1. I n t r o d u c t i o n The aim of this note is to explain how a well-known result from Moda~ Logic, S~hlqvist's Theorem, can be applied in the theory of Boolean Algebras with Operators to obtain a large class of identities, called Sahlqvist identities, that are preserved under canonical embedding algebras. These identities can be specified as follows. Let a = { fi : i E I } be a set of (nor...

In this paper, we associate canonically a precyclic mod- ule to a regular multiplier Hopf algebra endowed with a group-like projection and a modular pair in involution satisfying certain con- dition

How regular and irregular verbs are processed remains a matter of debate. Some English-speaking patients with nonfluent aphasia are especially impaired on regular past-tense forms like played, whether the task requires production, comprehension or even the judgement that "play" and "played" sound different. Within a dual-mechanism account of inflectional morphology, these deficits reflect disru...

In order to generalize the Kleene theorem from the free monoid to richer algebraic structures, we consider the non deterministic acceptance by a finite automaton of subsets of vertices of a graph. The subsets accepted in such a way are the equational subsets of vertices of the graph in the sense of Mezei and Wright. We introduce the notion of deterministic acceptance by finite automaton. A grap...

where x ∈ Ŝk is minimal such that ν = λ.x −1 satisfies νi < νi+1 for i = 1, 2 . . . k−1 and νi−νk ≥ 1−k−n, and μ = λ.xy. This conjecture is proved by Kazhdan-Lusztig [KL] and Kashiwara-Tanisaki [KT]. The proof relies on an equivalence between the category of finite-dimensional Uǫ(slk)-modules and a category of negative-level representations of the affine algebra ŝlk which are integrable with re...

The sandwiched Rényi \(\alpha \)-divergences of two finite-dimensional quantum states play a distinguished role among the many versions divergences as tight quantifiers trade-off between error probabilities in strong converse domain state discrimination. In this paper, we show same for normal on an injective von Neumann algebra, thereby establishing operational significance these quantities. Mo...

We present a new compositional tense-aspect deindexing mechanism that makes use of tense trees as components of discourse contexts. The mechanism allows reference episodes to be correctly identified even for embedded clauses and for discourse that involves shifts in temporal perspective, and permits deindexed logical forms to be automatically computed with a small number of deindexing rules. 1 ...

Let A and B be unital semi-simple commutative Banach algebras. In this paper we study two-variable polynomials p which satisfy the following property: a map T from A onto B such that the equality σ(p(Tf, T g)) = σ(p(f, g)), f, g ∈ A holds is an algebra isomorphism.

Let A be a C *-algebra, T be a locally compact Hausdorff space equipped with a probability measure P and let (A t) t∈T be a continuous field of operators in A such that the function t → A t is norm continuous on T and the function t → A t is integrable. Then the following equality including Bouchner integrals holds T A t − T A s dP 2 dP = T |A t | 2 dP − T A t dP 2. (0.1) This equality is relat...