We show how to calculate three low degree set-theoretic generators (i.e., algebraic surfaces) for all rational space curves of low degree (degree ≤ 6) as well as for all higher degree rational space curveswhere at least one element of theirμ-basis has degree 1 from a μ-basis of the parametrization. In addition to having low degree, at least two of these surface generators are always ruled surfa...

Let X ⊂ R be a set that is definable in an o-minimal expansion of R. This paper shows that, in a suitable sense, there are very few rational points of X that do not lie on some connected semialgebraic subset of X of positive dimension. 2000 Mathematics Subject Classification: 11G99, 03C64

We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is different from the original one, given by Douady and Hubbard and refined by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depen...

We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is di erent from the original one, given by Douady and Hubbard and re ned by Lavaurs, in several ways: it replaces analytic arguments by combinatorial ones; it does not use complex analytic depende...

To each pseudovariety of abelian groups residually containing the integers, there is naturally associated a proonite topology on any nite rank free abelian group. We show in this paper that if the pseudovariety in question has a decidable membership problem, then one can eeectively compute membership in the closure of a subgroup and more generally, in the closure of a rational subset of such a ...

We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring. We say that a subsemimodule of the free semimodule Sn over a semiring S is rational if it has a generating family that is a rational subset of Sn, Sn being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, r...

In this paper, we propose a new approach to deal with beliefs by supposing that a rational agent has a degree of trustiness for each information it disposes of. We propose (i) a new framework for dealing with imprecise beliefs and desires; (ii) two algorithms for updating the mental state of an agent in this new setting; (iii) three ways for comparing the resulting fuzzy set of desires and (iv)...