in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

The literature describes the presence of intra-articular structures in the zygapophyseal (facet) joint (Bogduk & Engel 1984, Bogduk 1997). The largest of these structures is attached via synovium to the inner surface of the superior and inferior capsules. They project up to 5mm into the joint space. The apex of these structures is wedge-shaped and consists of densely packed collagen. Their func...

We realise the first and second Grushin distributions as symmetry reductions of the 3-dimensional Heisenberg distribution and 4-dimensional Engel distribution respectively. Similarly, we realise the Martinet distribution as an alternative symmetry reduction of the Engel distribution. These reductions allow us to derive the integrability conditions for the Grushin and Martinet distributions and ...

1 Pediatric Institute (IPPMG), Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro, RJ, Brazil. Send correspondence and reprint requests to: Patricia de Carvalho Padilha, Rua Gramado 475, Bloco C, Apto. 202, Campo Grande, CEP 23050-090, Rio de Janeiro, RJ, Brasil; e-mail: [email protected] 2 Maternal and Child Health Research Group (GPSMI), Center for Micronutrient Research (NPq...

Mailing Address: Márcia Maria Carneiro Oliveira • Programa de Pós-Graduação em Medicina e Saúde da Universidade Federal da Bahia. Rua Acajutiba, Quadra 8, Lote 13 B, Pernambués. Postal Code 41120-700, Salvador, BA – Brazil E-mail: [email protected] Manuscript received June 21, 2015; revised manuscript June 26, 2015; accepted July 06, 2015.