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.     

Infima and complements in the lattice of quasi-uniformities

We show that the infimum of any family of proximally symmetric quasi-uniformities is proximally symmetric, while the supremum of two proximally symmetric quasi-uniformities need not be proximally symmetric. On the other hand, the supremum of any family of transitive quasi-uniformities is transitive, while there are transitive quasi-uniformities whose infimum with their conjugate quasi-uniformity is not transitive. Moreover we present two examples that show that neither the supremum topology nor the infimum topology of two transitive topologies need be transitive. Finally, we prove that several operations one can perform on and between quasi-uniformities preserve the property of having a complement.     

Bronze roman mirrors: the secret of brightness

The surface microchemical structure of high tin leaded bronze Roman mirrors has been studied by means of scanning electron microscopy combined with energy dispersive spectrometry (SEM-EDS), X-ray diffraction (XRD) and optical microscopy (OM) techniques. The results allowed understanding of the origin of their high chemical stability and silvery-lustrous appearance. Indeed, some areas of the selected Roman mirrors are still characterised by a highly reflective and silver coloured surface even though they have been buried in the soil for about 2000 years. The micro-chemical results obtained from these areas have revealed that the mirror surface was tin enriched via inverse-segregation phenomenon by tailoring the cooling parameters. Furthermore, the presence of tin could be likely enhanced via cycles of oxidation and selective copper corrosion processes, thus resulting in a tin surface enrichment as a semi-transparent amorphous-like tin oxide (SnO₂) film, as well as a copper depletion at the outer surfaces.     

Zinn und Antimon in Legierungen

Ohne Zusammenfassung     

Shape Optimization for Semi-Linear Elliptic Equations Based on an Embedding Domain Method

We study a class of shape optimization problems for semi-linear elliptic equations with Dirichlet boundary conditions in smooth domains in ℝ². A part of the boundary of the domain is variable as the graph of a smooth function. The problem is equivalently reformulated on a fixed domain. Continuity of the solution to the state equation with respect to domain variations is shown. This is used to obtain differentiability in the general case, and moreover a useful formula for the gradient of the cost functional in the case where the principal part of the differential operator is the Laplacian. Online publication 23 January 2004.     

Stable products of spheres in the non-linear coupling of oscillators or quasi-periodic motions

For generic families of vector fields or transformations, normally hyperbolic invariant products of spheres appear near partially elliptic rest points. To cite this article: M. Kammerer-Colin de Verdière, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Evolution in complex systems

What features characterize complex system dynamics? Power laws and scale invariance of fluctuations are often taken as the hallmarks of complexity, drawing on analogies with equilibrium critical phenomena. Here we argue that slow, directed dynamics, during which the system's properties change significantly, is fundamental. The underlying dynamics is related to a slow, decelerating but spasmodic release of an intrinsic strain or tension. Time series of a number of appropriate observables can be analyzed to confirm this effect. The strain arises from local frustration. As the strain is released through “quakes,” some system variable undergoes record statistics with accompanying log‐Poisson statistics for the quake event times. We demonstrate these phenomena via two very different systems: a model of magnetic relaxation in type II superconductors and the Tangled Nature model of evolutionary ecology and show how quantitative indications of aging can be found. © 2004 Wiley Periodicals, Inc. Complexity 10: 49–56, 2004     

Teaching proof in the context of physics

This paper describes an application of statics to geometrical proofs in the classroom. The aim of the study was to find out whether the use of concepts and arguments from statics can help students understand and produce proofs of geometrical theorems. The two theorems studied were (1) that the medians in a triangle meet at a single point which is the centre of gravity of the triangle, and (2) the Varignon theorem, that the lines joining the midpoints of successive sides of a quadrilateral form a parallelogram. The classroom experiment showed that most students were successful in using arguments from statics in their proofs, and that they gained a better understanding of the theorems. These findings lend support to the claim that the introduction of statics helps students produce proofs and grasp their meaning.     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.