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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Spectral properties of Levy Rosenzweig-Porter model via supersymmetric approach by Elizaveta Safonova, Mikhail Feigel'man, Vladimir Kravtsov

“…We show that $\rho(E)$ depends crucially on the control parameter that drives the system through the transition between the ergodic and the fractal phases and it can be used as an order parameter.…”
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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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Study on the mechanical properties and failure mechanism of a multi-lithologic layered rock mass by Bo Zeng, Guozhou Qiu, Haoyong Huang, Yintong Guo, Ersi Xu, Junchuan Gui, Junfeng Li

“…Interface characteristics were studied based on 3D scanning technology and fractal method, with an increase in the angle, the fractal dimension D showed first decreased, then increased, and further decreased, which was identical to the variation trend of the maximum load in the Brazilian splitting test and the maximum principal strain in the DIC test with the angle. …”
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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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Case studies in numerical simulation of crack trajectories in brittle materials by H. Jasarevic, S. Gagula

“…The “diffusion approximation” of the crack diffusion model represents cracktrajectories as a one-dimensional Wiener process with advantage of well-developed mathematical formalismand simplicity of creating computer generated realizations (fractal dimension d = 1.5). However, the most ofreported d values are in the range 1.1-1.3. …”
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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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Effect of pH on the Adsorption of Uranyl Ions by Peat Moss by Liu Zhirong, Zhou Shaoqi

“…The kinetics of the adsorption process were well described by the Elovich equation, while the equilibrium adsorption isotherm was fitted reasonably well by the Freundlich adsorption model. The calculated fractal dimension of granular peat moss was 2.3384.…”
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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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Pullback Exponential Attractor for Second Order Nonautonomous Lattice System by Shengfan Zhou, Hong Chen, Zhaojuan Wang

“…Moreover, we obtain the upper bound of fractal dimension and attracting rate for the attractor.…”
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Design and application of electrocardiograph diagnosis system based on multifractal theory by Chun-kai ZHANG, Ao,ZHANGJing-wang YIN, Pan-bo TIAN, Ying ZHOU, Chang-qing QI

“…An automatic segmentation algorithm for ECG data using differential threshold method was designed,which could identify the various ECG cycles of continuous ECG data.And it could obtain the multifractal features of multiple fractal and generalize hurst index feature of ECG data,these features were used to train artificial neural network in order to classify ECG data,the accuracy of the classifier could reach 97%.An ECG diagnosis system was implemented,which can automatically identify ECG sequences that contain multiple ECG cycles,and can automatically ignore the incomplete ECG cycle data,and could annotate every cycle of ECG data.…”
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Renormalization Group Equation for Tsallis Statistics by Airton Deppman

“…The nonextensive statistics proposed by Tsallis has found wide applicability, being present even in the description of experimental data from high energy collisions. A system with a fractal structure in its energy-momentum space, named thermofractal, was shown to be described thermodynamically by the nonextensive statistics. …”
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Discrete dynamics in transitional economies by J. Barkley Rosser, Jr., Marina Vcherashnaya Rosser

“…During recovery, transitional cobweb labor market dynamics exhibit chaos, fractal basin boundaries between coexisting non-chaotic attractors, discontinuous phase transitions, strange attractors, and cascades of infinitely many period-doubling bifurcations.…”
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Inventing the savage: the Sapara people of the Ecuadorian Amazon in 19th-century travel writing by Erika Rosado-Valencia, Silke Jansen, Andrés Gerique-Zipfel

“…We frame our analysis in the theoretical proposal of Irvine and Gal for the ideological construction of cultural difference through the semiotic processes known as rhematization, fractal recursivity, and erasure.…”
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Drawing Dynamical and Parameters Planes of Iterative Families and Methods by Francisco I. Chicharro, Alicia Cordero, Juan R. Torregrosa

“…The complex dynamical analysis of the parametric fourth-order Kim’s iterative family is made on quadratic polynomials, showing the MATLAB codes generated to draw the fractal images necessary to complete the study. The parameter spaces associated with the free critical points have been analyzed, showing the stable (and unstable) regions where the selection of the parameter will provide us the excellent schemes (or dreadful ones).…”
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Micropore Characteristics and Gas-Bearing Characteristics of Marine-Continental Transitional Shale Reservoirs in the East Margin of Ordos Basin by Yuanzhen Ma, Meng Wang, Ruying Ma, Jiamin Li, Asiya Bake, Yadi Shan

“…Based on the two-dimensional SEM image fractal theory to study different types of pores, the fractal dimension of shale pore fracture morphology is between 2.34 and 2.50, and the heterogeneity is moderate. …”
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Integrating social narratives of flood events into a text network analysis-based decision support framework to reduce vulnerability to climate change in Africa by Thomas E. O’Shea, Lena C. Grobusch, Mary Zhang, Jeff Neal, Joseph Daron, Richard G. Jones, Christopher Jack, Alice McClure, Gilbert Siame, Dorothy Ndhlovu, Sukaina Bharwani

“…Using a well-established network from the Future Resilience for African Cities And Lands (FRACTAL) group, a cross-disciplinary approach of natural and social sciences to support decision-making for flood resilience is presented as the Participatory Climate Information Distillation for Urban Flood Resilience in Lusaka (FRACTAL-PLUS) project. …”
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