Susceptibility to tuberculosis is multifactorial. The importance of host genetic factors on the susceptibility or resistance to tuberculosis has been emphasized by many workers. Host genetic factors such as human leucocyte antigens (HLA) and non-HLA genes that are associated with the susceptibility to tuberculosis will serve as genetic markers to predispose or predetermine the development of th...

We present a formalism within which the relationship (discovered by Drinfel’d in [Dr1, Dr2]) between associators (for quasi-triangular quasi-Hopf algebras) and (a variant of) the Grothendieck-Teichmuller group becomes simple and natural, leading to a great simplification of Drinfel’d’s original work. In particular, we re-prove that rational associators exist and can be constructed iteratively.

Eigenfunctions of the Laplacian on a negatively curved, rotationally symmetric manifold M = (Rn, ds2), ds2 = dr2+f(r)2dθ2, are constructed explicitly under the assumption that an integral of f(r) converges. This integral is the same one which gives the existence of nonconstant harmonic functions on M.