Special identities for Bol algebras

Bol algebras appear as the tangent algebra of Bol loops. A (left) Bol algebra is a vector space equipped with a binary operation [a, b] and a ternary operation {a, b, c} that satisfy five defining identities. If A is a left or right alternative algebra then A(b) is a Bol algebra, where [a, b] := ab - ba is the commutator and {a, b, c} := < b, c, a > is the Jordan associator. A special identity is an identity satisfied by Ab for all right alternative algebras A, but not satisfied by the free Bol algebra. We show that there are no special identities of degree <= 7, but there are special identities of degree 8. We obtain all the special identities of degree 8 in partition six-two. (C) 2011 Elsevier Inc. All rights reserved.

Miniversal deformations of matrices of bilinear forms

Arnold [V.I. Arnold, On matrices depending on parameters, Russian Math. Surveys 26 (2) (1971) 29-43] constructed miniversal deformations of square complex matrices under similarity; that is, a simple normal form to which not only a given square matrix A but all matrices B close to it can be reduced by similarity transformations that smoothly depend on the entries of B. We construct miniversal deformations of matrices under congruence. (C) 2011 Elsevier Inc. All rights reserved.

Kleiner's theorem for unitary representations of posets

A subspace representation of a poset S = {s(1), ..., S-t} is given by a system (V; V-1, ..., V-t) consisting of a vector space V and its sub-spaces V-i such that V-i subset of V-j if s(i) (sic) S-j. For each real-valued vector chi = (chi(1), ..., chi(t)) with positive components, we define a unitary chi-representation of S as a system (U: U-1, ..., U-t) that consists of a unitary space U and its subspaces U-i such that U-i subset of U-j if S-i (sic) S-j and satisfies chi 1 P-1 + ... + chi P-t(t) = 1, in which P-i is the orthogonal projection onto U-i. We prove that S has a finite number of unitarily nonequivalent indecomposable chi-representations for each weight chi if and only if S has a finite number of nonequivalent indecomposable subspace representations; that is, if and only if S contains any of Kleiner's critical posets. (c) 2012 Elsevier Inc. All rights reserved.

Remarks on the classification of a pair of commuting semilinear operators

Gelfand and Ponomarev [I.M. Gelfand, V.A. Ponomarev, Remarks on the classification of a pair of commuting linear transformations in a finite dimensional vector space, Funct. Anal. Appl. 3 (1969) 325-326] proved that the problem of classifying pairs of commuting linear operators contains the problem of classifying k-tuples of linear operators for any k. We prove an analogous statement for semilinear operators. (C) 2011 Elsevier Inc. All rights reserved.

Electron Interactions with Disulfide Bridges

Because of its electronic properties, sulfur plays a major role in a variety of metabolic processes and, more in general, in the chemistry of life. In particular, S-S bridges between cysteines are present in the amino acid backbone of proteins. Protein disulfur radical anions may decay following different paths through competing intra and intermolecular routes, including bond cleavage, disproportionation, protein-protein cross linking, and electron transfer. Indeed, mass spectrometry ECD (electron capture dissociation massspectroscopy) studies have shown that capture of low-energy (<0.2 eV) electrons by multiply protonated proteins is followed by dissociation of S-S bonds holding two peptide chains together. In view of the importance of organic sulfur chemistry, we report on electron interactions with disulphide bridges. To study these interactions we used as prototypes the molecules dimethyl sulfide [(CH3)2S] and dimethyl disulfide [(H3C)S2(CH3)]. We seek to better understand the electron-induced cleavage of the disulfide bond. To explore dissociative processes we performed electron scattering calculations with the Schwinger Multichannel Method with pseudopotentials (SMCPP), recently parallelized with OpenMP directives and optimized with subroutines for linear algebra (BLAS) and LAPACK routines. Elastic cross sections obtained for different S-S bond lengths indicate stabilization of the anion formed by electron attachment to a σ*SS antibonding orbital, such that dissociation would be expected.