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: In this article, the authors studied the Abel-Jacobiobis map of the family of elliptic quintics lying on a general cubic threefold and proved that it factors through a moduli component of stable rank 2 vector bundles.
Abstract: The Abel-Jacobi map of the family of elliptic quintics lying on a general cubic threefold is studied. It is proved that it factors through a moduli component of stable rank 2 vector bundles on the cubic threefold with Chern numbers c_1=0, c_2=2, whose general point represents a vector bundle obtained by Serre's construction from an elliptic quintic. The elliptic quintics mapped to a point of the moduli space vary in a 5-dimensional projective space inside the Hilbert scheme of curves, and the map from the moduli space to the intermediate Jacobian is etale. As auxiliary results, the irreducibility of families of elliptic normal quintics and of rational normal quartics on a general cubic threefold is proved. This implies the uniqueness of the moduli component under consideration. The techniques of Clemens-Griffiths and Welters are used for the calculation of the infinitesimal Abel-Jacobi map.
66 citations
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TL;DR: In this article, open string mirror symmetry for one-parameter Calabi-Yau hyper- surfaces in weighted projective space was studied and the corresponding Picard-Fuchs equations were derived.
Abstract: We study open string mirror symmetry for one-parameter Calabi-Yau hyper- surfaces in weighted projective space. We identify mirror pairs of D-brane configurations, derive the corresponding inhomogeneous Picard-Fuchs equations, and solve for the do- mainwall tensions as analytic functions over moduli space. Our calculations exemplify several features that had not been seen in previous work on the quintic or local Calabi-Yau manifolds. We comment on the calculation of loop amplitudes.
66 citations
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TL;DR: In this paper, the stability of the quintic and sextic functional equations in quasi-normed spaces via fixed point method was proved for the case of the quadratic functional equation.
Abstract: We achieve the general solution of the quintic functional equation and the sextic functional equation . Moreover, we prove the stability of the quintic and sextic functional equations in quasi-
-normed spaces via fixed point method.
65 citations
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TL;DR: The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrodinger equations described the propagation of ultra-short pulses in optical fibers of nonlinear media were derived by using an extended sinh-Gordon equation expansion method.
Abstract: The (2+1)-dimensional hyperbolic and cubic-quintic nonlinear Schrodinger equations describe the propagation of ultra-short pulses in optical fibers of nonlinear media. By using an extended sinh-Gordon equation expansion method, some new complex hyperbolic and trigonometric functions prototype solutions for two nonlinear Schrodinger equations were derived. The acquired new complex hyperbolic and trigonometric solutions are expressed by dark, bright, combined dark-bright, singular and combined singular solitons. The obtained results are more compatible than those of other applied methods. The extended sinh-Gordon equation expansion method is a more powerful and robust mathematical tool for generating new optical solitary wave solutions for many other nonlinear evolution equations arising in the propagation of optical pulses.
65 citations
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TL;DR: In this article, an algorithm for solving the Korteweg de-vries Burgers' (KdVB) equation, based on the collocation method with quintic B-spline finite elements, is set up to simulate the solutions of the KdV, Burgers, and KdVB equations.
65 citations