27 research outputs found

    A sofic group away from amenable groups

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    We give an example of a sofic group, which is not a limit of amenable groups.Comment: 6 pages, 0 figur

    The arithmetic of hyperelliptic curves

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    We summarise recent advances in techniques for solving Diophantine problems on hyperelliptic curves; in particular, those for finding the rank of the Jacobian, and the set of rational points on the curve

    Fixed points and amenability in non-positive curvature

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    Consider a proper cocompact CAT(0) space X. We give a complete algebraic characterisation of amenable groups of isometries of X. For amenable discrete subgroups, an even narrower description is derived, implying Q-linearity in the torsion-free case. We establish Levi decompositions for stabilisers of points at infinity of X, generalising the case of linear algebraic groups to Is(X). A geometric counterpart of this sheds light on the refined bordification of X (\`a la Karpelevich) and leads to a converse to the Adams-Ballmann theorem. It is further deduced that unimodular cocompact groups cannot fix any point at infinity except in the Euclidean factor; this fact is needed for the study of CAT(0) lattices. Various fixed point results are derived as illustrations.Comment: 33 page

    Sur les unités dans les corps biquadratiques primitifs du premier rang

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    Remarques sur les formes à plusieurs variables décomposables en facteurs linéaires

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    Modelling the impacts of maize decomposition on glyphosate dynamics in mulch

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    International audienceThe retention of crop residues as mulch on the soil surface in conservation agriculture systems greatly influences the fate of pesticides, as most of the applied pesticide is intercepted by mulch before moving to the soil. This work was conducted in order to model the effect of maize decomposition on glyphosate degradation in mulch and soil. Labelled 14C-glyphosate degradation was monitored for 49 days in three treatments with the same soils but with maize residues at different stages of decomposition (0, 20 and 49 days). Fresh residues of maize (0 days) exhibited an evolution of their biochemical fractions to a greater extent than decomposed residues. Glyphosate mineralization was faster in the 0-day treatment in mulch residues and in the soil layer below the mulch. However, a greater formation of non-extractable residues (NERs) was observed in mulch residues and soils in the 20- and 49-day treatments than in the 0-day treatment. Modelling maize mulch decomposition with the COP-soil model indicated that microbial activity was different in the three treatments and depended on the initial composition of maize residues. Glyphosate mineralization in mulch and soil can be simulated with an assumption of co-metabolism by coupling the modules of pesticide degradation and mulch carbon decomposition. Glyphosate and its metabolites, including soluble and adsorbed fractions, were simulated with the same adsorption coefficients for all treatments. The simulation of NER formation, however, suggested that more than one microbial population may be involved in the degradation process and could be added in the future development of the model

    Cycles of covers

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