Analytic maps of parabolic and elliptic type with trivial centralisers

We prove that for a dense set of irrational numbers α, the analytic centraliser of the map e^{2πiα} z+ z2 near 0 is trivial. We also prove that some analytic circle diffeomorphisms in the Arnold family, with irrational rotation numbers, have trivial centralisers. These provide the first examples of such maps with trivial centralisers

Correlation between capacitance and porosity in microporous carbon monoliths

Specific capacitance of carbons in aqueous KOH electrolyte seems to have two contributions, a double-layer capacitance and a pseudocapacitance. Moreover, the specific capacitance increases as the specific surface area does. Here, we report that the pseudocapacitance is associated with the K+ ion and the double-layer capacitance with both K+ and OH- ions. The former ion dominates the capacitance of a real two-electrode supercapacitor. Two microporous carbon monoliths with surface areas similar for micropores below 0.63 nm but different for larger micropores are chosen. There is a correlation between the double-layer capacitance due to those ions and the surface areas due to micropores with sizes above a certain value. It provides information on the size of those ions as they are electroadsorbed at the double layer. The dielectric permittivity associated with the K+ and OH - ion is discussed in relation to the confinement of these electroadsorbed ions in the micropores. © 2014 American Chemical Society.Financial support through the projects MAT2011-25198 and MP 1004 is gratefully acknowledged. V.B. thanks MINECO for R&C contract.Peer Reviewe