Unified min-max and interlacing theorems for linear operators

There exist striking analogies in the behaviour of eigenvalues of Hermitian compact operators, singular values of compact operators and invariant factors of homomorphisms of modules over principal ideal domains, namely diagonalization theorems, interlacing inequalities and Courant-Fischer type formulae. Carlson and Sa [D. Carlson and E.M. Sa, Generalized minimax and interlacing inequalities, Linear Multilinear Algebra 15 (1984) pp. 77-103.] introduced an abstract structure, the s-space, where they proved unified versions of these theorems in the finite-dimensional case. We show that this unification can be done using modular lattices with Goldie dimension, which have a natural structure of s-space in the finite-dimensional case, and extend the unification to the countable-dimensional case.

An experimental study to compare the interface pressure and experience of healthy participants when lying still for 20 minutes in a supine position on two different imaging surfaces

Introduction: Pressure ulcers are a high cost, high volume issue for health and medical care providers, affecting patients’ recovery and psychological wellbeing. The current research of support surfaces on pressure as a risk factor in the development of pressure ulcers is not relevant to the specialised, controlled environment of the radiological setting. Method: 38 healthy participants aged 19-51 were placed supine on two different imaging surfaces. The XSENSOR pressure mapping system was used to measure the interface pressure. Data was acquired over a time of 20 minutes preceded by 6 minutes settling time to reduce measurement error. Qualitative information regarding participants’ opinion on pain and comfort was recorded using a questionnaire. Data analysis was performed using SPSS 22. Results: Data was collected from 30 participants aged 19 to 51 (mean 25.77, SD 7.72), BMI from 18.7 to 33.6 (mean 24.12, SD 3.29), for two surfaces, following eight participant exclusions due to technical faults. Total average pressure, average pressure for jeopardy areas (head, sacrum & heels) and peak pressure for jeopardy areas were calculated as interface pressure in mmHg. Qualitative data showed that a significant difference in experiences of comfort and pain was found in the jeopardy areas (P<0.05) between the two surfaces. Conclusion: A significant difference is seen in average pressure between the two surfaces. Pain and comfort data also show a significant difference between the surfaces, both findings support the proposal for further investigation into the effects of radiological surfaces as a risk factor for the formation of pressure ulcers.

Projeto de desenvolvimento de App de apoio ao cliente para operador de telecomunicações

Trabalho de projeto apresentado à Escola Superior de Comunicação Social como parte dos requisitos para obtenção de grau de mestre em Publicidade e Marketing.