Etude asymptotique des enlacements du mouvement brownien autour des droites de l'espace

Summary The existence of a joint asymptotic distribution for the windings of a three-dimensional Brownian motion around a finite number of straight lines is obtained. This complements the recent studies, by Pitman- Yor, and the authors, of the joint asymptotic distribution for the windings of planar Brownian motion around a finite number of points.The following principle governs the passage from results in the plane to results in space:Let B be a three-dimensional Brownian motion, and P ₁, ..., P _k, k planes which intersect two by two. Then, the convergences in distribution concerning the planar Brownian motions B ⁱ (1ik), defined respectively as the orthogonal projections of B on P _i (1ik), take place jointly, and the corresponding limit variables are independent.     

160Tb nuclear orientation in yttrium single crystal

First experimental results of¹⁶⁰Tb nuclear orientation in yttrium single crystal matrix are described. The influence of external magnetic field in combination with the crystal field interaction is discussed.     

Quaternarisation de l'atome d'azote de systemes tautomeres de la serie des oxo-4 thiazoles. Cycloadditions dipolaires 1,3 des thiazoles mesoioniques formes in situ

4-Hydroxythiazoles and N-acylimino 4-thiazolidinones show similar tautomeric behaviour to azlactones. However, the mechanism of their reaction with dimethylacetylenedicarboxylate or with ethyl vinyl ether differs fundamentally. In the thiazole series, the first step is the quaternization of the nitrogen atom. The mesoionic thiazole intermediate is then trapped by a second molecule of the dipolarophile.     

19F NMR chemical shifts of n-F-alkyl compounds

The examination of ¹⁹F chemical shifts for ca. 650 F-alkylated compounds of general formula CF₃(CF₂)_nCF₂X led to the following conclusions: the CF₂ groups α to X are very sensitive to the nature of X, and are spread over a range of 85 ppm. The effect of the length of the F-alkyl chain decreases rapidly, so that δCF₂(α) can already be considered as characteristic of X for n = 1 or 2 for most practical purposes. Solvent effects (in 9 different solvents having ε = 1.8 to 52.1) were found to be rather small except for the F-alkyl iodides. A chart which indicates the domain in which the CF₂(α) resonance signal is to be expected is given for 42 different series of F-alkylated compounds; it is expected to provide the synthetic chemist with a useful tool for the identification and characterization of such compounds.     

Exposure dose assessment and discussion on radioisotope production and application

The exposure dose status on radioisotope production and application in China has been assessed in the paper. The average annual occupational exposure dose received by workers in the radioisotope production is about one tenth of the annual dose limit in normal situation. It is less than one twentieth for workers in the radioisotope applications. However, the annual collective dose for the latter is higher than the former by one oder of magnitude due to the larger number of workers in the application field. Although the output of radioisotopes increased doubly in 1980's as compared with 1970's, the increase on the annual collective dose was not obvious. For exposure to the public,¹³¹I for example, the collective dose in the radioisotope production decreased by one to two orders of magnitude and the releasing factor reduced by two orders of magnitude. Therefore, the exposure dose received by workers in radioisotope production and application is lower in normal situation. However, the facts worth paying attention to are that there were many events and accidents which happened in the radioisotope applications, especially at the irradiation facilities. The probability of fatal accident was as high as 10^–3 per irradiator year. In order to improve the radiation safety situation, it is imperative to conduct the safety assessment for irradiation facilities, to enhance management of the radioactive wastes and spent sources and to establish the experience feedback system.     

Quantifying uncertainty with ensembles of surrogates for blackbox optimization

Blackbox optimization tackles problems where the functions are expensive to evaluate and where no analytical information is available. In this context, a tried and tested technique is to build surrogates of the objective and the constraints in order to conduct the optimization at a cheaper computational cost. This work introduces an extension to a specific type of surrogates: ensembles of surrogates, enabling them to quantify the uncertainty on the predictions they produce. The resulting extended ensembles of surrogates behave as stochastic models and allow the use of efficient Bayesian optimization tools. The method is incorporated in the search step of the mesh adaptive direct search (MADS) algorithm to improve the exploration of the search space. Computational experiments are conducted on seven analytical problems, two multi-disciplinary optimization problems and two simulation problems. The results show that the proposed approach solves expensive simulation-based problems at a greater precision and with a lower computational effort than stochastic models.