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Sun's Log-concavity Conjecture on the Catalan–Larcombe–French Sequence

Acta Mathematica Sinica,English Series 2016年第5期32卷 553-558页

作者： James J.Y.ZHAO Center for Applied Mathematics Tianjin University

Let {Pn},n≥0 denote the Catalan-Larcombe-French sequence, which naturally came from the series expansion of the complete elliptic integral of the first kind. In this paper, we prove the strict log-concavity of the sequence { n√Pn}n≥1, which was originally conjectured by Z. W. Sun. We also obtain the strict log-concavity of the sequence {n√Vn}n≥1, where {Vn}n≥0 is the Fennessey-Larcombe- French sequence arising from the series expansion of the complete elliptic integral of the second kind.

关键词： The Catalan-Larcombe-French sequence the Fennessey-Larcombe-French sequence logconcavity three-term recurrence relation

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Recursive Schemes for Scattered Data Interpolation via Bivariate Continued Fractions

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Journal of Mathematical Research with Applications 2016年第5期36卷 583-607页

作者： Jiang QIAN Fan WANG Zhuojia FU Yunbiao WU College of Sciences Hohai University College of Engineering Nanjing Agricultural University College of Mechanics and Materials Hohai University Basic Research Department Hohai University Wentian College

In the paper,firstly,based on new non-tensor-product-typed partially inverse divided differences algorithms in a recursive form,scattered data interpolating schemes are constructed via bivariate continued fractions with odd and even nodes,*** equivalent identities are also obtained between interpolated functions and bivariate continued ***,by means of three-term recurrence relations for continued fractions,the characterization theorem is presented to study on the degrees of the numerators and denominators of the interpolating continued ***,some numerical examples show it feasible for the novel recursive ***,compared with the degrees of the numerators and denominators of bivariate Thiele-typed interpolating continued fractions,those of the new bivariate interpolating continued fractions are much low,respectively,due to the reduction of redundant interpolating ***,the operation count for the rational function interpolation is smaller than that for radial basis function interpolation.

关键词： Scattered data interpolation bivariate continued fraction three-term recurrence relation characterization theorem radial basis function

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