Families of orthogonal functions defined by the Weyl groups of compact Lie groups

Plusieurs familles de fonctions spéciales de plusieurs variables, appelées fonctions d'orbites, sont définies dans le contexte des groupes de Weyl de groupes de Lie simples compacts/d'algèbres de Lie simples. Ces fonctions sont étudiées depuis près d'un siècle en raison de leur lien avec les caractères des représentations irréductibles des algèbres de Lie simples, mais également de par leurs symétries et orthogonalités. Nous sommes principalement intéressés par la description des relations d'orthogonalité discrète et des transformations discrètes correspondantes, transformations qui permettent l'utilisation des fonctions d'orbites dans le traitement de données multidimensionnelles. Cette description est donnée pour les groupes de Weyl dont les racines ont deux longueurs différentes, en particulier pour les groupes de rang $2$ dans le cas des fonctions d'orbites du type $E$ et pour les groupes de rang $3$ dans le cas de toutes les autres fonctions d'orbites.

A study on the quality of life of the members of self help groups assisted by non-governmental organisations in Kerala

School of Management Studies, CUSAT

El estudio de los roles y funciones de los orientadores de secundaria utilizando la técnica de los grupos de discusión. 'The study of duties and roles of highschool counsellors by using the technique of focus groups'.

Resumen tomado de la publicación. Con el apoyo económico del departamento MIDE de la UNED

The role of protecting groups in the formation of organogels through a nano-fibrillar network formed by self-assembling terminally protected tripeptides

A series of eight synthetic self-assembling terminally blocked tripeptides have been studied for gelation. Some of them form gels in various aromatic solvents including benzene, toluene, xylene, and chlorobenzene. It has been found that the protecting groups play an important role in the formation of organogels. It has been observed that, if the C-terminal has been changed from methyl ester to ethyl ester the gelation property does not change significantly (keeping the N-terminal protecting group same), while the change of the protecting group from ethyl ester to isopropyl ester completely abolishes the gelation property. Similarly, keeping the identical C-terminal protecting group (methyl ester) the results of the gelation study indicate that the substitution of N-terminal protection Boc-(tert-butyloxycarbonyl) to Cbz-(benzyloxycarbonyl) does change the gelation property insignificantly, while the change from Boc- to pivaloyl (Piv-) or acetyl (Ac-) group completely eliminates the gelation property. Morphological studies of the dried gels of two of the peptides indicate the presence of an entangled nano-fibrillar network that might be responsible for gelation. FTIR studies of the gels demonstrate that an intermolecular hydrogen bonding network is formed during gelation. Results of X-ray powder diffraction studies for these gelator peptides in different states (dried gels, gel, and bulk solids) reflected that the structure in the wet gel is distinctly different from the dried gel and solid state structures. Single crystal X-ray diffraction studies of a non-gelator peptide, which is structurally similar to the gelator molecules reveal that the peptide forms an antiparallel beta-sheet structure in crystals. (c) 2007 Elsevier Ltd. All rights reserved.

The influence of pomegranate by-product and punicalagins on selected groups of human intestinal microbiota.

We have examined the gut bacterial metabolism of pomegranate by-product (POMx) and major pomegranate polyphenols, punicalagins, using pH-controlled, stirred, batch culture fermentation systems reflective of the distal region of the human large intestine. Incubation of POMx or punicalagins with faecal bacteria resulted in formation of the dibenzopyranone-type urolithins. The time course profile confirmed the tetrahydroxylated urolithin D as the first product of microbial transformation, followed by compounds with decreasing number of phenolic hydroxy groups: the trihydroxy analogue urolithin C and dihydroxylated urolithin A. POMx exposure enhanced the growth of total bacteria, Bifidobacterium spp. and Lactobacillus spp., without influencing the Clostridium coccoides–Eubacterium rectale group and the C. histolyticum group. In addition, POMx increased concentrations of short chain fatty acids (SCFA) viz. acetate, propionate and butyrate in the fermentation medium. Punicalagins did not affect the growth of bacteria or production of SCFA. The results suggest that POMx oligomers, composed of gallic acid, ellagic acid and glucose units, may account for the enhanced growth of probiotic bacteria.

