We extend to several combinatorial Hopf algebras the endomorphism of symmetric functions sending the first power-sum to zero and leaving the other ones invariant. As a “transformation of alphabets”, this is the (1 − E)-transform, where E is the “exponential alphabet,” whose elementary symmetric functions are en = 1 n! . In the case of noncommutative symmetric functions, we recover Schocker’s id...

We use category theory to propose a unified approach to the Schur–Weyl dualities involving the general linear Lie algebras, their polynomial extensions and associated quantum deformations. We define multiplicative sequences of algebras exemplified by the sequence of group algebras of the symmetric groups and use them to introduce associated monoidal categories. Universal properties of these cat...

There are two widely accepted notions of behavioural equivalence, formalizing the idea of observational indistinguishability: observational equivalence for algebras (which are models for sequential systems) and bisimulation equivalence (bisimilarity) for concurrent processes. In this paper we show that the observational equivalences for standard, partial and regular algebras are bisimulation eq...

In this paper we consider fuzzy relations compatible with algebraic operations, which are called fuzzy relational morphisms. In particular, we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations, called uniform fuzzy relational morphisms, and those which are partially uniform F -functions, called fuzzy homomorphisms. Both uniform fuzzy relations and partially...

Interpretation of Algebraic Polynomial Systems (Extended Abstract) Patrick Cousot 1 and Radhia Cousot 2 1 LIENS, ~cole Normale Sup4neure, 45 rue d'Ulm, 75230 Paris cedex 05, France [email protected] http://www.dmi.ens.fr/-cousot 2 LIX, CNRS & Ecole Polytechnique, 91140 Palaiseau cedex, France [email protected] http://lix.polytechnique.fr/-rcousot Abstract. We define a hierarchy of co...

Rate transition systems (RTS) are a special kind of transition systems introduced for defining the stochastic behavior of processes and for associating continuous-time Markov chains with process terms. The transition relation assigns to each process, for each action, the set of possible futures paired with a measure indicating the rates at which they are reached. RTS have been shown to be a uni...

It is shown that a uniform algebra can have nonzero bounded point derivation while having no nontrivial Gleason parts. Conversely, part nonzero, even possibly unbounded, derivations.