Normal Vietoris Implies Compactness: A Short Proof

One of the most celebrated results in the theory of hyperspaces says that if the Vietoris topology on the family of all nonempty closed subsets of a given space is normal, then the space is compact (Ivanova-Keesling-Velichko). The known proofs use cardinality arguments and are long. In this paper we present a short proof using known results concerning Hausdorff uniformities.     

Inorganic Sol-Gel Preparation of Medium Sized Microparticles of Li2TiO3 from TiCl4 as Tritium Breeding Material for Fusion Reactors

Microspheres of Li₂TiO₃ were fabricated by a classical, inorganic sol-gel process from commercially available TiCl₄. Elaborated process consists of the following main steps: (1) dissolving of TiCl₄ in concentrated aqueous HCl and addition of LiOH; (2) formation of sol emulsion in 2-ethylhexanol-1 containing the surfactant SPAN-80 (EH); (3) gelation of emulsion drops by extraction of water with partially dehydrated EH; (4) impregnation of gel to Li:Ti molar ratio MR = 2; (5) thermal treatment at 1200°C in order to receive chloride free product. This temperature can be significantly lowered (to 750°C) by dechlorination starting solution TiCl₄ by chemical treatment of the with nitric acid to form of nitrate-stabilized titania sols. Tritium release from sol-gel made Li₂TiO₃ microspheres were found very close to that observed for other traditional materials, however for the first sample process starts slightly earlier.     

A purely algebraic characterization of the hyperreal numbers

The hyperreal numbers of nonstandard analysis are characterized in purely algebraic terms as homomorphic images of a suitable class of rings of functions.

     

Double-thresholded estimator of extreme value index

The purpose of this Note is to propose an estimator of the extreme value index constructed by using only the number of points exceeding random thresholds. We prove the weak consistency and the asymptotic normality of this estimator. We deduce from this last result that the rate of convergence of our estimator is in a power of the sample size. To our knowledge, this rate of convergence is not reached by any other estimate of the extreme value index. Through a simulation, we compare our estimator to the moment estimator (Dekkers et al., Ann. Statist. 17 (1989) 1833–1855). To cite this article: L. Gardes, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

A Wilson group of non-uniformly exponential growth

This Note constructs a finitely generated group W whose word-growth is exponential, but for which the infimum of the growth rates over all finite generating sets is 1 – in other words, of non-uniformly exponential growth.This answers a question by Mikhael Gromov (Structures métriques pour les variétés riemanniennes, in: J. Lafontaine, P. Pansu (Eds.), CEDIC, Paris, 1981).The construction also yields a group of intermediate growth V that locally resembles W in that (by changing the generating set of W) there are isomorphic balls of arbitrarily large radius in V and W's Cayley graphs. To cite this article: L. Bartholdi, C. R. Acad. Sci. Paris, Ser. I 336 (2003).     

Berezin-Toeplitz Operators, a Semi-Classical Approach

This article is devoted to the Toeplitz Operators [4] in the context of the geometric quantization [11, 15]. We propose an ansatz for their Schwartz kernel. From this, we deduce the main known properties of the principal symbol of these operators and obtain new results : we define their covariant and contravariant symbols, which are full symbols, and compute the product of these symbols in terms of the Kähler metric. This gives canonical star products on the Kählerian manifolds. This ansatz is also useful to introduce the notion of microsupport.     

Assignments of methanol laser lines by frequency measurements and Fourier transform spectroscopy

We have measured the frequencies of four CH₃OH far-infrared laser lines that were previously known only by wavelength measurement. Two of these lines turned out to be doublets, bringing the total number of measured lines to six. We can now confirm the assignments of five of them and definitely disprove the assignments proposed for the sixth.In particular we confirm the assignments for the four strong laser lines at 205 and 208 µm pumped by the 9-P(34) CO₂ laser line. These lines share a common upper level in the first excited CO-stretch state, and terminate in the upper and lower levels of a hybrid state with J=5. Heterodyne frequency measurements and conventional microwave spectroscopy show that both lines are split into two components approximately 3.5 MHz apart. The origin of this further splitting is interpreted as a perturbed K-splitting.Work supported by Consiglio Nazionale delle Ricerche -Italia     

Access to Paullone Analogues by Intramolecular Heck Reaction

The syntheses of paullone ( 1a ) and three paullone derivatives, including a sulfur analogue ( 2a ), a tricyclic derivative ( 2b ), and a ring‐enlarged variant ( 2c ), are described, Pd‐catalyzed intramolecular Heck reaction being the key step. The kinase‐inhibitory properties of the novel paullone analogues were investigated.     

Growth of single-crystal magnetite nanowires from Fe3O4 nanoparticles in a surfactant-free hydrothermal process

Single-crystal magnetite nanowires with average diameter of ca. 20 nm and length of up to several micrometers were prepared by a simple alkaline surfactant-free hydrothermal process. The crystallinity, purity, morphology, and structural features of the as-prepared magnetite nanowires were investigated by powder X-ray diffraction, transmission electron microscopy (TEM) and selected area electron diffraction. The composition and length of nanowires depends on the pH, with higher pH favoring longer nanowires composed entirely of Fe₃O₄. A mechanism for nanowire growth is proposed.