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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Expanded (G/G2) Expansion Method to Solve Separated Variables for the 2+1-Dimensional NNV Equation by Yong Meng

“…By using this method, the solution to the detached variables of the symmetric extended form of the 2+1-dimensional NNV equation can be solved, also the soliton structure and fractal structure of Dromion can be studied well.…”
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Complex Dynamics in Nonlinear Triopoly Market with Different Expectations by Junhai Ma, Xiaosong Pu

“…Numerical simulations are presented to show that the triopoly game model behaves chaotically with the variation of the parameters. We obtain the fractal dimension of the strange attractor, bifurcation diagrams, and Lyapunov exponents of the system.…”
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Julia and Mandelbrot Sets of Transcendental Function via Fibonacci-Mann Iteration by Nihal Özgür, Swati Antal, Anita Tomar

“…Also, we explore the effect of involved parameters on the deviance of color, appearance, and dynamics of generated fractals. It is well known that fractal geometry portrays the complexity of numerous complicated shapes in our surroundings. …”
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Left ventricular trabecular complexity for risk stratification of cancer therapy–related cardiac dysfunction in breast cancer by Hesong Shen, Qian Xu, Chunrong Tu, Yangling Peng, Yuhang Xie, Zhiming Miao, Rui Yang, Jiuquan Zhang

“…Abstract The left ventricular trabecular fractal dimension (LVTFD) derived from cardiac magnetic resonance reflects myocardial trabecular complexity, which is associated with cardiovascular disease risk. …”
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A constitutive model for coal gangue coarse-grained subgrade filler incorporating particle breakage by Zong-Tang Zhang, An Liu, Si-Chun Yu, Shun-Kai Liu, Chuan-Feng Fang, Ze Liu, Wei Hu

“…A modified quadratic polynomial fractal model gradation equation was proposed to describe the gradation of samples after particle breakage. …”
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Arithmetic-Analytic Representation of Peano Curve by Guangjun Yang, Xiaoling Yang, Ping Wang

“…Applying the iteration method of fractal, we established a simple arithmetic-analytic representation of the Peano curve as a function of ternary numbers. …”
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Experimental Study on Gas Permeability Semiempirical Model of Granite after Heat Treatment by Jinquan Wu

“…Finally, the temperature-permeability model of granite after the high temperature was proposed combined with the pore fractal model. The new model was verified with experimental data.…”
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Hβ-Hausdorff Functions and Common Fixed Points of Multivalued Operators in a b-Metric Space and Their Applications by Fahad Sameer Alshammari, Naif R. Alrashedi, Reny George

“…In order to demonstrate applications of our result, we have proven an existence theorem for a unique common multivalued fractal of a pair of iterated multifunction systems and also an existence theorem for a common solution of a pair of Volterra-type integral equations.…”
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