Blow-up for hyperbolic systems in diagonal form

We prove a blow-up result for classical solutions of the Cauchy problem for a nonlinear hyperbolic system in one space dimension. The initial conditions are periodic and the system is supposed to be in diagonal form. We give an estimate of the lifespan of the classical solutions. Received May 2000     

Portable X-ray fluorescence device reveals the artistic palette of Carlo Bononi,Baroque artist from Ferrara

The principal aim of the in situ X-ray fluorescence (XRF) analysis on the canvas “The Coronation of the Virgin” was to characterise the colour palette of Carlo Bononi (Ferrara, 1580–1632), a lesser-known artist of the early Baroque period in Ferrara. More than 100 points were collected by means of an XRF spectrometer, but the presence of many overlapping painted layers left some doubts about the preparation and the background layers. The scanning electron microscopy with energy dispersive spectrometer analysis on two samples resolved some of these doubts. The results obtained indicate the use of typical 17th century pigments, such as lead white, vermilion, azurite and a copper-based green. For yellow pigments, the artist used the yellow ochre in some cases, while in others he used lead-tin yellow. We also individuated at least three different shades of umber. Almost all the pigments have been identified and they are the first step in establishing the technical apparatus necessary to understand the modus operandi of the Ferrarese artist.     

Untersuchungen über die quantitative Analyse des Antimontrisulfids und seiner Röstprodukte

Ohne ZusammenfassungEs sei mir an dieser Stelle gestattet, meinem hochverehrten Lehrer, Herrn Prof. Dr. B. Reinitzer, für die wertvollen Ratschläge und die stets hilfsbereite Unterstützung, die er mir bei meiner, unter seiner Aufsicht ausgeführten Arbeit, hat zuteil werden lassen, meinen wärmsten Dank auszusprechen.     

A realistic pattern of lepton mixing and masses from $$S_4$$ and CP

We calculate the combined angular-distribution functions of the polarized photons ( $\gamma _1$ and $\gamma _2$ ) and electron ( $e^-$ ) produced in the cascade process $\bar{p}p\rightarrow {^3{D_3}}\rightarrow {^3{P_2}}+\gamma _1 \rightarrow (\psi +\gamma _2)+\gamma _1\rightarrow (e^++e^-)+\gamma _1+\gamma _2$ , when the colliding $\bar{p}$ and $p$ are unpolarized. Our results are independent of any dynamical models and are expressed in terms of the spherical harmonics whose coefficients are functions of the angular-momentum helicity amplitudes of the individual processes. Once the joint angular distribution of ( $\gamma _1$ , $\gamma _2$ ) and that of ( $\gamma _2$ , $e^-$ ) with the polarization of either one of the two particles are measured, our results will enable one to determine the relative magnitudes as well as the relative phases of all the angular-momentum helicity amplitudes in the radiative decay processes ${^3{D_3}}\rightarrow {^3{P_2}}+\gamma _1$ and ${^3{P_2}}\rightarrow \psi +\gamma _2$ .     

Detection of genetic modification in cured tobacco leaf: proficiency testing using polymerase chain reaction-based methods

The Cooperation Centre for Scientific Research Relative to Tobacco (CORESTA; Paris, France) "Task Force Genetically Modified Tobacco-Detection Methods" investigated the performance of qualitative and quantitative methods based on the polymerase chain reaction (PCR) for the detection and quantitation of genetically modified (GM) tobacco. In the 4 successful rounds of proficiency testing, the cauliflower mosaic virus 35S RNA promoter (CaMV 35S) and the Agrobacterium tumefaciens nopaline synthase terminator (NOS) were selected as target sequences. Blind-coded reference materials containing from 0.1 to 5.0% and from 0.15 to 4% GM tobacco were used in 2 rounds of qualitative and quantitative PCR, respectively. Eighteen laboratories from 10 countries participated in this study. Considering all methods and 2 rounds, the different laboratories were able to detect GM tobacco at the 0.1% level in 46 out of 58 tests in qualitative assays. The results of the proficiency test indicate that both end point screening and real-time quantitative methods are suitable for the detection of genetically modified organisms in tobacco leaf samples having a GM content of 0.1% or higher. The CORESTA proficiency study represents a first step towards the interlaboratory evaluation of accuracy and precision of PCR-based GM tobacco detection, which may lead to the harmonization of analytical procedures and to the enhancement of comparability of testing results produced by different laboratories.     

