The realizations of the exceptional non-linear (quadratically generated, or W type) N = 8 and N = 7 superconformal algebras with Spin(7) and G2 affine symmetry currents are reviewed. Both the N = 8 and N = 7 algebras admit unitary realizations in terms of a single boson and free fermions in 8 of Spin(7) and 7 of G2, with the central charges c8 = 26/5 and c7 = 5, respectively. They can also be r...

We characterise the class SRaCAn of subalgebras of relation algebra reducts of ndimensional cylindric algebras (for finite n ≥ 5) by the notion of a ‘hyper-basis’, analogous to the cylindric basis of Maddux, and by relativised representations. A corollary is that SRaCAn = SRa(CAn ∩ Crsn) = SRa(CAn ∩ Gn). We outline a game-theoretic approximation to the existence of a representation, and how to ...

A new IPM (Interior Point Method) for LPs has been discussed in [9, 10] based on a centering step that attempts to maximize the radius of the inscribed sphere with center on the current objective plane, and using descent directions derived without using matrix inversions. The method is a descent method and may be called the sphere method for LP. In contrast to all the existing IPMs which involv...

A symplified axiomatization of pseudo-BCK algebras is given. In addition, we obtain a system of axioms defining bounded commutative pseudoBCK algebras and show that these axioms are independent (that is, none follows from the others). 2010 Mathematics Subject Classification: 03G25, 06F05, 06F35