Examples of Self-Iterating Lie Algebras, 2

We study properties of self-iterating Lie algebras in positive characteristic. Let R = K[t(i)vertical bar i is an element of N]/(t(i)(p)vertical bar i is an element of N) be the truncated polynomial ring. Let partial derivative(i) = partial derivative/partial derivative t(i), i is an element of N, denote the respective derivations. Consider the operators v(1) = partial derivative(1) + t(0)(partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...))))); v(2) = partial derivative(2) + t(1)(partial derivative(3) + t(2)(partial derivative(4) + t(3)(partial derivative(5) + t(4)(partial derivative(6) + ...)))). Let L = Lie(p)(v(1), v(2)) subset of Der R be the restricted Lie algebra generated by these derivations. We establish the following properties of this algebra in case p = 2, 3. a) L has a polynomial growth with Gelfand-Kirillov dimension lnp/ln((1+root 5)/2). b) the associative envelope A = Alg(v(1), v(2)) of L has Gelfand-Kirillov dimension 2 lnp/ln((1+root 5)/2). c) L has a nil-p-mapping. d) L, A and the augmentation ideal of the restricted enveloping algebra u = u(0)(L) are direct sums of two locally nilpotent subalgebras. The question whether u is a nil-algebra remains open. e) the restricted enveloping algebra u(L) is of intermediate growth. These properties resemble those of Grigorchuk and Gupta-Sidki groups.

Crossed products by twisted partial actions and graded algebras

For a twisted partial action e of a group G on an (associative non-necessarily unital) algebra A over a commutative unital ring k, the crossed product A x(Theta) G is proved to be associative. Given a G-graded k-algebra B = circle plus(g is an element of G) B-g with the mild restriction of homogeneous non-degeneracy, a criteria is established for B to be isomorphic to the crossed product B-1 x(Theta) G for some twisted partial action of G on B-1. The equality BgBg-1 B-g = B-g (for all g is an element of G) is one of the ingredients of the criteria, and if it holds and, moreover, B has enough local units, then it is shown that B is stably isomorphic to a crossed product by a twisted partial action of G. (c) 2008 Elsevier Inc. All rights reserved.

Torsion theories induced from commutative subalgebras

We begin a study of torsion theories for representations of finitely generated algebras U over a field containing a finitely generated commutative Harish-Chandra subalgebra Gamma. This is an important class of associative algebras, which includes all finite W-algebras of type A over an algebraically closed field of characteristic zero, in particular, the universal enveloping algebra of gl(n) (or sl(n)) for all n. We show that any Gamma-torsion theory defined by the coheight of the prime ideals of Gamma is liftable to U. Moreover, for any simple U-module M, all associated prime ideals of M in Spec Gamma have the same coheight. Hence, the coheight of these associated prime ideals is an invariant of a given simple U-module. This implies the stratification of the category of U-modules controlled by the coheight of the associated prime ideals of Gamma. Our approach can be viewed as a generalization of the classical paper by Block (1981) [4]; it allows, in particular, to study representations of gl(n) beyond the classical category of weight or generalized weight modules. (C) 2011 Elsevier B.V. All rights reserved.

Commutative Moufang loops and alternative algebras

We describe bases of free commutative Moufang loop with seven generators and calculate the order of this loop. (c) 2011 Published by Elsevier Inc.

Representation type of Jordan algebras

The problem of classification of Jordan bit-nodules over (non-semisimple) finite dimensional Jordan algebras with respect to their representation type is considered. The notions of diagram of a Jordan algebra and of Jordan tensor algebra of a bimodule are introduced and a mapping Qui is constructed which associates to the diagram of a Jordan algebra J the quiver of its universal associative enveloping algebra S(J). The main results are concerned with Jordan algebras of semi-matrix type, that is, algebras whose semi-simple component is a direct sum of Jordan matrix algebras. In this case, criterion of finiteness and tameness for one-sided representations are obtained, in terms of diagram and mapping Qui, for Jordan tensor algebras and for algebras with radical square equals to 0. (c) 2010 Elsevier Inc. All rights reserved.

