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Abstract: In this article, we study using model theory certain classes of real functions: restricted quasi-analytic classes. Let E be such a class of functions, we introduce a natural language , including E and a theory T in such that T admits quantifiers elimination, is o-minimal and is equivalent to the complete theory of in . To cite this article: A. Rambaud, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]

Abstract: Rivaroxaban (Xarelto®) is a new oral, direct and selective inhibitor of the factor Xa of the coagulation cascade. The main pharmacokinetic characteristics of rivaroxaban are a bioavailability of approximately 80-100%, a maximum concentration obtained in 2 to 4 hours, a terminal half-life of elimination of 7 to 11 hours, a renal elimination for 1/3 for the active hepatic metobolism from the cytochrome P450 (3A4) for the other 2/3. The main sources of variability are the renal and the liver function and potential interactions with some strong inhibitors or inducers of the CYP450 3A4. Phase II clinical studies have shown that this compound can be orally administrated, once or twice daily, without any biological monitoring and without any need for dose adjustment. There is a contra-indication in case of severe liver insufficiency and not recommended in case of severe renal impairment. Pharmacodynamically, Rivaroxaban is a direct and selective factor Xa inhibitor without any effect on the factor IIa and without any interaction on platelets. Four phases II with 2787 patients were carried out to for venous thromboembolic (VTE) prophylaxis after major orthopaedic surgery, showing that 10 mg once daily could be the optimal dose regimen to assess in phase III. Two phases II with 1446 patients were carried out for the treatment of VTE showing that 15 mg twice daily for 3 weeks and then 20 mg once daily could be the optimal dose regimen to evaluate in the following phases 3. No strong signal for a potential liver toxicity was shown during these 6 phases II. [Copyright &y& Elsevier]

Abstract: We describe a nonlinear technique to eliminate oscillations appearing in the discretization of diffusion operators with hybrid schemes. [Copyright &y& Elsevier]

Abstract: We give here a counter-example to an old conjecture in the theory of singularities. This conjecture is that the function that appears in the strong Artin approximation theorem is bounded by an affine function. First we study Diophantine approximation between the field of power series in several variables and its completion for the -adic topology. We show, with an example, that there is no Liouville theorem in this case. This example gives us our counter-example (cf. théorème 1.2). As an application, we give a new proof of the fact that there is no theory of elimination of quantifiers for the field of fractions of the ring of power series in several variables. [Copyright &y& Elsevier]