Results 131 to 140 of about 12,741 (164)
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Some Cantor Sets and Cantor Functions
Mathematics Magazine, 1972(1972). Some Cantor Sets and Cantor Functions. Mathematics Magazine: Vol. 45, No. 1, pp. 2-7.
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On the intersection of Cantor τ-sets
Russian Mathematical Surveys, 2002This article extends earlier topological results for intersections of Cantor \(\tau\)-sets. The central result is the following assertion: Theorem 1. Let \(F_j={\mathcal J}_j\setminus \cup^\infty_{\nu=1} \Delta^\nu_j\), \(j=1,2\), be two linked \(\tau\)-sets with the same sufficiently large \(\tau\).
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Maximal Operators and Cantor Sets
Canadian Mathematical Bulletin, 2000AbstractWe consider maximal operators in the plane, defined by Cantor sets of directions, and show such operators are not bounded on L2 if the Cantor set has positive Hausdorff dimension.
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Percolation in Random Cantor Sets
Fractals, 1997The d-dimensional random Cantor set is a generalization of the classical "middle-thirds" Cantor set. Starting with the unit cube [0, 1]d, at every stage of the construction we divide each cube remaining into Nd equal subcubes, and select each of these at random with probability p. The resulting limit set is a random fractal C.
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THE SUM OF THE CANTOR SET WITH ITSELF
1993Using ternary representation of the classical Cantor set \(C\subset[0,1]\), the author proves that \(C+C=[0,2]\) and derives a formula for the number of pairs \((x,y)\in C\times C\) for which \(x+y=k\in[0,2]\). The latter result is formulated in terms of the coefficients in the ternary expansion of \(k\).
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A Note on the History of the Cantor Set and Cantor Function
Mathematics Magazine, 1994A search through the primary and secondary literature on Cantor yields little about the history of the Cantor set and Cantor function. In this note, we would like to give some of that history, a sketch of the ideas under consideration at the time of their discovery, and a hypothesis regarding how Cantor came upon them. In particular, Cantor was not the
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Mechanical properties of Cantor alloys driven by additional elements: a review
Journal of Materials Research and Technology, 2021Ye Wang
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Optimization of micromixer with Cantor fractal baffle based on simulated annealing algorithm
Chaos, Solitons and Fractals, 2021Xueye Chen
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