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Quintic function

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


Papers
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Journal ArticleDOI
TL;DR: In this article, Jacobi's quartic theta function identity and its relation to the Eisenstein series are investigated. And the quintic transformation formulas are used to describe series multisections for modular forms in terms of simple matrix operations.

8 citations

Posted Content
01 Jul 2018-viXra
TL;DR: The Triple Conformal Geometric Algebra (TCGA) as discussed by the authors extends CGA as the product of three orthogonal CGAs, and thereby the representation of geometric entities to general cubic plane curves and certain cyclidic (or roulette) quartic, quintic, and sextic plane curves.
Abstract: The Triple Conformal Geometric Algebra (TCGA) for the Euclidean R^2-plane extends CGA as the product of three orthogonal CGAs, and thereby the representation of geometric entities to general cubic plane curves and certain cyclidic (or roulette) quartic, quintic, and sextic plane curves. The plane curve entities are 3-vectors that linearize the representation of non-linear curves, and the entities are inner product null spaces (IPNS) with respect to all points on the represented curves. Each IPNS entity also has a dual geometric outer product null space (OPNS) form. Orthogonal or conformal (angle-preserving) operations (as versors) are valid on all TCGA entities for inversions in circles, reflections in lines, and, by compositions thereof, isotropic dilations from a given center point, translations, and rotations around arbitrary points in the plane. A further dimensional extension of TCGA, also provides a method for anisotropic dilations. Intersections of any TCGA entity with a point, point pair, line or circle are possible. TCGA defines commutator-based differential operators in the coordinate directions that can be combined to yield a general n-directional derivative.

8 citations

Dissertation
01 Jun 2011
TL;DR: In this paper, the Bring-Jerrard quintic polynomial equation is investigated for a formula, and an explanation given as to why finding a formula and the equation being unsolvable by radicals may appear contradictory when read out of context.
Abstract: In this research the Bring-Jerrard quintic polynomial equation is investigated for a formula. Firstly, an explanation given as to why finding a formula and the equation being unsolvable by radicals may appear contradictory when read out of context. Secondly, the reason why some mathematical software programs may fail to render a conclusive test of the formula, and how that can be corrected is explained. As an application, this formula is used to determine another formula that expresses the gravitational constant in terms of other known physical constants. It is also explained why up to now it has been impossible to determine this expression using the current underlying theoretical basis.

8 citations

Posted Content
Abstract: We prove that the incidence scheme of rational curves of degree 11 on quintic threefolds is irreducible. This implies a strong form of the Clemens conjecture in degree 11. Namely, on a general quintic threefold $F$ in $\mathbb{P}^4$, there are only finitely many smooth rational curves of degree 11, and each curve $C$ is embedded in $F$ with normal bundle $\mathcal{O}(-1) \oplus \mathcal{O}(-1)$. Moreover, in degree 11, there are no singular, reduced, and irreducible rational curves, nor any reduced, reducible, and connected curves with rational components on $F$.

8 citations

Journal ArticleDOI
TL;DR: In this article, intersection theory is applied to construction of n-point finite-difference equations associated with classical integrable systems and exact discretizations of one-dimensional cubic and quintic Duffing oscillators are presented.
Abstract: Application of intersection theory to construction of n-point finite-difference equations associated with classical integrable systems is discussed. As an example, we present a few exact discretizations of one-dimensional cubic and quintic Duffing oscillators sharing form of Hamiltonian and canonical Poisson bracket up to the integer scaling factor.

8 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202397
2022254
2021109
2020104
201993
201893