We give a dimension bound on the irreducible components of the characteristic variety of a system of linear partial di.erential equations de0ned from a suitable 0ltration of the Weyl algebra An. This generalizes an important consequence of the fact that a characteristic variety de0ned from the order 0ltration is involutive. More explicitly, we consider a 0ltration of An induced by any vector (u...

Algorithmic issues concerning Elliott local semigroups are seldom considered in the literature, although these combinatorial structures completely classify AF algebras. In general, the addition operation of an Elliott local semigroup is partial, but for every AF algebra B whose Murray-von Neumann order of projections is a lattice, this operation is uniquely extendible to the addition of an invo...

Among P−pseudo-Hermitian Hamiltonians H = P HP with real spectra, the “weakly pseudo-Hermitian” ones (i.e., those employing non-self-adjoint P 6 = P) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P 6 = P, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasiparity...

We consider the relation of the dual calculus of Wadler (2003) to the λμ-calculus of Parigot (1992). We give translations from the λμ-calculus into the dual calculus and back again. The translations form an equational correspondence as defined by Sabry and Felleisen (1993). In particular, translating from λμ to dual and then ‘reloading’ from dual back into λμ yields a term equal to the original...

Let be the class of odd involutive even notion partial lex products is not sufficiently general. One more tweak needed, a slightly complex construction, called sublex product, introduced here.

We give necessary and sufficient geometric conditions for a distribution (or a Pfaffian system) to be locally equivalent to the canonical contact system on J(R, R). We study the geometry of that class of systems, in particular, the existence of corank one involutive subdistributions. We also distinguish regular points, at which the system is equivalent to the canonical contact system, and singu...

We axiomatically define (pre-)Hilbert categories. The axioms resemble those for monoidal Abelian categories with the addition of an involutive functor. We then prove embedding theorems: any locally small pre-Hilbert category whose monoidal unit is a simple generator embeds (weakly) monoidally into the category of pre-Hilbert spaces and adjointable maps, preserving adjoint morphisms and all fini...

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant 0, namely ¬φ isφ → 0. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which i...

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...