Showing papers on "Quintic function published in 1995"
01 Jan 1995
TL;DR: A homogeneous polynomial equation in five variables determines a quintic 3-fp;d in ℂP4.
Abstract: A homogeneous polynomial equation in five variables determines a quintic 3-fp;d in ℂP4. Hodge numbers of a nonsingular quintic are know to be: h p, p = 1, p = 0, 1, 2, 3 (Kahler form and its powers), h3, 0 = h0,3 = 1 (a quintic happens to bear a holomorphic volume form), h2,1 = h1, 2 = 101 = 126 - 25 (it is the dimension of the space of all quintics modulo projective transformations, and h2,1 is responsible here for infinitesimal variations of the complex structure) and all the other h p,q = 0.
224 citations
TL;DR: In this paper, the authors proposed a method for finding stationary pulse solutions of the complex Ginzburg-Landau equation, which can be applied to both cubic and quintic models.
Abstract: We propose a method for finding stationary pulse solutions of the complex Ginzburg-Landau equation, which can be applied to both cubic and quintic models. In particular, we discover previously unknown arbitrary-amplitude pulse solutions for both the cubic and quintic models. Numerical simulations show that these solutions are stable relative to small perturbations.
92 citations
01 May 1995
TL;DR: In this article, the case when the quintic consists of the quartic and a line was studied. But the main focus was on rational quartics, and the cases of primary interest for this purpose were the rational quadratic curves.
Abstract: In recent work [5] which involved enumeration of singularity types of highly singular quintic curves, it was necessary to use rather detailed information on the geometry of quartic curves (for the case when the quintic consists of the quartic and a line). The present paper was written to supply this background. The cases of primary interest for this purpose are the rational quartics, and we concentrate on these.
26 citations
TL;DR: In this article, the collocation method was used in conjunction with quintic Hermite elements to solve the system of flow equations, which provided high resolution required in the solution of discontinuities, thereby producing satisfactorily stable solutions.
Abstract: The one-dimensional hydrodynamic equations based on shallow-water theory are used to compute the flood wave resulting from the total instantaneous collapse of a dam. The collocation method is used in conjunction with quintic Hermite elements to solve the system of flow equations. Quintic Hermite elements are used to provide the high resolution required in the solution of discontinuities, thereby producing satisfactorily stable solutions. The model can simulate both subcritical and supercritical flows in different parts of the channel or in a sequence in time. The model is stable, although there are no second-order pseudoviscosity terms in it. No upwinding of the basis function is required. Linear stability analysis reveals the selective damping of short wavelengths and excellent phase accuracy of the model and insensitivity to parameter variation. The computed results are compared with the test results of the U.S. Corps of Engineers, Waterways Experiment Station. Close agreement between computed and measu...
22 citations
TL;DR: In this paper, necessary and sufficient conditions for the origin to be a center, an unstable focus, or a stable focus of a homogeneous polynomial vector field whose degree is arbitrary are investigated.
16 citations
TL;DR: In this paper, the authors present a full description of new pulse-like solutions of the complex quintic Ginzburg-Landau equation (CGLE) with a Lorentzian intensity profile and exist only when certain relations between the coefficients of the CGLE are satisfied.
9 citations
01 Jan 1995
TL;DR: It is proved that, if this data is extracted from a convexity-preserving Non-Uniform Degree Polynomial Spline (a new spline recently proposed by the authors), the resulting quintic spline also preserves the conveXity properties of the data points.
Abstract: Quintic splines lead to efficient algorithms for constructing a curvature-continuous parametric interpolant to a given set of planar points, provided that a robust procedure is available for choosing (estimating) tangent vectors and curvature values at the given points In this paper it is proved that, if this data is extracted from a convexity-preserving Non-Uniform Degree Polynomial Spline (a new spline recently proposed by the authors), the resulting quintic spline also preserves the convexity properties of the data points A fully automatic procedure, based on the above spline, is proposed for constructing convexity-preserving curvature-continuous quintic interpolants to arbitrary planar points Three examples are presented demonstrating the efficiency of the method
9 citations
02 Jan 1995
TL;DR: In this article, the authors present efficient algorithms to model a collection of scattered function data defined on a given smooth domain surface D in three dimensional real space (lR3 ), by a C 1 cubic or a C 2 quintic piecewise trivariate polynomial approximation F (a mapping from D into lR ).
Abstract: We present efficient algorithms to model a collection of scattered function data defined on a given smooth domain surface D in three dimensional real space (lR3 ), by a C1 cubic or a C2 quintic piecewise trivariate polynomial approximation F (a mapping from D into lR ). The smooth polynomial pieces or finite elements of F are defined on a three dimensional triangulation called the simplicial hull and defined over the domain surface D. Our smooth polynomial approximations allows one to additionally control the local geometry of the modeled function F. We also present two different techniques for visualizing the graph of the function F.
4 citations
TL;DR: In this paper, a four-point function of $E_6$ singlets, of interest in elucidating the moduli space of (0,2) deformations of the quintic string vacuum, is computed using analytic and numerical methods.
