Algorithms to Compute the Lyndon Array

We first describe three algorithms for computing the Lyndon array that have been suggested in the literature, but for which no structured exposition has been given. Two of these algorithms execute in quadratic time in the worst case, the third achieves linear time, but at the expense of prior computation of both the suffix array and the inverse suffix array of x. We then go on to describe two variants of a new algorithm that avoids prior computation of global data structures and executes in worst-case n log n time. Experimental evidence suggests that all but one of these five algorithms require only linear execution time in practice, with the two new algorithms faster by a small factor. We conjecture that there exists a fast and worst-case linear-time algorithm to compute the Lyndon array that is also elementary (making no use of global data structures such as the suffix array)

Gust–Airfoil Coupling with a Loaded Airfoil

The unsteady load response of an airfoil encountering a gust is often modeled using analytical transfer functions, which assume idealized behavior of both the flow and the airfoil. One such transfer function is the Sears function, which models a pure transverse gust interacting with a flat-plate airfoil at zero mean incidence. The function was extended by Goldstein and Atassi (“A Complete Second-Order Theory for the Unsteady Flow About an Airfoil due to a Periodic Gust,” Journal of Fluid Mechanics, Vol. 74, No. 4, 1976, pp. 741–765) to account for camber and incidence, as well as the presence of a streamwise gust component. Atassi (“The Sears Problem for a Lifting Airfoil Revisited-New Results,” Journal of Fluid Mechanics, Vol. 141, April 1984, pp. 109–122) showed that the effects of camber and incidence (that is, nonzero mean airfoil loading) are not negligible when there is a streamwise gust component. In this work, new experimental data are shown for an airfoil with nonzero loading encountering a gust with both streamwise and transverse components. As well as giving validation to the Atassi model, the flow physics behind the model is shown, including the superposition of the gust onto the airfoil potential field and the propagation of the gust along the airfoil surface

Secondary literacy across the curriculum: Challenges and possibilities

This paper discusses the challenges and possibilities attendant upon successfully implementing literacy across the curriculum initiatives – or ‘school language policies’ as they have come to be known - particularly at the secondary or high school level. It provides a theoretical background to these issues, exploring previous academic discussions of school language policies, and highlights key areas of concern as well as opportunity with respect to school implementation of such policies. As such, it provides a necessary conceptual background to the subsequent papers in this special issue, which focus upon the Secondary Schools’ Literacy Initiative (SSLI) – a New Zealand funded programme that aims to establish cross-curricular language and literacy policies in secondary schools

Micronutrient fertilization on a typic acrorthox at Manaus, Brazil.

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Phosphorus fertilizer placement and profitability.

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Lime and gypsum applications.

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Lime requirements and downward movement of Ca and Mg.

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Nutrient dynamics.

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