In vitro fermentation of a red wine extract by human gut microbiota: changes in microbial groups and formation of phenolic metabolites

An in vitro batch culture fermentation experiment was conducted with fecal inocula from three healthy volunteers in the presence and absence of a red wine extract. Changes in main bacterial groups were determined by FISH during a 48 h fermentation period. The catabolism of main flavonoids (i.e., flavan-3-ols and anthocyanins) and the formation of a wide a range of phenolic microbial metabolites were determined by a targeted UPLC-PAD-ESI-TQ MS method. Statistical analysis revealed that catechol/pyrocatechol, as well as 4-hydroxy-5-(phenyl)-valeric, 3- and 4-hydroxyphenylacetic, phenylacetic, phenylpropionic, and benzoic acids, showed the greatest increases in concentration during fermentation, whereas 5-(3′-hydroxyphenyl)-γ-valerolactone, its open form 4-hydroxy-5-(3′-hydroxyphenyl)-valeric acid, and 3,4-dihydroxyphenylacetic acid represented the largest interindividual variations in the catabolism of red wine polyphenols. Despite these changes, microbial catabolism did not produce significant changes in the main bacterial groups detected, although a slight inhibition of the Clostridium histolyticum group was observed.

In vitro fermentation of grape seed flavan-3-ol fractions by human faecal microbiota: changes in microbial groups and phenolic metabolites

With the aim of investigating the potential of flavan-3-ols to influence the growth of intestinal bacterial groups, we have carried out the in vitro fermentation, with human faecal microbiota, of two purified fractions from grape seed extract (GSE): GSE-M (70% monomers and 28% procyanidins) and GSE-O (21% monomers and 78 % procyanidins). Samples were collected at 0, 5, 10, 24, 30 and 48 h of fermentation for bacterial enumeration by fluorescent in situ hybridization and for analysis of phenolic metabolites. Both GSE-M and GSE-O fractions promoted growth of Lactobacillus/Enterococcus and decrease in the Clostridium histolyticum group during fermentation, although the effects were only statistically significant with GSE-M for Lactobacillus/Enterococcus (at 5 and 10 h of fermentation) and GSE-O for C. histolyticum (at 10 h of fermentation). Main changes in polyphenol catabolism also occurred during the first 10 h of fermentation, however no significant correlation coefficients (P>0.05) were found between changes in microbial populations and precursor flavan-3-ols or microbial metabolites. Together these data suggest that the flavan-3-ol profile of a particular food source could affect the microbiota composition and its catabolic activity, inducing changes that could in turn affect the bioavailability and potential bioactivity of these compounds.

Mutual binding of polymer end-groups by complementary π–π-stacking: a molecular “Roman Handshake”

Self-complementary tweezer-molecules based on a naphthalenediimide core self-assemble into supramolecular dimers through mutual π–π-stacking and hydrogen bonding. The resulting motif is extremely stable in solution (Ka = 105 M−1), and its attachment to one terminal position of a poly(ethylene glycol) chain leads to a doubling of the polymer's apparent molecular weight.

Determination of orientations of aromatic groups in self-assembled peptide fibrils by polarised Raman spectroscopy

In this paper we describe a novel combination of Raman spectroscopy, isotope editing and X-ray scattering as a powerful approach to give detailed structural information on aromatic side chains in peptide fibrils. The orientation of the tyrosine residues in fibrils of the peptide YTIAALLSPYS with respect to the fibril axis has been determined from a combination of polarised Raman spectroscopy and X-ray diffraction measurements. The Raman intensity of selected tyrosine bands collected at different polarisation geometries is related to the values and orientation of the Raman tensor for those specific vibrations. Using published Raman tensor values we solved the relevant expressions for both of the two tyrosine residues present in this peptide. Ring deuteration in one of the two tyrosine side chains allowed for the calculation to be performed individually for both, by virtue of the isotopic shift that eliminates band overlapping. Sample disorder was taken into account by obtaining the distribution of orientations of the samples from X-ray diffraction experiments. The results provide previously unavailable details about the molecular conformation of this peptide, and demonstrate the value of this approach for the study of amyloid fibrils.

THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

Group algebras of torsion groups and Lie nilpotence

Let * be an involution of a group algebra FG induced by an involution of the group G. For char F not equal 2, we classify the torsion groups G with no elements of order 2 whose Lie algebra of *-skew elements is nilpotent.

The reactivity of oytho-methoxy-substituted catechol radicals with sulfhydryl groups: Contribution for the comprehension of the mechanism of inhibition of NADPH oxidase by apocynin

Redox processes are involved in the mechanism of action of NADPH oxidase inhibitors such as diphenyleneiodonium and apocynin. Here, we studied the structure-activity relationship for apocynin and analogous ortho-methoxy-substituted catechols as inhibitors of the NADPH oxidase in neutrophils and their reactivity with peroxidase. Aiming to alter the reduction potential, the ortho-methoxy-catechol moiety was kept constant and the substituents at para position related to the hydroxyl group were varied. Two series of compounds were employed: methoxy-catechols bearing electron-withdrawing groups (MC-W) such as apocynin, vanillin, 4-nitroguaiacol, 4-cyanoguaiacol, and methoxy-catechol bearing electron-donating groups (MC-D) such as 4-methylguaiacol and 4-ethylguaiacol. We found that MC-D were weaker inhibitors compared to MD-W. Furthermore, the radicals generated by oxidation of MC-W via MPO/H(2)O(2), but not for MC-D, were able to oxidize glutathione (GSH) as verified by the formation of thiyl radicals, depletion of GSH, and recycling of the ortho-methoxy-catechols during their oxidations. The capacity of oxidizing sulfhydryl (SH) groups was also verified when ovalbumin was incubated with MC-W, but not for MC-D. Since the effect of apocynin has been correlated with inactivation of the cytosolic fractions of the NADPH oxidase complex and its oxidation during the inhibitory process develops a special role in this process, we suggest that the close relationship between the reactivity of the radicals of MC-W compounds with thiol groups and their efficacy as NADPH oxidase inhibitor could be the chemical pathway behind the mechanism of action of apocynin and should be taken into account in the design of new and specific NADPH oxidase inhibitors. (c) 2007 Elsevier B.V. All rights reserved.

Application of cellulose modified with p-aminobenzoic groups in preconcentration system for determination of Cu, Fe, Ni, and Zn in fuel ethanol samples by flame atomic absorption spectrometry

Cellulose chemically modified with p-aminobenzoic groups, abbreviated as Cel-PAB, was used for preconcentration of copper, iron, nickel, and zinc from ethanol fuel, normally used in Brazil as engine fuel. The surface characteristics and the surface area of the cellulose were obtained before and after chemical modification using FT-IR, elemental analysis, and surface area analysis (B.E.T.). The retention and recovery of the analyte elements were studied by applying batch and column techniques.

Determination of copper, iron, nickel and zinc in gasoline by FAAS after sorption and preconcentration on silica modified with 2-aminotiazole groups

Silica gel chemically modified with 2-aminotiazole groups (SiAT), was used for preconcentration of cupper, zinc, nickel and iron from gasoline, normally used as a engine fuel. Surface characteristics and surface area of the silica gel were obtained before and after chemical modification using FT-IR, Kjeldhal and surface area analysis (B.E.T.). The retention and recovery of the analyte elements were studied by applying batch and column techniques. The experimental parameters, such as shaking time in batch technique, flow rate and concentration of the eluent (HCl-0.25-2.00 mol 1(-1)) and the amount of silica, on retention and elution, have been investigated. Detection limits of the method for cupper, iron, nickel and zinc are 0.8, 3, 2 and 0.1 mug 1(-1), respectively. The sorption-desorption of the studied metal ions made possible the development of a preconcentration method for metal ions at trace level in gasoline using flame AAS for their quantification. (C) 2004 Published by Elsevier Ltd.