Hierarchies in φ‐spaces and applications

We establish some results on the Borel and difference hierarchies in φ‐spaces. Such spaces are the topological counterpart of the algebraic directed‐complete partial orderings. E.g., we prove analogs of the Hausdorff Theorem relating the difference and Borel hierarchies and of the Lavrentyev Theorem on the non‐collapse of the difference hierarchy. Some of our results generalize results of A. Tang for the space Pω. We also sketch some older applications of these hierarchies and present a new application to the question of characterizing the ω‐ary Boolean operations generating a given level of the Wadge hierarchy from the open sets. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Enantiopure aryl-[1,2,5,6-tetrahydro-pyridinyl] methanols and their use for heterogeneous hydrogenation of ethyl pyruvate

Both enantiomers of two new chiral modifiers (naphthyl- and anthryl-[1,2,5,6-tetrahydro-pyridinyl] methanols, 4H and 5H) are obtained for the first time from inexpensive d-mannitol in 10 easy steps. Until now erythro-4H is the only synthetic chiral modifier available under both enantiomeric forms, which provide enantioselectivities almost as high as those obtained with natural cinchonidine, for which only one enantiomer is available. It is shown that the anthryl group may be less efficient than the naphthyl (the e.e.% drops from 75% with erythro-4H to 46% with erythro-5H) and that N-methyl substitution (trisubstituted nitrogen as in cinchonidine) leads also to a drop in the e.e.% (from 75% with 4H to 39% with 4Me).     

Uniform Asymptotic Expansions for Meixner Polynomials

Meixner polynomials m _n (x;β,c) form a postive-definite orthogonal system on the positive real line x > 0 with respect to a distribution step function whose jumps are Unlike classical orthogonal polynomials, they do not satisfy a second-order linear differential equation. In this paper, we derive two infinite asymptotic expansions for m _n (nα;β,c) as . One holds uniformly for , and the other holds uniformly for , where a and b are two small positive quantities. Both expansions involve the parabolic cylinder function and its derivative. Our results include all five asymptotic formulas recently given by W. M. Y. Goh as special cases. April 16, 1996. Date revised: October 30, 1996.     

La détection infrarouge avec les plans focaux non refroidis : état de l'artUncooled focal plane infrared detectors: the state of the art

The emergence of uncooled detectors has opened new opportunities for IR detection for both military and commercial applications. Development of such devices involves a lot of trade-offs between the different parameters that define the technological stack. These trade-offs explain the number of different architectures that are under worldwide development. The key factor is to find a high sensitivity and low noise thermometer material compatible with silicon technology in order to achieve high thermal isolation in the smallest area as possible. Ferroelectric thermometer based hybrid technology and electrical resistive thermometer based (microbolometer) technology are under development. LETI and ULIS have chosen from the very beginning to develop first a monolithic microbolometer technology fully compatible with commercially available CMOS technology and secondly amorphous silicon based thermometer. This silicon approach has the greatest potential for reducing infrared detector manufacturing cost. After the development of the technology, the transfer to industrial facilities has been performed in a short period of time and the production is now ramping up with ULIS team in new facilities. LETI and ULIS are now working to facilitate the IRFPA integration into equipment in order to address a very large market. Achievement of this goal needs the development of smart sensors with on-chip advanced functions and the decrease of manufacturing cost of IRFPA by decreasing the pixel pitch and simplifying the vacuum package. We present in this paper the technology developed by CEA/LETI and its improvement for being able to designs 384×288 and 160×120 arrays with a pitch of 35 μm. Thermographic application needs high stability infrared detector with a precise determination of the amount of absorbed infrared flux. Hence, infrared detector with internal temperature stabilized shield has been developed and characterized. These results will be presented. To cite this article: J.-L. Tissot, C. R. Physique 4 (2003).     

() reaction studies of Dy and Hf

Angular distributions for the ¹⁶³Dy(t,p) and ¹⁷⁷Hf(t,p) reactions were measured using 17 MeV tritons from the McMaster University Tandem Van de Graaff accelerator. Reaction products were analyzed with a magnetic spectrograph and detected with photographic emulsions. Favored L=0 transitions confirmed assignments of the 5/2⁻[523] band in ¹⁶⁵Dy and 7/2⁻[514] band in ¹⁷⁹Hf. Additional L=0 transitions in each nuclide identified previously unknown 5/2⁻ levels in ¹⁶⁵Dy and 7/2⁻ ones in ¹⁷⁹Hf. Overall trends of L=0 strengths support the existence of subshell closures at neutron numbers 98 and 108. On the basis of a relatively strong L=2 transition, the K^π=11/2⁻ γ-vibration based on the 7/2⁻[514] state is identified at 1689 keV in ¹⁷⁹Hf, about 440 keV above its previously-assigned K^π=3/2⁻ partner.     

Characterization of rankings generated by linear discriminant analysis

Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model.     

Extension theorems for Stokes and Lamé equations for nearly incompressible media and their applications to numerical solution of problems with highly discontinuous coefficients

We prove extension theorems in the norms described by Stokes and Lamé operators for the three‐dimensional case with periodic boundary conditions. For the Lamé equations, we show that the extension theorem holds for nearly incompressible media, but may fail in the opposite limit, i.e. for case of absolutely compressible media. We study carefully the latter case and associate it with the Cosserat problem. Extension theorems serve as an important tool in many applications, e.g. in domain decomposition and fictitious domain methods, and in analysis of finite element methods. We consider an application of established extension theorems to an efficient iterative solution technique for the isotropic linear elasticity equations for nearly incompressible media and for the Stokes equations with highly discontinuous coefficients. The iterative method involves a special choice for an initial guess and a preconditioner based on solving a constant coefficient problem. Such preconditioner allows the use of well‐known fast algorithms for preconditioning. Under some natural assumptions on smoothness and topological properties of subdomains with small coefficients, we prove convergence of the simplest Richardson method uniform in the jump of coefficients. For the Lamé equations, the convergence is also uniform in the incompressible limit. Our preliminary numerical results for two‐dimensional diffusion problems show fast convergence uniform in the jump and in the mesh size parameter. Copyright © 2002 John Wiley & Sons, Ltd.     

Aqueous Solution-Gel Synthesis of Strontium Bismuth Niobate (SrBi2Nb2O9)

The synthesis of multimetal oxides containing pentavalent elements like Nb and Ta out of an aqueous solution is very complicated due to the extremely high sensitivity of these metals towards hydrolysis. Moreover the only water-soluble starting compound is the oxalate which is not very suited for gel formation. Nevertheless, from Nb-oxalate it is possible to prepare a water-soluble Nb(V)-precursor by chemical modification. The synthesized precursor remains stable in the pH-range needed for gel formation. This Nb(V)-precursor is used for the synthesis of the ferroelectric material SrBi₂Nb₂O₉ (SBN). An aqueous acetate-citrate solution-gel precursor for SBN was prepared. The chemical homogeneity of this precursor was investigated by means of TEM-experiments. All metal ions were found to be homogeneously dispersed in the precursor gel at least down to 10 nm. The SBN phase formation is followed by means of X-ray Diffraction. It has been shown that the perovskite phase already forms at 550°C.     

Substrate-controlled diastereoselective aziridination of alkenes using 3-acetoxyaminoquinazolinone in the presence of hexamethyldisilazane

8-Phenylmenthol derived α,β-unsaturated esters were aziridinated highly diastereoselectively using 3-acetoxyamino-2-ethylquinazolinone. The yields of these aziridines were greatly improved in the presence of hexamethyldisilazane.