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.

Abstract
Eating behavior adopted during adolescence may persist into adulthood. The aims of this study were to identify eating behavior patterns among Portuguese adolescents and to explore whether groups differ in terms of early life and family characteristics, severity of depressive symptoms, and body mass index (BMI) z-score. Participants were 3601 13-year-olds enrolled in the birth cohort Generation XXI. Eating behavior was assessed using the self-reported Adult Eating Behavior Questionnaire (AEBQ), validated in this sample. The severity of depressive symptoms was measured through the Beck Depression Inventory (BDI-II), and data on sociodemographic and anthropometrics were collected at birth and 13-years-old. Latent class analysis was conducted, and associations were estimated using multinomial logistic regression models. Five patterns of individuals were identified: Picky eating, Disinterest towards food, Food neophilia, Emotional eating, and Food attractiveness. The adolescents' sex, maternal education, BMI z-score, and severity of depressive symptoms were significantly associated with the identified patterns. In particular, adolescents with a higher BMI z-score were more likely in Food neophilia while individuals with more severe depressive symptoms were in the Picky eating, Emotional eating, and Food attractiveness patterns. These findings suggest a starting point for the development and planning of targeted public health interventions.