Quintic function

About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.

Holomorphic Anomaly Equations for the Formal Quintic

Abstract: We define a formal Gromov–Witten theory of the quintic threefold via localization on $${\mathbb {P}}^4$$ . Our main result is a direct geometric proof of holomorphic anomaly equations for the formal quintic in precisely the same form as predicted by B-model physics for the true Gromov–Witten theory of the quintic threefold. The results suggest that the formal quintic and the true quintic theories should be related by transformations which respect the holomorphic anomaly equations. Such a relationship has been recently found by Q. Chen, S. Guo, F. Janda, and Y. Ruan via the geometry of new moduli spaces.

Algorithm 684: C1- and C2-interplation on triangles with quintic and nonic bivariate polynomials

Abstract: The innovative part of the algorithm is the formulation of a bivariate nonic Hermite polynomial with C2-property [7] contained in modules CBSIDE, CSINSD, and CSHORN. These formulas are of principal value. They describe a twice differentiable polynomial representation on a set of triangles. To be of immediate use, some interfaces were designed, and the new modules were integrated into Renka’s triangle interpolation package [9]. Especially all procedures related to the generation and the handling of triangles are taken or may be taken from that algorithm. Also, the method of derivative estimation is identical with Renka’s global method [S]. The higher derivatives of order n are generated by taking the derivatives of order n 1 as input (n = 2, 3, 4). For the sake of completeness, equivalent routines for Cl-interpolation (once differentiable) are supplied, based on the well known quintic triangular element [l, 3, 41. In general, the Cl-routines are approximately 3 times faster than their C ‘-equivalents and need less memory. The main user interfaces to the package are the routines C2GRID and ClGRID. They interpolate values of a rectangular grid to a given set of irregularly distributed points (scattered data interpolation in two dimensions). Because the array of grid points is scanned for every triangie, the coefficients for each polynomial are computed only once, and the fast evaluation phase of the Taylor representation [7] can be exploited most efficiently. If the mesh lines of the rectangular grid are relatively wide with respect to the irregularly distributed

An Arithmetic Progression on Quintic Curves

Abstract: Consider a degree five curve of the form y 2 = f(x) where f(x) ∈ Q[x]. Ulas previously showed the existence of an infinite family of curves C which contain an arithmetic progression (AP) of length 11. The author also found an example of said curve which contains 12 points in AP. In this paper, we construct an infinite family of curves with an AP of length 12.

Center conditions and bifurcation of limit cycles at degenerate singular points in a quintic polynomial differential system

Abstract: The center problem and bifurcation of limit cycles for degenerate singular points are far to be solved in general. In this paper, we study center conditions and bifurcation of limit cycles at the degenerate singular point in a class of quintic polynomial vector field with a small parameter and eight normal parameters. We deduce a recursion formula for singular point quantities at the degenerate singular points in this system and reach with relative ease an expression of the first five quantities at the degenerate singular point. The center conditions for the degenerate singular point of this system are derived. Consequently, we construct a quintic system, which can bifurcates 5 limit cycles in the neighborhood of the degenerate singular point. The positions of these limit cycles can be pointed out exactly without constructing Poincare cycle fields. The technique employed in this work is essentially different from more usual ones. The recursion formula we present in this paper for the calculation of singular point quantities at degenerate singular point is linear and then avoids complex integrating operations.