Porous Blasting Morphology and Resistivity Response Characteristics of Soft Coal Seam by Wenwang Yang, Sanlin He, Taotao Zhao, Chenying Ge

“…When single-hole blasting is performed, S < 0, the fractal dimension change rate of coal seam crack is only 5%, the control area presents a compaction phenomenon, and the resistivity decreases by about 20%. …”
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Relative Permeability of Porous Media with Nonuniform Pores by He Chen, Minghui Yang, Ke Chen, Chao Zhang

“…Moreover, the index factor can be captured by a newly defined parameter, called the nonuniformity factor, which is used to establish an extended Darcy’s law. Based on these, a fractal-based continuous analytical model and a fractal-based Monte Carlo model of relative permeability as well as a permeability-porosity model are established. …”
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Comparison of OCT Angiography Parameters after Administration of Intravitreal Brolucizumab versus Ranibizumab in Exudative Age-related Macular Degeneration by Sanjitha Vilma Moses, Aadithreya Varman, Dinesh Balakumar, Arulmozhi Varman

“…Central foveal thickness (CFT) and OCTA parameters like vessel density (VD), superficial capillary plexus (SCP), deep capillary plexus (DCP), foveal avascular zone, (FAZ), fractal dimension (FD) were assessed. The scans were repeated 1 month postinjection. …”
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Exponential Attractor for a First-Order Dissipative Lattice Dynamical System by Xiaoming Fan

“…We construct an exponential attractor for a first-order dissipative lattice dynamical system arising from spatial discretization of reaction-diffusion equations in ℝ𝑘. And we obtain fractal dimension of the exponential attractor.…”
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An Analysis of the Allometric and Multifractal Features of a Development in the Urban-Rural Area in the Lower Reaches of the Yangtze River: 2012 Cross-Sectional Data of Four Provin... by Zhi-jun Song, Yi Chen, Yun Li, Xin Zhao

“…This paper adopts the fitting function and the relevant parameters of the fractal dimension to quantify the evolution in particular fields. …”
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Experimental Study on the Effect of Coarse Grain Content on the Dilatancy and Particle Breakage Characteristics of Coarse-Grained Soils by Jun Du, Zhiming Xiong, Xinggang Shen, Chenchen Li

“…The coarse-grained soil particle size distribution before and after breakage conformed to the fractal characteristics, and the particle breakage rate increased significantly with larger soil particle size fractal dimension differences before and after the test. …”
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Evaporative Cracking Characteristics of the Embankment Soil Affected by the Saline Concentration by Jiawei Liu, Yingzhi Xia, Hui Li, Guoping Hu, Mingming Hu

“…The fractal dimension was gradually increased with the decrease of the moisture content and the increase of the saline concentration, respectively. …”
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Anterior Chamber Angle Shape Analysis and Classification of Glaucoma in SS-OCT Images by Soe Ni Ni, J. Tian, Pina Marziliano, Hong-Tym Wong

“…From the experimental results, the fkNN reveals the best classification accuracy (99.11±0.76%) and AUC (0.98±0.012) with the combination of fractal dimension and biometric parameters. It showed that the proposed approach has promising potential to become a computer aided diagnostic tool for angle closure glaucoma (ACG) disease.…”
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Finite Dimensional Uniform Attractors for the Nonautonomous Camassa-Holm Equations by Delin Wu

“…Assuming 𝑓=𝑓(𝑥,𝑡)∈𝐿2loc((0,𝑇);𝐷(𝐴−1/2)), we establish the existence of the uniform attractors in 𝐷(𝐴1/2) and 𝐷(𝐴). The fractal dimension is estimated for the kernel sections of the uniform attractors obtained.…”
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Interrelationships between Acoustic Emission and Cutting Force in Rock Cutting by Sifei Liu, Peng Shi, Zhijun Wan, Shuaifeng Lu, Jiakun Lv, Fanfei Meng

“…The results show that the development of AE energy can represent the different stages of the cutting process, and the time fractal dimension of AE energy can reveal the change law of coal structure stability. …”
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Self-Organized Crystallization Patterns from Evaporating Droplets of Common Wheat Grain Leakages as a Potential Tool for Quality Analysis by Maria Olga Kokornaczyk, Giovanni Dinelli, Ilaria Marotti, Stefano Benedettelli, Daniele Nani, Lucietta Betti

“…The evaluation of the patterns was performed both visually and by means of the fractal dimension analysis. From the results, it can be inferred that the wheat cultivars differed in their pattern-forming capacities. …”
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Research on the Impact of Coastal Land Reclamation on Geomorphic Complexity and Tidal Energy Dissipation—A Case Study of Zhoushan Islands, Hangzhou Bay by Shixia Zhang, Qiankun Hong, Huifang Guo

“…The model is constructed using fractal geometry theory and quantitative methods, while also incorporating principles from ocean dynamics theory. …”
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The Influences of Sand Content and Particle Size on the Desiccation Cracks of Compacted Expansive Soil by Dongdong Li, Shaowei Zhang

“…The changing law of the fractal dimension of cracks was the same as that of the surface crack ratio. …”
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Study on the Relationship between Pore Structure and Uniaxial Compressive Strength of Cemented Paste Backfill by Using Air-Entraining Agent by Fengwen Zhao, Jianhua Hu, Dongjie Yang, Ye Kuang, Hongxing Xiao, Minghua Zheng, Xueliang Wang

“…A higher proportion of small pores leads to a linear increase in strength; a higher proportion of medium pores leads to a linear decrease in strength; and a higher proportion of big pores leads to an exponential decrease in strength. And the fractal dimension has a linear negative correlation with the UCS by fractal theory analysis.…”
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Experimental Study of Fracture Characterizations of Rocks under Dynamic Tension Test with Image Processing by Dihao Ai, Yuechao Zhao, Beijing Xie, Chengwu Li

“…Using the extracted cracks and image processing technique, the relationship between loading condition (impact velocity), crack propagation process (crack velocity, crack fractal characteristic, and crack morphological features), and dynamic mechanical properties (absorbed energy and strain-stress parameters) was explored and analyzed. …”
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DEFINITION OF BUDGETING AS A COMPONENT OF A DESCRIPTIVE ASSESSMENT OF THE FINANCIAL SOLVENCY OF RUSSIAN ENTERPRISES by S. Yunusova, A. Bodiako

“…Problems of the implementation of the fractal, within branched budgeting system in Russian enterprises. …”
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Art and Science: Where Numerology and Mathematics Touch the Lung by S Marsh Tenney

“…Rigorous analysis or form and function in the biological sciences has been a more recent innovation. but introduction of' the principles of similarity. scaling, fractal geometry, harmony and proportion has hroadened our perspective. …”
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Chebyshev Wavelet Analysis by Emanuel Guariglia, Rodrigo Capobianco Guido

“…In particular, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry. Finally, we give two examples concerning the main properties proved.…”
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Influence of Drying–Wetting Cycles on the Water Retention and Microstructure of Residual Soil by Xu-tang Xu, Dao-qi Liu, Zhen-xing Xian, Feng Yang, Wen-bin Jian, Xiang Xu, Jian-bin Huang

“…Also, the fractal dimension can be approximated as a constant, because its attenuation is small with more drying–wetting cycles.…”
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Asymptotic Properties of Parameter Estimators in~Vasicek Model Driven by Tempered Fractional Brownian Motion by Yuliya Mishura, Kostiantyn Ralchenko, Olena Dehtiar

“…This work continues the investigation by Mishura and Ralchenko (Fractal and Fractional, 8(2:79), 2024), where these estimators were introduced and their strong consistency was proved.…”
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