This note provides a simpliied proof concerning the paper \A Primal-Dual Interior Point Method Whose Running Time Depends Only on the Constraint Matrix" by the same authors. In particular, we prove that Case II, one of the three cases in the method, can never occur.

The notion of anyonic Wick algebras is introduced and the corresponding second quantisation procedure is discussed. Applications to the physics of 2D anyonic matter are presented. In particular the existence of thermodynamics in the in nite volume for the case of Leinaas-Myrheim potentials is presented. Additionally a new class of states corresponding to quasifree thermal states on some Wick al...

We study interior operators and interior structures in a fuzzy setting. We investigate systems of “almost open” fuzzy sets and the relationships to fuzzy interior operators and fuzzy interior systems.

Recently in proving certain existence theorems for non-alternating and for interior transformations of a continuum onto a simple arc it was observed that when a transformation of one of these types was set up, usually it satisfied in large measure conditions which brought it also under transformations of the other type. This suggests the existence of common ground shared by these sorts of trans...

It is known that commutative BCK-algebras form a variety, but BCK-algebras do not [4]. Therefore H. Yutani introduced the notion of quasicommutative BCK-algebras. In this article we first present the notion and general theory of quasi-commutative BCI-algebras. Then we discuss the reduction of the type of quasi-commutative BCK-algebras and some special classes of quasicommutative BCI-algebras.

We discuss a method to construct a De Rham complex (diierential algebra) of Poincar e-Birkhoo-Witt-type on the universal enveloping algebra of a Lie algebra g. We determine the cases in which this gives rise to a diierential Hopf algebra that naturally extends the Hopf algebra structure of U(g). The construction of such diierential structures is interpreted in terms of colour Lie superalgebras.

A theorem of Bade proves that for a complete Boolean sublattice S£ of 3>(3if) the following holds: SS {PeS£"; P is orthogonal projection operator} We prove that this theorem does not hold for the physically interesting class of non-Boolean propositional systems embedded in a 3>(3if); we derive however a necessary and sufficient condition under which the theorem does hold. This condition is auto...

In the 1950’s I set out to revolutionize logic. I didn’t succeed (not yet!), but it wasn’t for want of trying. Logic has always fascinated me. In the common-sense sense of the word logic was easy; I had no inclination to commit the obvious errors of reasoning, and long chains of deductions were not intimidating. When I was told about syllogisms, I said “sure, obviously”, and didn’t feel that I ...

We propose the notion of q–characters for finite-dimensional representations of quantum affine algebras. It is motivated by our theory of deformed W– algebras.