The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invar...The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.展开更多
Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput...Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler's method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.展开更多
We construct a fermion analogue of the Fock representation of quantum toroidal algebra and construct the fermion representation of quantum toroidal algebra on the K-theory of Hilbert scheme.
文摘The explicit expressions for indecomposable representations of nine square-root Lie algebras of vector type, , are obtained on the space of universal enveloping algebra of two-state Heisenberg–Weyl algebra, the invariant subspaces and the quotient spaces. From Fock representations corresponding to these indecomposable representations, the inhomogeneous boson realizations of are given. The expectation values of in the angular momentum coherent states are calculated as well as the corresponding classical limits.
基金supported by the National Key Basic Research Project of China(No.2004CB318000)One Hundred Talent Project of the Chinese Academy of Sciences,the NSF of China(No.60225002,No.60533060)Doctorial Program of MOE of China and the 111 Project(No.B07033).
文摘Surface reconstruction from unorganized data points is a challenging problem in Computer Aided Design and Geometric Modeling. In this paper, we extend the mathematical model proposed by Juttler and Felis (Adv. Comput. Math., 17 (2002), pp. 135-152) based on tensor product algebraic spline surfaces from fixed meshes to adaptive meshes. We start with a tensor product algebraic B-spline surface defined on an initial mesh to fit the given data based on an optimization approach. By measuring the fitting errors over each cell of the mesh, we recursively insert new knots in cells over which the errors are larger than some given threshold, and construct a new algebraic spline surface to better fit the given data locally. The algorithm terminates when the error over each cell is less than the threshold. We provide some examples to demonstrate our algorithm and compare it with Juttler's method. Examples suggest that our method is effective and is able to produce reconstruction surfaces of high quality.
基金Supported by National Natural Science Foundation of China under Grant No.11031005Beijing Municipal Education Commission Foundation under Grant Nos.KZ201210028032 and KM201210028006
文摘We construct a fermion analogue of the Fock representation of quantum toroidal algebra and construct the fermion representation of quantum toroidal algebra on the K-theory of Hilbert scheme.