In two recent papers we overhauled the theory of ternary complementary pairs, focusing on questions relating to the possible weights of pairs, and special pairs from which all others can be derived, which we call “primitive.” Of particular interest at this time is a new refinement of the concept of primitivity, which necessitates some revisions to our tables. In this article we report on the st...

A semi-computable set S in a computable metric space need not be computable. However, in some cases, if S has certain topological properties, we can conclude that S is computable. It is known that if a semi-computable set S is a compact manifold with boundary, then the computability of ∂S implies the computability of S. In this paper we examine the case when S is a 1-manifold with boundary, not...

Ramanujan studied the analytic properties of many q-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious q-series fit into the theory of automorphic forms. The analytic theory of partial theta functions however, which have q-expansions resembling modular theta functions, is not well understood. Here we con...

We develop a new framework for location of competitive facilities by introducing non-constant expenditure functions into spatial interaction location models. This framework allows us to capture two key effects – market expansion and cannibalization – within the same model. We develop algorithmic approaches for finding optimal or near-optimal solutions for several models that arise from choosing...

A piecewise linear (PWL) function approximation scheme is described by a lattice algebra of modified operators that allows for the interpolation of PWL function vertexes. A new recursive method called Centred Recursive Interpolation (CRI) based on such modified operators is analysed for successive function smoothing and more accurate approximation. This approximation method, simple but accurate...

We describe a new method to represent (partial) recursive functions in type theory. For every recursive definition, we define a co-inductive type of prophecies that characterises the traces of the computation of the function. The structure of a prophecy is a possibly infinite tree, which is coerced by linearisation to a type of partial results defined by applying the delay monad to the co-domai...

In functional languages, iterative operations on data collections are naturally expressed using recursive functions on recursive data structures. In this paper, we present a method to extract data parallelism from recursive functions and generate data parallel programs. As the parallel model for object programs, we use polytypic parallel skeletons. This model can express data parallel operation...

The earlier SCM computer did not contain recursive function, so Trybulec and Nakamura proved the correctness of the Euclid’s algorithm only by way of an iterative program. However, the recursive method is a very important programming method, furthermore, for some algorithms, for example Quicksort, only by employing a recursive method (note push-down stack is essentially also a recursive method)...

in this paper, we propose to extend the hierarchical bivariatehermite interpolant to the spherical case. let $t$ be an arbitraryspherical triangle of the unit sphere $s$ and  let $u$ be a functiondefined over the triangle $t$. for $kin mathbb{n}$, we consider ahermite spherical interpolant problem $h_k$ defined by some datascheme $mathcal{d}_k(u)$ and which admits a unique solution $p_k$in the ...

Given two elementary embeddings from the collection of sets of rank less than λ to itself, one can combine them to obtain another such embedding in two ways: by composition, and by applying one to (initial segments of) the other. Hence, a single such nontrivial embedding j generates an algebra of embeddings via these two operations, which satisfies certain laws (for example, application distrib...