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Algebraic Curve

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Renhong Wang – 1st expert on this subject based on the ideXlab platform

  • Nöther-type theorem of piecewise Algebraic Curves on triangulation
    Science China-mathematics, 2007
    Co-Authors: Renhong Wang

    Abstract:

    The piecewise Algebraic Curve is a kind generalization of the classical Algebraic Curve. Nother-type theorem of piecewise Algebraic Curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space. In this paper, using the properties of bivariate splines, the Nother-type theorem of piecewise Algebraic Curves on the arbitrary triangulation is presented.

  • the nother and riemann roch type theorems for piecewise Algebraic Curve
    Science China-mathematics, 2007
    Co-Authors: Renhong Wang

    Abstract:

    A piecewise Algebraic Curve is a Curve determined by the zero set of a bivariate spline function. In this paper, the Nother type theorems for Cµ piecewise Algebraic Curves are obtained. The theory of the linear series of sets of places on the piecewise Algebraic Curve is also established. In this theory, singular cycles are put into the linear series, and a complete series of the piecewise Algebraic Curves consists of all effective ordinary cycles in an equivalence class and all effective singular cycles which are equivalent specifically to any effective ordinary cycle in the equivalence class. This theory is a generalization of that of linear series of the Algebraic Curve. With this theory and the fundamental theory of multivariate splines on smoothing cofactors and global conformality conditions, and the results on the general expression of multivariate splines, we get a formula on the index, the order and the dimension of a complete series of the irreducible Cµ piecewise Algebraic Curves and the degree, the genus and the smoothness of the Curves, hence the Riemann-Roch type theorem of the Cµ piecewise Algebraic Curve is established.

  • Nöther-type theorem of piecewise Algebraic Curves
    Progress in Natural Science, 2004
    Co-Authors: Renhong Wang

    Abstract:

    Abstract The piecewise Algebraic Curve is a generalization of the classical Algebraic Curve. This paper describes the improvement of the Nother-type theorem of piecewise Algebraic Curves on the star region. Moreover, the Nother-type theorem of piecewise Algebraic Curves on the cross-cut partition is discussed.

Pawel Laskośgrabowski – 2nd expert on this subject based on the ideXlab platform

  • surprises in the ads Algebraic Curve constructions wilson loops and correlation functions
    Nuclear Physics, 2012
    Co-Authors: Romuald A Janik, Pawel Laskośgrabowski

    Abstract:

    Abstract The Algebraic Curve (finite-gap) classification of rotating string solutions was very important in the development of integrability through comparison with analogous structures at weak coupling. The classification was based on the analysis of monodromy around the closed string cylinder. In this paper we show that certain classical Wilson loop minimal surfaces corresponding to the null cusp and q q ¯ potential with trivial monodromy can, nevertheless, be described by appropriate Algebraic Curves. We also show how a correlation function of a circular Wilson loop with a local operator fits into this framework. The latter solution has identical monodromy to the pointlike BMN string and yet is significantly different.

Guangxing Zeng – 3rd expert on this subject based on the ideXlab platform

  • computing the asymptotes for a real plane Algebraic Curve
    Journal of Algebra, 2007
    Co-Authors: Guangxing Zeng

    Abstract:

    The purpose of this paper is to present an algorithm for computing all the asymptotes of a real plane Algebraic Curve. By this algorithm, all the asymptotes of a real plane Algebraic Curve may be represented via polynomial real root isolation.

  • Determination of the tangents for a real plane Algebraic Curve
    Journal of Symbolic Computation, 2006
    Co-Authors: Guangxing Zeng

    Abstract:

    Abstract The purpose of this paper is to present an algorithm for computing the tangents of a real plane Algebraic Curve. By this algorithm, all the slopes of the tangents to a real plane Algebraic Curve at a particular point may be accurately represented via polynomial real root isolation.