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, Crilly et al. gave a Volumetric proof of the Sum of Squares formula, and showed that it can be computed in polynomial time.
Abstract: References 1. Ian Anderson, Sums of squares and binomial coefficients, Math. Gaz. 65 (June 1981) pp. 87-92. 2. D. R. Woodall, Finite sums, matrices, and induction, Math. Gaz. 65 (June 1981) pp. 92-103. 3. D. Desbrow, Sums of integer powers, Math. Gaz. 66 (June 1982) pp.97-100. 4. David Singmaster, Sums of squares and pyramidal numbers, Math. Gaz. 66 (June 1982) pp. 100-104. 5. D. Desbrow, Volumetric proof of the sum of squares formula, Math. Gaz. 83 (July 1999) pp. 256-257. TONY CRILLY 10 Lemsford Road, St Albans ALl 3PB e-mail: t.crilly@btinternet.com
11 citations
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TL;DR: An axisymmetric viscous flow, generated by two large parallel plates slowly approaching each other is investigated and the steady nonlinear governing equations are converted into a fourth-order nonlinear differential equation using integrability condition.
Abstract: An axisymmetric viscous flow, generated by two large parallel plates slowly approaching each other is investigated. The steady nonlinear governing equations are converted into a fourth-order nonlinear differential equation using integrability condition. The resulting nonlinear boundary value problem is solved using quintic B-spline collocation and sinc-collocation methods. The approach consists of reducing the problem to a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the techniques and a comparison is made with existing results in the literature.
11 citations
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TL;DR: In this article, an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schrodinger equation in the supercritical regime has been proved, that is, below the critical space (H^1(mathbb T^3) ).
Abstract: In this paper we prove an almost sure local well-posedness result for the periodic 3D quintic nonlinear Schrodinger equation in the supercritical regime, that is below the critical space $H^1(\mathbb T^3)$.
11 citations
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TL;DR: In this article, the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds was obtained.
Abstract: We use numerical methods to obtain moduli-dependent Calabi-Yau metrics, and from them, the moduli-dependent massive tower of Kaluza-Klein states for the one-parameter family of quintic Calabi-Yau manifolds. We then compute geodesic distances in their K\"ahler and complex structure moduli space using exact expressions from mirror symmetry, approximate expressions, and numerical methods, and we compare the results. Finally, we fit the moduli dependence of the massive spectrum to the geodesic distance to obtain the rate at which states become exponentially light. The result is indeed of order 1, as suggested by the swampland distance conjecture. We also observe level crossing in the eigenvalue spectrum and find that states in small irreducible representations of the symmetry group tend to become lighter than states in larger irreducible representations.
11 citations
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TL;DR: The scalar-vector representation is used to derive a simple algorithm to obtain the roots of a quadratic quaternion polynomial, which is illustrated by computed examples, and used to analyze the root structure of quadratically quaternions polynomials that generate quintic curves with rational rotation-minimizing frames (RRMF curves).
11 citations