Field et al (1991 J. Nonlinear Sci. 1 201-23) consider the steady-state bifurcations of reaction-diffusion equations defined on the hemisphere with Neumann boundary conditions on the equator. We consider Hopf bifurcations for these equations. We show the effect of the hidden symmetries on spherical domains for the type of Hopf bifurcations that can occur. We obtain periodic solutions for the hemisphere problem by extending the problem to the sphere and then finding periodic solutions with spherical spatial symmetries containing the reflection across the equator. The equations on the hemisphere have O(2)-symmetry and the equations on the sphere have spherical symmetry. We find orbits of periodic solutions for the sphere problem containing multiple periodic solutions that restrict to periodic solutions of the Neumann boundary value problem on the hemisphere lying on different O(2)-orbits.

The population characterized is an elderly one, mainly female and with HFpEF. Nearly a third of patients died and/or were rehospitalized in the year following discharge.

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This paper is an extension of work originally presented at the 2 nd International Conference of the Portuguese Society for Engineering Education and aims to describe an interdisciplinarity teaching experiment involving three subjects of the scientific area ofMathematics and a fourth one in the area of Management. Using only one project, the students developed skills, in an integrated way, in the fields of the subjects involved. The structure of the project is described in detail. It is shown how the knowledge obtained in the different subjects is needed and how it connects together to answer the proposed challenges. We report the progress of the students' work, the main difficulties and the skills developed during this process. We conclude with a reflection on the main problems and gains that may arise in similar projects.

Objective: This study aims to characterize patients hospitalized for acute heart failure (HF) in an internal medicine department and their one-year mortality and rate of rehospitalization for decompensated HF. Methods: This retrospective observational study enrolled all patients discharged in 2012 after hospitalization for acute HF. Discharge summaries, clinical records and telephone interviews were analysed. The data reports to the year before implementation of a heart failure clinic. Results: Four hundred and twenty-nine patients were enrolled, with a mean age of 79 years, 62.5% female. The most prevalent comorbidity and etiology was hypertension (86.7%) and the most frequent decompensation trigger was infection. HF with preserved ejection fraction (HFpEF) was present in 70.5%. In-hospital mortality was 7.9%. At discharge more than half of the patients were prescribed beta-blockers (52.8%) and angiotensin-converting enzyme inhibitors (52% FEp, p<0,001, respetivamente). No primeiro ano, a taxa de mortalidade foi 34,3% e de rehospitalização por IC 30,5%. Conclusões: A população estudada é idosa, predominantemente feminina e apresenta IC com FEp. Um terço morreu e/ou foi reinternada no ano seguinte. PALAVRAS-CHAVE

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In this work, we describe an interdisciplinary teaching experiment involving three subjects of the scientific area of Mathematics and a fourth one in the area of Management. Using only one project, the students developed skills, in an integrated way, in the fields of the subjects involved. The structure of the project is described in detail. It is shown how the knowledge obtained in the different subjects is needed and how it connects together to answer the proposed challenges. We report the progress of the students' work, the main difficulties and the skills developed during this process. We conclude with a reflection on the main problems and gains that may arise in projects of this kind.