Results 21 to 30 of about 12,741 (164)
A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals
Mathematics, 2021 How many fractals exist in nature or the virtual world? In this paper, we partially answer the second question using Mandelbrot’s fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure.
Mohsen Soltanifar
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On the Design of Soret Zone Plates Based on Binary Sequences Using Directional Transducers
Sensors, 2021 In this work, we analyze the effect of the distribution of transparent Fresnel regions over the focusing profile of Soret Zone Plates (SZP) based on binary sequences. It is shown that this effect becomes very significant in those fields where directional
Pilar Candelas +2 more
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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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Maxwell’s Equations on Cantor Sets: A Local Fractional Approach
Advances in High Energy Physics, 2013 Maxwell’s equations on Cantor sets are derived from the local fractional vector calculus. It is shown that Maxwell’s equations on Cantor sets in a fractal bounded domain give efficiency and accuracy for describing the fractal electric and magnetic fields.
Yang Zhao +4 more
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Cantor Paradoxes, Possible Worlds and Set Theory
Mathematics, 2019 In this paper, we illustrate the paradox concerning maximally consistent sets of propositions, which is contrary to set theory. It has been shown that Cantor paradoxes do not offer particular advantages for any modal theories.
José-Luis Usó-Doménech +4 more
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A mixing dynamical system on the cantor set
International Journal of Mathematics and Mathematical Sciences, 1995 In this paper we give mixing properties (ergodic, weak-mixng and strong-mixing) to a dynamical system on the Cantor set by showing that the one-sided (12,12)-shift map is isomorphic to a measure preserving transformation defined on the Cantor ...
Jeong H. Kim
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On the Fractal Langevin Equation
Fractal and Fractional, 2019 In this paper, fractal stochastic Langevin equations are suggested, providing a mathematical model for random walks on the middle- τ Cantor set.
Alireza Khalili Golmankhaneh
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Generalized Differentiability of Continuous Functions
Fractal and Fractional, 2020 Many physical phenomena give rise to mathematical models in terms of fractal, non-differentiable functions. The paper introduces a broad generalization of the derivative in terms of the maximal modulus of continuity of the primitive function.
Dimiter Prodanov
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Data block decomposition and intelligent secure acquisition of microdata
Scientific Reports, 2023 P-sets (P stands for Packet) is a set model with dynamic characteristics, which is obtained by introducing dynamic characteristics into Cantor set and improving Cantor set. According to the fact that the characteristics of class I big data are completely
Xiuquan Zhang, Lin Shen, Kaiquan Shi
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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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