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.     

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.

     

On the support of the Ashtekar-Lewandowski measure

We show that the Ashtekar-Isham extension of the configuration space of Yang-Mills theories is (topologically and measure-theoretically) the projective limit of a family of finite dimensional spaces associated with arbitrary finite lattices.These results are then used to prove that is contained in a zero measure subset of with respect to the diffeomorphism invariant Ashtekar-Lewandowski measure on . Much as in scalar field theory, this implies that states in the quantum theory associated with this measure can be realized as functions on the extended configuration space .     

Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

Magnetic penetration depth in V3Si and LiTi2O4 measured by μSR

Muon spin relaxation (SR) studies have been performed in the normal spinel LiTi₂O₄ and the A-15 superconductor V₃Si to measure the magnetic penetration depth . The relaxation rate(T) 1/² in field-cooled measurements shows a sharp increase belowT _c followed by saturation at low temperatures in both systems. This feature implies an isotropic energy gap without anomalous zeros, and most likelys-wave pairing. The low temperature penetration depth (T 0) is determined to be 2100Å for LiTi₂O₄ and 1300Å for V₃Si respectively. Assuming a clean limit relation ^–2 n _s /m ^*, we derive the Fermi temperatureT _F n _s/ ^2/3 m ^* from the relaxation rate and the Sommerfeld constant asT _F ^3/4–1/4. Unlike conventional superconductors, both LiTi₂O₄ and V₃Si have a large ratio ofT _c /T _F 0.01, only slightly smaller than those ratios in more exotic superconductors.We thank C. Ballard and K. Hoyle for technical assistance. Work at Columbia University is supported by NSF Grant No. DMR-89-13784 and Packard Foundation (YJU). Ames Laboratory is operated for the U. S. Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. Work at Ames was supported by the Director for Energy Research, Office of Basic Energy Sciences.