Nil graded self-similar algebras

In [19], [24] we introduced a family of self-similar nil Lie algebras L over fields of prime characteristic p > 0 whose properties resemble those of Grigorchuk and Gupta-Sidki groups. The Lie algebra L is generated by two derivations v(1) = partial derivative(1) + t(0)(p-1) (partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...))))), v(2) = partial derivative(2) + t(1)(p-1) (partial derivative(3) + t(2)(p-1) (partial derivative(4) + t(3)(p-1) (partial derivative(5) + t(4)(p-1) (partial derivative(6) + ...)))) of the truncated polynomial ring K[t(i), i is an element of N vertical bar t(j)(p) =0, i is an element of N] in countably many variables. The associative algebra A generated by v(1), v(2) is equipped with a natural Z circle plus Z-gradation. In this paper we show that for p, which is not representable as p = m(2) + m + 1, m is an element of Z, the algebra A is graded nil and can be represented as a sum of two locally nilpotent subalgebras. L. Bartholdi [3] andYa. S. Krylyuk [15] proved that for p = m(2) + m + 1 the algebra A is not graded nil. However, we show that the second family of self-similar Lie algebras introduced in [24] and their associative hulls are always Z(p)-graded, graded nil, and are sums of two locally nilpotent subalgebras.

Comparative bioavailability of three ibuprofen formulations in healthy human volunteers

Objective: To assess the bioequivalence of three ibuprofen formulations (Test formulation: ibuprofen (400 mg capsule) manufactured by Cardinal Health Brasil 402 Ltda. (Sorocaba, Brazil) and licensed to Boehringer Ingelheim do Brasil Quim. e Farm. Ltda. (Sao Paulo, Brazil); Reference formulation (1): ibuprofen (Advil (R); 2 x 200 mg coated tablet) from Wyeth-Whitehall Ltda. (Itapevi, Brazil); Reference formulation (2): ibuprofen (Alivium (R); 8 ml x 50 mg/ml solution) from Schering Plough S.A. (Rio de Janeiro, Brazil)) in 24 healthy volunteers of both sexes. Methods: The study was conducted using an open, randomized, three-period crossover design with at least 5-day washout interval. Plasma samples were obtained over a 24-h period. Plasma ibuprofen concentrations were analyzed by liquid chromatography coupled to tandem mass spectrometry (LC-MS/MS) with negative ion electrospray ionization using multiple reaction monitoring (MRM). The following pharmacokinetic parameters were obtained from the ibuprofen plasma concentration vs. time curves: AUC(last), AUC(trunctmax) AUC(inf) and C-max. Results: The limit of quantification for ibuprofen was 0.1 mu g x ml(-1). The geometric mean with corresponding 90% confidence interval (CI) for Test/Reference (1) percent ratios were 114.24% (90% CI = 105.67, 123.50%) for C-max, 98.97% (90% CI = 94.69, 103.44%) for AUC(last) and 99.40% (90% CI = 95.21, 103.78%) for AUCinf. The geometric mean and respective 90% confidence interval (CI) for Test/Reference (2) percent ratios were 108.38% (90% Cl = 100.195, 117.25%) for C-max, 100.79% (90% CI = 96.39, 105.40%) for AUC(last) and 101.26% (90% CI = 96.94, 105.77%) for AUC(inf); t(max) for the 400 mg Test capsule was shorter than that for the 2 x 200 mg Reference (1) tablets (p < 0.002). Conclusion: Since the 90% CI for AUC(last), AUC(inf) and C-max ratios were within the 80 - 125% interval proposed by the US FDA, it was concluded that ibuprofen formulation manufactured by Cardinal Health Brasil 402 Ltda. and licensed to Boehringer Ingelheim do Brasil Quim. e Farm. Ltda. is bioequivalent to the Advil (R) and Alivium (R) formulations with regard to both the rate and the extent of absorption.

Lipopeptides Produced by a Soil Bacillus Megaterium Strain

A soil microorganism identified as Bacillum megaterium was found to produce several antibiotics substances after growth for 20 h at 37A degrees C in a mineral culture medium. Analysis both by electron spray ionization (ESI) and matrix-assisted laser desorption ionization-time of flight (MALDI-TOF) mass spectrometry (MS) identified these substances as lipopeptides. Predominant peaks at m/z 1,041 and m/z 1,065 revealed ions which are compatible with surfactins and lichenysins, respectively. Two other ions m/z 1,057 and m/z 1,464 were further studied by collision-induced dissociation (CID) unveiling an iturin A at the first and fengycins A and B at the second m/z peaks. The CID spectrum of the m/z 1,464 ion also suggests the existence of fengycins A and B variants in which Ile was changed to Val in the position 10 of the peptide moiety. Raw mixtures of all these compounds were also assayed for antibiotic features. The data enlighten the unusual diversity of the lipopeptide mixture produced by a sole Bacillus species.

