High temperature limit in static backgrounds

We prove that the hard thermal loop contribution to static thermal amplitudes can be obtained by setting all the external four-momenta to zero before performing the Matsubara sums and loop integrals. At the one-loop order we do an iterative procedure for all the one-particle irreducible one-loop diagrams, and at the two-loop order we consider the self-energy. Our approach is sufficiently general to the extent that it includes theories with any kind of interaction vertices, such as gravity in the weak field approximation, for d space-time dimensions. This result is valid whenever the external fields are all bosonic.

Prevalence of long face pattern in brazilian individuals of different ethnic backgrounds

Conclusions: Black individuals had greater prevalence of long face pattern, followed by Brown, White and Yellow individuals. The prevalence of long face pattern was 14.06% in which 13.39% and 0.68% belonged to moderate and severe subtypes, respectively.