Showing papers on "Quintic function published in 2000"
TL;DR: In this article, the authors study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models.
Abstract: We study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models recently constructed by Recknagel and Schomerus, to begin sketching a picture of D-branes in the stringy regime. We also make first steps towards computing superpotentials on the D-brane world-volumes.
407 citations
Posted Content•
TL;DR: In this article, the zeta-functions for a one parameter family of quintic three-folds defined over finite fields and for their mirror manifolds were studied and their structure was analyzed.
Abstract: We study zeta-functions for a one parameter family of quintic threefolds defined over finite fields and for their mirror manifolds and comment on their structure. The zeta-function for the quintic family involves factors that correspond to a certain pair of genus 4 Riemann curves. The appearance of these factors is intriguing since we have been unable to `see' these curves in the geometry of the quintic. Having these zeta-functions to hand we are led to comment on their form in the light of mirror symmetry. That some residue of mirror symmetry survives into the zeta-functions is suggested by an application of the Weil conjectures to Calabi-Yau threefolds: the zeta-functions are rational functions and the degrees of the numerators and denominators are exchanged between the zeta-functions for the manifold and its mirror. It is clear nevertheless that the zeta-function, as classically defined, makes an essential distinction between Kahler parameters and the coefficients of the defining polynomial. It is an interesting question whether there is a `quantum modification' of the zeta-function that restores the symmetry between the Kahler and complex structure parameters. We note that the zeta-function seems to manifest an arithmetic analogue of the large complex structure limit which involves 5-adic expansion.
79 citations
[...]
TL;DR: In this paper, the authors discuss the general theory of D-branes on Calabi-Yau, recent results from the theory of boundary states and new results on the spectrum of branes on the quintic Calabi Yau.
Abstract: We discuss the general theory of D-branes on Calabi-Yau, recent results from the theory of boundary states and new results on the spectrum of branes on the quintic Calabi-Yau.
75 citations
TL;DR: In this article, an algorithm for solving the Korteweg de-vries Burgers' (KdVB) equation, based on the collocation method with quintic B-spline finite elements, is set up to simulate the solutions of the KdV, Burgers, and KdVB equations.
65 citations
03 Oct 2000
TL;DR: In this article, the authors present a motion planning primitive for car-like vehicles, which is a completely parametrized quintic spline, denoted as /spl eta/-spline, that allows interpolation of an arbitrary sequence of points with overall second order geometric continuity.
Abstract: Presents a motion planning primitive for car-like vehicles. It is a completely parametrized quintic spline, denoted as /spl eta/-spline, that allows interpolation of an arbitrary sequence of points with overall second order geometric (G/sup 2/-) continuity. Issues such as minimality, regularity, symmetry, and flexibility of these G/sup 2/-splines are addressed in the exposition. The development of the new primitive is tightly connected to the flatness based control of nonholonomic car-like vehicles.
59 citations
TL;DR: Exact and approximate solutions to higher-order evolution equations developed for propagation in two-dimensions are obtained and are shown to exhibit quasi-soliton behavior based on propagation and collision studies.
Abstract: Scalar and vector nonlinear nonparaxial evolution equations are developed for propagation in two-dimensions Using standard soliton scalings, it is found that nonparaxial propagation is accompanied by higher-order linear and nonlinear terms and an effective quintic nonlinear index The presence of an intrinsic quintic nonlinearity arising from χ(5) must also be considered at the order of the analysis These terms represent corrections to the well-known nonlinear Schrodinger equation Exact and approximate solutions to these higher-order evolution equations are obtained and are shown to exhibit quasi-soliton behavior based on propagation and collision studies
45 citations
TL;DR: In this article, the Galois group of irreducible sextic polynomials with Gal(f) = G is defined and a common formula for finding the roots of all polynomial f(x) ∈ Q[x] is given.
34 citations
TL;DR: In this article, the conditions to achieve stable soliton propagation are analyzed within the domain of validity of soliton perturbation theory, and an analytical expression for the soliton amplitude corresponding to the quintic Ginzburg-Landau equation (CGLE) is also obtained.
Abstract: Stable soliton propagation in a system with linear and nonlinear gain and spectral filtering is investigated. Different types of exact analytical solutions of the cubic and the quintic complex Ginzburg-Landau equation (CGLE) are reviewed. The conditions to achieve stable soliton propagation are analyzed within the domain of validity of soliton perturbation theory. We derive an analytical expression defining the region in the parameter space where stable pulselike solutions exist, which agrees with the numerical results obtained by other authors. An analytical expression for the soliton amplitude corresponding to the quintic CGLE is also obtained. We show that the minimum value of this amplitude depends only on the ratio between the linear gain and the quintic gain saturating term.
29 citations
03 Oct 2000
TL;DR: In this paper, the authors deal with the generation of optimal paths for the automated steering of autonomous vehicles, where the path is parametrized by quintic G/sup 2/splines, or /spl eta/-spline, devised to guarantee the overall second order geometric continuity of a composite path interpolating an arbitrary sequence of points.
