A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval

According to Thurston's stability theorem, every group of C^1 diffeomorphisms of the closed interval is locally indicable (.e., every finitely generated subgroup factors through Z). We show that, even for finitely generated groups, the converse of this statement is not true. More precisely, we show that the semi-direct product between F_2 an Z^2, although locally indicable, does not embed into Diff_+^1 (]0,1[). (Here F_2 is any free subgroup of SL(2,Z), and its action on Z^2 is the projective one.) Moreover, we show that for every non-solvable subgroup G of SL(2,Z), the semi-direct product between G and Z^2 does not embed into Diff^1_+(S^1).Comment: 8 pages, no figur

Asymmetric trade liberalization, sector heterogeneity and Innovation

Innovation, mark-ups and the degree of trade openness vary substantially across sectors. This paper builds a multi-sector endogenous growth model to study the influence that asymmetric trade liberalization and sectorial differences in the degree of product market competition has on the effect of trade openness on R&D investments at a firm level. I find that differences in the degree of competition generate large differences on firm innovative response to trade liberalization. A movement from autarky to free trade promotes innovation and productivity growth in those sectors which are initially less competitive. However, when the initial tariff level is common across sectors, a homogeneous tariff reduction promotes innovation in those sectors which are initially more competitive. The paper suggests that trade liberalization could be a source of industry productivity divergence: firms that are located in industries with greater exposure to foreign trade, invest a greater amount in R&D contributing to industry productivity growth. Finally the paper finds that these asymmetries generate important reallocative effects that contribute to enlarge these differences.Sectorial productivity; international trade; innovation.

Describing all bi-orderings on Thompson's group F

We describe all possible ways of bi-ordering Thompson group F: its space of bi-orderings is made up of eight isolated points and four canonical copies of the Cantor set.Comment: Final versio

A multiplexing architecture for mixed-signal CMOS fuzzy controllers

Limits to precision impose limits to the complexity of analog circuits, hence fuzzy analog controllers are usually oriented to fast low-power systems with low-medium complexity. This paper presents a strategy to preserve most of the advantages of an analog implementation, while allowing a marked increment in system complexity.The works in this papaer has been partially funded by the spanish C.I.C.Y.T. under contract TIC96-1392-C02-02 (SIVA