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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: The principal n-th root of a complex number is defined, the Vieta's formulas for polynomial equations of degree 2, 3 and 4 are formalized and the solution of Cubic and Quartic Equations is presented.
Abstract: Summary. In this article, the principal n-th root of a complex number is defined, the Vieta’s formulas for polynomial equations of degree 2, 3 and 4 are formalized. The solution of quadratic equations, the Cardan’s solution of cubic equations and the Descartes-Euler solution of quartic equations in terms of their complex coecients are also presented [5].
44 citations
TL;DR: In this article, a new finite element is developed for free vibration analysis of high speed rotating beams using basis functions which use a linear combination of the solution of the governing static differential equation of a stiff-string and a cubic polynomial.
44 citations
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TL;DR: In this article, it was shown that the moduli space on the Higgs branch exactly reproduces the modulus space of degree N hypersurfaces in the quintic endowed with the appropriate line bundle.
Abstract: It is proposed that the quantum mechanics of N D4-branes and M D0-branes on the quintic is described by the dimensional reduction of a certain U(N)xU(M) quiver gauge theory, whose superpotential encodes the defining quintic polynomial. It is shown that the moduli space on the Higgs branch exactly reproduces the moduli space of degree N hypersurfaces in the quintic endowed with the appropriate line bundle, and that the cohomology growth reproduces the D4-D0 black hole entropy.
44 citations
TL;DR: It has been shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons, whereas theSelf-focusing quintal non linearity will enhance the repulsive interaction and increase soliton separation.
Abstract: We investigate analytically and numerically the interactions of dark solitons under competing nonlocal cubic and local quintic nonlinearities. It is shown that the self-defocusing quintic nonlinearity will strengthen the attractive interaction and decrease the relative distance between solitons, whereas the self-focusing quintic nonlinearity will enhance the repulsive interaction and increase soliton separation. We demonstrate these results by approximate variational approach and direct numerical simulation.
44 citations
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TL;DR: The first part of the project toward an effective algorithm to evaluate genus Gromov-Witten invariants of quintic Calabi-Yau threefolds is described in this paper.
Abstract: This is the first part of the project toward an effective algorithm to evaluate all genus Gromov-Witten invariants of quintic Calabi-Yau threefolds. In this paper, we introduce the notion of Mixed-Spin-P fields, construct their moduli spaces, and construct the virtual cycles of these moduli spaces.
43 citations