L'ensemble des algèbres de Lie algébriques n'est pas Zariski-dense dans la variété des algèbres de Lie de dimensionM≧9

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Comparisons between model equations for long waves

Summary Considered here are model equations for weakly nonlinear and dispersive long waves, which feature general forms of dispersion and pure power nonlinearity. Two variants of such equations are introduced, one of Korteweg-de Vries type and one of regularized long-wave type. It is proven that solutions of the pure initial-value problem for these two types of model equations are the same, to within the order of accuracy attributable to either, on the long time scale during which nonlinear and dispersive effects may accumulate to make an order-one relative difference to the wave profiles.This research was supported in part by the National Science Foundation. A considerable portion of the project was completed while the first author was resident at the Institute for Mathematics and Its Applications, University of Minnesota.     

Synthesis and thermal crosslinking of oxazolidine‐functionalized polyurethanes

A new oxazolidine derivative was obtained from phenol, 2‐amino‐2‐methylpropane‐1,3‐diol and paraformaldehyde. The reaction of this novel oxazolidine diol with phenylisocyanate lead to a urethane model compound which can be polymerized thermally by oxazolidine ring opening to give a Mannich bridge structure. Linear segmented polyurethanes were prepared by reaction of different ratios of oxazolidine diol and commercial polyethylenglycol (M_w ～ 400) with 4,4′‐methylenbis (cyclohexylisocyanate) (HMDI, 90% isomers mixture). The polyurethanes were thermally characterized and crosslinked by oxazolidine ring opening to obtain materials which showed improved thermal stability. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4965–4973, 2007     

Alternative syntheses of the D2d symmetric 1,3,5,7-tetraiodotricyclo[3.3.0.0]octane

Three alternative syntheses of 1,3,5,7-tetraiodotricyclo[3.3.0.0^3,7]octane are described. Reaction of this tetraiodide with sodium amalgam in the presence of dienes or with molten sodium in boiling 1,4-dioxane in the absence of trapping agents led to very complex mixtures of products, presumably due to competitive 1,2- and 1,3-deiodination reactions.     

Secret Sharing Schemes with Detection of Cheaters for a General Access Structure

In a secret sharing scheme, some participants can lie about the value of their shares when reconstructing the secret in order to obtain some illicit benefit. We present in this paper two methods to modify any linear secret sharing scheme in order to obtain schemes that are unconditionally secure against that kind of attack. The schemes obtained by the first method are robust, that is, cheaters are detected with high probability even if they know the value of the secret. The second method provides secure schemes, in which cheaters that do not know the secret are detected with high probability. When applied to ideal linear secret sharing schemes, our methods provide robust and secure schemes whose relation between the probability of cheating and the information rate is almost optimal. Besides, those methods make it possible to construct robust and secure schemes for any access structure.     

Ab-initio molecular dynamics based on non-local density functional procedure with Gaussian basis; study of structural and temperature behaviour of metallic clusters

An ab-initio molecular dynamics procedure without precalculation of the Born-Oppenheimer energy surface based on an iterative non-local density functional method employing Gaussian atomic basis has been developed. Analytical gradients are calculated and used for the propagation of nuclei. Sufficiently long trajectories can be calculated at an acceptable computational cost, allowing for analysis of dynamical behaviour of small metallic clusters. This is illustrated on an example of the Li₈ cluster. Temperature behaviour of different type of isomers has been investigated. Calculated power spectra allow to identify the presence of more than one isomeric forms along the given trajectories.     

Chips and Qi: microcomponent-based analysis in traditional Chinese medicine

Over the last 50 years or so Traditional Chinese medicine (TCM) has been subject to intensive basic and clinical research. Although the effectiveness and remarkable safety of TCM have been documented after controlled clinical studies, there are several herbal and animal parts that are toxic or difficult to identify. DNA polymorphism-based assays have recently been developed for the identification of herbal medicines. In this approach, small amounts of DNA are amplified by the polymerase chain reaction and the reactions products are analyzed by gel electrophoresis, sequencing, or hybridization with species-specific probes. With the DNA based identification of TCM materials as an example, chip-based analytical micro devices were developed with the goal of fabricating an integrated device that will enable sample preparation, amplification, and analysis on a single microchip-based device ("lab-on-a-chip"). The application of a silicon-based polymerase chain reaction microreactor and a DNA microarray for the DNA sequence-based identification of toxic medicinal plants is reported here.     

Standardization of multi-nuclide mixtures by a new spectrum unfolding method

A new spectrum unfolding method has been applied to double-labeled mixtures with excellent results, while the CIEMAT/NIST method has been used for gels. The convenience of applying both methods has been demonstrated with mixtures containing more than three components.⁹⁰Sr+⁹⁰Y,⁸⁹Sr,²⁰⁴TI,⁴⁵Ca and³⁵S nuclides were combined as three, four and five components, and the different quench values and activity ratios were assayed. The discrepancies between computed and experimental activities were also obtained. Mixtures with some of their components below background have been prepared in order to test low-level activities.     

Nucleation mechanisms and speciation of metal oxide clusters

The self-assembly mechanisms of polyoxometalates (POMs) are still a matter of discussion owing to the difficult task of identifying all the chemical species and reactions involved. We present a new computational methodology that identifies the reaction mechanism for the formation of metal-oxide clusters and provides a speciation model from first-principles and in an automated manner. As a first example, we apply our method to the formation of octamolybdate. In our model, we include variables such as pH, temperature and ionic force because they have a determining effect on driving the reaction to a specific product. Making use of graphs, we set up and solved 2.8 × 10⁵ multi-species chemical equilibrium (MSCE) non-linear equations and found which set of reactions fitted best with the experimental data available. The agreement between computed and experimental speciation diagrams is excellent. Furthermore, we discovered a strong linear dependence between DFT and empirical formation constants, which opens the door for a systematic rescaling.

The self-assembly mechanisms of polyoxometalates (POMs) are still a matter of discussion owing to the difficult task of identifying all the chemical species and reactions involved. The POMSimulator deals with that complexity in an automated manner.