Abstract: A four-point function of $E_6$ singlets, of interest in elucidating the moduli space of (0,2) deformations of the quintic string vacuum, is computed using analytic and numerical methods. The conformal field theory amplitude satisfies the requisite selection rules and monodromy conditions, but the integrated string amplitude vanishes. Together with selection rules coming from the spacetime R-symmetry \dksecond, this demonstrates the flatness of the gauge-singlet spacetime superpotential through fourth order. Relevance to the more general program of determining the (0,2) moduli space and superpotential is discussed.
3 citations
TL;DR: In this paper, the family of quartic surfaces is parametrized by ℙ4 and the equation for {Δ = 0} ⊂ ℓ 4 parametrization of all Kummer surfaces is well known.
Abstract: AnH2,2-invariant quartic surface in ℙ3 is a quartic surface in ℙ3 invariant under the Heisenberg groupH2,2 of level (2, 2), the family ofH2,2-invariant quartic surfaces is parametrized by ℙ4. For each ν e ℙ4, the corresponding quartic surfaceX ν will be a Kummer surface, ifX ν is singular. The equation for {Δ = 0} ⊂ ℙ4 parametrizing all Kummer surfaces is well known. We find another more symmetric form (with respect to a 5-dimensional representation of the symmetric group S6) for this equation.
3 citations
TL;DR: In this article, it was shown that in the presence of cubic and quintic nonlinearities above a certain critical power, multidimensional optical solitary waves could propagate stably in bulk media.
Abstract: We show analytically that in the presence of cubic and quintic nonlinearities above a certain critical power, multidimensional optical solitary waves could propagate stably in bulk media. To investigate the stability an analytical expression for the solitary-wave fields with an arbitrary transverse dimension is derived through the combined use of Galerkin’s method and self-consistent-field approximation.
Book•
06 Jul 1995
TL;DR: An Efficient Algorithm for Evaluating Polynomials in the Polya Basis and a Hybrid Method for Shape-Preserving Interpolation with Curvature-Continuous Quintic Splines are presented.
Abstract: Parametric Offset Surface Approximation.- Unimodal Properties of Generalized Ball Bases.- Nef Polyhedra: A Brief Introduction.- Complex PDE Surface Generation for Analysis and Manufacture.- Weight Estimation of Rational Bezier Curves and Surfaces.- The Use of Multiple Knots for B-spline Finite Element Approximations to PDE Surfaces.- Geometric Design with Trimmed Surfaces.- The Shape of the Overhauser Spline.- Local Energy Fairing of B-spline Curves.- Integrating Analysis Tools into the Design Process through Constrained Parametric Structures.- Localized Radial Basis Methods Using Rational Triangle Patches.- Repeated Knots in Least Squares Multiquadric Functions.- Stability Concept for Surfaces.- A Quartic Spline Based on a Variational Approach.- A Knowledge-Based System for Geometric Design.- Bezier Representation of Trim Curves.- Control Point Representations of Trigonometrically Specified Curves and Surfaces.- Towards Optimality in Automated Feature Recognition.- Solid Modeling with Constrained Form Features.- A Hybrid Method for Shape-Preserving Interpolation with Curvature-Continuous Quintic Splines.- Scale-Invariant Functionals for Smooth Curves and Surfaces.- The C-Tree: A Dynamically Balanced Spatial Index.- Piecewise Linear Approximation of Trimmed Surfaces.- An Efficient Algorithm for Evaluating Polynomials in the Polya Basis.
Journal Article•
TL;DR: In this article, a family of normal quintic surfaces in $P^3$ which are birationally isomorphic to Enriques surfaces is presented. And they prove that the dimension of the moduli space of these surfaces is 6.
Abstract: In this paper, we show one family of normal quintic surfaces in $P^3$ which are birationally isomorphic to Enriques surfaces. We prove that the dimension of the moduli space of these Enriques surfaces is 6.
TL;DR: In this article, the applicability of cubic pseudosplines is explored via numerical comparison with previously obtained results from the implementation of the quintic ones for ray-optical field evaluations, when the antenna secondary field is calculated by integration of physical-optics-induced currents.
Abstract: A recent study demonstrated the superior stability of quintic pseudosplines, when compared with usual oscillatory series expansions, for global interpolation of numerically defined reflector surfaces presenting critical behavior of their principal curvatures. Although interpolating functions with continuous derivatives up to second order are necessary for ray-optical field evaluations, C-class surface descriptions are sufficient when the antenna secondary field is calculated by integration of physical-optics-induced currents. In this connection, the applicability of cubic pseudosplines is explored via numerical comparison with previously obtained results from the implementation of the quintic ones. © 1995 John Wiley & Sons. Inc.
TL;DR: A joint interpolation strategy is proposed which uses joint variable reference data calculated from inverse kinematics, along with a polynomial equation or quintic equation as the parametric equation of the joint variables.
Abstract: The concept of tension is introduced and applied to a robot's trajectories, then new joint interpolation strategies are implemented. A joint interpolation strategy is proposed which uses joint variable reference data calculated from inverse kinematics, along with a polynomial equation or quintic equation as the parametric equation of the joint variables. This method can use any polynomial equation which has the C 2 continuity property and has intermediate points which pass through the reference data. For the time variable, first order linear equations can be used where the number of equations is n−1, n being the number of points in the reference data. Due to large reductions in computational burden resulting from this form, this method may be suited for real time applications