Mean directionally curved lines on surfaces immersed in R4

The notion of principal configuration of immersions of surfaces into R3, due to Sotomayor and Gutierrez [16] for lines of curvature and umbilics, is extended to that of mean directional configuration for immersed surfaces in R4. This configuration consists on the families of mean directionally curved lines, along which the second fundamental form points in the direction of the mean curvature vector, and their singularities, called here H-singularities. The concepts of H-singularities and periodic mean directionally curved lines are studied here in detail. Also the notion of principal structural stability of immersions of surfaces into R3 is extended to that of mean directional structural stability, for the case of surfaces in R4. Sufficient conditions for immersions to be mean directional structurally stable are provided in terms of H-singularities, periodic mean directionally curved lines and the asymptotic behavior of all the other mean directionally curved lines

Bifurcation Analysis of the Watt Governor System

This paper pursues the study carried out by the authors in {\it Stability and Hopf bifurcation in the Watt governor system} \cite{smb}, focusing on the codimension one Hopf bifurcations in the centrifugal Watt governor differential system, as presented in Pontryagin's book {\it Ordinary Differential Equations}, \cite{pon}. Here are studied the codimension two and three Hopf bifurcations and the pertinent Lyapunov stability coefficients and bifurcation diagrams, illustrating the number, types and positions of bifurcating small amplitude periodic orbits, are determined. As a consequence it is found a region in the space of parameters where an attracting periodic orbit coexists with an attracting equilibrium.Comment: 34 pages, 9 figure

Extradural hematoma: comparative radiological study between, comatous and noncomatous patients

A series of 129 patients harbouring extradural hematomas was analysed considering the neurological state immediately before operation as the most consistent variable. Seventy eight patients were considered to be comatous (Group I) and 51 were noncomatous. Among the comatous group, 30 were investigated with computerized tomography (23.3% mortality, 50% good results), 31 were submitted to angiography (48.3% mortality, 38.7% good results), and 17 were operated based on the neurological examination and skull radiography (47% mortality, 35.2% good results). The presence or absence of skull fracture and the density of hematoma did not change the final outcome. Associated intracranial lesions increased the mortality and lowered the good results in both groups. Frontal hematomas (10 cases) in the comatous group were associated with high mortality (52.6%) due to bad neurological state (Glasgow 3-5) and to isolated or multiple intracranial associated lesions (6 patients).Considerando o estado neurológico imediatamente antes da operação como a variável miais fidedigna para antecipação do prognóstico dos hematomas extradurais, os autores realizaram estudo radiológico comparativo de 129 pacientes operados por esta patologia. Desta amostra, 78 casos se encontravam em coma (Grupo I) e 51 eram não comatosos (Grupo II). No grupo I, os 30 casos investigados pré-operatoriamente com tomografia tiveram 23,3% de mortalidade e 50% de bons resultados; dos 31 casos submetidos a angiografia, 48,3% faleceram e 38,7% tiveram bons resultados; 17 casos foram operados pela radiografia simples de crânio e exame neurológico, com 47% de mortalidade e 35,2% de bons resultados. A presença de fratura de crânio e a densidade tomográfica do hematoma não interferiram nos resultados. A presença de lesão associada intracraniana aumentou a mortalidade e diminuiu a quantidade de bons resultados tanto no Grupo I quanto no Grupo II. A localização frontal do hematoma foi associada a elevada mortalidade (52,6%) no grupo comatoso, por estarem todos os pacientes entre 3 a 5 pontos na Escala de Glasgow e seis deles por apresentarem lesões associadas intracranianas únicas ou múltiplas.Hospital Santa IsabelEscola Paulista de MedicinaUNIFESP, EPMSciEL

When parallels and meridians are limit cycles for polynomial vector fields on quadrics of revolution in the euclidean 3-space

Agraïments: The first and third authors are partially supported by CNPq grant 472321/2013-7 and by FAPEMIG grant APQ-00130-13. The third author is partially supported by CNPq grant 301758/2012-3 and by FAPEMIG grant PPM-00516-15. All authors are also supported by the joint project CAPES CSF-PVE grant 88881.030454/2013-0.We study polynomial vector fields of arbitrary degree in R^3 with an invariant quadric of revolution. We characterize all the possible configurations of invariant meridians and parallels that these vector fields can exhibit. Furthermore we analyze when these invariant meridians and parallels can be limit cycles

Kite planar central configurations

Neste artigo estudamos configurações centrais planares do tipo pipa para o problema de quatro corpos. Mostramos a existência de tais configurações para as pipas côncavas, quando uma das massas está no interior do triângulo formado pelas outras três massas, e para as pipas convexas, quando uma das massas está no exterior do triângulo formado pelas outras três massas.In this paper we study the kite planar central configurations for the 4-body problem. We show the existence of such configurations for the 4-body problem in two cases: kite concave and kite convex