Showing papers on "Quintic function published in 1986"

Comparison of three curve intersection algorithms

Abstract: This paper treats the problem of how one can best compute the points of intersection of two planar rational curves. Three different algorithms are compared: the well known Bezier subdivision algorithm, a subdivision algorithm based on interval arithmetic, and the implicitization approach. Implementation considerations are discussed, with particular focus on how to make the implicitization method robust and fast. Report is made on a test in which the algorithms solved hundreds of randomly generated problems to eight digits of accuracy. The implicitization algorithm was faster than the others by a factor of five for degree two curves; by a factor of four for cubic curves; by a factor of three for quartic curves; and the interval method was faster for quintic curves by a factor of two.

Quasi-soliton and other behaviour of the nonlinear cubic-quintic Schrodinger equation

Abstract: The stability of the solitary-wave solutions of the nonlinear cubic–quintic Schrodinger equation (NLCQSE) is examined numerically. The solutions are found not to be solitons, but quasi-soliton behaviour is found to persist over wide regions of parameter space. Outside these regions dispersive and explosive behaviour is observed in solitary-wave interactions.

On quintic surfaces of general type

Abstract: The study of quintic surfaces is of special interest because 5 is the lowest degree of surfaces of general type. The aim of this paper is to give a classification of the quintic surfaces of general type over the complex number field C. We show that if S is an irreducible quintic surface of general type then it must be normal, and it has only elliptic double or triple points as essential singularities. Then we classify all such surfaces in terms of the classification of the elliptic double and triple points. We give many examples in order to verify the existence of various types of quintic surfaces of general type. We also make a study of the double or triple covering of a quintic surface over p2 obtained by the projection from a triple or double point on the surface. This reduces the classification of the surfaces to the classification of branch loci satisfying certain conditions. Finally we derive some properties of the Hilbert schemes of some types of quintic surfaces.

An aspect of the invariant of degree 4 of the binary quintic

Abstract: A binary form of odd degree,has a quadratic covariant Г, (ab2maxbx in Aronhold's notation, and the discriminant Δ of Г is an invariant of ƒ For m = 2Δ was obtained by Cayley in 1856 [3, p. 274]; it was curiosity as to how Δ could be interpreted geometrically that triggered the writing of this note. An interpretation, in projective space [2m + 1], that does not seem to be on record, of Γ and Δ is found below. If m = 1 one has merely the Hessian and discriminant of a binary cubic whose interpretations in the geometry of the twisted cubic are widely known [5, pp. 241–2].

A Posteriori Corrections for Non-periodic Cubic and Quintic Interpolating Splines at Equally Spaced Knots

Abstract: Extension aux fonctions splines non periodiques de degre 5 au plus d'une methode proposee recemment par Lucas pour la correction a posteriori des fonctions splines periodiques d'interpolation de degre impair

The polylogarithm in the field of two irreducible quintics

Abstract: A brief review of the polylogarithmic ladder and its cyclotomic equation is followed by an application to the roots of two irreducible quintic equations. The first is unique in its class and possesses four accessible and two inaccessible valid ladders. The other equation gives rise to a single ladder determinable, at the present time, only by numerical computation, and is a member of a completely new category.