Conjugate points and Maslov index in locally symmetric semi-Riemannian manifolds

We study the singularities of the exponential map in semi Riemannian locally symmetric manifolds. Conjugate points along geodesics depend only on real negative eigenvalues of the curvature tensor, and their contribution to the Maslov index of the geodesic is computed explicitly. We prove that degeneracy of conjugate points, which is a phenomenon that can only occur in semi-Riemannian geometry, is caused in the locally symmetric case by the lack of diagonalizability of the curvature tensor. The case of Lie groups endowed with a bi-invariant metric is studied in some detail, and conditions are given for the lack of local injectivity of the exponential map around its singularities.     

A validated spectrofluorometric method for the determination of celecoxib in capsules

A rapid, selective, sensitive and simple fluorescence method was developed for the direct determination of celecoxib in capsules. The capsules were emptied, pulverized and dissolved in either ethanol or acetonitrile, sonicated and filtered. Direct fluorescence emission was measured at 355±5 nm (exciting at 272 nm). The method was fully validated and the recoveries were excellent, even in presence of excipients.     

DAC-FECS Affairs

DAC-FECS Affairs

The Division of Analytical Chemistry     

Indirect automatic atomic absorption determination of sulphate based on its precipitation with barium

A continuous precipitation flame atomization atomic absorption spectrometric method for the indirect determination of sulphate is proposed. By using a reversed flow-injection configuration for precipitation as barium sulphate, this anion was determined in the range 10–150 g/ml, with a relative standard deviation of 2.6%. The sensitivity was increased by a factor of seven by using a nitrous oxide-acetylene flame to measure barium.     

Hydride generation atomic fluorescence spectrometric determination of ultratraces of selenium and tellurium in cow milk

A sensitive procedure has been developed for selenium and tellurium determination in milk by hydride generation atomic fluorescence spectrometry (HG-AFS) after microwave-assisted sample digestion. The method provides sensitivity values of 1591 and 997 fluorescence units ng⁻¹ ml⁻¹ with detection limits of 0.005 and 0.015 ng ml⁻¹ for Se and Te, respectively. The application of the developed methodology to the analysis of cow milk samples of the Spanish market evidenced the presence of concentration ranges from 11.1 to 26.0 ng ml⁻¹ for Se, and from 1.04 to 9.7 ng ml⁻¹ for Te having found a good comparability with data obtained after dry-ashing of samples.     

Attenuated Total Reflection-Fourier transform infrared analysis of the fermentation process of pineapple

A direct and reagent free procedure has been developed to monitor the fermentation process of pine apple nectar using Attenuated Total Reflectance Fourier-transform mid-infrared spectrometry (FT-IR) and multivariate analysis. A classical 4² design for standards was employed for calibration using the information in the spectral range from 907 to 1531 cm⁻¹ of the first order derivative spectra after mean centering of infrared data. The root mean square error of calibration (RMSEC) of 0.040, 0.021, 0.063 and 0.074% w/w were obtained for glucose, fructose, saccharose and ethanol, respectively, and a mean relative validation error of 2.9, 2.1, 2.6 and 3.6% was achieved for glucose, fructose, saccharose and ethanol. Results obtained by the proposed procedure for the alcohol content at different fermentation levels were statistically comparable with those obtained by a reference spectrometric method. So, FT-IR spectrometry provides a fast alternative to long and tedious classical procedures to ethanol determination and sugar enzymatic analysis.     

Inorganic-metalorganic hybrids based on copper(II)-monosubstituted Keggin polyanions and dinuclear copper(II)-oxalate complexes. Synthesis, X-ray structural characterization, and magnetic properties

Reaction of in situ generated copper(II)-monosubstituted Keggin polyoxometalates and copper(II)-bipyridine-oxalate complexes in the corresponding alkaline acetate buffer led to the formation of hybrid metal organic-inorganic compounds K(2)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(H(2)O)(2)(mu-ox)}(2)].14H(2)O (1), K(14)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}](2)[SiW(11)O(39)Cu(H(2)O)].55H(2)O (2), (NH(4))(4)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}].10H(2)O (3), and Rb(4)[{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}].10H(2)O (4). Their structures have been established by single-crystal X-ray diffraction. The main structural feature of these compounds is the presence of copper(II)-monosubstituted alpha-Keggin polyoxoanions as inorganic building blocks, on which the mu-oxalatodicopper metalorganic blocks are supported. Compound 1contains the discrete hybrid polyanion [{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(H(2)O)(2)(mu-ox)}(2)](2)(-), whereas the polymeric hybrid polyanion [{SiW(11)O(39)Cu(H(2)O)}{Cu(2)(bpy)(2)(mu-ox)}(2)](n)(4)(n)(-) gives a monodimensional character to compounds 2-4. Magnetic and EPR results are discussed with respect to the crystal structure of the compounds. DFT calculations on both the [Cu(2)(bpy)(2)(H(2)O)(4)(mu-ox)](2+) cationic complex and the metalorganic blocks have been performed in order to determine the optimized geometry and the magnetic coupling constants, respectively.