Synthesis of 1,7-epoxycyclononanes and 1,8-epoxycyclodecanes by β-fragmentation reactions using LTA and I2

The reaction of derivatives on C3 of 6-hydroxy-2,7-dimethyl-11-oxatricyclo[6.2.1.0^2,6]undecan-4-one with lead tetraacetate and iodine, gave, in a good yield, 1,7-epoxycyclononanes. These compounds are the result of a β-fragmentation at the level of C2-C6 respect to the tertiary hydroxyl group on C6, with an unexpected contraction from a ten to a nine-membered ring system, via a radical addition to the carbonyl group on C4. The treatment of precursors (non-functionalized on C3) with LTA and iodine produced again a β-fragmentation without any structural rearrangement, affording a typical 1,8-epoxycyclodecane system. The transformation of the carbonyl group on C4 into acetate avoided radical additions and rearrangements affording, in high yield, the corresponding cyclodecanes. By this methodology, either 1,7-epoxy-cyclononane or 1,8-epoxycyclodecane could be synthesized, in a good yield, from the same versatile precursor.     

Une procédure de Calderón-Zygmund pour le problème de la racine <Emphasis Type="Italic">k</Emphasis>-ième

Soit f une fonction définie sur un ouvert de ℝ ^d , à valeurs positives ou nulles, de classe C ^k , où k est un entier ≥2. Un résultat de Colombini–Jannelli–Spagnolo assure que ∇(f ^{1/ k} ) appartient à L ¹ _loc. Nous démontrons ici que ∇(f ^{1/ k} )∈L _w ^{k / k −2}, ce qui fournit une amélioration optimale du résultat ci-dessus et une généralisation d’un théorème classique de Glaeser sur la racine carrée. La méthode de preuve requiert l’usage d’une décomposition de Calderón–Zygmund de la fonction f qui nous permet de nous ramener à des formes normales de manipulation simple. Nous montrons également que la régularité C ^k est essentiellement nécessaire au résultat. Nous donnons quelques applications à des problèmes d’équations aux dérivées partielles faiblement hyperboliques. L’adaptabilité des méthodes de décomposition de Calderón-Zygmund, utilisées en analyse harmonique et pseudo-différentielle, trouve dans ces résultats une nouvelle illustration.

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Received: December 13, 2001?Published online: April 14, 2003     

Time-Dependent Loss of Derivatives for Hyperbolic Operators with Non Regular Coefficients

In this paper we will study the Cauchy problem for strictly hyperbolic operators with low regularity coefficients in any space dimension N ≥ 1. We will suppose the coefficients to be log-Zygmund continuous in time and log-Lipschitz continuous in space. Paradifferential calculus with parameters will be the main tool to get energy estimates in Sobolev spaces and these estimates will present a time-dependent loss of derivatives.     

Unprecedented double benzylic rearrangement: regio- and stereospecific tandem 1,4-shift and Curtin rearrangement

An α-benzyloxyketone forming part of a strained cyclopentane carbon framework when treated with 10 equiv of anhydrous NaOH in absolute ethanol, for 2 h, affords in a 65% yield a new 2-benzyl-2-hydroxyketone, resulting from an unprecedented double benzylic rearrangement. This new rearrangement could be interpreted as an initial benzylic 1,4-shift between the O-enolate alkoxide of the ketone group and the oxygen atom of the benzyloxy ether, followed by a Curtin type benzylic 1,2-shift. Apart from the novelty and the synthetic application of this transformation it is worth noting the complete regio- and stereoselectivity observed. The structures of both substrate and product have been confirmed by X-ray diffraction studies. A tentative mechanism is herein proposed.