Diastereoselective cycloaddition of (S)-N-(1-phenylethylimino)trifluoropropionate and trifluoroethylphosphonate with diazomethane

The cycloaddition reaction of (S)-(α-phenylethylimino)trifluoropropionate with diazomethane leads to a diastereomeric mixture (4.5:1) of 5-trifluoromethyl-1,2,3-triazoline-5-carboxylates. Enantiopure diastereomers were isolated by column chromatography and converted into their respective non-racemic 2-trifluoromethyl-aziridine-2-carboxylates and carboxylic acids. The absolute configuration of newly formed stereogenic centers was determined by XRD analysis. The stereoselective reaction between (S)-N-(α-phenylethyl)trifluoroacetimidoylphosphonate and diazomethane produces a diastereomeric mixture (2.5:1) of 5-trifluoromethyltriazoline-5-phosphonates readily separated by column chromatography in diastereomerically pure forms.     

Small Ball Probabilities of Fractional Brownian Sheets via Fractional Integration Operators

We investigate the small ball problem for d-dimensional fractional Brownian sheets by functional analytic methods. For this reason we show that integration operators of Riemann–Liouville and Weyl type are very close in the sense of their approximation properties, i.e., the Kolmogorov and entropy numbers of their difference tend to zero exponentially. This allows us to carry over properties of the Weyl operator to the Riemann–Liouville one, leading to sharp small ball estimates for some fractional Brownian sheets. In particular, we extend Talagrand's estimate for the 2-dimensional Brownian sheet to the fractional case. When passing from dimension 1 to dimension d2, we use a quite general estimate for the Kolmogorov numbers of the tensor products of linear operators.     

KAM theory in configuration space

A new approach to the Kolmogorov-Arnold-Moser theory concerning the existence of invariant tori having prescribed frequencies is presented. It is based on the Lagrangian formalism in configuration space instead of the Hamiltonian formalism in phase space used in earlier approaches. In particular, the construction of the invariant tori avoids the composition of infinitely many coordinate transformations. The regularity results obtained are applied to invariant curves of monotone twist maps. The Lagrangian approach has been prompted by a recent study of minimal foliations for variational problems on a torus by J. Moser. This research has been supported by the Nuffields Foundation under grant SCI/180/173/G and by the Stiftung Volkswagenwerk.     

Metalloid derivatives for synthesis the preparation of macrocyclic tetrathiolactones

The preparation of macrocyclic thiolactones by condensation of diacyl chlorides with siladithianes is described.     

Folding and unfolding of an elastinlike oligopeptide: "inverse temperature transition," reentrance, and hydrogen-bond dynamics

The temperature-dependent behavior of a solvated oligopeptide, GVG(VPGVG), is investigated. Spectroscopic measurements, thermodynamic measurements, and molecular dynamics simulations find that this elastinlike octapeptide behaves as a two-state system that undergoes an "inverse temperature" folding transition and reentrant unfolding close to the boiling point of water. A molecular picture of these processes is presented, emphasizing changes in the dynamics of hydrogen bonding at the protein/water interface and peptide backbone librational entropy.     

String Jacobi Matrices with Very Fast Decreasing Weights

In this work we investigate a class of string, compact Jacobi matrices with very rapidly decreasing weights. In particular, we have found Hellinger-Weyls function representation as ratio of two entire functions with known Taylor series representation. The asymptotical estimations of zeroes of this entire functions and of eigenvalues of a corresponding operator are found. The application of this theory to Rogers-Ramanujans functions is considered.Submitted: November 18, 2002 Revised: October 30, 2003     

Über die Nitrierung der Opiansäureester und Abkömmlinge der Nitroopiansäure

Ohne Zusammenfassung     

Oracle convergence rate of posterior under projection prior and Bayesian model selection

We apply the Bayes approach to the problem of projection estimation of a signal observed in the Gaussian white noise model and we study the rate at which the posterior distribution concentrates about the true signal from the space ℓ₂ as the information in observations tends to infinity. A benchmark is the rate of a so-called oracle projection risk, i.e., the smallest risk of an unknown true signal over all projection estimators. Under an appropriate hierarchical prior, we study the performance of the resulting (appropriately adjusted by the empirical Bayes approach) posterior distribution and establish that the posterior concentrates about the true signal with the oracle projection convergence rate. We also construct a Bayes estimator based on the posterior and show that it satisfies an oracle inequality. The results are nonasymptotic and uniform over ℓ₂. Another important feature of our approach is that our results on the oracle projection posterior rate are always stronger than any result about posterior convergence with the minimax rate over all nonparametric classes for which the corresponding projection oracle estimator is minimax over this class. We also study implications for the model selection problem, namely, we propose a Bayes model selector and assess its quality in terms of the so-called false selection probability.