Abstract: This paper deals with the generation of optimal paths for the automated steering of autonomous vehicles. The path is parametrized by quintic G/sup 2/-splines, or /spl eta/-spline, devised to guarantee the overall second order geometric continuity of a composite path interpolating an arbitrary sequence of points. Starting from the closed-form /spl eta/-parametrization of the spline an optimization criterion is proposed to design smooth curves. The aim is to plan curves where the curvature variability is kept as small as possible. With good approximation, in a flatness based control scheme, this corresponds to minimize the change-rate of the steering control. Various examples are included to highlight the ductility and effectiveness of the planning.
26 citations
TL;DR: In this paper, a new proof of the rigidity of a smooth quintic 4-fold into fibrations with general fibre of Kodaira dimension zero was given. But the results were not generalized to smooth hypersurfaces of degree in in the case of equal to 6, 7, or 8.
Abstract: The birational geometry of an arbitrary smooth quintic 4-fold is studied using the properties of log pairs. As a result, a new proof of its birational rigidity is given and all birational maps of a smooth quintic 4-fold into fibrations with general fibre of Kodaira dimension zero are described.In the Addendum similar results are obtained for all smooth hypersurfaces of degree in in the case of equal to 6, 7, or 8.
25 citations
TL;DR: This paper aims to describe the tensorial basis spline collocation method applied to Poisson's equation, and shows it to be competitive with both iterative BSCM and FFT-based methods in the case of a localized 3D charge distribution in vacuum.
TL;DR: In this paper, the authors studied the structure of the function field K of the quintic Fermat curve F(5) in the following way: Let K m be a g-maximal rational subfield of K, and the field extension K/K m is obtained by the projection from F (5) to a line with a center p, ∈ F(1).
Abstract: We study the structure of the function field K of the quintic Fermat curve F(5) in the following way: Let K m be a g-maximal rational subfield of K. Then the field extension K/K m is obtained by the projection from F(5) to a line with a center p, ∈ F(5). By using this fact, we consider the field extension K/K m from several point of view.
TL;DR: This paper investigates the family of Thue equations F(x,y) originating from Emma Lehmer's family of quintic fields, and shows that for |t| > 3.28.10 15 the only solutions are the trivial ones with x= 0 or y = 0.
Abstract: For an integral parameter t ∈ Z we investigate the family of Thue equations F(x,y) = x 5 + (t - 1) 2 x 4 y - (2t 3 + 4t + 4)x 3 y 2 + (t 4 + t 3 + 2t 2 + 4t - 3)x 2 y 3 + (t 3 + t 2 + 5t + 3)xy 4 + y 5 = ±1, originating from Emma Lehmer's family of quintic fields, and show that for |t| > 3.28.10 15 the only solutions are the trivial ones with x= 0 or y = 0. Our arguments contain some new ideas in comparison with the standard methods for Thue families, which gives this family a special interest.
TL;DR: In this article, a global collocation method for the integration of the special second-order ordinary initial value problem (IVP) y″=f(x,y) is proposed.
Posted Content•
TL;DR: In this paper, a purely analytic introduction to the phenomenon of mirror symmetry for quintic three-folds via classical hypergeometric functions and differential equations for them is given. But the existence of non-linear equations for the mirror map is not discussed.
Abstract: In this work, we give a purely analytic introduction to the phenomenon of mirror symmetry for quintic threefolds via classical hypergeometric functions and differential equations for them. Starting with a modular map and recent transcendence results for its values, we regard a mirror map $z(q)$ as a concept generalizing the modular one. We give an alternative approach demonstrating the existence of non-linear differential equations for the mirror map, and exploit both an elegant construction of Klemm-Lian-Roan-Yau and the Ax theorem to prove that the Yukawa coupling $K(q)$ does not satisfy any algebraic differential equation of order less than 7 with coefficients from $\mathbb{C}(q)$.
01 Jan 2000
TL;DR: Here the cases of approximation order O(h(sup 8)) are studied which need piecewise quartic curves in the plane and piecewise quinticCurves in space.
Abstract: : Parametric approximation of curves offers the possibility of increasing the order of approximation by using the additional parameters in the parameterization of the curve. This has been studied in several papers, see e.g.,. The resulting problems are highly nonlinear. Here the cases of approximation order O(h(sup 8)) are studied which need piecewise quartic curves in the plane and piecewise quintic curves in space.
TL;DR: In this paper, the authors completely solved the family of Thue equations with the method of Bilu and Hanrot, where is an integral parameter and the only solutions are the trivial ones with x = 0 or y = 0.
Abstract: In this paper we completely solve the family of Thue equations
where is an integral parameter. In particular, for , the only solutions are the trivial ones with x = 0 or y = 0. The result is achieved by sharpening the estimates of part I of the paper and by solving Thue equations with the method of Bilu and Hanrot.
Posted Content•
TL;DR: In this article, the authors gave the closed form solution for the five roots of the General Quintic Equation, which can be generated on Maple V or on the new version Maple VI.
