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.

Polymerization kinetics and reactivity of alternative initiators systems for use in light-activated dental resins

Objectives. The purpose of this study was to evaluate the reactivity and polymerization kinetics behavior of a model dental adhesive resin with water-soluble initiator systems. Methods. A monomer blend based on Bis-GMA, TEGDMA and HEMA was used as a model dental adhesive resin, which was polymerized using a thioxanthone type (QTX) as a photoinitiator. Binary and ternary photoinitiator systems were formulated using 1 mol% of each initiator. The co-initiators used in this study were ethyl 4-dimethylaminobenzoate (EDAB), diphenyliodonium hexafluorophosphate (DPIHFP), 1,3-diethyl-2-thiobarbituric acid (BARB), p-toluenesulfinic acid and sodium salt hydrate (SULF). Absorption spectra of the initiators were measured using a UV-Vis spectrophotometer, and the photon absorption energy (PAE) was calculated. The binary system camphorquinone (CQ)/amine was used as a reference group (control). Twelve groups were tested in triplicate. Fourier-transform infrared spectroscopy (FTIR) was used to investigate the polymerization reaction during the photoactivation period to obtain the degree of conversion (DC) and maximum polymerization rate (R-p(max)) profile of the model resin. Results. In the analyzed absorption profiles, the absorption spectrum of QTX is almost entirely localized in the UV region, whereas that of CQ is in the visible range. With respect to binary systems, CQ + EDAB exhibited higher DC and R-p(max) values. In formulations that contained ternary initiator systems, the group CQ + QTX + EDAB was the only one of the investigated experimental groups that exhibited an R-p(max) value greater than that of CQ + EDAB. The groups QTX + EDAB + DPIHFP and QTX + DPIHFP + SULF exhibited values similar to those of CQ + EDAB with respect to the final DC; however, they also exhibited lower reactivity. Significance. Water-soluble initiator systems should be considered as alternatives to the widely used CQ/amine system in dentin adhesive formulations. (C) 2012 Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.