On Self-Similar Sets with Overlaps and Inverse Theorems for Entropy in $\mathbb {R}^d$ Susanna C. Calkins to meet pressing twenty-first-century concerns

to meet pressing twenty-first-century concerns

drawing on cutting-edge research about the stages of learning

see through deception

published in collections from Brunizem in 1988 to Pure Lizard in 2008

university faculty members remain largely unaware of the findings of SoTL research

On Self-Similar Sets with Overlaps and Inverse Theorems for Entropy in $\mathbb {R}^d$ Susanna C. Calkins to meet pressing twenty-first-century concernsThe author studies self similar sets and measures on $\mathbb{R}^{d}$. Assuming that the defining iterated function system $\Phi$ does not preserve a proper affine subspace, he shows that one of the following holds: (1) the dimension is equal to the trivial bound (the minimum of $d$ and the similarity dimension $s$); (2) for all large $n$ there are $n$ fold compositions of maps from $\Phi$ which are super exponentially close in $n$; (3) there is a non