Results 201 to 210 of about 69,620 (237)

Brownian Motion on Cantor Sets

International Journal of Nonlinear Sciences and Numerical Simulation, 2020
AbstractIn this paper, we have investigated the Langevin and Brownian equations on fractal time sets usingFα-calculus and shown that the mean square displacement is not varied linearly with time. We have also generalized the classical method of deriving the Fokker–Planck equation in order to obtain the Fokker–Planck equation on fractal time sets.
Ali Khalili Golmankhaneh, Saleh Ashrafi, Dumitru Baleanu, Arran Fernandez   +3 more
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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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Cantor Set Fractals from Solitons

Nonlinear Guided Waves and Their Applications, 1999
We show how a nonlinear system that supports solitons can be driven to generate exact (regular) Cantor set fractals. As an example, we use numerical simulations to demonstrate the formation of Cantor set fractals by temporal optical solitons. This fractal formation occurs in a cascade of nonlinear optical fibers through the dynamical evolution from a ...
, Sears, , Soljacic, , Segev, , Krylov, , Bergman   +4 more
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Percolation in Random Cantor Sets

Fractals, 1997
The 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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Maximal Operators and Cantor Sets

Canadian Mathematical Bulletin, 2000
AbstractWe 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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Cantor Sets And Dejean's Conjecture

1996
Let $k\in\mathbb{R}$ be given, $1 \lt k \lt 2$. It is shown that for a large enough alphabet $\Sigma$, the set of $\omega$-words over $\Sigma$ avoiding powers greater than $k$ is a Cantor set. In particular, a new method for showing the existence of $\omega$-words over $\Sigma$ avoiding powers greater than $k$ is given. This presents a new way in which
Currie, James D., Shelton, Robert O.
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Hausdorff Measure of Homogeneous Cantor Set

Acta Mathematica Sinica, English Series, 2001
In this short note, the authors give an exact expression of the Hausdorff measure of a class of homogeneous Cantor sets refining the results of \textit{D. J. Feng}, \textit{H. Rao} and \textit{J. Wu} [Progr. Nat. Sci. 6, 673-678 (1996) (per bibl.)] and \textit{D. J. Feng}, \textit{Z. Y. Wen} and \textit{J. Wu} [Sci. China, Ser. A 40, No.
Qu, Cheng Qin, Rao, Hui, Su, Wei Yi
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Void distribution of random Cantor sets

Physical Review A, 1989
A simple method to compute void distributions of random Cantor sets is developed. In particular, a detailed calculation is presented for the void distribution of the random Cantor set used in a recent theory of fractal growth. The exact results allow us to clarify and rediscuss some of the implicit assumptions made previously in this theory.
TREMBLAY, RR, SIEBESMA, AP
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A CANTOR LIMIT SET

Russian Mathematical Surveys, 1980
Barkovskij, Yu. S., Levin, G. M.
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Cantor set and interpolation

Moscow University Mathematics Bulletin, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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