An alternating direction scheme on a nonuniform mesh for reaction-diffusion parabolic problems

In this paper we develop a numerical method for two-dimensionaltime-dependent reaction-diffusion problems. This method, whichcan immediately be generalized to higher dimensions, is shownto be uniformly convergent with respect to the diffusion problems.This method, which can immediately be generalized to higherdimensions, is shown to be uniformly convergent with respectto the diffusion parameter.     

Intramolecular rearrangement of α-amino acid amide derivatives of 2-aminobenzothiazoles

We have found that α-amino acid amide derivatives of 2-aminobenzothiazoles undergo a time-dependent, thermal rearrangement in which the amine group attacks the 2-position carbon of the thiazole ring to form a 5,5-spiro ring system. This is followed by sulfur leaving and air oxidation to the corresponding symmetrical disulfide. The isolated yields of such products are quite high (>70%) if there is conformational bias to further promote the intramolecular reaction such as for the 2-aminobenzothiazole amides derived from proline or 4-aminopiperidine-4-carboxylic acid. This rearrangement has not been described previously for α-amino acid amide derivatives of 2-aminobenzothiazoles. However, a related reaction involving 2-semicarbazido benzothiazoles has been recently reported.     

Characteristic vector fields of generic distributions of corank 2

We study generic distributions D⊂TM$D\subset TM$ of corank 2 on manifolds M   of dimension n?5$n?5$. We describe singular curves of such distributions, also called abnormal curves. For n   even the singular directions (tangent to singular curves) are discrete lines in D(x)$D(x)$, while for n   odd they form a Veronese curve in a projectivized subspace of D(x)$D(x)$, at generic x∈M$x\in M$. We show that singular curves of a generic distribution determine the distribution on the subset of M where they generate at least two different directions. In particular, this happens on the whole of M if n is odd. The distribution is determined by characteristic vector fields and their Lie brackets of appropriate order. We characterize pairs of vector fields which can appear as characteristic vector fields of a generic corank 2 distribution, when n is even.     

Fast and high-resolution ion chromatography at high pH on short columns packed with 1.8 microm surfactant coated silica reverse-phase particles

Rapid ion chromatographic separations of small inorganic anions are performed on columns packed with high-pH resistant Zorbax Extend-C18 1.8 microm silica particles. Seven anions (iodate, chloride, nitrite, bromide, nitrate, phosphate, sulphate) are separated with 1.3 and 2 cm long x 0.46 cm I.D. C18 columns coated with the surfactant didodecyldimethylammonium bromide (DDAB). A 40 s separation is achieved at 2 mL/min with a 2.5 mM 4-hydroxybenzoic acid eluent at pH 10. Finally, the DDAB removal procedure is improved to eliminate the pressure build-up caused by precipitation of the surfactant in the column upon uncoating.     

Electronically variable imino-phenanthrolinyl-cobalt complexes; synthesis, structures and ethylene oligomerisation studies

The 2-imino-1,10-phenanthroline ligands, 1,10-C₁₂H₇N₂-2-CRN(2,6-i-Pr₂-4-R¹-C₆H₂) [R = R¹ = H (L1); R = H, R¹ = Br (L2); R = H, R¹ = CN (L3); R = H, R¹ = i-Pr (L4); R = Me, R¹ = H (L5); R = Me, R¹ = i-Pr (L6)], have been prepared in high yield from the condensation reaction of 1,10-C₁₂H₇N₂-2-CRO (R = H, Me) with one equivalent of the corresponding 4-substituted 2,6-diisopropylaniline. The molecular structures of L2, L5 and L6 reveal the imino nitrogen atoms to adopt a transoid configuration with respect to the phenanthrolinyl nitrogen atoms. Treatment of Lx with one equivalent of CoCl₂ in n-BuOH at 90 °C gives the high spin complexes, (Lx)CoCl₂ [Lx = L1 (1a), L2 (1b), L3 (1c), L4 (1d), L5 (1e), L6 (1f)], in which the metal centres exhibit distorted square pyramidal geometries. Activation of 1a-1f with excess methylaluminoxane (MAO) gives catalysts that are modestly active for the oligomerisation of ethylene affording mainly linear α-olefins along with some degree of internal olefins. While the donor capability of the 4-position of the N-aryl group does not appear to affect the activity of the catalyst, it does have an influence on the ratio of α-olefins to internal olefins. Single crystal X-ray diffraction studies have been performed on L2, L5, L6, 1a, 1c and 1f.     

Characterization of the drastic increase in molecular mobility of a deformed amorphous polymer

Original experiments of dynamic mechanical analysis and small angle x-ray scattering on a deformed amorphous polymer below its glass transition temperature are reported. The mechanical treatment reveals high mobility zones induced by shearing and leads to a drastic increase in the molecular mobility of the system. These domains are evidenced by small angle x-ray scattering measurements, and their geometrical characteristics are independent of the applied deformation. An experimental procedure is proposed to determine an apparent activation energy associated with high mobility domains. The energy values obtained for intermediate modes rise from the beta to the alpha relaxation ones.     

Large and moderate deviations principles for kernel estimators of the multivariate regression

In this paper, we prove large deviations principle for the Nadaraya-Watson estimator and for the semi-recursive kernel estimator of the regression in the multidimensional case. Under suitable conditions, we show that the rate function is a good rate function. We thus generalize the results already obtained in the one-dimensional case for the Nadaraya-Watson estimator. Moreover, we give a moderate deviations principle for these two estimators. It turns out that the rate function obtained in the moderate deviations principle for the semi-recursive estimator is larger than the one obtained for the Nadaraya-Watson estimator.      

On Quantales and Spectra of C*-Algebras

We study properties of the quantale spectrum MaxA of an arbitrary unital C^*-algebra A. In particular we show that the spatialization of MaxA with respect to one of the notions of spatiality in the literature yields the locale of closed ideals of A when A is commutative. We study under general conditions functors with this property, in addition requiring that colimits be preserved, and we conclude in this case that the spectrum of A necessarily coincides with the locale of closed ideals of the commutative reflection of A. Finally, we address functorial properties of Max, namely studying (non-)preservation of limits and colimits. Although Max is not an equivalence of categories, therefore not providing a direct generalization of Gelfand duality to the noncommutative case, it is a faithful complete invariant of unital C^*-algebras.