one of the central questions in CAGD[1] is blending surfaces whichprovides the theoretical baJsis for the design technology of space surfaces. We willdiscuss the general theories and algorithms for multivariate hyperf...one of the central questions in CAGD[1] is blending surfaces whichprovides the theoretical baJsis for the design technology of space surfaces. We willdiscuss the general theories and algorithms for multivariate hyperfinite interpolationand their aPplication to the blending of implicit algebraic surfaces, and investigate theexistence conditions of hyperfinite interpolation. Based on Wu's theory on blendingimplicit algebraic surfaces, the problem of blending two quadric surfaces is studied.The conditions for the coefficient of gi under which there exists the cubic blendingsurface S(f) (the lowest degree) are obtained and the concrete expressions of f arepresented if they exist. These results can be applied directly to CAGD.展开更多
We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the resul...We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.展开更多
In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial di...In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations, we characterize all the Darboux invariants, the irreducible Darboux polynomials, the rational first integrals and the algebraic integrability of this system.展开更多
We study two-dimensional irreducible projective smooth algebraic semigroups. Minimal surface semigroups with Kodaira dimension at most one are partially classified. We also calculate the local dimension of the moduli ...We study two-dimensional irreducible projective smooth algebraic semigroups. Minimal surface semigroups with Kodaira dimension at most one are partially classified. We also calculate the local dimension of the moduli scheme parameterizing all algebraic semigroup laws on a fixed minimal surface.展开更多
We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its...We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.展开更多
In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the ...In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.展开更多
文摘one of the central questions in CAGD[1] is blending surfaces whichprovides the theoretical baJsis for the design technology of space surfaces. We willdiscuss the general theories and algorithms for multivariate hyperfinite interpolationand their aPplication to the blending of implicit algebraic surfaces, and investigate theexistence conditions of hyperfinite interpolation. Based on Wu's theory on blendingimplicit algebraic surfaces, the problem of blending two quadric surfaces is studied.The conditions for the coefficient of gi under which there exists the cubic blendingsurface S(f) (the lowest degree) are obtained and the concrete expressions of f arepresented if they exist. These results can be applied directly to CAGD.
文摘We give a local analytic characterization that a minimal surface in the 3-sphere S3 C R4 defined by an irreducible cubic polynomial is one of the Lawson＇s minimal tori. This provides an alternative proof of the result by Perdomo （Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 （2007）, 23 34）.
基金supported by the NNSF of China (11171191 and 11201266)
文摘In this paper, we study the invariant algebraic surfaces of a system, which generalizes the Lorenz system. Using the weight homogeneous polynomials and the method of characteristic curves for solving linear partial differential equations, we characterize all the Darboux invariants, the irreducible Darboux polynomials, the rational first integrals and the algebraic integrability of this system.
文摘We study two-dimensional irreducible projective smooth algebraic semigroups. Minimal surface semigroups with Kodaira dimension at most one are partially classified. We also calculate the local dimension of the moduli scheme parameterizing all algebraic semigroup laws on a fixed minimal surface.
基金partially supported by a MINECO-FEDER(Grant No.MTM2016-77278-P)a MINECO(Grant No.MTM2013-40998-P)+1 种基金an AGAUR(Grant No.2014SGR-568)partially supported by FCT/Portugal through UID/MAT/04459/2013
文摘We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.
基金This paper is partially supported by the National Fundamental Research 973 Program of China under Grant No.2004CB318000.
文摘In this paper, we present a proper reparametrization algorithm for rational ruled surfaces. That is, for an improper rational parametrization of a ruled surface, we construct a proper rational parametrization for the same surface. The algorithm consists of three steps. We first reparametrize the improper rational parametrization caused by improper supports. Then the improper rational parametrization is transformed to a new one which is proper in one of the parameters. Finally, the problem is reduced to the proper reparametrization of planar rational algebraic curves.
