Showing papers on "Quintic function published in 1992"
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TL;DR: In this article, the authors give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold, using the interpretation of Yukawa couplings in terms of variations of Hodge structure and a new $q$-expansion principle for functions on the moduli space of Calabi-Yau manifolds.
Abstract: We give a mathematical account of a recent string theory calculation which predicts the number of rational curves on the generic quintic threefold. Our account involves the interpretation of Yukawa couplings in terms of variations of Hodge structure, a new $q$-expansion principle for functions on the moduli space of Calabi-Yau manifolds, and the ``mirror symmetry'' phenomenon recently observed by string theorists.
148 citations
TL;DR: Part I. Curve Design: Properties of Minimal Energy Splines G. Brunnett Minimal energy splines with Various End Constraints and Algorithms for Geometric spline Curves and Non-Tensor Product Surfaces.
Abstract: Part I. Curve Design: Properties of Minimal Energy Splines G. Brunnett Minimal Energy splines with Various End Constraints E. Jou and W. Han Interval Weighted Tau- splines D. Lasser and H. Hagen Curve and surface Interpolation using Quintic Weight Tau-splines D. Neuser Weighted splines Based on Piecewise Polynomial Weighted Functions K. Salkauskas Algorithms for Geometric spline Curves M. Eck On the Problem of Determining the distance Between parametric curves F. Fritsch and G. Nielson Part II. Non-Tensor Product Surfaces: A survey of scattered Data Fitting Using Triangular Interpolants T. De Rose Free-form surfaces from Partial Differential Equations M. I. G. Bloor and M. J. Wilson Modeling with Box spline surfaces M. Daehlen.
87 citations
40 citations
TL;DR: In this paper, the stability of the nonlinear cubic-quintic Schrodinger equation was studied using collision simulations and a single value and a bistable region of the high order parameter were studied and quasi soliton behaviour was found.
35 citations
TL;DR: A C 2 piecewise quintic interpolating scheme is described for values of position, gradient and Hessian at scattered points in two variables on the triangulation with minimal split and an open problem is solved.
22 citations
TL;DR: This algorithm is based on the isomorphism of the A5 alternating Galois group of the general quintic equation to the symmetry group ofThe icosahedron, coupled with the ability to partition an object of icosahedral symmetry into five equivalent objects of tetrahedral or octahedral symmetry.
Abstract: An algorithm has been implemented on a microcomputer for solving the general quintic equation. This algorithm is based on the isomorphism of the A5 alternating Galois group of the general quintic equation to the symmetry group of the icosahedron, coupled with the ability to partition an object of icosahedral symmetry into five equivalent objects of tetrahedral or octahedral symmetry. A detailed discussion is presented of the portions of this algorithm relating to these symmetry properties of the icosahedron. In addition, the entire algorithm is summarized.
7 citations
3 citations