Abstract: The motivation behind this note, is due to the non success in finding the complete solution to the General Quintic Equation The hope was to have a solution with all the parameters precisely calculated in a straight forward manner This paper gives the closed form solution for the five roots of the General Quintic Equation They can be generated on Maple V, or on the new version Maple VI On the new version of maple, Maple VI, it may be possible to insert all the substitutions calculated in this paper, into one another, and construct one large equation for the Tschirnhausian Transformation The solution also uses the Generalized Hypergeometric Function which Maple V can calculate, robustly
10 Apr 2000
TL;DR: The Quintic Reciprocity Law is used to produce an algorithm, that runs in polynomial time, that determines the primality of numbers M such that M 4 − 1 is divisible by a power of 5 which is larger that \(\sqrt{M}\), provided that a small prime p, p ≡ 1 (mod 5) is given.
Abstract: The Quintic Reciprocity Law is used to produce an algorithm, that runs in polynomial time, and that determines the primality of numbers M such that M4 − 1 is divisible by a power of 5 which is larger that \(\sqrt{M}\), provided that a small prime p, p ≡ 1 (mod 5) is given, such that M is not a fifth power modulo p. The same test equations are used for all such M.
01 Jun 2000
TL;DR: In this paper, Nieto's quintic is studied from the point of view of abelian and Kummer surfaces and their moduli, which is analogous to the Segre cubic and the Burkhardt quartic.
Abstract: We study, from the point of view of abelian and Kummer surfaces and their moduli, the special quintic threefold known as Nieto's quintic. It is, in some ways, analogous to the Segre cubic and the Burkhardt quartic and can be interpreted as a moduli space of certain Kummer surfaces. It contains 30 planes and has 10 singular points: we describe how some of these arise from bielliptic and product abelian surfaces and their Kummer surfaces.
TL;DR: In this article, the authors prove a conjecture made earlier concerning a beautiful algebraic fourfold, a quintic in projective five-space invariant under the Weyl group of typeE 6, to the effect that a certain birational model of this variety is a smooth compactification of a ball quotient.
Abstract: We prove a conjecture made earlier concerning a beautiful algebraic fourfold, a quintic in projective five-space invariant under the Weyl group of typeE
6, to the effect that a certain birational model of this variety is a smooth compactification of a ball quotient. To prove this, we first state and prove a general result which gives a criterion for checking whether a variety of dimensionN≥3 is a (compactification of a) ball quotient. We then go on to identify the group up to commensurability class.
TL;DR: In this paper, the authors proposed analytical dark solitary wave solutions for the higher order nonlinear Schrodinger equation with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short (femtosecond) optical soliton propagation in non-Kerr media.
Abstract: By means of the coupled amplitude-phase method we find analytical dark solitary wave solutions for the higher order nonlinear Schrodinger equation with cubic-quintic terms describing the effects of quintic nonlinearity on the ultra-short (femtosecond) optical soliton propagation in non-Kerr media. The dark solitary wave solution exists even for the coefficients of quintic terms much larger than those of cubic terms. PACS: 42.65.Tg, 42.81Dp, 02.30.Jr, 42.79.Sz
Journal Article•
TL;DR: In this paper, a new conservative difference scheme is proposed for a class of nonlinear Schrdinger equation involving quintic term, and its convergence and stability are proved.
Abstract: in this paper, a new conservative difference scheme is proposed for a class of nonlinear Schrdinger equation involving quintic term, and its convergence and stability are proved. It is denostrated by numerical test results that the scheme is reliable in computing this class of equations.
Posted Content•
01 Jan 2000
TL;DR: In this paper, the authors gave a closed form solution for the five roots of the General Quintic Equation on Maple V and on the new version of Maple VI. But they did not give a solution to the Tschirnhausian transformation.
Abstract: The motivation behind this note, is due to the non success in finding the complete solution to the General Quintic Equation. The hope was to have a solution with all the parameters precisely calculated in a straight forward manner. This paper gives the closed form solution for the five roots of the General Quintic Equation. They can be generated on Maple V, or on the new version Maple VI. On the new version of maple, Maple VI, it may be possible to insert all the substitutions calculated in this paper, into one another, and construct one large equation for the Tschirnhausian Transformation. The solution also uses the Generalized Hypergeometric Function which Maple V can calculate, robustly.
TL;DR: A forced parameter in the quintic splines is used to satisfy the solution in the first and third subregions after getting the solution of a pair of differential equations which are of the FitzHugh–Nagumo (F–N) type.
Abstract: This paper is devoted to study the numerical solution of a pair of differential equations which are of the FitzHugh–Nagumo (F–N) type. Existence and uniqueness for such system has been given in 1978 by Rauch and Smoller. Our main concern in this article is to use high ordered splines as basis for the collocation method to solve numerically such differential equations. Finite difference methods were used in 1979 by Khalifa as well as collocation with cubic and quadratic splines but higher order ones were not used because of the discontinuity in the second derivative of the solution. In this paper, we considered the problem under the same basis in three separate regions and end up with a forced parameter in the quintic splines to satisfy the solution in the first and third subregions after getting the solution in the middle region, in which we overcome the difficulty of the discontinuity in the second derivative. Numerical results obtained are good and more accurate than the previous ones.