A simple relation between the Leimkuhler curve and the mean residual life

In this paper, a simple relation between the Leimkuhler curve and the mean residual life is established. The result is illustrated with several models commonly used in informetrics, such as exponential, Pareto and lognormal. Finally, relationships with some other reliability concepts are also presented. (C) 2010 Elsevier Ltd. All rights reserved.

COMMUTATIVE FINITE-DIMENSIONAL ALGEBRAS SATISFYING x(x(xy))=0 ARE NILPOTENT

We investigate the structure of commutative non-associative algebras satisfying the identity x(x(xy)) = 0. Recently, Correa and Hentzel proved that every commutative algebra satisfying above identity over a field of characteristic not equal 2 is solvable. We prove that every commutative finite-dimensional algebra u over a field F of characteristic not equal 2, 3 which satisfies the identity x(x(xy)) = 0 is nilpotent. Furthermore, we obtain new identities and properties for this class of algebras.

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.

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.