A Verified Optimization Technique to Locate Chaotic Regions of Hénon Systems

We present a new verified optimization method to find regions for Hénon systems where the conditions of chaotic behaviour hold. The present paper provides a methodology to verify chaos for certain mappings and regions. We discuss first how to check the set theoretical conditions of a respective theorem in a reliable way by computer programs. Then we introduce optimization problems that provide a model to locate chaotic regions. We prove the correctness of the underlying checking algorithms and the optimization model. We have verified an earlier published chaotic region, and we also give new chaotic places located by the new technique.     

Electronic properties of model quantum-dot structures in zero and finite magnetic fields

We have computed electronic structures and total energies of circularly confined two-dimensional quantum dots and their lateral dimers in zero and finite uniform external magnetic fields using different theoretical schemes: the spin-density-functional theory (SDFT), the current-and-spin-density-functional theory (CSDFT), and the variational quantum Monte Carlo (VMC) method. The SDFT and CSDFT calculations employ a recently-developed, symmetry-unrestricted real-space algorithm allowing solutions which break the spin symmetry. Results obtained for a six-electron dot in the weak confinement limit and in zero magnetic field as well as in a moderate confinement and in finite magnetic fields enable us to draw conclusions about the reliability of the more approximative SDFT and CSDFT schemes in comparison with the VMC method. The same is true for results obtained for the two-electron quantum dot dimer as a function of inter-dot distance. The structure and role of the symmetry-breaking solutions appearing in the SDFT and CSDFT calculations for the above systems are discussed. Received 16 October 2001 and Received in final form 17 January 2002     

Tracing Possible Structural Asymmetry of Silica Gel Used for Precoating Thin-Layer Chromatography Plates

JPC – Journal of Planar Chromatography – Modern TLC - We have previously described unexpected two-dimensionality in the thin-layer chromatographic separation of pairs of enantiomers of...     

Orderings of uniquely colorable hypergraphs

For a mixed hypergraph H=(X,C,D), where C and D are set systems over the vertex set X, a coloring is a partition of X into ‘color classes’ such that every C∈C meets some class in more than one vertex, and every D∈D has a nonempty intersection with at least two classes. A vertex-orderx₁,x₂,…,x_n on X (n=|X|) is uniquely colorable if the subhypergraph induced by {x_j:1?j?i} has precisely one coloring, for each i (1?i?n). We prove that it is NP-complete to decide whether a mixed hypergraph admits a uniquely colorable vertex-order, even if the input is restricted to have just one coloring. On the other hand, via a characterization theorem it can be decided in linear time whether a given color-sequence belongs to a mixed hypergraph in which the uniquely colorable vertex-order is unique.     

Optical properties of in situ doped and undoped titania nanocatalysts and doped titania sol-gel nanofilms

In this paper we present spectroscopic properties of doped and undoped titanium dioxide (TiO₂) as nanofilms prepared by the sol-gel process with rhodamine 6G doping and studied by photoacoustic absorption, excitation and emission spectroscopy. The absorption spectra of TiO₂ thin films doped with rhodamine 6G at very low concentration during their preparation show two absorption bands, one at 2.3 eV attributed to molecular dimmer formation, which is responsible for the fluorescence quenching of the sample and the other at 3.0 eV attributed to TiO₂ absorption, which subsequently yields a strong emission band at 600 nm. The electronic band structure and optical properties of the rutile phase of TiO₂ are calculated employing a fully relativistic, full-potential, linearized, augmented plane-wave (FPLAPW) method within the local density approximation (LDA). Comparison of this calculation with experimental data for TiO₂ films prepared for undoped sol-gels and by sputtering is performed.     

A Multidimensional Branch-and-Prune Method for Interval Global Optimization

In this paper a new multidimensional extension of the recently developed one-dimensional enclosure method called kite is given for interval global optimization. A more sophisticated version of the pruning technique based on the kite method is introduced. By the new componentwise approach all the one-dimensional theoretical results and procedures can be used in the higher-dimensional case. The possibilities in the implementation of the new algorithm together with numerical results on 40 standard test problems are presented.     

Penetration of radionuclides across the skin: Rat age dependent promethium permeation through skin in vitro

The composition and the permeation properties of the skin are dependent on age. In the animal models for permation studies, age affects the mechanical as well as the permeation properties significantly. The time dependence of permeation of ¹⁴⁷Pm³⁺ from aqueous solution was established by the animal skin model and the age dependence of promethium permeation through the skin was examined. The aim was to find the optimum rat skin age model for radionuclide permeation studies and to assess the relative importance of the main permeation pathways: transepidermal and transfollicular permeation. The skin from 5-day-old rats (5DR) was found to represent the optimum animal model to study transepidermal permeation of ions. The skin from 9-day-old rats (9DR) was selected to study transfollicular permeation of ions. Comparison of the permeated amounts of promethium through the skin without hairs (3 DR to 6 DR) and with hairs (7DR to 12DR) showed that the additional permation mode via follicles significantly contributed to the permeation rate and extent.     

Asymptotically balanced schemes for non-homogeneous hyperbolic systems – application to the Shallow Water equations

In this work we introduce a class of balanced numerical schemes, up to second order, for the solution of general non-homogeneous hyperbolic systems of conservation laws. We give a general technique to build such schemes. We also prove that they balance up to second order a large class of steady solutions in the whole domain but some subset whose measure tends to zero as the grid size decreases to zero. We finally present an application to Shallow Water equations that exhibit the good performances of some of the schemes introduced. To cite this article: T. Chacón Rebollo et al., C. R. Acad. Sci. Paris, Ser. I 338 (2004).