Closed Expressions for Lie Algebra Invariants and Finite Transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.Comment: 34 pages, ps file, no figure

The Stellar Content of Obscured Galactic Giant HII Regions. VI: W51A

We present K-band spectra of newly born OB stars in the obscured Galactic giant H II region W51A and ~ 0.8'' angular resolution images in the J, H and K_S-bands. Four objects have been spectroscopically classified as O-type stars. The mean spectroscopic parallax of the four stars gives a distance of 2.0 \pm 0.3 kpc (error in the mean), significantly smaller than the radio recombination line kinematic value of 5.5 kpc or the values derived from maser propermotion observations (6--8 kpc). The number of Lyman continuum photons from the contribution of all massive stars (NLyc ~ 1.5 x 10^{50} s^{-1}) is in good agreement with that inferred from radio recombination lines (NLyc = 1.3 x 10^{50} s^{-1}) after accounting for the smaller distance derived here. We present analysis of archival high angular resolution images (NAOS CONICA at VLT and T-ReCS at Gemini) of the compact region W51 IRS2. The K_S--band images resolve the infrared source IRS~2 indicating that it is a very young compact HII region. Sources IRS2E was resolved into compact cluster (within 660 AU of projected distance) of 3 objects, but one of them is just bright extended emission. W51d1 and W51d2 were identified with compact clusters of 3 objects (maybe 4 in the case of W51d1) each one. Although IRS~2E is the brightest source in the K-band and at 12.6 \micron, it is not clearly associated with a radio continuum source. Our spectrum of IRS~2E shows, similar to previous work, strong emission in Br$\gamma$ and HeI, as well as three forbidden emission lines of FeIII and emission lines of molecular hydrogen (H_2) marking it as a massive young stellar object.Comment: 31 pages and 9 figures, submitted to A

Foliations and Chern-Heinz inequalities

We extend the Chern-Heinz inequalities about mean curvature and scalar curvature of graphs of $C^{2}$-functions to leaves of transversally oriented codimension one $C^{2}$-foliations of Riemannian manifolds. That extends partially Salavessa's work on mean curvature of graphs and generalize results of Barbosa-Kenmotsu-Oshikiri \cite{barbosa-kenmotsu-Oshikiri} and Barbosa-Gomes-Silveira \cite{barbosa-gomes-silveira} about foliations of 3-dimensional Riemannian manifolds by constant mean curvature surfaces. These Chern-Heinz inequalities for foliations can be applied to prove Haymann-Makai-Osserman inequality (lower bounds of the fundamental tones of bounded open subsets $\Omega \subset \mathbb{R}^{2}$ in terms of its inradius) for embedded tubular neighborhoods of simple curves of $\mathbb{R}^{n}$.Comment: This paper is an improvment of an earlier paper titled On Chern-Heinz Inequalities. 8 Pages, Late

Structural and chemical characterization of silica spheres before and after modification by silanization for trypsin immobilization.

In the last decades, silica particles of a variety of sizes and shapes have been characterized and chemically modified for several applications, from chromatographic separation to dental supplies. The present study proposes the use of aminopropyl triethoxysilane (APTS) silanized silica particles to immobilize the proteolytic enzyme trypsin for the development of a bioreactor. The major advantage of the process is that it enables the polypeptides hydrolysis interruption simply by removing the silica particles from the reaction bottle. Silanized silica surfaces showed significant morphological changes at micro- and nanoscale level. Chemical characterization showed changes in elemental composition, chemical environment, and thermal degradation. Their application as supports for trypsin immobilization showed high immobilization efficiency at reduced immobilization times, combined with more acidic conditions. Indirect immobilization quantification by reversed-phase ultrafast high performance liquid chromatography proved to be a suitable approach due to its high linearity and sensitivity. Immobilized trypsin activities on nonmodified and silanized silica showed promising features (e.g., selective hydrolysis) for applications in proteins/peptides primary structure elucidation for proteomics. Silanized silica system produced some preferential targeting peptides, probably due to the hydrophobicity of the nanoenvironment conditioned by silanization

Honey sugars analysis by ion chromatography method with Integrated Pulsed Amperometric Detection (IPAD)

Glucose and fructose are the most important monosaccharides in honey, these sugars combined in various forms comprise the di- and trisaccharide fractions of floral honey. Frutose/glucose ratio can influence the flavor of honey since fructose is sweeter than glucose. Honeys with higher fructose/glucose ratios remain liquid for longer periods. Several Chromatographic methods have been used to evaluate the sugar content of honey, although the Integrated Pulsed Amperometric Detection (IPAD) only recently became to be used. In order to characterize the sugar content in honey from different botanical origins a Dionex ICS3000 ion chromatograph was used. Separation was performed in a column “CarboPacTM PA20 3x150mm”, with a precolumn “CarboPacTM PA20 3x30mm”. Electrochemical detector in Integrated Pulsed Amperometric Detection (IPAD) mode was used. The elution was performed with a gradient with two NaOH solutions (10 and 200 mM). Standard solutions of glucose, fructose and sucrose, were used to identify and quantify the individual sugar components in the honey samples. The method showed a good separation between the compounds (resolution> 3.3 and more than 9000 theoretical plates). The response was linear in the range (0.05 to 1.00 mg/L for fructose and glucose and 0.01 to 0.20 mg/L for sucrose). The detection limits were 0.014 mg/L for glucose, 0.007 mg/L for fructose and 0.003 mg/L for sucrose. Twenty six monofloral honey samples from Erica, Citrus, Lavandula and Eucalyptus were tested. 5,000 g of each honey sample was diluted to 1 mg/L and filtered with a 0.45 m polypropylene filter prior to HPLC analysis. The results show that the fructose/glucose ratios are in accordance with the different honeys analyzed and the HPLC-IPAD is a good methodology to determine the sugar content in honey, with low solvent consumption and residues