Congruences on direct products of transformation and matrix monoids

Malcev described the congruences of the monoid Tn of all full transformations on a finite set Xn={1,…,n}. Since then, congruences have been characterized in various other monoids of (partial) transformations on Xn, such as the symmetric inverse monoid Inn of all injective partial transformations, or the monoid PTn of all partial transformations. The first aim of this paper is to describe the congruences of the direct products Qm×Pn, where Q and P belong to {T,PT,In}. Malcev also provided a similar description of the congruences on the multiplicative monoid Fn of all n×n matrices with entries in a field F, our second aim is provide a description of the principal congruences of Fm×Fn. The paper finishes with some comments on the congruences of products of more than two transformation semigroups, and a fairly large number of open problems

Congruences on monoids of order-preserving or order-reversing transformations on a finite chain

Glasgow Mathematical Journal, nº 47 (2005), pg. 413-424This paper is mainly dedicated to describing the congruences on certain monoids of transformations on a finite chain Xn with n elements. Namely, we consider the monoids ODn and PODn of all full, respectively partial, transformations on Xn that preserve or reverse the order, as well as the submonoid POn of PODn of all its order-preserving elements. The inverse monoid PODIn of all injective elements of PODn is also considered. We show that in POn any congruence is a Rees congruence, but this may not happen in the monoids ODn, PODIn and PODn. However in all these cases the congruences form a chain.This work was developed within the activities of Centro de ´Algebra da Universidade de Lisboa, supported by FCT and FEDER, within project POCTI ”Fundamental and Applied Algebra

Congruences on monoids of transformations preserving the orientation on a finite chain

Journal of Algebra, 321 (2009), p. 743–757Congruences on monoids of transformations preserving the orientation on a finite chai

The cardinal and the idempotent number of various monoids of transformations on a finite chain

Bulletin of the Malaysian Mathematical Sciences Society, 2, 34 (1),(2011), p. 79–85We consider various classes of monoids of transformations on a finite chain, in particular transformations that preserve or reverse either the order or the orientation. Being finite monoids we are naturally interested in computing both their cardinals and the number of their idempotents. In this note we present a short survey on these questions which have been approached by various authors and close the problem by computing the number of idempotents of those monoids not considered before. Fibonacci and Lucas numbers play an essential role in the last computations

Takahasi semigroups

Takahasi's Theorem on chains of subgroups of bounded rank in a free group is generalized to several classes of semigroups. As an application, it is proved that the subsemigroups of periodic points are finitely generated and periodic orbits are bounded for arbitrary endomorphisms for various semigroups. Some of these results feature classes such as completely simple semigroups, Clifford semigroups or monoids defined by balanced one-relator presentations

Incentivando o vínculo mãe-filho em situação de prematuridade: as intervenções de enfermagem no Hospital das Clínicas de Ribeirão Preto

This study aims at describing nursing actions performed in the high-risk neonatal units at a university hospital of the University of São Paulo at Ribeirão Preto so as to favor mother-child attachment in prematurity situations. The nurse accompanies parents in their first visit, giving them support as well as information concerning the equipment surrounding the newborn and encouraging skin-to-skin contact, touching and talking. Parents' access to and staying with high-risk newborns is permanently allowed. A visiting program by grandparents and siblings of pre-term newborns was implemented, even when under intensive care, which encourages family contact. Parents participate in a support group with other parents who experienced the situation of having their pre-term children in serious conditions and hospitalized. We consider that our experience has favored the establishment of mother-child and family attachment, observing greater interaction between the family and the newborn, particular involving the mother. Greater interest in learning about care as well as satisfaction concerning the assistance received have also been expressed by families.El objetivo de este estudio es describir las acciones de enfermería realizadas en las unidades neonatales de riesgo de un hospital-escuela de la ciudad de Ribeirão Preto - USP, en el sentido de favorecer el vinculo y apego madre-hijo en situación de prematuridad. La enfermera acompaña los padres en la primera visita, procurando apoyarlos e informar sobre los equipos que cercan al recién-nacido, incentivando el contacto piel a piel, el toque y habla. El acceso y permanencia de los padres junto a los bebes de riesgo son permitidos. Implantamos un programa de visitas de los abuelos y hermanos del prematuro, aunque estén en cuidado intensivo, con el objetivo de incentivar el contacto familiar. Los padres participan en un grupo de apoyo, conjuntamente con otros padres que pasan por la experiencia de tener sus hijos prematuros en estado grave y hospitalizados. Consideramos que nuestra experiencia favoreció el establecimiento del vinculo y apego madre-hijo y familia, resultando en una mayor interacción de la familia con el bebe, en especial, de la madre, y mayor interés en el aprendizaje de sus cuidados, además de la satisfacción manifestada por la atención recibida.O objetivo deste estudo é descrever as ações da enfermagem realizadas nas unidades neonatais de risco de um hospital-escola de Ribeirão Preto-USP, no sentido de favorecer o vínculo e apego mãe-filho em situação de prematuridade. A enfermeira acompanha os pais na primeira visita, procurando apoiá-los e informando-os sobre os equipamentos que cercam o recém-nascido, incentivando o contato pele-a-pele, o toque e a fala. O acesso e permanência dos pais junto aos bebês de risco são liberados.Foi implantado programa de visitas dos avós e irmãos do prematuro aos bebês, mesmo quando em cuidado intensivo, incentivando o contato familiar. Os pais participam de um grupo de apoio, juntamente com outros pais que passam pela experiência de terem seus filhos prematuros em estado grave e hospitalizados. Consideramos que a nossa experiência tem favorecido o estabelecimento do vínculo e apego mãe-filho e família, observando-se maior interação da família com o bebê, em especial da mãe, e maior interesse no aprendizado de seus cuidados, além da satisfação manifestada pela assistência recebida