266 research outputs found
Computational Group Theory
This was the seventh workshop on Computational Group Theory. It showed that Computational Group Theory has significantly expanded its range of activities. For example, symbolic computations with groups and their representations and computations with infinite groups play a major role nowadays. The talks also presented connections and applications to cryptography, number theory and the algorithmic theory of algebras
Analytic cell decomposition and analytic motivic integration
The main results of this paper are a Cell Decomposition Theorem for Henselian
valued fields with analytic structure in an analytic Denef-Pas language, and
its application to analytic motivic integrals and analytic integrals over
\FF_q((t)) of big enough characteristic. To accomplish this, we introduce a
general framework for Henselian valued fields with analytic structure, and
we investigate the structure of analytic functions in one variable, defined on
annuli over . We also prove that, after parameterization, definable analytic
functions are given by terms. The results in this paper pave the way for a
theory of \emph{analytic} motivic integration and \emph{analytic} motivic
constructible functions in the line of R. Cluckers and F. Loeser
[\emph{Fonctions constructible et int\'egration motivic I}, Comptes rendus de
l'Acad\'emie des Sciences, {\bf 339} (2004) 411 - 416]
Panorama of p-adic model theory
ABSTRACT. We survey the literature in the model theory of p-adic numbers since\ud
Denef’s work on the rationality of Poincaré series. / RÉSUMÉ. Nous donnons un aperçu des développements de la théorie des modèles\ud
des nombres p-adiques depuis les travaux de Denef sur la rationalité de séries de Poincaré,\ud
par une revue de la bibliographie
A Geometric Index Reduction Method for Implicit Systems of Differential Algebraic Equations
This paper deals with the index reduction problem for the class of
quasi-regular DAE systems. It is shown that any of these systems can be
transformed to a generically equivalent first order DAE system consisting of a
single purely algebraic (polynomial) equation plus an under-determined ODE
(that is, a semi-explicit DAE system of differentiation index 1) in as many
variables as the order of the input system. This can be done by means of a
Kronecker-type algorithm with bounded complexity
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