1. CMB 2015 (vol 58 pp. 402)
 Tikuisis, Aaron Peter; Toms, Andrew

On the Structure of Cuntz Semigroups in (Possibly) Nonunital C*algebras
We examine the ranks of operators in semifinite $\mathrm{C}^*$algebras
as measured by their densely defined lower semicontinuous traces.
We first prove that a unital simple $\mathrm{C}^*$algebra whose
extreme tracial boundary is nonempty and finite contains positive
operators of every possible rank, independent of the property
of strict comparison. We then turn to nonunital simple algebras
and establish criteria that imply that the Cuntz semigroup is
recovered functorially from the Murrayvon Neumann semigroup
and the space of densely defined lower semicontinuous traces.
Finally, we prove that these criteria are satisfied by notnecessarilyunital
approximately subhomogeneous algebras of slow dimension growth.
Combined with results of the firstnamed author, this shows that
slow dimension growth coincides with $\mathcal Z$stability,
for approximately subhomogeneous algebras.
Keywords:nuclear C*algebras, Cuntz semigroup, dimension functions, stably projectionless C*algebras, approximately subhomogeneous C*algebras, slow dimension growth Categories:46L35, 46L05, 46L80, 47L40, 46L85 

2. CMB 2013 (vol 56 pp. 745)
 Fu, Xiaoye; Gabardo, JeanPierre

Dimension Functions of SelfAffine Scaling Sets
In this paper, the dimension function of a selfaffine generalized scaling set associated with an $n\times n$ integral expansive dilation $A$ is studied. More specifically, we consider the dimension function of an $A$dilation generalized scaling set $K$ assuming that $K$ is a selfaffine tile satisfying $BK = (K+d_1) \cup (K+d_2)$, where $B=A^t$, $A$ is an $n\times n$ integral expansive matrix with $\lvert \det A\rvert=2$, and $d_1,d_2\in\mathbb{R}^n$. We show that the dimension function of $K$ must be constant if either $n=1$ or $2$ or one of the digits is $0$, and that it is bounded by $2\lvert K\rvert$ for any $n$.
Keywords:scaling set, selfaffine tile, orthonormal multiwavelet, dimension function Category:42C40 

3. CMB 2011 (vol 56 pp. 354)
 Hare, Kathryn E.; Mendivil, Franklin; Zuberman, Leandro

The Sizes of Rearrangements of Cantor Sets
A linear Cantor set $C$ with zero Lebesgue measure is associated with
the countable collection of the bounded complementary open intervals. A
rearrangment of $C$ has the same lengths of its complementary
intervals, but with different locations. We study the Hausdorff and packing
$h$measures and dimensional properties of the set of all rearrangments of
some given $C$ for general dimension functions $h$. For each set of
complementary lengths, we construct a Cantor set rearrangement which has the
maximal Hausdorff and the minimal packing $h$premeasure, up to a constant.
We also show that if the packing measure of this Cantor set is positive,
then there is a rearrangement which has infinite packing measure.
Keywords:Hausdorff dimension, packing dimension, dimension functions, Cantor sets, cutout set Categories:28A78, 28A80 
