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1. CMB 2011 (vol 56 pp. 292)

Dai, Mei-Feng
 Quasisymmetrically Minimal Moran Sets M. Hu and S. Wen considered quasisymmetrically minimal uniform Cantor sets of Hausdorff dimension $1$, where at the $k$-th set one removes from each interval $I$ a certain number $n_{k}$ of open subintervals of length $c_{k}|I|$, leaving $(n_{k}+1)$ closed subintervals of equal length. Quasisymmetrically Moran sets of Hausdorff dimension $1$ considered in the paper are more general than uniform Cantor sets in that neither the open subintervals nor the closed subintervals are required to be of equal length. Keywords:quasisymmetric, Moran set, Hausdorff dimensionCategories:28A80, 54C30

2. 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, cut-out setCategories:28A78, 28A80

3. CMB 2009 (vol 52 pp. 105)

Okoudjou, Kasso A.; Rogers, Luke G.; Strichartz, Robert S.
 Generalized Eigenfunctions and a Borel Theorem on the Sierpinski Gasket We prove there exist exponentially decaying generalized eigenfunctions on a blow-up of the Sierpinski gasket with boundary. These are used to show a Borel-type theorem, specifically that for a prescribed jet at the boundary point there is a smooth function having that jet. Categories:28A80, 31C45

4. CMB 2004 (vol 47 pp. 168)

Baake, Michael; Sing, Bernd
 Kolakoski-$(3,1)$ Is a (Deformed) Model Set Unlike the (classical) Kolakoski sequence on the alphabet $\{1,2\}$, its analogue on $\{1,3\}$ can be related to a primitive substitution rule. Using this connection, we prove that the corresponding bi-infinite fixed point is a regular generic model set and thus has a pure point diffraction spectrum. The Kolakoski-$(3,1)$ sequence is then obtained as a deformation, without losing the pure point diffraction property. Categories:52C23, 37B10, 28A80, 43A25

5. CMB 2001 (vol 44 pp. 61)

Kats, B. A.
 The Inequalities for Polynomials and Integration over Fractal Arcs The paper is dealing with determination of the integral $\int_{\gamma} f \,dz$ along the fractal arc $\gamma$ on the complex plane by terms of polynomial approximations of the function~$f$. We obtain inequalities for polynomials and conditions of integrability for functions from the H\"older, Besov and Slobodetskii spaces. Categories:26B15, 28A80
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