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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.
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TL;DR: In this paper, the effects of filter and linear dissipation parameters on explosion excitation and wave amplitude modulation were studied, and exact solutions of discrete conformable fractional complex cubic cubic cubic-quintic Ginzburg-Landau model possessing non-local quintic term were derived.
9 citations
TL;DR: In this paper, it was shown that the number of digits in the integers of a creative telescoping relation of expected minimal order for a bivariate proper hypergeometric term has essentially cubic growth with the problem size.
9 citations
TL;DR: In this paper, a complex plane representation for strongly resonant PDEs with analytic solutions and an extra conserved quantity is developed and explored, and simple closed form expressions for families of stationary states bifurcating from all individual modes are given.
Abstract: Weakly nonlinear energy transfer between normal modes of strongly resonant PDEs is captured by the corresponding effective resonant systems. In a previous article, we have constructed a large class of such resonant systems (with specific representatives related to the physics of Bose-Einstein condensates and Anti-de Sitter spacetime) that admit special analytic solutions and an extra conserved quantity. Here, we develop and explore a complex plane representation for these systems modelled on the related cubic Szego and LLL equations. To demonstrate the power of this representation, we use it to give simple closed form expressions for families of stationary states bifurcating from all individual modes. The conservation laws, the complex plane representation and the stationary states admit furthermore a natural generalization from cubic to quintic nonlinearity. We demonstrate how two concrete quintic PDEs of mathematical physics fit into this framework, and thus directly benefit from the analytic structures we present: the quintic nonlinear Schroedinger equation in a one-dimensional harmonic trap, studied in relation to Bose-Einstein condensates, and the quintic conformally invariant wave equation on a two-sphere, which is of interest for AdS/CFT-correspondence.
8 citations
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TL;DR: In this article, the authors show that all conics invariant under a residual Z2 symmetry reduce to an algebraic problem at the limit of our computational capabilities, where the main results are of arithmetic flavor: the extension of the moduli space by the algebraic cycle splits in the large complex structure limit into groups each governed by an algebraIC number field.
Abstract: Irrational invariants from D-brane superpotentials are pursued on the mirror quintic, systematically according to the degree of a representative curve. Lines are completely understood: the contribution from isolated lines vanishes. All other lines can be deformed holomorphically to the van Geemen lines, whose superpotential is determined via the associated inhomogeneous Picard-Fuchs equation. Substantial progress is made for conics: the families found by Mustata contain conics reducible to isolated lines, hence they have a vanishing superpotential. The search for all conics invariant under a residual Z2 symmetry reduces to an algebraic problem at the limit of our computational capabilities. The main results are of arithmetic flavor: the extension of the moduli space by the algebraic cycle splits in the large complex structure limit into groups each governed by an algebraic number field. The expansion coefficients of the superpotential around large volume remain irrational. The integrality of those coefficients is revealed by a new, arithmetic twist of the di-logarithm: the D-logarithm. There are several options for attempting to explain how these invariants could arise from the A-model perspective. A successful spacetime interpretation will require spaces of BPS states to carry number theoretic structures, such as an action of the Galois group.
8 citations
TL;DR: In this paper, it was shown that a piecewise defined polynomial P of degree six can be used to give at any point of [a, b] better orders of approximation to y and its derivatives than those obtained from Q.
8 citations