Results 31 to 40 of about 6,429 (238)
On the Cantor set and the Cantor-Lebesgue functions
, 2021 The ternary Cantor set $\mathcal{C}$, constructed by George Cantor in 1883, is the best known example of a perfect nowhere-dense set in the real line. The present article we study the basic properties $\mathcal{C}$ and also study in detail the ternary expansion characterization $\mathcal{C}$.
Liu, Lihang, Urbina, Wilfredo O.
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Solving Fokker-Planck Equations on Cantor Sets Using Local Fractional Decomposition Method
Abstract and Applied Analysis, 2014 The local fractional decomposition method is applied to approximate the solutions for Fokker-Planck equations on Cantor sets with local fractional derivative.
Shao-Hong Yan +4 more
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Local Fractional Z-Transforms with Applications to Signals on Cantor Sets
Abstract and Applied Analysis, 2014 The Z-transform has played an important role in signal processing. In this paper the Z-transform has been generalized by the coupling of both the Z-transform and the local fractional complex calculus. In the literature the local fractional Z-transform is
Kai Liu +5 more
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Descriptions of Cantor Sets: A Set‑Theoretic Survey and Open Problems
Chaos and FractalsThis paper synthesizes the principal descriptive set-theoretic perspectives on deterministic Cantor sets on the real line and charts directions for future study.
Mohsen Soltanifar
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All projections of a typical Cantor set are Cantor sets
Topology and its Applications, 2020 In 1994, John Cobb asked: given $N>m>k>0$, does there exist a Cantor set in $\mathbb R^N$ such that each of its projections into $m$-planes is exactly $k$-dimensional? Such sets were described for $(N,m,k)=(2,1,1)$ by L.Antoine (1924) and for $(N,m,m)$ by K.Borsuk (1947). Examples were constructed for the cases $(3,2,1)$ by J.Cobb (1994), for $
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Squeezing functions and Cantor sets [PDF]
ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE, 2020 We construct "large" Cantor sets whose complements resemble the unit disk arbitrarily well from the point of view of the squeezing function, and we construct "large" Cantor sets whose complements do not resemble the unit disk from the point of view of the squeezing function.
Arosio, L +3 more
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On G-transitive version of perfectly meager sets [PDF]
Mathematica Moravica, 2020 We study the G-invariant version of perfectly meager sets (a generalization of the notion of AFC sets). We find the necessary and sufficient conditions for the inclusion AFC'G ⊆ I.
Nowik Andrzej
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Lebesgue Constants for Cantor Sets
Experimental MathematicsWe evaluate the values of the Lebesgue constants in polynomial interpolation for three types of Cantor sets. In all cases, the sequences of Lebesgue constants are not bounded. This disproves the statement by Mergelyan.
Alexander Goncharov, Yaman Paksoy
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Remainders, Singular Sets and the Cantor Set
Rocky Mountain Journal of Mathematics, 1994 The authors characterize when, for nonlocally compact \(X\), there is a compactification \(\alpha X\) of \(X\) for which the closure of \(\alpha X\smallsetminus X\) is homeomorphic to the Cantor set \(2^ \omega\).
Hatzenbuhler, James P., Mattson, Don A.
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Advanced Engineering Materials, EarlyView.Geometry‐driven thermal behavior in wire‐arc additive manufacturing (WAAM) influences microstructural evolution during nonequilibrium solidification of a chemically complex Fe–Cr–Nb–W–Mo–C nanocomposite system. By comparing different deposits configurations, distinct entropy–cooling rate correlations, segregation, and carbide evolution are revealed ...
Blanca Palacios +5 more
wiley +1 more source