The Experts below are selected from a list of 11919 Experts worldwide ranked by ideXlab platform
Renhong Wang - One of the best experts on this subject based on the ideXlab platform.
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Nöther-type theorem of piecewise Algebraic Curves on triangulation
Science China-mathematics, 2007Co-Authors: Renhong WangAbstract: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.
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the nother and riemann roch type theorems for piecewise Algebraic Curve
Science China-mathematics, 2007Co-Authors: Renhong WangAbstract: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.
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Nöther-type theorem of piecewise Algebraic Curves
Progress in Natural Science, 2004Co-Authors: Renhong WangAbstract: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.
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Cayley-Bacharach theorem of piecewise Algebraic Curves
Journal of Computational and Applied Mathematics, 2004Co-Authors: Renhong WangAbstract:The piecewise Algebraic Curve, determined by a bivariate spline function, is a generalization of the classical Algebraic Curve. In this paper, by using Bezout's theorem and Nother-type theorem of piecewise Algebraic Curves, the Cayley-Bacharach theorem and Hilbert function of C0 piecewise Algebraic Curves are presented.
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estimation of the bezout number for piecewise Algebraic Curve
Science China-mathematics, 2003Co-Authors: Renhong Wang, Zhiqiang XuAbstract:A piecewise Algebraic Curve is a Curve determined by the zero set of a bivariate spline function. In this paper, a conjecture on triangulation is confirmed. The relation between the piecewise linear Algebraic Curve and four-color conjecture is also presented. By Morgan-Scott triangulation, we will show the instability of Bezout number of piecewise Algebraic Curves. By using the combinatorial optimization method, an upper bound of the Bezout number defined as the maximum finite number of intersection points of two piecewise Algebraic Curves is presented.
Pawel Laskośgrabowski - One of the best experts on this subject based on the ideXlab platform.
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surprises in the ads Algebraic Curve constructions wilson loops and correlation functions
Nuclear Physics, 2012Co-Authors: Romuald A Janik, Pawel LaskośgrabowskiAbstract: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 - One of the best experts on this subject based on the ideXlab platform.
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computing the asymptotes for a real plane Algebraic Curve
Journal of Algebra, 2007Co-Authors: Guangxing ZengAbstract: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.
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Determination of the tangents for a real plane Algebraic Curve
Journal of Symbolic Computation, 2006Co-Authors: Guangxing ZengAbstract: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.
Romuald A Janik - One of the best experts on this subject based on the ideXlab platform.
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surprises in the ads Algebraic Curve constructions wilson loops and correlation functions
Nuclear Physics, 2012Co-Authors: Romuald A Janik, Pawel LaskośgrabowskiAbstract: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.
Guoliang Xu - One of the best experts on this subject based on the ideXlab platform.
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regular Algebraic Curve segments iii applications in interactive design and data fitting
Computer Aided Geometric Design, 2001Co-Authors: Chandrajit L Bajaj, Guoliang XuAbstract:In this paper (part three of the trilogy) we use low degree G 1 and G 2 continuous regular Algebraic spline Curves defined within parallelograms, to interpolate an ordered set of data points in the plane. We explicitly characterize Curve families whose members have the required interpolating properties and possess a minimal number of inflection points. The regular Algebraic spline Curves considered here have many attractive features: They are easy to construct. There exist convenient geometric control handles to locally modify the shape of the Curve. The error of the approximation is controllable. Since the spline Curve is always inside the parallelogram, the error of the fit is bounded by the size of the parallelogram. The spline Curve can be rapidly displayed, even though the Algebraic Curve segments are implicitly defined. 2001 Elsevier Science B.V. All rights reserved.
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regular Algebraic Curve segments ii interpolation and approximation
Computer Aided Geometric Design, 2000Co-Authors: Guoliang Xu, Chandrajit L BajajAbstract:Abstract In this paper (part two of the trilogy) we introduce three classes of reduced form D -regular Algebraic Curve splines and use them for interpolation and approximation of various Algebraic Curves. Explicit formulas for interpolation and approximation are also given in some low degree cases.
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regular Algebraic Curve segments i definitions and characteristics
Computer Aided Geometric Design, 2000Co-Authors: Chandrajit L Bajaj, Guoliang XuAbstract:Abstract In this paper (part one of a trilogy), we introduce the concept of a discriminating family of regular Algebraic Curves (real, nonsingular and connected). Several discriminating families are obtained which yield different characterizations of the Bernstein–Bezier (BB) bivariate polynomials over the plane triangle and the quadrilateral domain such that their zero contours are smooth and connected. These regular Curve segments in BB basis can be smoothly joined together to form Algebraic Curve splines or A-splines. Algorithms for the efficient graphics display of these new A-spline families are also provided.
