Finite-dimensional non-associative algebras and codimension growth

Let A be a (non-necessarily associative) finite-dimensional algebra over a field of characteristic zero. A quantitative estimate of the polynomial identities satisfied by A is achieved through the study of the asymptotics of the sequence of codimensions of A. It is well known that for such an algebra this sequence is exponentially bounded. Here we capture the exponential rate of growth of the sequence of codimensions for several classes of algebras including simple algebras with a special non-degenerate form, finite-dimensional Jordan or alternative algebras and many more. In all cases such rate of growth is integer and is explicitly related to the dimension of a subalgebra of A. One of the main tools of independent interest is the construction in the free non-associative algebra of multialternating polynomials satisfying special properties. (C) 2010 Elsevier Inc. All rights reserved.

Processing of electroactive nanostructured films incorporating carbon nanotubes and phthalocyanines for sensing

The use of carbon nanotubes (CNTs) combined with other materials in nanostructured films has demonstrated their versatility in tailoring specific properties. In this study, we produced layer-by-layer (LbL) films of polyamidoamine-PAMAM-incorporating multiwalled carbon nanotubes (PAMAM-NT) alternated with nickel tetrasulfonated metallophthalocyanine (NiTsPc), in which the incorporation of CNTs enhanced the NiTsPc redox process and its electrocatalytic properties for detecting dopamine. Film growth was monitored by UV-vis spectroscopy, which pointed to an exponential growth of the multilayers, whose roughness increased with the number of bilayers according to atomic force microscopy (AFM) analysis. Strong interactions between -NH3+ terminal groups from PAMAM and -SO3- from NiTsPc were observed via infrared spectroscopy, while the micro-Raman spectra confirmed the adsorption of carbon nanotubes (CNTs) onto the LbL film containing NiTsPc. Cyclic voltammograms presented well-defined electroactivity with a redox pair at 0.86 and 0.87 V, reversibility, a charge-transfer controlled process, and high stability up to 100 cycles. The films were employed successfully in dopamine (DA) detection, with limits of detection and quantification of 10(-7) and 10(-6) mol L-1, respectively. Furthermore, films containing immobilized CNTs could distinguish between DA and its natural interferent, ascorbic acid (AA).

Fluorimetric determination of intra- and extracellular free amino acids in the microalgae Tetraselmis gracilis (Prasinophyceae) using monolithic column in reversed phase mode

This paper describes the development and application of an RP HPLC method using a C(18) monolithic stationary phase for the separation and quantification of extra- and intracellular amino acids in a batch cultivation of the marine alga Tetraselmis gracilis. Fluorimetric detection was made after separation of the o-phthaldialdehyde 2-mercaptoethanol (OPA-2MCE) derivatives using a binary gradient elution. Separation of 19 amino acids was achieved with resolution >1.5 in about 39 min at a flow rate of 1.5 mL/min. RSD of analyses in seawater medium ranged from 0.36% for Orn (0.50 mu mol/L) to 12% for Ile (0.10 mu mol/L). The main constituents of the intracellular dissolved free amino acids (DFAAs) in the exponential growth phase were arginine (Arg), asparagine (Asn), alanine (Ala), aspartic acid (Asp), glutamic acid (Glu), serine (Ser), glycine (Gly), glutamine (Gln), and leucine (Leu). The major amino acids excreted to the media were valine (Val), Ala, Ser, and Gly. The monolithic phase facilitates the analysis by shortening the separation time and saving solvents and instrumentation costs (indeed conventional HPLC instrumentation can be used, running at lower pressures than those ones used with packed particle columns).

INDEFINITE QUASILINEAR ELLIPTIC EQUATIONS IN EXTERIOR DOMAINS WITH EXPONENTIAL CRITICAL GROWTH

This paper is concerned with the existence of solutions for the quasilinear problem {-div(vertical bar del u vertical bar(N-2) del u) + vertical bar u vertical bar(N-2) u = a(x)g(u) in Omega u = 0 on partial derivative Omega, where Omega subset of R(N) (N >= 2) is an exterior domain; that is, Omega = R(N)\omega, where omega subset of R(N) is a bounded domain, the nonlinearity g(u) has an exponential critical growth at infinity and a(x) is a continuous function and changes sign in Omega. A variational method is applied to establish the existence of a nontrivial solution for the above problem.