Characterization of a beta-1,3-glucanase active in the alkaline midgut of Spodoptera frugiperda larvae and its relation to beta-glucan-binding proteins

Spodoptera frugiperda beta-1,3-glucanase (SLam) was purified from larval midgut. It has a molecular mass of 37.5 kDa, an alkaline optimum pH of 9.0, is active against beta-1,3-glucan (laminarin), but cannot hydrolyze yeast beta-1,3-1,6-glucan or other polysaccharides. The enzyme is an endoglucanase with low processivity (0.4), and is not inhibited by high concentrations of substrate. In contrast to other digestive beta-1,3-glucanases from insects, SLam is unable to lyse Saccharomyces cerevisae cells. The cDNA encoding SLam was cloned and sequenced, showing that the protein belongs to glycosyl hydrolase family 16 as other insect glucanases and glucan-binding proteins. Multiple sequence alignment of beta-1,3-glucanases and beta-glucan-binding protein supports the assumption that the beta-1,3-glucanase gene duplicated in the ancestor of mollusks and arthropods. One copy originated the derived beta-1,3-glucanases by the loss of an extended N-terminal region and the beta-glucan-binding proteins by the loss of the catalytic residues. SLam homology modeling suggests that E228 may affect the ionization of the catalytic residues, thus displacing the enzyme pH optimum. SLam antiserum reacts with a single protein in the insect midgut. Immunocytolocalization shows that the enzyme is present in secretory vesicles and glycocalyx from columnar cells. (C) 2010 Elsevier Ltd. All rights reserved.

Electronic Structure of the Ground and Low-Lying Electronic States of MoB and MoB(+)

Multiconfigurational second-order perturbation theory (CASSCF//CASPT2) and quadruple-zeta ANO-RCC basis sets were employed to investigate the ground and low-lying electronic states of MoB and MoB(+). Spectroscopic constants, potential energy curves, wavefunctions, Mulliken population analyses, and ionization energies are given. The ground state of MoB is of X(6)Pi symmetry (R(e) = 1.968 angstrom, omega(e) = 664 cm(-1), and mu = 2.7 D), giving rise to a Omega = 7/2 ground state after including spin-orbit coupling. For MoB(+), the ground state is computed to be of X(7)Sigma(+) symmetry (R(e) = 2.224 angstrom, omega(e) = 141 cm(-1), and mu = 1.2 D), with an adiabatic ionization energy of 7.19 eV and a vertical one of 7.53 eV. (C) 2011 Wiley Periodicals, Inc. Int J Quantum Chem 111: 3362-3370, 2011

Optimization of a method for determination of phenolic acids in exotic fruits by capillary electrophoresis

In this work, the separation of nine phenolic acids (benzoic, caffeic, chlorogenic, p-coumaric, ferulic, gallic, protocatechuic, syringic, and vanillic acid) was approached by a 32 factorial design in electrolytes consisting of sodium tetraborate buffer(STB) in the concentration range of 10-50 mmol L(-1) and methanol in the volume percentage of 5-20%. Derringer`s desirability functions combined globally were tested as response functions. An optimal electrolyte composed by 50 mmol L(-1) tetraborate buffer at pH 9.2, and 7.5% (v/v) methanol allowed baseline resolution of all phenolic acids under investigation in less than 15 min. In order to promote sample clean up, to preconcentrate the phenolic fraction and to release esterified phenolic acids from the fruit matrix, elaborate liquid-liquid extraction procedures followed by alkaline hydrolysis were performed. The proposed methodology was fully validated (linearity from 10.0 to 100 mu g mL(-1), R(2) > 0.999: LOD and LOQ from 1.32 to 3.80 mu g mL(-1) and from 4.01 to 11.5 mu g mL(-1), respectively; intra-day precision better than 2.8% CV for migration time and 5.4% CV for peak area; inter-day precision better than 4.8% CV for migration time and 4.8-11% CV for peak area: recoveries from 81% to 115%) and applied successfully to the evaluation of phenolic contents of abiu-roxo (Chrysophyllum caimito), wild mulberry growing in Brazil (Morus nigra L.) and tree tomato (Cyphomandra betacea). Values in the range of 1.50-47.3 mu g g(-1) were found, with smaller amounts occurring as free phenolic acids. (C) 2009 Elsevier B.V. All rights reserved.

