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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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55 citations
TL;DR: In this paper, two explicit representations of a C1 quintic interpolant over triangles are derived by generalization of Coons' methods and Bernstein-Bezier methods, respectively.
Abstract: Two explicit representation of a C1 quintic interpolant over triangles are given. These representations are derived by generalization of Coons' methods and Bernstein-Bezier methods, respectively.
55 citations
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TL;DR: In this paper, an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrodinger equations (NLS) is presented.
Abstract: This paper introduces an extension of the time-splitting sine-spectral (TSSP) method for solving damped focusing nonlinear Schrodinger equations (NLS). The method is explicit, unconditionally stable and time transversal invariant. Moreover, it preserves the exact decay rate for the normalization of the wave function if linear damping terms are added to the NLS. Extensive numerical tests are presented for cubic focusing nonlinear Schrodinger equations in 2d with a linear, cubic or a quintic damping term. Our numerical results show that quintic or cubic damping always arrests blowup, while linear damping can arrest blowup only when the damping parameter $\dt$ is larger than a threshold value $\dt_{\rm th}$. We note that our method can also be applied to solve the 3d Gross-Pitaevskii equation with a quintic damping term to model the dynamics of a collapsing and exploding Bose-Einstein condensate (BEC).
55 citations
TL;DR: Estimates of covariance functions and genetic parameters were obtained for growth of Angus cattle from birth to 820 days of age and showed good agreement for all models at ages with many records, but differed at the highest ages and at very early ages with few weights available.
Abstract: Estimates of covariance functions and genetic parameters were obtained for growth of Angus cattle from birth to 820 days of age. Data comprised 84,533 records on 20,731 animals in 43 herds, with a high proportion of animals with 4 or more weights recorded. Changes in weights were modelled through random regression on orthogonal polynomials of age at recording. A total of 11 combinations of quadratic, cubic, quartic and quintic polynomials to model direct and maternal genetic effects and permanent environmental effects were considered. Results showed good agreement for all models at ages with many records, but differed at the highest ages and at very early ages with few weights available. Cubic polynomials appeared to be most problematic. The order of polynomial fit for permanent environmental effects of the animal dominated estimates of phenotypic variances and mean squares for residual errors. A model fitting a quartic polynomial for these effects and quadratic polynomials for the other random effects, appeared to be the best compromise between detailedness of the model which could be supported by the data, plausibility of results, and fit, measured as mean square error.
54 citations
TL;DR: The reduced quintic triangular finite element is shown to be well suited for elliptic problems, anisotropic diffusion, the Grad-Shafranov-Schluter equation, and the time-dependent MHD or extended MHD equations.
54 citations