منابع مشابه
Karpińska’s Paradox in Dimension Three
For 0 < λ < 1/e the Julia set of λez is an uncountable union of pairwise disjoint simple curves tending to infinity [Devaney and Krych 1984], the Hausdorff dimension of this set is two [McMullen 1987], but the set of curves without endpoints has Hausdorff dimension one [Karpińska 1999]. We show that these results have three-dimensional analogues when the exponential function is replaced by a qu...
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Non-crossing knight‟s tour in 3-dimension is a new field of research. The author has shown its possibility in small cuboids and in cubes up to 8x8x8 size. It can also be extended to larger size cubes and cuboids. The author has achieved jumps of length 15, 46, 88, 159, 258 and 395 in cubes of size 3x3x3, 4x4x4, 5x5x5, 6x6x6, 7x7x7 and 8x8x8 respectively. This amounts to covering 59%, 73%, 71%, ...
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ژورنال
عنوان ژورنال: Duke Mathematical Journal
سال: 2010
ISSN: 0012-7094
DOI: 10.1215/00127094-2010-047