Structural and spectroscopic properties of the diazocarbene radical (CNN) and its ions CNN(+) and CNN(-): a high-level theoretical investigation

The diazocarbene radical, CNN, and the ions CNN(+) and CNN(-) were investigated at a high level of theory. Very accurate structural parameters for the states X(3)Sigma(-) and A(3)Pi of CNN, and X(2)Pi of both CNN(+) and CNN(-) were obtained with the UCCSD(T) method using correlated-consistent basis functions with extrapolations to the complete basis set limit, with valence only and also with all electrons correlated. Harmonic and anharmonic frequencies were obtained for all species and the Renner parameter and average frequencies evaluated for the Pi states. At the UCCSD(T)/CBS(T-5) level of theory, Delta(f)H(0 K) = 138.89 kcal/mol and Delta(f)H(298 K) = 139.65 kcal/mol were obtained for diazocarbene; for the ionization potential and the electron affinity of CNN, 10.969 eV (252.95 kcal/mol), and 1.743 eV (40.19 kcal/mol), respectively, are predicted. Geometry optimization was also carried out with the CASSCF/MRCI/CBS(T-5) approach for the states X(3)Sigma(-) A(3)Pi, and a(1)Delta of CNN, and with the CASSCF/MRSDCI/aug-cc-pVTZ approach for the states b(1)Sigma(+), c(1)Pi, d(1)Sigma(-), and B(3)Sigma(-), and excitation energies (T(e)) evaluated. Vertical energies were calculated for 15 electronic states, thus improving on the accuracy of the five transitions already described, and allowing for a reliable overview of a manifold of other states, which is expected to guide future spectroscopic experiments. This study corroborates the experimental assignment for the vertical transition X (3)Sigma(-) <- E (3)Pi.

Synthesis of alpha,beta-unsaturated aryl esters via Heck reaction of unsymmetrical aryl tellurides

A variety of alpha,beta-unsaturated aryl esters were prepared by the direct reaction of unsymmetrical aryltellurides and ethyl acrylate, catalyzed by PdCl(2) via a Heck cross-coupling reaction. (C) 2009 Elsevier Ltd. All rights reserved.

Simple method for determination of cocaine and main metabolites in urine by CE coupled to MS

in this work, a simple method for the simultaneous determination of cocaine (COC) and five COC metabolites (benzoylecgonine, cocaethylene (CET), anhydroecgonine, anhydroecgonine methyl ester and ecgonine methyl ester) in human urine using CE coupled to MS via electrospray ionization (CE-ESI-MS) was developed and validated. Formic acid at 1 mol/L concentration was used as electrolyte whereas formic acid at 0.05 mol/L concentration in 1:1 methanol:water composed the coaxial sheath liquid at the ESI nozzle. The developed method presented good linearity in the dynamic range from 250 ng/mL to 5000 ng/mL (coefficient of determination greater than 0.98 for all compounds). LODs (signal-to-noise ratio of 3) were 100 ng/mL for COC and CET and 250 ng/mL for the other studied metabolites whereas LOQ`s (signal-to-noise ratio of 10) were 250 ng/mL for COC and CET and 500 ng/mL for all other compounds. Intra-day precision and recovery tests estimated at three different concentration levels (500, 1500 and 5000 ng/mL) provided RSD lower than 10% (except anhydroecgonine, 18% RSD) and recoveries from 83-109% for all analytes. The method was successfully applied to real cases. For the positive urine samples, the presence of COC and its` metabolites was further confirmed by MS/MS experiments.

New Relativistic Atomic Natural Orbital Basis Sets for Lanthanide Atoms with Applications to the Ce Diatom and LuF3

New basis sets of the atomic natural orbital (ANO) type have been developed for the lanthanide atoms La-Lu. The ANOs have been obtained from the average density matrix of the ground and lowest excited states of the atom, the positive ions, and the atom in an electric field. Scalar relativistic effects are included through the use of a Douglas-Kroll-Hess Hamiltonian. Multiconfigurational wave functions have been used with dynamic correlation included using second-order perturbation theory (CASSCF/CASPT2). The basis sets are applied in calculations of ionization energies and some excitation energies. Computed ionization energies have an accuracy better than 0.1 eV in most cases. Two molecular applications are inluded as illustration: the cerium diatom and the LuF3 molecule. In both cases it is shown that 4f orbitals are not involved in the chemical bond in contrast to an earlier claim for the latter molecule.