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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 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 Mustat¸ya 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 ofthe 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, a numerical scheme for finding minimizing surfaces of functionals of the form F [S]= ∫ S [α+β(H−H 0 ) 2 −γK] d σ, where H and K are the mean and Gaussian curvatures, respectively, of the surface S, in the particular case of open surfaces represented as graphs.
8 citations
23 Jul 2006
TL;DR: The polynomials do not only give all the quintic cyclic extensions over the rationals by choosing the parameters but also classify all such extensions.
Abstract: We study cyclic extensions arising from Kummer theory of norm algebraic tori. In particular, we compute quintic cyclic polynomials defining ‘Kummer extension’. The polynomials do not only give all the quintic cyclic extensions over the rationals by choosing the parameters but also classify all such extensions. Some arithmetic properties of the polynomials are also derived.
7 citations
TL;DR: In this paper, the existence of solitons in a fifth-order nonlinear quintic Schrodinger equation is investigated through the use of a Hirota's differential operator, which utilizes only one auxiliary function.
7 citations
TL;DR: In this paper, the authors consider two classical cases in which such kind of phenomena occur: the case of the self focusing cubic nonlinearity, and the cases of competing quintic and cubic non-linearity.
Abstract: Abstract An optical vortex can appear when a light beam with nonzero angular momentum propagates in a suitable nonlinear medium. In some situations has been observed that the light intensity vanish at the center of the vortex (where the phase of the electromagnetic field is undefined), while the light beam assumes a ring-shaped structure. In this paper we consider two classical cases in which such kind of phenomena occur: the case of the self focusing cubic nonlinearity, and the case of competing quintic and cubic nonlinearity. In both cases we study the nonlinear Schrödinger equation of the optical field (with various boundary conditions) by means of min-max methods, and we prove the existence of saddle point type solutions, as well as minimum type solutions.
7 citations