Topic
Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: This article gives an efficient algorithm for computing relative power integral bases in cubic relative extensions and illustrated by examples of relative cubic extensions of quintic and sextic fields which emphasizes the power of the method.
Abstract: We give an efficient algorithm for computing relative power integral bases in cubic relative extensions. The problem leads to solving relative Thue equations as described by [Gaal and Pohst 1999] using the enumeration method of [Wildanger 1997]. The article is illustrated by examples of relative cubic extensions of quintic and sextic fields which emphasizes the power of the method. This is the first case that unit equations of 12 unknown exponents are completely solved. The experiences of our computations may be useful for other related calculations, as well.
15 citations
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Abstract: We obtain homological properties of the second symmetric product of P^4 and the double cover of the symmetric determinantal quintic hypersurface in P^{14} (the double quintic symmetroids), which indicate the homological projective duality between (suitable noncommutative resolutions of) them. Among other things, we construct their good desingularizations and also (dual) Lefschetz collections in the derived categories of the desingularizations. These are expected to give (dual) Lefschetz decompositions of suitable noncommutative resolutions. The desingularization of the double quintic symmetroids also contains its interesting birational geometries.
15 citations
TL;DR: In this paper, it was shown that a curve of degree dk on a very general surface of degree n ≥ 5 in P 3 has geometric genus at least d k (d − 5 ) + k 2 + 1.
15 citations
01 Jan 2016
TL;DR: In this paper, a linear stability analysis based on von Neu-mann approximation theory of the numerical scheme is investigated to demonstrate the precise and efficiency of the proposed method, the motion of solitary wave is studied by calculating the error norms L2 and L1.
Abstract: In this paper, the Rosenau-KdV equation that is one of the significant equations in physics was discussed. The collo- cation finite element method is implemented to find the numerical simulation of the dispersive shallow water waves with Rosenau-KdV equation using the quintic B-spline basis functions. A linear stability analysis based on von Neu- mann approximation theory of the numerical scheme is investigated. To demonstrate the precise and efficiency of the proposed method, the motion of solitary wave is studied by calculating the error norms L2 and L1. The invariants I1, I2 and their relative changes have been computed to define the conservation properties of the simulation. As a result, the obtained results are found better than some recent results. MSC: 35Q51 † 35Q53 † 35Q58
15 citations
TL;DR: A general spline-based method for differential quadrature with two-stage scheme for the cubic, quartic, quintic and sextic cases is proposed and compared with another methods that appear in the literature.
15 citations