Representation theory of the Galilean group to , and applying Hamilton's equations, we obtain the mass-velocity relation . The hypersurface is parametrized by this velocity In . Consider the stabilizer of a point on the orbit, (), where the velocity is . Because of transitivity, we know the unitary irrep contains a nontrivial linear subspace with these energy-momentum eigenvalues. (This subspace only exists in a rigged Hilbert space, because the momentum spectrum is continuous.) The subspace is spanned by , , and . We already know how the subspace of the irrep transforms under all operators but the angular momentum. Note that the rotation subgroup is
Body mass index what category an individual falls into for a given height. The BMI also fails to take into account loss of height through aging. In this situation, BMI will increase without any corresponding increase in weight. Assumptions about the distribution between muscle mass and fat mass are inexact. BMI generally overestimates adiposity on those with more lean body mass (e.g., athletes) and underestimates excess adiposity on those with less lean body mass. A study in June 2008 by Romero-Corral et al. examined 13,601 subjects from the United States' third National Health and Nutrition Examination Survey (NHANES III) and found that BMI-defined