On automorphisms of order three of division algebras

AbstractLet A be a finite dimensional division algebra (not necessarily associative) over a field. The automorphisms of A having order three are characterized by giving a canonical matrix representation for each of the possible types (there are three). Examples are given to show that each type does exist. Some general results concerning automorphisms of prime power order are included

Effect of light, food additives and heat on the stability of sorghum 3-deoxyanthocyanins in model beverages.

This work aimed to evaluate the stability of sorghum 3-deoxyanthocyanins (DXA) in model beverages (pH 3.5) elaborated with crude sorghum phenolic extract, containing ascorbic acid and sulphite, under fluorescent light exposure and subjected to heat treatment. There was no significant difference in the DXA degradation during storage under light exposure (24.16%) and absence of light (20.72%). DXA degradation did not differ in the presence of ascorbic acid during storage under light exposure (23.99-25.38%) and absence of light (19.87-21.74%). The addition of sulphite caused an initial bleaching reaction, but as a reversible reaction, the anthocyanin content was higher on the last day of storage compared to the first day. There were no significant differences in total anthocyanin content of all treatments subjected to the heat treatment (80 °C for 5 and 25 min). Thus, crude DXA are very stable under light, additives and heat, and may be useful as natural food colourants

The maximum dimension of a subspace of nilpotent matrices of index 2

A matrix M is nilpotent of index 2 if M² = 0. Let V be a space of nilpotent n x n matrices of index 2 over a field k where card k > n and suppose that r is the maximum rank of any matrix in V. The object of this paper is to give an elementary proof of the fact that dim V ≤ r(n − r). We show that the inequality is sharp and construct all such subspaces of maximum dimension. We use the result to find the maximum dimension of spaces of anti-commuting matrices and zero subalgebras of special Jordan Algebras