| An {dollar}alpha{dollar}-resolvable uniform frame on the point set {dollar}{lcub}cal V{rcub}{dollar} is a group divisible design such that (1) the groups are all of the same size, (2) the blocks can be partitioned into classes associated with the groups, (3) the classes associated with the group G contain every point of {dollar}{lcub}cal V{rcub}{dollar}/G exactly {dollar}alpha{dollar} times.; An {dollar}alpha{dollar}-resolvable balanced incomplete block design is a BIBD whose blocks can be partitioned into classes that contain every point of the design exactly {dollar}alpha{dollar} times.; In this thesis we show that the necessary conditions for the existence of {dollar}alpha{dollar}-resolvable uniform frames with block size 3 are sufficient, with the possible exception of multiples of a very small number of frames. We are also able to make considerable progress in determining the spectrum of {dollar}alpha{dollar}-resolvable uniform frames with block size 4.; We show that the necessary conditions for the existence of {dollar}alpha{dollar}-resolvable designs are sufficient, with one exception, when the block size is 3 and are often sufficient when the block size is 4.; The spectrum of near resolvable designs, a special type of frame, is investigated for block sizes 2, 3, 4, 5, and 6.; These results are obtained, in part, through the use of difference families and P B D-closure. |
