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Fractal Sturm–Liouville Theory
Fractal and FractionalThis paper provides a short summary of fractal calculus and its application to generalized Sturm–Liouville theory. It presents both the fractal homogeneous and non-homogeneous Sturm–Liouville problems and explores the theory’s applications in optics.
Alireza Khalili Golmankhaneh +3 more
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This paper introduces fractal probability theory, a novel extension to standard probability theory that incorporates a fundamental balance between probability and its complement. For any event A with standard probability µ(A), we define a fractal probability measure µr(A) = (1 − r)µ(A) + rµ(Ac), where r ∈ [0, 1/2] is the fractal ratio parameter ...
Jason Evanoff
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Urban spatial form analysis based on the architectural layout -- Taking Zhengzhou City as an example
PLoS ONE, 2022 The analysis of urban spatial form is the basic research of urban development. Traditional fractal research often focuses on the urban spatial layout, which cannot visually express the specific form, change characteristics and development trend of urban ...
Qindong Fan +3 more
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Distribution theory on P.C.F. fractals [PDF]
Journal d'Analyse Mathématique, 2010 38 ...
Rogers, Luke G., Strichartz, Robert S.
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Seepage–Fractal Model of Embankment Soil and Its Application
Fractal and Fractional, 2022 Over time and across space, the hydraulic conductivity, fractal dimension, and porosity of embankment soil have strong randomness, which makes analyzing seepage fields difficult, affecting embankment risk analysis and early disaster warning.
Xiaoming Zhao +4 more
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Fractal Dimension Complexity of Gravitation Fractals in Central Place Theory
Scientific Reports, 2022 Abstract Settlement centers of various types, including cities, produce basins of attraction whose shape can be regular or complexly irregular (from the point of view of geometry). It depends, among others, on the properties of the space surrounding a city.
Banaszak, Michał +3 more
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Advances in Mechanical Engineering, 2020 To analyze the fractal form of the vascular network in the human circulatory system, the optimal transport effect has been achieved from the point of view of biological evolution.
Yan-li Chen +7 more
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Historical aspects of fractal theory appearance
Физика волновых процессов и радиотехнические системы, 2021 In paper short definition of a fractal is made, its basic properties are resulted, historical preconditions of origination fractal theories in a context of terms «assemblage» and «function» which development is observed from the moment of their ...
Viktor A. Kuznetsov
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, 2013 This thesis aims at getting a better understanding of the properties, scalings and similarities of turbulent axisymmetric wakes, as well as possible applications that arise from the information learnt.
Nedic, Jovan
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Slope Deformation Prediction Based on IVDF-SVR Coupling Model
Renmin Zhujiang, 2022 Given the shortcomings of improved variable-dimension fractal in the fitting and prediction of fractal dimensions,this paper proposes a fractal prediction model based on the coupling of the improved variable-dimension fractal (IVDF) theory and the ...
HOU Taiping +5 more
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