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 descent, with a higher risk of type 2 diabetes mellitus and atherosclerotic cardiovascular disease at BMIs lower than the WHO cut-off point for overweight, 25 kg/m, although the cut-off for observed risk varies among different Asian populations. Adolphe Quetelet, a Belgian astronomer, mathematician, statistician and sociologist, devised the basis of the BMI between 1830 and 1850 as he developed what he called "social physics". The modern term "body mass index" (BMI) for the ratio of human body weight to squared height was coined in a paper published in the July 1972 edition of the "Journal of Chronic Diseases" by Ancel