This is easily established, since according to the theorem of Euler mentioned above, if d denotes the distance between the centers of the circumscribed and inscribed circles, then d = R2rR. It follows that R~2rR^0, and therefore R^2r. Equality holds only if the two circles are concentric, that is, if the triangle is equilateral. The problem of generalizing the above result to space was proposed...

Healthy adults are advised to perform at least 150 min of moderate-intensity physical activity weekly, but this advice is based on studies using self-reports of questionable validity. This study examined the dose-response relationship of accelerometer-measured physical activity and sedentary behaviors on all-cause mortality using segmented Cox regression to empirically determine the break-point...

This paper studies a criteria-based mechanism for nurturing and enhancing agents’ group-benefiting individual efforts whenever the agents are self-interested. The idea is that only those agents that meet the criteria get to benefit from the group effort, giving an incentive to contribute even when it is otherwise individually irrational. Specifically, the paper provides a comprehensive equilibr...

Time-dependent buckling phenomena of polysilicon micro beams have been demonstrated and reported. These beams are suspended 2 mm above the silicon substrate with dimensions of 100 mm (length) × 2 mm (width) × 2 mm (thickness). When a constant input current is supplied at or above a threshold value, electro-thermally induced buckling occurs. It is observed and recorded that the beams exhibit tim...

OBJECTIVE It was to investigate the cluster of four main risk behaviors (smoking, alcohol, physical inactivity and low consumption of fruits and vegetables) related to chronic diseases from Northeastern Brazil. METHODS Cross-sectional study with a representative sample (n = 600) of high school students from public schools in Caruaru, Pernambuco, Brazil. The cluster was evaluated by comparing ...