Symmetries of BLT-Sets

We do the tentative beginnings of a study of BLT-sets of generalised quadrangles via their symmetries. In particular, the study of whorls about a line leads us to hyperbolic reflections preserving a BLT-set of Q(4, q).     

Weak density of smooth maps for the Dirichlet energy between manifolds

We prove that given a simply connected compact manifold M and a closed manifold N, any map in the Sobolev space W ^1,2(M,N) can be approximated weakly by smooth maps between M and N. Submitted: September 2002, Final version: November 2002.     

Functional Quantization and Small Ball Probabilities for Gaussian Processes

Quantization consists in studying the L ^r -error induced by the approximation of a random vector X by a vector (quantized version) taking a finite number n of values. We investigate this problem for Gaussian random vectors in an infinite dimensional Banach space and in particular, for Gaussian processes. A precise link proved by Fehringer⁽⁴⁾ and Dereich et al. ⁽³⁾ relates lower and upper bounds for small ball probabilities with upper and lower bounds for the quantization error, respectively. We establish a complete relationship by showing that the same holds for the direction from the quantization error to small ball probabilities. This allows us to compute the exact rate of convergence to zero of the minimal L ^r -quantization error from logarithmic small ball asymptotics and vice versa.     

A comparison theorem for a piecewise Lipschitz continuous Hamiltonian and application to Shape-from-Shading problems

Summary The reconstruction from a shaded image of a Lambertian and not self-shadowing surface illuminated by a single distant pointwise light source may be written as a first-order Hamilton-Jacobi equation.In this paper, we continue the investigation begun in E. Rouy and A. Tourin into the uniqueness of the solution of this equation; the approach is based on the viscosity solutions theory and the dynamic programming principle.More precisely, we concentrate here on the uniqueness of the viscosity solution of this equation in case the measured luminous intensity reflected by the surface is discontinuous along a smooth curve. We prove a general comparison result for a piecewise Lipschitz continuous Hamiltonian and illustrate it by numerical experiments.     

Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.     

Characteristic classes of flat bundles, II

On a smooth varietyX defined over a fieldK of characteristic zero, one defines characteristic classes of bundles with an integrableK-connection in a group lifting the Chow group, which map, whenK is the field of complex numbers andX is proper, to Cheeger-Simons' secondary analytic invariants, compatibly with the cycle map in the Deligne cohomology.     

A short note on the generalized Euler transform for the summation of power series

Applying the generalized Euler transform to the firstn partial sums of a power series results in a triangular array whose inferior diagonal givesn approximate values of the sum of this series. The aim of this short note is to estimate the best of thesen values and to compare it with the actual best one for a collection of test series.     

Trace Functionals for a Class of Pseudo-Differential Operators in R n

In this paper we define trace functionals on the algebra of pseudo-differential operators with cone-shaped exits to infinity. Furthermore, we improve the Weyl formula on the asymptotic distribution of eigenvalues and make use of it in order to establish inclusion relations between the interpolation normed ideals of compact operators in L ²(R ⁿ ) and the above operator classes.     

Probing the Conformational Stability of Two Different Copper Proteins: A Dynamic Fluorescence Study on Azurin and Ascorbate Oxidase

Tryptophan fluorescence is extremely useful to monitor structural conformational transitions in proteins. Denaturant-induced unfolding of azurin and ascorbate oxidase has been studied by dynamic fluorescence measurements in the frequency domain and the results have been interpreted in terms of continuous distribution of lifetimes. The data add new information on the unfolding mechanism that was previously analyzed by steady-state emission spectroscopy. In particular, the existence of multiple, parallel unfolding pathways may be envisaged and correlated, in both cases, to the two protein structures. The effect of metal depletion has been also characterized by fluorescence lifetime measurements. In the case of azurin, a monomeric protein, the data demonstrate that copper removal yields a totally different unfolding pathways with respect to the holo protein, indicating that metal ion plays a fundamental structural role in the wild type, native protein. In the case of ascorbate oxidase a dimer of 140 kDa, only minor effects have been detected by copper removal. However, the analysis of the fluorescence decay in presence of different amounts of guanidinium hydrochloride gives new important insights on the unfolding intermediates. In particular the data support the hypothesis of a partial exposure of an outer layer of dimer at intermediate denaturant concentration. This ability of dynamic fluorescence to pinpoint the presence of structural micro-heterogeneity in the unfolding pathways of proteins demonstrates the greater power of this technique compared to the most commonly used steady-state measurements.