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     

Über die Darstellung der Methylpropylessigsäure aus Acetessigester und Malonsäurediäthylester und die Löslichkeitsbestimmungen einiger Salze dieser Säure und der Trimethylessigsäure

Ohne Zusammenfassung