1,215 research outputs found

    Mean convergence of orthogonal series and lagrange interpolation

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    Three notes on orthogonal polynomials

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    We love open source software. No, you can’t have our code

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    Librarians are among the strongest proponents of open source software. Paradoxically, libraries are also among the least likely to actively contribute their code to open source projects. This article identifies and discusses six main reasons this dichotomy exists and offers ways to get around them

    Certain rational functions whose power series have positive coefficients

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    Thomas Brussig: Helden wie wir

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    Berlin: Volk und Welt, 1995. 322 p

    Equilibrium Positions, Shape Invariance and Askey-Wilson Polynomials

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    We show that the equilibrium positions of the Ruijsenaars-Schneider-van Diejen systems with the trigonometric potential are given by the zeros of the Askey-Wilson polynomials with five parameters. The corresponding single particle quantum version, which is a typical example of "discrete" quantum mechanical systems with a q-shift type kinetic term, is shape invariant and the eigenfunctions are the Askey-Wilson polynomials. This is an extension of our previous study [1,2], which established the "discrete analogue" of the well-known fact; The equilibrium positions of the Calogero systems are described by the Hermite and Laguerre polynomials, whereas the corresponding single particle quantum versions are shape invariant and the eigenfunctions are the Hermite and Laguerre polynomials.Comment: 14 pages, 1 figure. The outline of derivation of the result in section 2 is adde

    Eight lectures on orthogonal polynomials

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    Drivers of on-farm performance of irrigation water management practices: Empirical Evidence from eastern Arkansas

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    Unsustainable agricultural practices are putting a strain on freshwater supplies in many parts of the world. More efficient irrigation techniques are going to be critical to feed a growing population. Data from the 2016 Arkansas Irrigation Survey was used to assess the adoption of three Irrigation Water Management (IWM) practices: multiple inlet rice irrigation, tailwater recovery, and storage reservoirs. Results indicate that these practices do not always lead to reported pumping time reductions, a proxy for water use savings. Large variations in pumping time reduction are observed across producers for all three practices. A Tobit model was used to examine the relationship between pumping time reduction and a set of producer, farm, and water supply characteristics. Operators that owned their land had a more significant reduction in pumping time when using tailwater recovery systems and storage reservoirs than those who did not. Land ownership had no discernible influence on pumping time reduction for multiple inlet rice irrigation. More formal education and years of farming experience both had a negative relationship with pumping time reduction for multiple inlet irrigation. Users of tailwater recovery systems achieved sizeable pumping time reductions when faced with a declining groundwater table compared to those who implement multiple inlet irrigation. This reduction in pumping time is consistent with the role of on-farm reservoirs as an infrastructure-based solution to convert groundwater to surface water. Counter to expectations, having an agriculture-related formal education or flow meters did not influence reported pumping time savings. By providing empirical evidence on how different factors can affect the effectiveness of IWM practices, findings from this paper provide insight for IWM implementation programs

    An inequality for the classical polynomials

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