Abstract
We use a new R&D investment function in a Cournot competition model inspired in the logistic equation. We present the full characterization of the associated gam; and study the short and long term economical effects derived from using this new R&D investment function. We observe the existence of four different Nash investment equilibria regions and fully characterize the boundaries of these regions.

Abstract
We introduce a renormalization scheme to study the asymptotic dynamical behaviour of a family of mechanical systems with non-isochronous potentials with an elliptic equilibrium. This renormalization scheme acts on a family of orbits of these mechanical systems, all of which are contained on neighbourhoods of the elliptic equilibrium, by rescaling space and shifting time in an appropriate way. We present some new results regarding the properties of this renormalization scheme, and examine the strong connection it has with the focal decomposition for the Euler-Lagrange equation of this family of mechanical systems.

Abstract
We consider an international trade economical model where two firms of different countries compete in quantities and can use three different strategies: (i) repealed collusion, (ii) deviation from the foreigner firm followed by punishment by he home country and then followed by repeated Cournot, or (iii) repeated deviation followed by punishment. In some cases (ii) and (iii) can be interpreted as dumping, We compute the profits of both firms for each strategy and we characterize the econc,mical parameters where each strategy is adopted by the firms.

Abstract

Abstract
Twelve adolescent athletes underwent, in a crossover-design study, 3 separate 90-min training sessions in the following conditions: no fluid ingestion allowed (NF), ad libitum ingestion of water (W), and ad libitum ingestion of a commercial 8% carbohydrate-electrolyte sports beverage (CSB). After each session athletes performed a set of basketball drills (2-point, 3-point, and free-throw shootout, suicide sprints, and defensive zigzags). Body weight (before and after sessions), rating of perceived exertion (RPE), urine color, and beverage acceptability were determined in each session. Athletes also completed a survey about their knowledge and behaviors regarding hydration and fluid replacement. The percentage of weight loss was significantly higher in NF (2.46% +/- 0.87%) than in the other 2 conditions (W, 1.08% +/- 0.67%, p = .006; CSB, 0.65% +/- 0.62%, p = .001) but also higher in W than CSB (p = .012). RPE was higher in NF (16.8 +/- 1.96) than in the W (14.2 +/- 1.99, p = .004) and CSB (13.3 +/- 2.06, p = .002) trials. Athletes' fluid intake was positively correlated with proper self-reported behaviors (r = .75, p = .005) and knowledge (r = .76, p = .004) about fluid and hydration. In conclusion, fluid restriction during exercise was associated with a greater level of dehydration and increased perceived exertion but had no impact on basketball performance compared with ad libitum drinking of water or a CSB. Athletes with more knowledge about hydration and better self-reported hydration behaviors ingested more fluids during training sessions.

Abstract
Objective: To estimate the prevalence of overweight and obesity in schoolchildren from Aveiro, Portugal, according to two criteria: the International Obesity Task Force (IOTF) and the US Centers for Disease Control and Prevention (CDC) cut-offs. Design: Weight, height and waist circumference were measured. Using the BMI, gender- and age-specific prevalences of overweight and obesity were determined according to the IOTF cut-offs extrapolated from an adult BMI of 25 and 30 kg/m(2) and the CDC cut-off values of 85th and 95th BMI percentile. Setting: Aveiro, Portugal. Subjects: A random representative sample of 905 children (457 boys; 448 girls) aged 7-9 years. Results: The prevalence of excess weight (overweight and obesity) was lowest according to IOTF cut-offs compared to CDC (28.1% v. 31.2%), especially obesity (8.1% v. 14.0%). However, the CDC and IOTF criteria have a strong agreement (Cohen's k=0.755; P<0.001). There were significant differences in excess weight between boys and girls according to the CDC (26.9% v. 35.7%; P=0.003). Obese children are younger and the majority present abdominal obesity. Conclusions: The present study shows a high prevalence of excess weight in Aveiro children, similar to other Portuguese regions and among the highest in Europe, especially in the female gender. The IOTF cut-off values give a lower prevalence of excess weight, namely obesity.