Search results for "monoid"

Languages associated with saturated formations of groups

2013

International audience; In a previous paper, the authors have shown that Eilenberg's variety theorem can be extended to more general structures, called formations. In this paper, we give a general method to describe the languages corresponding to saturated formations of groups, which are widely studied in group theory. We recover in this way a number of known results about the languages corresponding to the classes of nilpotent groups, soluble groups and supersoluble groups. Our method also applies to new examples, like the class of groups having a Sylow tower.; Dans un article précédent, les auteurs avaient montré comment étendre le théorème des variétés d'Eilenberg à des structures plus g…

On Sets of Words of Rank Two

2019

Given a (finite or infinite) subset X of the free monoid A∗ over a finite alphabet A, the rank of X is the minimal cardinality of a set F such that X⊆ F∗. A submonoid M generated by k elements of A∗ is k-maximal if there does not exist another submonoid generated by at most k words containing M. We call a set X⊆ A∗ primitive if it is the basis of a |X|-maximal submonoid. This extends the notion of primitive word: indeed, w is a primitive set if and only if w is a primitive word. By definition, for any set X, there exists a primitive set Y such that X⊆ Y∗. The set Y is therefore called a primitive root of X. As a main result, we prove that if a set has rank 2, then it has a unique primitive …

External derivations of internal groupoids

2008

If His a G-crossed module, the set of derivations of Gin H is a monoid under the Whitehead product of derivations. We interpret the Whitehead product using the correspondence between crossed modules and internal groupoids in the category of groups. Working in the general context of internal groupoids in a finitely complete category, we relate derivations to holomorphisms, translations, affine transformations, and to the embedding category of a groupoid. (C) 2007 Elsevier B.V. All rights reserved.

2006

Phenology of the Braconidae (Hymenoptera, Ichneumonoidea) at Andorra has been conducted/studied using a Malaise trap after a one-year cycle during 1993. A total of 1.892 specimens, representing 23 subfamilies and 79 genera were sampled. About 93.7% of the captures were koinobiont braconids, whereas 6.3% belonged to idiobiont braconids. The annual phenology has been characterized through the correlation between the evolution of the collected braconids and the weather (meteorological conditions). The maximum of the populations were registered between the two rain periods. In fact, the family Braconidae shows an abundance peak from middle of May to end of August, due to the xerothermic conditi…

Dinotrema cavernicola sp. n. (Hymenoptera, Braconidae, Alysiinae), a new species of the genus Dinotrema Foerster from caves of Spain

2014

Dinotrema cavernicola sp. n. was collected in two caves in Spain. This is the first Dinotrema species known to occur in caves. This new species is described and compared to D. affine (Fischer, 1973) and D. collybiae Munk & Peris-Felipo, 2014, species sharing a mid-longitudinal carina on the propodeum.

Aspilota-group (Hymenoptera: Braconidae: Alysiinae) diversity in Mediterranean Natural Parks of Spain

2014

This work analyses the biodiversity of the Aspilota-group (Hymenoptera: Braconidae: Alysiinae) in three Mediterranean Natural parks: Natural Park of La Font Roja, Natural Park of Las Lagunas de la Mata-Torrevieja and Natural Park of La Tinença de Benifassà. Samples were carried out from April 2004 to December 2007. In total, 822 specimens, belonging to 52 species, were collected. Alpha, beta and gamma diversities were analysed, and the Tinença Park was proven to have higher diversity than the Font Roja and Torrevieja. Also, the structure of the Aspilota-group community was analysed.

Chemical constituents from leaves and root bark of Trichilia monadelpha (Meliaceae)

2018

Abstract Two new limonoid derivatives designated, monadelphin A (1) and monadelphin B (2) and two new sesquiterpene derivatives named trichins A (3) and B (4) were isolated together with six known compounds (5–10) from the mixture of methylene chloride/methanol (1:1) extract of leaves and root bark of Trichilia monadelpha (Meliaceae) collected in Cameroon. The structures of the new compounds were unambiguously established by detailed spectroscopic analysis including 1D and 2D NMR data in conjunction with high resolution mass spectrometry data and by comparison of these data with those of related compounds described in the literature. Compounds 1–4 were screened for their cytotoxic potential…

FULL MONOIDS AND MAXIMAL CODES

2012

In recent years codes that are not Uniquely Decipherable (UD) were studied partitioning them in classes that localize the ambiguities of the code. A natural question is how we can extend the notion of maximality to codes that are not UD. In this paper we give an answer to this question. To do this we introduce a partial order in the set of submonoids of a free monoid showing the existence, in this poset, of maximal elements that we call full monoids. Then a set of generators of a full monoid is, by definition, a maximal set. We show how this definition extends, in a natural way, the existing definition concerning UD codes and we find a characteristic property of a monoid generated by a max…

CODING PARTITIONS OF REGULAR SETS

2009

A coding partition of a set of words partitions this set into classes such that whenever a sequence, of minimal length, has two distinct factorizations, the words of these factorizations belong to the same class. The canonical coding partition is the finest coding partition that partitions the set of words in at most one unambiguous class and other classes that localize the ambiguities in the factorizations of finite sequences. We prove that the canonical coding partition of a regular set contains a finite number of regular classes and we give an algorithm for computing this partition. From this we derive a canonical decomposition of a regular monoid into a free product of finitely many re…

The Many Faces of a Translation

2000

First-order translations have recently been characterized as the maps computed by aperiodic single-valued nondeterministic finite transducers (NFTs). It is shown here that this characterization lifts to "V-translations" and "V-single-valued-NFTs", where V is an arbitrary monoid pseudovariety. More strikingly, 2-way V-machines are introduced, and the following three models are shown exactly equivalent to Eilenberg's classical notion of a bimachine when V is a group variety or when V is the variety of aperiodic monoids: V-translations, V-single-valued-NFTs and 2-way V-transducers.