A complex continued fraction can be represented by a sequence of Möbius transformations in such a way that the continued fraction converges if and only if the sequence converges at the origin. The set of divergence of the sequence of Möbius transformations is equivalent to the conical limit set from Kleinian group theory, and it is closely related to the Julia set from complex dynamics. We dete...

The current prognostic parameters, including tumor volume, biochemistry, or immunohistochemistry, are not sufficient to reflect the properties of cancer cells that distinguish them from normal cells. Our focus is to evaluate the effects of a combination of microtubule-polymerizing Taxol and -depolymerizing colchicine on IAR20 PC1 liver cells by measuring the surface fractal dimension as a descr...

This paper studies labeled sample compression for multi-label concept classes. For a specific extension of the notion of VC-dimension to multi-label classes, we prove that every maximum multilabel class of dimension d has a sample compression scheme in which every sample is compressed to a subset of size at most d. We further show that every multi-label class of dimension 1 has a sample compres...

Let A, B, be finite subsets of an abelian group, and let G ⊂ A×B be such that #A,#B,#{a + b : (a, b) ∈ G} ≤ N . We consider the question of estimating the quantity #{a − b : (a, b) ∈ G}. In [2] Bourgain improved the trivial upper bound of N to N 1 13 , and applied this to the Kakeya conjecture. We improve Bourgain’s estimate further to N 1 6 , and conclude that Besicovitch sets in Rn have Hausd...

The study aims to identify the possibilities offered by academic studies in Cuba for the training of information professionals as marketing managers. A theoretical analysis is conducted of the basic functions of marketing and its information dimension, the specific features of the work of the marketing manager, and the Revista Cubana de Información en Ciencias de la Salud 2014;25(2):234-248 htt...

In this paper we use the theory of computing to study fractal dimensions of projections in Euclidean spaces. A fundamental result in fractal geometry is Marstrands projection theorem, which shows that for every analytic set E, for almost every line L, the Hausdorff dimension of the orthogonal projection of E onto L is maximal. We use Kolmogorov complexity to give two new results on the Hausdorf...

Minkowski dimension is one of the most widely used dimensions. Its popularity is largely due to its relative ease of mathematical calculation. The definition goes back at least to the 1930’s and it has been variously termed Kolmogorov entropy, metric dimension, information dimension, ... etc. Let F be any non-empty bounded subset of R and let Nγ(F ) be the smallest number of sets of diameter at...

Lyapunov exponents represent important quantities to characterize the properties of dynamical systems. We show that the Lyapunov exponents of two di€erent dynamical systems that can be converted to each other by a transformation of variables are identical. Moreover, we derive sucient conditions on the transformation for this invariance property to hold. In particular, it turns out that the tra...

Let $(R, m)$ be a commutative noetherian local ring and let $Gamma$ be a finite group. It is proved that if $R$ admits a dualizing module, then the group ring $Rga$ has a dualizing bimodule as well. Moreover, it is shown that a finitely generated $Rga$-module $M$ has generalized Gorenstein dimension zero if and only if it has generalized Gorenstein dimension zero as an $R$-module.