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De toute façon, les considérations exposées ici se prêtentà des généralisations variées, qu'il n'entrait pas dans notre propos d'examiner pour l'instant.A. Weil [Wei62] AbstractAn integer may be represented by a quadratic form over each ring of p-adic integers and over the reals without being represented by this quadratic form over the integers.More generally, such failure of a local-global principle may occur for the representation of one integral quadratic form by another integral quadratic form. We show that many such examples may be accounted for by a Brauer-Manin obstruction for the existence of integral points on schemes defined over the integers. For several types of homogeneous spaces of linear algebraic groups, this obstruction is shown to be the only obstruction to the existence of integral points. RésuméUne forme quadratique entière peutêtre représentée par une autre forme quadratique entière sur tous les anneaux d'entiers p-adiques et sur les réels, sans l'être sur les entiers. On en trouve de nombreux exemples dans la littérature. Nous montrons qu'une partie de ces exemples s'explique au moyen d'une obstruction de type Brauer-Manin pour les points entiers. Pour plusieurs types d'espaces homogènes de groupes algébriques linéaires, cette obstruction est la seule obstructionà l'existence d'un point entier.

This present study deals with synthesis, characterization and antibacterial activity of cross-linked chitosan-glutaraldehyde. Results from this study indicated that cross-linked chitosan-glutaraldehyde markedly inhibited the growth of antibiotic-resistant Burkholderia cepacia complex regardless of bacterial species and incubation time while bacterial growth was unaffected by solid chitosan. Furthermore, high temperature treated cross-linked chitosan-glutaraldehyde showed strong antibacterial activity against the selected strain 0901 although the inhibitory effects varied with different temperatures. In addition, physical-chemical and structural characterization revealed that the cross-linking of chitosan with glutaraldehyde resulted in a rougher surface morphology, a characteristic Fourier transform infrared (FTIR) band at 1559 cm−1, a specific X-ray diffraction peak centered at 2θ = 15°, a lower contents of carbon, hydrogen and nitrogen, and a higher stability of glucose units compared to chitosan based on scanning electron microscopic observation, FTIR spectra, X-ray diffraction pattern, as well as elemental and thermo gravimetric analysis. Overall, this study indicated that cross-linked chitosan-glutaraldehyde is promising to be developed as a new antibacterial drug.

A series of 1-alkyl-3-methylimidazolium fluorohydrogenate salts (C(x)MIm(FH)(2)F, x=8, 10, 12, 14, 16, and 18) have been characterized by thermal analysis, polarized optical microscopy, IR spectroscopy, X-ray diffraction, and anisotropic ionic conductivity measurements. Liquid crystalline mesophases with a smectic A interdigitated bilayer structure are observed from C(10) to C(18), showing a fan-like or focal conic texture. The temperature range of the mesophase increases with the increase in the alkyl chain length (from 10.1 °C for C(10)MIm(FH)(2)F to 123.1 °C for C(18)MIm(FH)(2)F). The distance between the two layers in the smectic structure gradually increases with increasing alkyl chain length and decreases with increasing temperature. Conductivity parallel to the smectic layers is around 10 mS cm(-1) regardless of the alkyl chain length, whereas that perpendicular to the smectic layers decreases with increasing alkyl chain length because of the thicker insulating sheet with the longer alkyl chain.

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