We calculate the fragmentation function for a heavy quark to go into quarkonia + X including relativistic and binding corrections. We use a systematic gauge invariant method which starts directly from QCD and which allows for a systematic expansion in quark relative v elocity, which is a small natural parameter for heavy quark systems. Inclusion of these O(v 2 ) corrections modies the fragmentation functions appreciably.

A systematic gauge-invariant method, which starts directly from QCD, is used to calculate the rate for an upsilon meson to decay inclusively into a prompt photon. An expansion is made in the quark relative velocity v, which is a small natural parameter for heavy quark systems. Inclusion of these O(v 2 ) corrections tends to increase the photon rate in the middle z range and to lower it for larger z, a feature supported by the data.

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The quadrupole gluon distribution, which exists only for hadrons with spin 2 1 , is investigated for a typical light nucleus using the convolution model and a OCD inspired parton recombination model. The effects of an exotic quadrupole gluon component upon asymmetries in prompt photon production and Jlv lepton production are estimated.