Search results for "semigroups"
showing 10 items of 19 documents
A reduction theorem for the generalised Rhodes' Type II Conjecture
2018
One of the milestones in the theory of semigroups and automata is the Krohn-Rhodes Theorem. It states that every finite semigroup S divides a wreath product of finite simple groups, each of them divisor of S, and finite aperiodic semigroups, i. e. semigroups with trivial maximal subgroups. The smallest number of groups in any Kohn-Rhodes decomposition is called the group complexity of the semigroup. Since there is no obvious way to compute the complexity of a finite semigroup in general, the decidability of this number is one of the most important open problems in finite semigroup theory and the search for the solution has led to the development of many tools and ideas that are useful in fi…
The ideal duplication
2021
AbstractIn this paper we present and study the ideal duplication, a new construction within the class of the relative ideals of a numerical semigroup S, that, under specific assumptions, produces a relative ideal of the numerical duplication $$S\bowtie ^b E$$ S ⋈ b E . We prove that every relative ideal of the numerical duplication can be uniquely written as the ideal duplication of two relative ideals of S; this allows us to better understand how the basic operations of the class of the relative ideals of $$S\bowtie ^b E$$ S ⋈ b E work. In particular, we characterize the ideals E such that $$S\bowtie ^b E$$ S ⋈ b E is nearly Gorenstein.
Hybrid bases for varieties of semigroups
2003
We consider the lower part of the lattice of varieties of semigroups. We present finite bases of hybrid identities for the varieties of normal bands, commutative bands and abelian groups of finite exponent. The variety A n,0 of abelian groups provides an example of a variety which has no finite base of hyperidentities (cf. [12]) but has a finite base of hybrid identities.
Incomparable Banach spaces and operator semigroups
2002
Using the notions of total incomparability and total coincomparability of Banach spaces, we define two families of operator semigroups. We show that these semigroups are minimal, in the sense that they admit a perturbative characterization. Moreover, they allow us to characterize the corresponding incomparability classes.
Stability of solution for Rao-Nakra sandwich beam model with Kelvin-Voigt damping and time delay
2022
This paper deals with stability of solution for a one-dimensional model of Rao?Nakra sandwich beam with Kelvin?Voigt damping and time delay given by ??1?1?????? ? ??1?1?????? ? ??(??? + ?? + ??????) ? ?????????? ? ??????????( ? , ?? ? ??) = 0, ??3?3?????? ? ??3?3?????? + ??(??? + ?? + ??????) ? ?????????? = 0, ????????? + ?????????????? ? ????(??? + ?? + ??????)?? ? ?????????? = 0. A sandwich beam is an engineering model that consists of three layers: two stiff outer layers, bottom and top faces, and a more compliant inner layer called ?core layer?. Rao?Nakra system consists of three layers and the assumption is that there is no slip at the interface between contacts. The top and bottom lay…
Representation of Autonomous Automata
2001
An autonomous automaton is a finite automaton with output in which the input alphabet has cardinality one when special reduced. We define the transition from automata to semigroups via a representation successful if given two incomparable automata (neither simulate the other), the semigroups representing the automata are distinct. We show that representation by the transition semigroup is not successful. We then consider a representation of automata by semigroups of partial transformations. We show that in general transition from automata to semigroups by this representation is not successful either. In fact, the only successful transition presented is the transiton to this semigroup of par…
Geometrical characterization of non-Markovianity
2013
We introduce a new tool for the quantitative characterisation of the departure form Markovianity of a given dynamical process. Our tool can be applied to a generic $N$-level system and extended straightforwardly to Gaussian continuous-variable systems. It is linked to the change of the volume of physical states that are dynamically accessible to a system and provides qualitative expectations in agreement with some of the analogous tools proposed so far. We illustrate its prediticve power by tackling a few canonical examples.
Formations of finite monoids and formal languages: Eilenberg’s variety theorem revisited
2014
International audience; We present an extension of Eilenberg's variety theorem, a well-known result connecting algebra to formal languages. We prove that there is a bijective correspondence between formations of finite monoids and certain classes of languages, the formations of languages. Our result permits to treat classes of finite monoids which are not necessarily closed under taking submonoids, contrary to the original theory. We also prove a similar result for ordered monoids.; Nous présentons une extension du théorème des variétés d'Eilenberg, un résultat célèbre reliant l'algèbre à la théorie des langages formels. Nous montrons qu'il existe une correspondance bijective entre les form…
Formations of Monoids, Congruences, and Formal Languages
2015
The main goal in this paper is to use a dual equivalence in automata theory started in [25] and developed in [3] to prove a general version of the Eilenberg-type theorem presented in [4]. Our principal results confirm the existence of a bijective correspondence between three concepts; formations of monoids, formations of languages and formations of congruences. The result does not require finiteness on monoids, nor regularity on languages nor finite index conditions on congruences. We relate our work to other results in the field and we include applications to non-r-disjunctive languages, Reiterman s equational description of pseudovarieties and varieties of monoids.
A C0-Semigroup of Ulam Unstable Operators
2020
The Ulam stability of the composition of two Ulam stable operators has been investigated by several authors. Composition of operators is a key concept when speaking about C0-semigroups. Examples of C0-semigroups formed with Ulam stable operators are known. In this paper, we construct a C0-semigroup (Rt)t&ge