For general information on bar recursion the reader should consult the papers of Spector [8], where it was introduced, Howard [2] and Tait [11]. In this note we shall prove that the terms of Godel's theory T (in its extensional version of Spector [8]) are closed under the rule BRo•1 of bar recursion of types 0 and 1. Our method of proof is based on the notion of an infinite term introduced by T...

Abstract. We present here generalization of the recursion method of Haydock et al [1] for the calculation of Green matrices (in angular momentum space). Earlier approaches concentrated on the diagonal elements, since the focus was on spectral densities. However, calculations of configuration averaged response functions or neutron scattering cross-sections require the entire Green matrices and s...

We present a structured interior-point method for the efficient solution of the optimal control problem in model predictive control. The cost of this approach is linear in the horizon length, compared with cubic growth for a naive approach. We use a discrete-time Riccati recursion to solve the linear equations efficiently at each iteration of the interior-point method, and show that this recurs...

Bézier curve flattening by recursive subdivision requires that the maximum excursion of the subdivided curve segment be known so that recursion can be terminated once this value drops below the specified flatness criterion. A much more accurate method than the most commonly used techniques to evaluate this distance is presented. This method stops recursion sooner, significantly reducing the num...

We observe that application of a recursion operator of Burgers equation does not produce the expected symmetries. This is explained by the incorrect assumption that D−1 x Dx = 1. We then proceed to give a method to compute the symmetries using the recursion operator as a first order approximation.

We propose a method for encoding iterators (recursion operators) using interaction nets. The method can be used to obtain a visual notation for functional programs, and also to extend with recursion the many translations of the λ-calculus into interaction nets, which have been proposed as efficient implementation mechanisms. We exemplify the method with a number of list-processing examples that...

This paper presents structural recursion as the basis of the syntax and semantics of query languages for semistructured data and XML. We describe a simple and powerful query language based on pattern matching and show that it can be expressed using structural recursion, which is introduced as a top-down, recursive function, similar to the way XSL is deened on XML trees. On cyclic data, structur...

Let F be a finite real abelian extension of Q. Let M be an odd positive integer. For every squarefree positive integer r the prime factors of which are congruent to 1 modulo M and split completely in F, the corresponding Kolyvagin class κr ∈ F×/F×M satisfies a remarkable and crucial recursion which for each prime number l dividing r determines the order of vanishing of κr at each place of F abo...