Lie algebra methods for the applications to the statistical theory of turbulence

Approximate Lie symmetries of the Navier-Stokes equations are used for the applications to scaling phenomenon arising in turbulence. In particular, we show that the Lie symmetries of the Euler equations are inherited by the Navier-Stokes equations in the form of approximate symmetries that allows to involve the Reynolds number dependence into scaling laws. Moreover, the optimal systems of all finite-dimensional Lie subalgebras of the approximate symmetry transformations of the Navier-Stokes are constructed. We show how the scaling groups obtained can be used to introduce the Reynolds number dependence into scaling laws explicitly for stationary parallel turbulent shear flows. This is demonstrated in the framework of a new approach to derive scaling laws based on symmetry analysis [11]-[13].

Hypercentral unit groups and the hyperbolicity of a modular group algebra

We classify groups G such that the unit group U-1 (ZG) is hypercentral. In the second part, we classify groups G whose modular group algebra has hyperbolic unit groups U-1 (KG).

Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

CLASSIFICATION OF SUBALGEBRAS OF THE CAYLEY ALGEBRA OVER A FINITE FIELD

We classify all unital subalgebras of the Cayley algebra O(q) over the finite field F(q), q = p(n). We obtain the number of subalgebras of each type and prove that all isomorphic subalgebras are conjugate with respect to the automorphism group of O(q). We also determine the structure of the Moufang loops associated with each subalgebra of O(q).

Coincidence Wecken homotopies versus Wecken homotopies relative to a fixed homotopy in one of the maps

We study the 1-parameter Wecken problem versus the restricted Wecken problem, for coincidence free pairs of maps between surfaces. For this we use properties of the function space between two surfaces and of the pure braid group on two strings of a surface. When the target surface is either the 2-sphere or the torus it is known that the two problems are the same. We classify most pairs of homotopy classes of maps according to the answer of the two problems are either the same or different when the target is either projective space or the Klein bottle. Some partial results are given for surfaces of negative Euler characteristic. (C) 2010 Elsevier B.V. All rights reserved.

Free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus (Omega(R)/dR)

In this paper we construct two free field realizations of the elliptic affine Lie algebra sl(2, R) circle plus Omega(R)/dR where R = C[t. t(-1), u vertical bar u(2) = t(3) - 2bt(2) + t]. The first realization provides an analogue of Wakimoto`s construction for Affine Kac-Moody algebras, but in the setting of the elliptic affine Lie algebra. The second realization gives new types of representations analogous to Imaginary Verma modules in the Affine setting. (c) 2009 Elsevier B.V. All rights reserved.

INSECT CHYMOTRYPSINS: CHLOROMETHYL KETONE INACTIVATION AND SUBSTRATE SPECIFICITY RELATIVE TO POSSIBLE COEVOLUTIONAL ADAPTATION OF INSECTS AND PLANTS

Insect digestive chymotrypsins are present in a large variety of insect orders but their substrate specificity still remains unclear. Ewer insect chymotrypsins from 3 different insect orders (Dictyoptera, Coleoptera and two Lepidoptera) were isolated using affinity chromatography. Enzymes presented molecular masses in the range of 20 to 31 kDa and pH optima in the range of 7.5 to 10.0. Kinetic characterization. using different, colorimetric and fluorescent substrates indicated that insect chymotrypsins differ from, bovine chymotrypsin in their primary specificity toward small substrates (like N-benzoyl-L-Tyr p-nitroanilide) rather than on their preference for large substrates (exemplified by Succynil-Ala-Ala-Pro-Phe P-nitroanilide). Chloromethyl ketones (TPCK, N-alpha-tosyl-L-Phe chloromethyl ketone and Z-GGF-CK, N-carbobenzoxy-Gly-Gly-phe-CK) inactivated all chymotrypsins legated. Inactivation rates follow apparent first-order kinetics with variable second order rates (TPCK, 42 to 130 M(-1)s(-1); Z-GGF-CK, 150 to 450 M(-1)s(-1) that may be remarkably low for S. frugiperda chymotrypsin (TPCK, 6 M(-1)s(-1); Z-GGF-CK, 6.1 M(-1) s(-1)). Homology modelling and sequence alignment showed that. in lepidopteran chymotrypsins, differences in the amino acid residues in the neighborhood of the catalytic His 57 may affect its pKa, value. This is Proposed as the cause of the decrease in His 57 reactivity toward chloromethyl ketones. Such amino acid replacement in the active site is proposed. to be an adaptation to the presence of dietary ketones. (C) 2009 Wiley Periodicals, Inc.

Tellurium in organic synthesis: a new approach to trisubstituted gamma-butyrolactones with trans-trans relative stereochemistry. Total enantioselective synthesis of (-)-Blastmycinolactol, (+)-Blastmycinone, (-)-NFX-2, and (+)-Antimycinone

The total synthesis of (-)-Blastmycinolactol, (+)-Blastmycinone, (-)-NFX-2, and (+)-Antimycinone was accomplished in few steps in high yields and ee, starting from enantiomerically enriched (S)-Z-vinylic hydroxytellurides. (C) 2010 Published by Elsevier Ltd.