Topic

# Quintic function

About: Quintic function is a(n) research topic. Over the lifetime, 1677 publication(s) have been published within this topic receiving 26780 citation(s).

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TL;DR: In this article, the authors consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients and investigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities.

Abstract: We consider the Lagrangian of gravity covariantly amended by the mass and polynomial interaction terms with arbitrary coefficients and reinvestigate the consistency of such a theory in the decoupling limit, up to the fifth order in the nonlinearities. We calculate explicitly the self-interactions of the helicity-0 mode, as well as the nonlinear mixing between the helicity-0 and -2 modes. We show that ghostlike pathologies in these interactions disappear for special choices of the polynomial interactions and argue that this result remains true to all orders in the decoupling limit. Moreover, we show that the linear and some of the nonlinear mixing terms between the helicity-0 and -2 modes can be absorbed by a local change of variables, which then naturally generates the cubic, quartic, and quintic Galileon interactions, introduced in a different context. We also point out that the mixing between the helicity-0 and -2 modes can be at most quartic in the decoupling limit. Finally, we discuss the implications of our findings for the consistency of the effective field theory away from the decoupling limit, and for the Boulware-Deser problem.

1,222 citations

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TL;DR: In this paper, the authors formulate semi-direct MP2 methods that utilize disk space (which is usually much larger than memory size) for the steps that require most storage, and show that these methods are superior to conventional algorithms despite requiring less disk space.

Abstract: The cost (via the number of two-electron integral evaluations) and the maximum size of a direct second-order Mooller-Plesset (MP2) energy or gradient calculation are both determined by the available computer memory. Therefore we formulate semi-direct MP2 methods that utilize disk space (which is usually much larger than memory size) for the steps that require most storage. In terms of the molecular basis set size, they require as little as quadratic memory and cubic disk. The amount of input/output transfer between memory and disk is quartic plus the cost of transpositions, which is between quartic and quintic. A variety of calculations are presented comparing the fully direct, semi-direct and conventional algorithms. The semi-direct methods are shown to be superior to conventional algorithms despite requiring less disk space, and are also often preferred over the direct methods.

1,139 citations

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TL;DR: In this article, the authors study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models.

Abstract: We study D-branes on the quintic CY by combining results from several directions: general results on holomorphic curves and vector bundles, stringy geometry and mirror symmetry, and the boundary states in Gepner models recently constructed by Recknagel and Schomerus, to begin sketching a picture of D-branes in the stringy regime. We also make first steps towards computing superpotentials on the D-brane world-volumes.

404 citations

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19 Feb 2003TL;DR: An online method for obtaining smooth, jerk-bounded trajectories has been developed and implemented and a method for blending these straight-line trajectories over a series of way points is also discussed.

Abstract: An online method for obtaining smooth, jerk-bounded trajectories has been developed and implemented. Jerk limitation is important in industrial robot applications, since it results in improved path tracking and reduced wear on the robot. The method described herein uses a concatenation of fifth-order polynomials to provide a smooth trajectory between two way points. The trajectory approximates a linear segment with parabolic blends trajectory. A sine wave template is used to calculate the end conditions (control points) for ramps from zero acceleration to nonzero acceleration. Joining these control points with quintic polynomials results in a controlled quintic trajectory that does not oscillate, and is near time optimal for the jerk and acceleration limits specified. The method requires only the computation of the quintic control points, up to a maximum of eight points per trajectory way point. This provides hard bounds for online motion algorithm computation time. A method for blending these straight-line trajectories over a series of way points is also discussed. Simulations and experimental results on an industrial robot are presented.

355 citations

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TL;DR: In this paper, the Dvali-Gabadadze-Porrati model reduces to the theory of a scalar field with interactions including a specific cubic self-interaction, the Galileon term.

Abstract: In the decoupling limit, the Dvali-Gabadadze-Porrati model reduces to the theory of a scalar field $\ensuremath{\pi}$, with interactions including a specific cubic self-interaction---the Galileon term. This term, and its quartic and quintic generalizations, can be thought of as arising from a probe 3-brane in a five-dimensional bulk with Lovelock terms on the brane and in the bulk. We study multifield generalizations of the Galileon and extend this probe-brane view to higher codimensions. We derive an extremely restrictive theory of multiple Galileon fields, interacting through a quartic term controlled by a single coupling, and trace its origin to the induced brane terms coming from Lovelock invariants in the higher codimension bulk. We explore some properties of this theory, finding de Sitter like self-accelerating solutions. These solutions have ghosts if and only if the flat space theory does not have ghosts. Finally, we prove a general nonrenormalization theorem: multifield Galileons are not renormalized quantum mechanically to any loop in perturbation theory.

264 citations