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Journal of Low Frequency Noise, Vibration and Active Control, 2022 This paper uses the two-scale fractal dimension transform and He’s formula derived from the ancient Chinese algorithm Ying Bu Zu Shu to find the approximate frequency–amplitude expression of the fractal and forced anharmonic oscillator that can be used ...
Alex Elías-Zúñiga +3 more
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A new nonlinear fractal vibration of the Euler–Bernoulli beams in a microgravity space
Journal of Low Frequency Noise, Vibration and Active Control, 2023 Microgravity is an extreme physical environment, where many theories deduced on the earth’s surface become invalid. So a fractal vibration of Euler–Bernoulli beams in a microgravity space is presented in this paper via He’s fractal derivative.
Pei-Ling Zhang, Kang-Jia Wang
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Fractal transforms and feature invariance [PDF]
Proceedings 15th International Conference on Pattern Recognition. ICPR-2000, 2002 In this paper, fractal transforms are employed with the aim of image recognition. It is known that such transforms are highly sensitive to distortions like a small shift of an image. However, by using features based on statistics kept during the actual decomposition we can derive features from fractal transforms, which are invariant to perturbations ...
Zeeuw, Paul M. de, Schouten, Ben
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Wavelet-based 3D reconstruction of microcalcification clusters from two mammographic views: new evidence that fractal tumors are malignant and Euclidean tumors are benign. [PDF]
PLoS ONE, 2014 The 2D Wavelet-Transform Modulus Maxima (WTMM) method was used to detect microcalcifications (MC) in human breast tissue seen in mammograms and to characterize the fractal geometry of benign and malignant MC clusters.
Kendra A Batchelder +6 more
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Petroleum, 2015 Based on fractal geometry, fractal medium of coalbed methane mathematical model is established by Langmuir isotherm adsorption formula, Fick's diffusion law, Laplace transform formula, considering the well bore storage effect and skin effect. The Laplace
Lei Wang +4 more
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Dynamics research of Fangzhu’s nanoscale surface
Journal of Low Frequency Noise, Vibration and Active Control, 2022 In this paper, we mainly focus on a fractal model of Fangzhu’s nanoscale surface for water collection which is established through He’s fractal derivative. Based on the fractal two-scale transform method, the approximate analytical solutions are obtained
Pinxia Wu +4 more
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Fractal Transformation of Krein–Feller Operators
Zurnal matematiceskoj fiziki, analiza, geometrii, 2023 Summary: We consider a fractal transformed doubly reflected Brownian motion with state space being a Cantor-like set. By applying the theory of fractal transformations as developped by Barnsley, et al., together with an application of a generalised Taylor expression we show that its infinitesimal generator is given in terms of a second order measure ...
Menzel, Max, Freiberg, Uta
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An Efficient Computational Technique for Fractal Vehicular Traffic Flow
Entropy, 2018 In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local ...
Devendra Kumar +3 more
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IEEE Access, 2020 Texture in synthetic aperture radar (SAR) images is a combination of the intrinsic texture of scene backscattering and the texture due to noncoherent high-frequency multiplicative noise (HMN) interactions that reflect erroneous information and lead to ...
Iman Heidarpour Shahrezaei +1 more
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Fractal Dimensions and Random Transformations [PDF]
Transactions of the American Mathematical Society, 1996 Summary: I start with random base expansions of numbers from the interval \([0,1]\) and, more generally, vectors from \([0,1]^d\), which leads to random expanding transformations on the \(d\)-dimensional torus \(\mathbb{T}^d\). As in the classical deterministic case of Besicovitch and Eggleston I find the Hausdorff dimension of random sets of numbers ...
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