Interplay between an elusive 4-(isopropylamino)imidazol-2-ylidene and its isolable mesoionic tautomer, and associated reactivities

An elusive free 4-(isopropylamino)imidazol-2-ylidene is engaged in a tautomeric equilibrium with its mesoionic tautomer, 4-(isopropylamido)imidazolium, which displays the typical reactivity of a cyclic diaminocarbene; once coordinated to a Rh(I) centre, it undergoes a smooth 4e(-) oxidation of its backbone to yield an amido-amidino-carbene, a weak electron donor viable only in its complexed form.     

Long-range intramolecular S → N acyl migration: a study of the formation of native peptide analogues via 13-, 15-, and 16-membered cyclic transition states

The intramolecular long-range S → N acyl migration via 13-, 15-, and 16-membered cyclic transition states to form native tetra- and pentapeptide analogues was studied on S-acylcysteine peptides containing β- or γ-amino acids. The pH-dependency study of the acyl migration via a 15-membered cyclic transition state indicated that the reaction is favored at a pH range from 7.0 to 7.6. Experimental observations are supported by structural and computational investigations.     

Spectral measure and approximation of homogenized coefficients

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation formula to design and analyze effective and computable approximations of the homogenized coefficients. In particular, we show that information on the edge of the spectrum of the generator of the environment viewed by the particle projected on the local drift yields bounds on the approximation error, and conversely. Combined with results by Otto and the first author in low dimension, and results by the second author in high dimension, this allows us to prove that for any dimension d?≥ 2, there exists an explicit numerical strategy to approximate homogenized coefficients which converges at the rate of the central limit theorem.     

A concavity inequality for symmetric norms

We review some recent convexity results for Hermitian matrices and we add a new one to the list: Let A be semidefinite positive, let Z be expansive, Z^∗Z?I, and let f:[0,∞)→[0,∞) be a concave function. Then, for all symmetric norms

‖f(Z^∗AZ)‖?‖Z^∗f(A)Z‖.     

Exponential mixing for the Teichmüller flow

We study the dynamics of the Teichmüller flow in the moduli space of Abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of Hölder observables. A geometric consequence is that the $SL(2,\mathbb{R})We study the dynamics of the Teichmüller flow in the moduli space of Abelian differentials (and more generally, its restriction to any connected component of a stratum). We show that the (Masur-Veech) absolutely continuous invariant probability measure is exponentially mixing for the class of H?lder observables. A geometric consequence is that the action in the moduli space has a spectral gap.     

A matrix reverse Hölder inequality

A matrix reverse Hölder inequality is given. This result is a counterpart to the concavity property of matrix weighted geometric means. It extends a scalar inequality due to Gheorghiu and contains several Kantorovich type inequalities.