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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: A result characterising the covariants for these models in terms of their restrictions to the family of curves parametrised by the modular curve X(5) is proved.
Abstract: A genus one curve C of degree 5 is defined by the 4 x 4 Pfaffians of a 5 x 5 alternating matrix of linear forms on P^4. We prove a result characterising the covariants for these models in terms of their restrictions to the family of curves parametrised by the modular curve X(5). We then construct covariants describing the covering map of degree 25 from C to its Jacobian and give a practical algorithm for evaluating them.
10 citations
TL;DR: In this article, a class of periodic discrete spline interpolates in one and two independent variables was developed, and explicit error bounds were derived for the periodic quintic and biquintic discrete splines interpolates.
10 citations
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TL;DR: In this paper, a purely analytic introduction to the phenomenon of mirror symmetry for quintic three-folds via classical hypergeometric functions and differential equations for them is given. But the existence of non-linear equations for the mirror map is not discussed.
Abstract: In this work, we give a purely analytic introduction to the phenomenon of mirror symmetry for quintic threefolds via classical hypergeometric functions and differential equations for them. Starting with a modular map and recent transcendence results for its values, we regard a mirror map $z(q)$ as a concept generalizing the modular one. We give an alternative approach demonstrating the existence of non-linear differential equations for the mirror map, and exploit both an elegant construction of Klemm-Lian-Roan-Yau and the Ax theorem to prove that the Yukawa coupling $K(q)$ does not satisfy any algebraic differential equation of order less than 7 with coefficients from $\mathbb{C}(q)$.
10 citations
TL;DR: In this paper, an efficient time-splitting Fourier spectral method for the quintic complex Swift-Hohenberg equation is presented, which is easy to apply and second-order in time and spectrally accurate in space.
Abstract: In this paper, we present an efficient time-splitting Fourier spectral method for the quintic complex Swift-Hohenberg equation. Using the Strang time-splitting tech- nique, we split the equation into linear part and nonlinear part. The linear part is solved with Fourier Pseudospectral method; the nonlinear part is solved analytically. We show that the method is easy to be applied and second-order in time and spectrally accurate in space. We apply the method to investigate soliton propagation, soliton interaction, and generation of stable moving pulses in one dimension and stable vortex solitons in two dimensions. AMS subject classifications: 65M70, 65Z05
10 citations
TL;DR: In this paper, the authors proved homological mirror symmetry for the quintic Calabi-Yau hypersurface 3-fold and showed that for the quartic surface, the symmetry can be maintained.
Abstract: We prove homological mirror symmetry for the quintic Calabi‐Yau 3‐fold. The proof follows that for the quartic surface by Seidel [16] closely, and uses a result of Sheridan [23]. In contrast to Sheridan’s approach [22], our proof gives the compatibility of homological mirror symmetry for the projective space and its Calabi‐Yau hypersurface. 53D37; 14J33
10 citations