Infinite dimensional Lie algebra associated with conformal transformations of the two-point velocity correlation tensor from isotropic turbulence

We deal with homogeneous isotropic turbulence and use the two-point velocity correlation tensor field (parametrized by the time variable t) of the velocity fluctuations to equip an affine space K3 of the correlation vectors by a family of metrics. It was shown in Grebenev and Oberlack (J Nonlinear Math Phys 18:109–120, 2011) that a special form of this tensor field generates the so-called semi-reducible pseudo-Riemannian metrics ds2(t) in K3. This construction presents the template for embedding the couple (K3, ds2(t)) into the Euclidean space R3 with the standard metric. This allows to introduce into the consideration the function of length between the fluid particles, and the accompanying important problem to address is to find out which transformations leave the statistic of length to be invariant that presents a basic interest of the paper. Also we classify the geometry of the particles configuration at least locally for a positive Gaussian curvature of this configuration and comment the case of a negative Gaussian curvature.

The potentially toxic diatom Pseudo-nitzschia H. Peragallo in the Parana and Santa Catarina States, Southern Brazil

A taxonomic survey of the diatom Pseudo-nitzschia H. Peragallo was carried out in the Parana and Santa Catarina coasts, Southern Brazil. Samples were taken in various localities along the coastline using vertical hauls from the bottom to the surface. Electron microscopy revealed five species: the potentially toxic P. australis Frenguelli, P calliantha Lundholm, Moestrup & Has le, P multiseries (Has le) Has le and P pungens (Grunow ex Cleve) Has le (plus P pungens var. cingulata Villac), and the non-toxic P linea Lundholm, Has le & G. A. Fryxell. Southern Brazilian strains of P. calliantha and P multiseries have previously been shown to be toxic, raising concerns about a potential contamination of mussels and oysters being commercially grounded in the region. High morphological variability was observed in valve characters of P calliantha and P pungens, in some cases confirmed in the literature. In P calliantha there was a conspicuous differentiation in two morphotypes separated from each other by the width and the shape of the valve, and the density of the poroids. P linea has not previously been found in Brazilian waters, and P pungens var. cingulata is a new record in Western Atlantic waters. Future investigations using molecular techniques will elucidate whether the genetic variability corresponds to the morphological variation and unveil the possible existence of semicryptic species of Pseudo-nitzschia inhabiting the South Brazilian coast.

Curves in the Minkowski plane and their contact with pseudo-circles

We study the caustic, evolute, Minkowski symmetry set and parallels of a smooth and regular curve in the Minkowski plane.

Generalizations of Lie Algebras

The generalizations of Lie algebras appeared in the modern mathematics and mathematical physics. In this paper we consider recent developments and remaining open problems on the subject. Some of that developments have been influenced by lectures given by Professor Jaime Keller in his research seminar. The survey includes Lie superalgebras, color Lie algebras, Lie algebras in symmetric categories, free Lie tau-algebras, and some generalizations with non-associative enveloping algebras: tangent algebras to analytic loops, bialgebras and primitive elements, non-associative Hopf algebras.

COMMUTATIVE ALGEBRAS IN DRINFELD CATEGORIES OF ABELIAN LIE ALGEBRAS

We describe (braided-) commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over these algebras and classify commutative algebras with a finite number of simple local modules.

Effectiveness, against tuberculosis, of pseudo-ternary complexes: Peptide-DNA-cationic liposome

We report the effects of a synthetic peptide designed to act as a nuclear localization signal on the treatment of tuberculosis. The peptide contains 21 amino acid residues with the following specific domains: nuclear localization signal from SV 40T, cationic shuttle sequence, and cysteamide group at the C-terminus. The peptide was complexed with the plasmid DNAhsp65 and incorporated into cationic liposomes, forming a pseudo-ternary complex. The same cationic liposomes, composed of egg chicken L-alpha-phosphatidylcholine, 1,2-dioleoyl-3-trimethylammonium-propane, and 1,2-dioleoyl-3-trimethylammonium-propane (2:1:1 M), were previously evaluated as a gene carrier for tuberculosis immunization protocols with DNAhsp65. The pseudo-ternary complex presented a controlled size (250 nm), spherical-like shape, and various lamellae in liposomes as evaluated by transmission electron microscopy. An assay of fluorescence probe accessibility confirmed insertion of the peptide/DNA into the liposome structure. Peptide addition conferred no cytotoxicity in vitro, and similar therapeutic effects against tuberculosis were seen with four times less DNA compared with naked DNA treatment. Taken together, the results indicate that the pseudo-ternary complex is a promising gene vaccine for tuberculosis treatment. This work contributes to the development of multifunctional nanostructures in the search for strategies for in vivo DNA delivery. (C) 2011 Elsevier Inc. All rights reserved.

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

Transverse pseudo-nonlinear effects measured in solid-state laser materials using a sensitive time-resolved technique

We present a detailed study of the Baryscan technique, a new efficient alternative to the widespread Z-scan technique which has been demonstrated [Opt. Lett. 36:8, 2011] to reach among the highest sensitivity levels. This method is based upon the measurement of optical nonlinearities by means of beam centroid displacements with a position sensitive detector and is able to deal with any kind of lensing effect. This technique is applied here to measure pump-induced electronic refractive index changes (population lens), which can be discriminated from parasitic thermal effects by using a time-resolved Baryscan experiment. This method is validated by evaluating the polarizability variation at the origin of the population lens observed in the reference Cr3+:GSGG laser material.

On simple Lie algebras over a field of characteristic 2

We prove that the simple Lie algebras constructed by G. Jurman (2004) in 121 are isomorphic to Hamiltonian algebras. As a corollary we answer all questions formulated in G. Jurman (2004) [2] about isomorphisms of these algebras. (C) 2012 Elsevier Inc. All rights reserved.