Local classification of singular hexagonal 3-webs with holomorphic Chern connection form and infinitesimal symmetries

Implicit ODE, cubic in derivative, generically has no infinitesimal symmetries even at regular points with distinct roots. Cartan showed that at regular points, ODEs with hexagonal 3-web of solutions have symmetry algebras of the maximal possible dimension 3. At singular points such a web can lose all its symmetries. In this paper we study hexagonal 3-webs having at least one infinitesimal symmetry at singular points. In particular, we establish sufficient conditions for the existence of non-trivial symmetries and show that under natural assumptions such a symmetry is semi-simple, i.e. is a scaling in some coordinates. Using the obtained results, we provide a complete classification of hexagonal singular 3-web germs in the complex plane, satisfying the following two conditions: 1) the Chern connection form is holomorphic at the singular point, 2) the web admits at least one infinitesimal symmetry at this point. As a by-product, a classification of hexagonal weighted homogeneous 3-webs is obtained.

Seqüelas em dentes permanentes após trauma nos predecessores decíduos e sua implicação clínica

In regarding to the high prevalence of traumatic dental injuries in primary teeth and the possible disturbances on developing permanent successor germs, an early diagnosis and an adequate establishment of treatment planning are very important to minimize the damage caused by the trauma. Sequelaes can affect the coronal portion (white or yellow-brown discoloration associated or not with enamel hipoplasia, dilacerations of the crown), the root portion (dilaceration, duplication or cessation of root formation) or the whole successor permanent tooth (odontoma sequestration or disturbances of permanent successor eruption). The aim of this study is to make a literature review of the developmental disturbances of permanent teeth followed by traumatic injuries to theirs primary predecessors and to present cases reports to advise the dentists, their patients and parents about the damage that developing permanents teeth can undergo.

Tratamiento Quirúrgico de Mesiodens en Odontopediatría

Supernumerary teeth are a relatively frequent disorder of odontogenesis that can interfere with the development of the germs teeth. This pathology is most common in the maxillary anterior area, called mesiodens, and their prevalence is generally reported to occur more frequently in male than female, in a ratio of 2:1. The aim of this article was to report the clinical procedures performed in the Clinic of Pediatric Dentistry at the Araraquara School of Dentistry when the presence of two mesiodens, radiographically shown, caused retention of permanent anterior teeth, resulting in esthetic and funcional disturb. All the surgical procedures, etiology and the importancy of the early diagnostic for the appropriate treatment was detailed described.

Tratamiento quirúrgico de mesiodents en odontopediatría

Supernumerary teeth are a relatively frequent disorder of odontogenesis that can interfere with the development of the germs teeth. This pathology is most common in the maxillary anterior area, called mesiodens, and their prevalence is generally reported to occur more frequently in male than female, in a ratio of 2:1. The aim of this article was to report the clinical procedures performed in the Clinic of Pediatric Dentistry at the Araraquara School of Dentistry when the presence of two mesiodens, radiographically shown, caused retention of permanent anterior teeth, resulting in esthetic and funcional disturb. All the surgical procedures, etiology and the importancy of the early diagnostic for the appropriate treatment was detailed described.

Controvérsias no tratamento das fraturas mandibulares em crianças: relato de caso clínico

Introduction: The treatment of mandibular fractures has undergone many changes, especially after the introduction of rigid internal fixation techniques. Currently, the use of resorbable materials presents some advantages over metallic devices, particularly when applied in children. Objective: The authors discuss the controversies involved in the treatment of mandibular fractures in children, mainly related to fixation of fractures. Case Report: In this paper, we present a case of a 5 years treatment patient with mandibular angle fracture treated by open reduction and internal fixation with plates and screws. Final Comments: Aiming to not interfere in the development of tooth germs and mandibular bone growth a second surgery for removal of the fixation devices is indicated.

Epigenetic and genetic approach to the transmissibility of dental characteristics in twins: report of two cases

Transmissibility of dental and jaw characteristics is strongly influenced by environmental factors during the years of extra uterine life when odontogenesis occurs. Through biochemical factors, such as enzymes, proteins, hormones and other mediators, genes are activated or silenced to suit the cell or organism to its environment. These changes are not transmitted to our descendants, because of that, these factors are called epigenetic. Among the most cited epigenetic factors are food, pollution, drugs and exercise. The objective of this study was to assess the transmissibility of dental characteristics in two pairs of twins. In one case, 13-year-old boys had the same basic dental and jaw characteristics with prolonged retention of the second upper deciduous molars and the presence of permanent successors. In the other case, 14-year-old boys had prolonged retention of lower deciduous second molars and absence of permanent successors, but only one of them had the germs of third lower molars. The phenotypic difference in the dentition of twins from clinical case 2 could be due to epigenetic factors, showing the absence of genetic determinism in the transmissibility of dental characteristics.

Número de Milnor associado a curvas reduzidas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Singularidades do tipo D(q,p)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)