Ernst Schuster

Uniformly resolvable designs with index one and block sizes three and four - with three or five parallel classes of block size four

Each parallel class of a uniformly resolvable design (URD) contains blocks of only one block size. A URD with v points and with block sizes three and four means that at least one parallel class has block size three and at least one has block size four. Danziger [P. Danziger, Uniform restricted resolvable designs with r=3, ARS Combin. 46 (1997) 161-176] proved that for all v=12(mod24) there exist URDs with index one, some parallel classes of block size three, and exactly three parallel classes with block size four, except when v=12 and except possibly when v=84156. We extend Danzigers work by showing that there exists a URD with index one, some parallel classes with block size three, and exactly three parallel classes with block size four if, and only if, v=0(mod12), v 12. We also prove that there exists a URD with index one, some parallel classes of block size three, and exactly five parallel classes with block size four if, and only if, v=0(mod12), v 12. New labeled URDs, which give new URDs as ingredient designs for recursive constructions, are the key in the proofs. Some ingredient URDs are also constructed with difference families.

Group divisible designs with block size four and group type gum1 where g is a multiple of 8

We determine, up to some possible exceptions, the spectrum for 4-GDDs of type g^um^1, where g is a multiple of 8 until 48, g is a multiple of 24 until 144, respectively. These spectra are without exceptions for g=8, 16, 24, 48, 72, 96, 120 and 144. Furthermore, we establish, up to a finite number of possible exceptions, the spectra for 4-GDDs of types 30^um^1 and 90^um^1. Finally, we provide nine {3, 5}-URDs which were the last possible exceptions in their classes.

Markov Chain Monte Carlo methods for handling missing covariates in longitudinal mixed models

Handling missing covariates in longitudinal mixed effect models is demonstrated on a medical example.