It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple computation of the value of words in this system and easy constructions for the recognition of recognisable sets of numbers. It is also shown that conversely...

This paper presents a method for computing the explicitly rational solutions of a trivariate rational system of autonomous ordinary differential equations (ODEs) based on the proper parametrization of its invariant algebraic space curve. It is the generalization of the method in [11]. First, an undetermined coefficients method is given for computing the invariant algebraic space curves of the t...

Past parametric tests of demand system rank employed polynomial Engel curve systems. However, by Gorman’s (1981) theorem, the maximum possible rank of a utility derived polynomial demand system is three. The present paper proposes a class of demand systems that are utility derived, are close to polynomial, and have rank four. These systems nest rational polynomial demands, and so can be used to...

2 mation is actually a rational model with a time delay. Through illustrations, we show that the pseudo-rational approximation is simple and effective. It commensurate form. Useful MATLAB codes are also included in the appendix.

In this paper, a spectral collocation approach based on the rational Chebyshev functions for solving the axisymmetric stagnation point flow on an infinite stationary circular cylinder is suggested. The Navier-Stokes equations which govern the flow, are changed to a boundary value problem with a semi-infinite domain and a third-order nonlinear ordinary differential equation by applying proper si...

A rational language can be studied from different points of view. For instance, it can be seen as a part of the free monoid or as a set recognized by a finite automaton; this leads to combinatoric or graphic studies. It can also be considered as a series with coefficients in the boolean semiring; this second point of view is richer since it leads to generalize naturally the theory of rational l...

Meta-reasoning can improve numerous search algorithms, but necessitates collection of statistics to be used as probability distributions, and involves restrictive meta-reasoning assumptions. The recently suggested scheme of type systems in search algorithms is used in this paper for collecting these statistics. The statistics are then used to better estimate the unknown quantity of expected reg...

In this paper I defend the view that there are rational methodological criteria for preferring one system design1 over another and that they are substantially the same as those of the scientific method. The parallels between the notion of a rational system design and the notion of a rational scientific theory are not coincidental: they reflect a fundamental similarity between the invention of d...