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Abstract. This article deals with the transposition of "fractal robustness" to automatic control. The considered dynamic model which g o verns this phenomenon is a non integer order linear di erential equation where the natural frequency and the damping ratio of the oscillatory mode of the solution are determined. A remarkable result is that the damping ratio is exclusively linked to the non integer order of the di erential equation. This is the corner stone of the CRONE control. The dynamic behaviour of this control is described in tracking and in regulation. The robustness of the damping ratio and of the resonance ratio is demonstrated. An open loop is de ned using closed loop performance speci cations. A C R ONE regulator is approximated by a n i n teger order transmittance. Finally, the principle of the CRONE suspension, the synthesis method and the performance are developed.R esum e. Cet article traite de la transposition en automatique de la "robustesse fractale". Le mod ele dynamique consid er e e s t u n e equation diff erentielle lin eaire d'ordre non entier dont l a f r equence propre et le facteur d'amortissement du mode oscillatoire de la solution sont d etermin es. Un r esultat remarquable tient a ce que le facteur d'amortissement est exclusivement li e a l'ordre non entier de l' equation di erentielle. Un tel r esultat est a l'origine de la commande C R ONE. Le comportement dynamique de cette commande est d ecrit en asservissement e t e n r egulation. La robustesse du facteur de r esonance est d emontr ee. Un transfert en boucle ouverte est d e ni a partir des sp eci cations des performances en boucle ferm ee. Un r egulateur CRONE est synth etis e par une transmittance d'ordre entier. En n, le principe de la suspension CRONE, sa m ethode de synth ese et ses performances s o n t d evelopp es.

SUMMARY BackgroundFew data are available on the incidence, risk factors and contamination pathways involved in acute indigenous hepatitis E in developed countries.

Ester-way to heaven: Unexpected formation of bicyclo[3.1.0]hexene 4 was the main focus of combined experimental and theoretical studies on the Au-catalyzed cycloisomerization of branched dienyne 1 (see scheme), which provided better understanding of the mechanistic details governing the cyclization of enynes bearing a propargylic ester group.Experimental and theoretical studies on Au- and Pt-catalyzed cycloisomerization of a branched dienyne with an acetate group at the propargylic position are presented. The peculiar architecture of the dienyne precursor, which has both a 1,6- and a 1,5-enyne skeleton, leads, in the presence of alkynophilic gold catalysts, to mixtures of bicyclic compounds 3, 4, and 5. Formation of unprecedented bicyclo[3.1.0]hexene 5 is the main focus of this study. The effect of the ancillary ligand on the gold center was examined and found to be crucial for formation of 5. Further mechanistic studies, involving cyclization of an enantioenriched dienyne precursor, (18)O-labeling experiments, and DFT calculations, allowed an unprecedented reaction pathway to be proposed. We show that bicyclo[3.1.0]hexene 5 is likely formed by a 1,3-OAc shift/allene-ene cyclization/1,2-OAc shift sequence, as calculated by DFT and supported by Au-catalyzed cyclization of isolated allenenyl acetate 7, which leads to improved selectivity in the formation of 5. Additionally, the possibility of OAc migration from allenyl acetates was supported by a trapping experiment with styrene that afforded the corresponding cyclopropane derivative. This unprecedented generation of a vinyl metal carbene from an allenyl ester supports a facile enynyl ester/allenenyl ester equilibrium. Further examination of the difference in reactivity between enynyl acetates and their corresponding [3,3]-rearranged allenenyl acetates toward Au- and Pt-catalyzed cycloisomerization is also presented.

Polycyclic derivatives incorporating a cyclopropyl group have been efficiently synthesized from propargyl acetates using platinum(II), gold(I) and goldA C H T U N G T R E N N U N G (III) catalysis. These reactions which are also viable for the preparation of medium-sized rings, proceed with a complete diastereocontrol and can also be run in neat conditions.

Catalytic asymmetric vinylogous Mukaiyama reactions on ketones, leading to the formation of alpha,beta-unsaturated lactones with tertiary alcohols, have been described (11 examples, up to 93% ee). This methodology has been applied in a formal enantioselective synthesis of taurospongin A (12 steps, 6% overall yield).