Abstract
We consider a continuous lifetime model for investor whose lifetime is a random variable. We assume the investor has an access to the social welfare system, the financial market and the life insurance market. The investor aims to find the optimal strategies that maximize the expected utility obtained from consumption, investing in the financial market, buying life insurance, registering in the social welfare system, the size of his estate in the event of premature death and the size of his fortune at time of retirement if he lives that long. We use dynamic programming techniques to derive a second-order nonlinear partial differential equation whose solution is the maximum objective function. We use special case of discounted constant relative risk aversion utilities to find an explicit solutions for the optimal strategies. Finally, we have shown a numerical solution for the problem under consideration and study some properties for the optimal strategies.

Abstract
We show that in finite settings with identical firms and consumers, asymmetric pure price equilibria with positive profits exist. We consider a price competition duopoly for a homogeneous product. Demand stems from a second-stage consumption game at posted prices, with consumers' behavior impacted by negative network effects. We characterize equilibrium prices and demand. In all subgame-perfect pure price equilibria, both firms have positive profits, and in some, firms charge different prices.

Abstract

Abstract
An important problem in directional statistics is to test the null hypothesis of a common mean direction for several populations. The Analysis of Variance (ANOVA) test for vectorial data may be used to test the hypothesis of the equality of the mean directions for several von Mises-Fisher populations. As this test is valid only for large concentrations, we propose in this paper to apply the resampling techniques of bootstrap and permutation to the ANOVA test. We carried out an extensive simulation study in order to evaluate the performance of the ANOVA test with the resampling techniques, for several sphere dimensions and different sample sizes and we compare with the usual ANOVA test for data from von Mises-Fisher populations. The purpose of this simulation study is also to investigate whether the proposed tests are preferable to the ANOVA test, for low concentrations and small samples. Finally, we present an example with spherical data.

Abstract

We implemented Discord as a pedagogical tool in the academic year of 2021/2022 in two mathematics curricular units of the first year of an Informatics Engineering university program. We analyze and discuss the experience, reflecting on usability and influence on learning processes and engagement. We compare the impact of using the platform: 1) when combined with different methodological and pedagogical approaches and 2) to previous years with other (or none) classic virtual forums.

Abstract
Malnutrition is widespread among older adults, and its determinants may differ between countries. We compared Portuguese and Turkish non-institutionalized older adults regarding nutritional status, sociodemographic, health and anthropometric characteristics and studied the relationships between nutritional status and those characteristics. This cross-sectional study analyzed data from 430 Portuguese and 162 Turkish non-institutionalized older adults regarding sociodemographics, health conditions, the Mini-Nutritional Assessment (MNA-FF) and anthropometry. Turkish older adults were more likely to be malnourished or at risk of malnutrition and had lower average BMI but a higher calf circumference. A higher proportion of the Portuguese sample had tooth loss, diabetes, hypertension, oncologic diseases, kidney diseases, osteoarticular problems or eye problems, while less had anemia. A better nutritional status (higher MNA-FF score) was found among the Portuguese, males, people using dentures, those without tooth loss, hypertension, cardiovascular diseases, anemia or oncological diseases and was related to younger age, higher BMI and a higher calf circumference. Malnutrition and its risk were higher among older adults from Turkey, despite Portuguese older adults presenting a higher prevalence of chronic diseases. Being female, older age, tooth loss, hypertension, anemia, CVD or oncological disorders and having a lower BMI or CC were associated with higher rates of malnutrition among older adults from Portugal and Turkey.