural Science Foundation of China (Grant No. 40730527)National Natural Science Foundation of China (Grant No. 41001224)
文摘We propose a new Geographic Information System (GIS) three-dimensional (3D) data model based on conformal geometric algebra (CGA). In this approach, geographic objects of different dimensions are mapped to the corresponding basic elements (blades) in Clifford algebra, and the expressions of multi-dimensional objects are unified without losing their geometric meaning. Geometric and topologic computations are also processed in a clear and coordinates-free way. Under the CGA framework, basic geometrics are constructed and expressed by the inner and outer operators. This expression combined geometrics of different dimensions and metric relations. We present the structure of the framework, data structure design, and the data storage, editing and updating mechanisms of the proposed 3D GIS data model. 3D GIS geometric and topological analyses are performed by CGA metric, geometric and topological operators using an object-oriented approach. Demonstrations with 3D residence district data suggest that our 3D data model expresses effectively geometric objects in different dimensions, which supports computation of both geometric and topological relations. The clear and effective expression and computation structure has the potential to support complex 3D GIS analysis, and spatio-temporal analysis.
文摘In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are considered. It is proved that, for any Lie algebra W of generalized Witt type, all Lie bialgebras on W are the coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group H1(W, W(?)W) is trivial.
文摘A Kalman filter used in strapdown AHRS (Attitude Heading Reference System) based on micro machined inertial sensors is introduced. The composition and principle of the system are described. The attitude algorithm and error model of the system are derived based on the quaternion formulation. The real time quaternion based Kalman filter is designed. Simulation results show that accuracy of the system is better than 0.04 degree without disturbance of lateral acceleration and reduced to 0.44 degree with l...
基金Supported by National Natural Science Foundation of China （Grant Nos. 10825101, 11047030） and Natural Science Foundation of He＇nan Provincial Education Department （Grant No. 2010Bl10003）
文摘Hom-Leibniz algebra is a natural generalization of Leibniz algebras and Hom-Lie algebras. In this paper, we develop some structure theory （such as （co）homology groups, universal central extensions） of Hom-Leibniz algebras based on some works of Loday and Pirashvili.
