A simple proof of an inequality of Bourgain,Brezis and Mironescu

A simpler proof of a recent inequality of Bourgain, Brezis and Mironescu is given. To cite this article: J. Van Schaftingen, C. R. Acad. Sci. Paris, Ser. I 338 (2004).     

tert‐Butyl (6S)‐4‐hydroxy‐6‐isobutyl‐2‐oxo‐1,2,5,6‐tetra­hydropyridine‐1‐carboxyl­ate and tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxopiperidine‐1‐carboxyl­ate

X‐ray studies reveal that tert‐butyl (6S)‐6‐iso­butyl‐2,4‐dioxo­piperidine‐1‐carboxyl­ate occurs in the 4‐enol form, viz. tert‐butyl (6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo‐1,2,5,6‐tetra­hydropyri­dine‐1‐carboxyl­ate, C₁₄H₂₃NO₄, when crystals are grown from a mixture of di­chloro­methane and pentane, and has an axial orientation of the iso­butyl side chain at the 6‐position of the piperidine ring. Reduction of the keto functionality leads predominantly to the corresponding β‐hydroxy­lated δ‐lactam, tert‐butyl (4R,6S)‐4‐hydroxy‐6‐iso­butyl‐2‐oxo­piperidine‐1‐car­boxyl­ate, C₁₄H₂₅NO₄, with a cis configuration of the 4‐hydroxy and 6‐iso­butyl groups. The two compounds show similar molecular packing driven by strong O—H⋯O=C hydrogen bonds, leading to infinite chains in the crystal structure.     

Photothermal microanalysis of thermal discontinuities in metallic samples

Modeling the behavior of a protective coating during a thermal shock not only requires the knowledge of its own thermophysical characteristics, but also those of the coating–substrate discontinuity. According to its nature, this discontinuity can be modeled as a zero-thickness interface (thermal contact resistance) or a finite thickness layer (thermal third body). This paper presents an experimental device and two associated thermal transfer models developed in view of the microscale characterization of such discontinuities.     

Metallo‐supramolecular micelles: Studies by analytical ultracentrifugation and electron microscopy

In aqueous solutions, amphiphilic block copolymers in which a polystyrene (PS) segment is connected to a poly(ethylene oxide) (PEO) block via a bis(2,2′:6′,2″‐ terpyridine ruthenium) complex can form micelles. Such micelles of the protomer type PS₂₀‐[Ru]‐PEO₇₀, according to the preparation procedure representing frozen micelles, were studied by sedimentation velocity and sedimentation equilibrium analysis in an analytical ultracentrifuge and by transmission electron microscopy, with different techniques applied for the sample preparation. The particles obtained were surprisingly multifarious in size. In ultracentrifugation experiments performed at relatively low salt concentrations, the distributions of the sedimentation coefficient s_20,w showed a pronounced peak at 9.6 S and a broad, only partly separated second peak around 14 S. The molar mass of the particles at the peak was around 430,000 g/mol, corresponding to an aggregation number of approximately 85. The average hydrodynamic diameter of the particles in the peak fraction was approximately 13 nm. In electron micrographs of negatively stained samples, spheres of diameters between 10 and 25 nm were the most abundant particles, but larger ones with a wide size range were also visible. The latter particles apparently were composed of smaller ones. The data from both sedimentation analysis and electron microscopy showed that (1) the studied compound formed primary micelles of diameters around 20 nm and (2) the primary micelles had a tendency toward aggregation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3159–3168, 2003     

Positive value of information in games

We exhibit a general class of interactive decision situations in which all the agents benefit from more information. This class includes as a special case the classical comparison of statistical experiments à la Blackwell. AMS 2000 Subject Classification:Primary 91A35.The work of Bruno Bassan and Marco Scarsini was partially supported by MIUR-COFIN. The authors express their thanks to Sylvain Sorin for enlightening comments.     

Thermodynamic non-additivity in disordered systems with extended phase space

Non-additivity effects in coupled dynamic-stochastic systems are investigated. It is shown that there is a mapping of the replica approach to disordered systems with finite replica indexn on Tsallis non-extensive statistics, if the average thermodynamic entropy of the dynamic subsystem differs from the information entropy for the probability distribution in the stochastic subsystem. The entropic indexq is determined by the entropy difference ΔS. In the case of incomplete information, the entropic indexq=1−n is shown to be related to the degree of lost information.     

Boundary blow-up for differential equations with indefinite weight

We obtain results of existence and multiplicity of solutions for the second-order equation x″+q(t)g(x)=0, with x(t) defined for all t∈]0,1[ and such that x(t)→+∞ as t→0⁺ and t→1⁻. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0,1].     

Properties of levels in22Ne

Levels up to 9.3 MeV excitation in²²Ne were studied with the¹⁹ F(α, pγ) ²²Ne reaction atE _α = 12 MeV. Level energies, branching ratios, mean lifetimes, spins and mixing ratios were obtained for a number of levels. Relevant results are compared with many-particle shell-model calculations.