Cantor Set
The Cantor set
... following construction ofthe Cantor set. are obviously in the Cantor set. We obtain another point in. the Cantor set by either adding or subracting ^ with the[r] ...
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Lebesgue Measure of Generalized Cantor Set
... 4. M.J.Islam and M.S.Islam, Generalized Cantor set and its fractal dimension, Bangladesh Journal of Scientific and Industrial Research, 46(4) (2011) 499-506. 5. H.L.Royden, Real Analysis, Macmillan ...
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Correct a Wide Spread Conclusion of Cantor Set Theory
... 1874, Cantor started to consider whether there is a one-one correspondence between the points on the line and the points in the n-dimensional ...Since Cantor set theory had been published, mathe- ...
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Amenable purely infinite actions on the non compact Cantor set
... Free, minimal (topological) actions on the non-compact Cantor set K ∗ were constructed by Matui and Rørdam [11] and Danilenko [4] (see also [3]). Fur- thermore, the action constructed in [4] is amenable ...
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Analysis and Investigation of a Cantor Set Fractal UWB Antenna with a Notch-Band Characteristic
... using cantor set ...are set at the bottom of the wide ...a cantor set fractal radiation patch, a T-shaped tuning stub and a 50 Ω CPW-fed ...
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DNA Sequences with Forbidden Words and the Generalized Cantor Set
... generalized Cantor set, which can naturally correspond to multifractals, and then in Section 3, we will induce Hao’s frame representation according to the principle that the correspondence between line ...
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Multifractal two-scale Cantor set model for slow solar wind turbulence in the outer heliosphere during solar maximum
... This paper is organized as follows. In Sect. 2 a generalized two-scale Cantor set model is summarised, and the data are presented in Sect. 3. The methods related the concept of the generalized dimensions ...
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An Exploration Of The Generalized Cantor Set
... If we apply 𝐿 to the portion of 𝐶 3 in 0, 1/3 , we see that 𝐿 maps this portion onto the entire Cantor set. Indeed, 𝐿 maps 1 9 , 2/9 to 1 3 , 2/3 , 1 27 , 2/27 to 1 9 , 2/9 , and so forth (Fig. 2). Each of ...
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An orthonormal system on the construction of the generalized cantor set
... n The Cantor N, n contains 2 closed Interval each of length 3 For each n set can be associated with a monotone non-decreaslng continuous function Lebesgue function and defined by the fol[r] ...
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A mixing dynamical system on the cantor set
... In Section 4 we show that the one-sided shift transformation is isomorphic to a measure preserving transformation defined on the Cantor ternary set so that a dynamical system on the Cant[r] ...
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Central limit theorems for the spectra of classes of random fractals
... The main technical tool we develop is a central limit theorem for the general Crump-Mode- Jagers branching process. In our setting the random fractal sets, the random Cantor set boundary of the string, or ...
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Vol 9, No 5 (2018)
... This approach is used to construct the Cantor sets. Here, segments can be computed independent of each other. This approach uses the numerators of the upper bound. The Upper Bound Numerator Generator Approach ...
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International Journal of Emerging Technology and Advanced Engineering Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 9, Issue 5, May 2019)
... 64 As with the Cantor set, the von-Koch curve is also constructed recursively. Westart with a s traight line, partition it into three equal parts, then replace the middle part by an equilateral triangle and ...
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The diffraction of monsters from complex apertures
... the Cantor set [10] or, more precisely, a slightly modified version of what might be interpreted as the ‘traditional’ Cantor set from ...’ Cantor set and, in a sense, inverts it ...
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An Analytical Model for Multifractal Systems
... In conclusion, an analytical model (named Jake-Jun model) for multifractal systems was developed by combin- ing and improving the Jake model, Tyler fractal model and Gompertz curve. Previous multifractal theories fail to ...
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Nanocapacitor with a Cantor Multi Layered Structure
... We calculate numerically the quantum capacitance of a nanocapacitor formed of oxide-silicon layers deposited alter- nately with their widths following a Cantor set structure. We show that this configuration ...
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The Electromagnetic Properties of the Generalized Cantor Stack in Spherical Multilayered Systems
... known Cantor set is created by repeatedly deleting the open central third of a set of line ...the set by, say, cutting the segments into a different number of intervals or choosing another ...
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Voyager 2 observation of the multifractal spectrum in the heliosphere and the heliosheath
... weighted Cantor set model using the partition technique (Macek, 2007; Macek and Szczepaniak, 2008), which leads to complementary informa- tion about the multifractal nature of the fluctuations as the ...
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Attractor of Cantor type with positive measure
... It is well-known that the attractor of this IFS is the Cantor set (see e.g. [6, Chapter 9]), which has Lebesgue measure zero. The problem is that the gap ( 1 3 , 2 3 ) leads to the gaps ( 1 9 , 2 9 ) and ( ...
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On the Construction of Two Dimensional Cantor like Sets and Determination of Hausdorff Dimension
... dimensional Cantor like set S from any sequence { } with 0 < < 1, ∑ = ∞ with the help of sequence of sets { } of subsets of unit square [0, 1] × [0, 1] such that ⊃ , S = ∩ and m(S) = ...dimensional ...
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