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For $i, j > 0, i + j = 1$, the set of badly approximable vectors with weight $(i, j)$ is defined by $Bad(i, j) = \{(x, y) \in \R^2 : \exists c > 0 \forall q\in\N, \;\; \max\{q||qx||^{1/i}, q||qy||^{1/...
Abstract: We prove that only for powers of 2 and 3 could occur counterexamples to the local-global divisibility principle for elliptic curves defined over the rationals. For we refine our previous cri...
Let K be a subfield of the real field, D  K be a closed and discrete set and f : Dn ! K be such that f(Dn) is somewhere dense. Then (K, f) defines Z. We present several applications of this result. W...
Aichholzer et al. [{\it Graphs and Combinatorics}, Vol. 23, 481-507, 2007] introduced the notion of pseudo-convex partitioning of planar point sets and proved that the pseudo-convex partition number ...

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