Andrew J. Walker

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We present a general scheme to derive higher-order members of the Painlevé VI (PVI) hierarchy of ODE's as well as their difference analogues. The derivation is based on a discrete structure that sits on the background of the PVI equation and that consists of a system of partial difference equations on a multidimensional lattice. The connection with the(More)
INTRODUCTION The present study aimed to explore how athletes respond to different behaviors of their opponents. METHODS Twelve moderately to highly physically active participants with at least two years of cycling experience completed four 4-km time trials on a Velotron cycle ergometer. After a familiarization time trial (FAM), participants performed(More)
We consider the class of trees for which all vertices of degree at least 3 lie on a single induced path of the tree. For such trees, a new superposition principle is proposed to generate all possible ordered multiplicity lists for the eigenvalues of symmetric (Hermitian) matrices whose graph is such a tree. It is shown that no multiplicity lists other than(More)
Nekrashevych conjectured that iterated monodromy groups of quadratic poly-nomials with a pre-periodic kneading sequence have intermediate growth. In this paper we prove intermediate growth for two such groups. We also provide a new proof of intermediate growth for a class of groups containing the Grigorchuk group, previously known to have intermediate(More)
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