A second-order shape optimization algorithm for solving the exterior Bernoulli free boundary problem using a new boundary cost functional

The exterior Bernoulli problem is rephrased into a shape optimization problem using a new type of objective function called the Dirichlet-data-gap cost function which measures the L^2-distance between the Dirichlet data of two state functions. The first-order shape derivative of the cost function is explicitly determined via the chain rule approach. Using the same technique, the second-order shape derivative of the cost function at the solution of the free boundary problem is also computed. The gradient and Hessian informations are then used to formulate an efficient second-order gradient-based descent algorithm to numerically solve the minimization problem. The feasibility of the proposed method is illustrated through various numerical examples.ファイル公開：2021/09/01journal articl

Factors associated with good self-rated health of non-disabled elderly living alone in Japan: a cross-sectional study

<p>Abstract</p> <p>Background</p> <p>Self-rated health (SRH) is reported as a reliable predictor of disability and mortality in the aged population and has been studied worldwide to enhance the quality of life of the elderly. Nowadays, the elderly living alone, a particular population at great risk of suffering physical and mental health problems, is increasing rapidly in Japan and could potentially make up the majority of the aged population. However, few data are available pertaining to SRH of this population. Given the fact that sufficient healthcare is provided to the disabled elderly whereas there is little support for non-disabled elderly, we designed this population-based survey to investigate SRH of non-disabled elderly living alone and to identify the factors associated with good SRH with the purpose of aiding health promotion for the elderly.</p> <p>Methods</p> <p>A cross-sectional study was conducted in a metropolitan suburb in Japan. Questionnaires pertaining to SRH and physical conditions, lifestyle factors, psychological status, and social activities, were distributed in October 2005 to individuals aged ≥ 65 years and living alone. Response rate was 75.1%. Among these respondents, a total of 600 male and 2587 female respondents were identified as non-disabled elderly living alone and became our subjects. Multivariate logistic regression was used to identify the factors associated with good SRH and sex-specific effect was tested by stepwise logistic regression.</p> <p>Results</p> <p>Good SRH was reported by 69.8% of men and 73.8% of women. Multivariate logistic regression analysis showed that good SRH correlated with, in odds ratio sequence, "can go out alone to distant places", no depression, no weight loss, absence of self-rated chronic disease, good chewing ability, and good visual ability in men; whereas with "can go out alone to distant places", absence of self-rated chronic disease, no weight loss, no depression, no risk of falling, independent IADL, good chewing ability, good visual ability, and social integration (attend) in women.</p> <p>Conclusion</p> <p>For the non-disabled elderly living alone, sex-appropriate support should be considered by health promotion systems from the view point of SRH. Overall, the ability to go out alone to distant places is crucial to SRH of both men and women.</p