Analysis on characteristics and mechanism for rock fracture in deep rock with cracks under dynamic-static coupling effect by Jinjin Ge, Yongqi Jia, Wei Huang, Meilu Yu, Suqian Ni, Ying Xu, Leilei Yu, Keke Gu

“…The study revealed three key findings: (1)The dynamic compressive strength of specimens with pre-existing cracks exhibited a non-monotonic relationship with crack inclination angle under uniaxial stress, contrasting with an increasing trend under confining pressure, highlighting the significant effects of confining pressure and strain rate. (2)Confining pressure significantly altered the failure modes, with specimens failing predominantly in axial tension at 0° and 90° crack inclinations, and a mix of axial tension and shear at 30° and 60°, indicating complex failure mechanisms. (3)The pre-existing crack angle under confining pressure influenced the propagation path and fractal dimension of the specimen, with an increasing angle correlating to higher fractal dimensions and a positive impact on compression peak stress. …”
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Study on the Regulation Effect of Optogenetic Technology on LFP of the Basal Ganglia Nucleus in Rotenone-Treated Rats by Zongya Zhao, Yanxiang Niu, Peiqi Chen, Yu Zhu, Liangliang Shi, Xuewei Zhao, Chang Wang, Yehong Zhang, Zhixian Gao, Wenshuai Jiang, Wu Ren, Renjun Gu, Yi Yu

“…Approximate entropy and fractal dimension algorithm can be used as an effective index to study LFP changes in rotenone-treated rats.…”
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Simulation of the Radiation Reaction Orbits of a Classical Relativistic Charged Particle with Generalized Off-Shell Lorentz Force by Aviad Roitgrund, Lawrence Horwitz

“…The attractor may acquire fractal characteristics in the presence of an external field and thus become a strange attractor.…”
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Complex Dynamics of an Adnascent-Type Game Model by Baogui Xin, Junhai Ma, Qin Gao

“…Its complex dynamics is demonstrated by means of the largest Lyapunov exponents, fractal dimensions, bifurcation diagrams, and phase portraits. …”
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Student Models for a Risky Asset with Dependence: Option Pricing and Greeks by Nikolai Leonenko, Anqi Liu, Nataliya Schestyuk

“… We propose several new models in finance known as the Fractal Activity Time Geometric Brownian Motion (FATGBM) models with Student marginals. …”
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The Question of Metropolitan Form: Introduction by David Prosperi, Anne Vernez Moudon, François Claessens

“…Soja’s six metaphors (post-Fordist industrial, cosmopolis, expolis, fractal city, carceral archipelago, simcities) are being indicative of the wide range of possible images.[2] The eight papers in this issue of Footprint take an opposite approach. …”
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Laplace Transform Methods for a Free Boundary Problem of Time-Fractional Partial Differential Equation System by Zhiqiang Zhou, Xuemei Gao

“…We study the pricing of the American options with fractal transmission system under two-state regime switching models. …”
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Nonlinear Behaviors of Tail Dependence and Cross-Correlation of Financial Time Series Model by Wei Deng, Jun Wang

“…Further, the multifractality of cross-correlations for return series is studied by multifractal detrended cross-correlation analysis, which indicates the analogous cross-correlations and some fractal characters for both actual data and simulative data and provides an intuitive evidence for market inefficiency.…”
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Limiting Behavior of Travelling Waves for the Modified Degasperis-Procesi Equation by Jiuli Yin, Liuwei Zhao, Shanyu Ding

“…Besides some popular exotic solutions including peaked waves, and looped and cusped waves, this equation also admits some very particular waves, such as fractal-like waves, double stumpons, double kinked waves, and butterfly-like waves. …”
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The Question of Metropolitan Form: Introduction by Anne Vernez Moudon, François Claessens, David Prosperi

“…Soja’s six metaphors (post-Fordist industrial, cosmopolis, expolis, fractal city, carceral archipelago, simcities) are being indicative of the wide range of possible images.[2] The eight papers in this issue of Footprint take an opposite approach. …”
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Design of a tensile-type 3-D multi-scroll chaotic system and its application in secure communication by Jun-peng MA, Li-dan WANG, Shu-kai DUAN, Jie-ning WU

“…Then, some basic dynamical properties, such as Lyapunov exponents, fractal dimension, chaotic dynamical behaviors of the new chaotic system were introduced, either numerically or analytically. …”
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MULTI-OBJECTIVE PARAMETER OPTIMIZATION OF SYNCHRONIZER BASED ON IMPROVED PARTICLE SWARM OPTIMIZATION ALGORITHM by WANG ChunHua, GUO ZhiWei

“…To meet the requirements of shorter synchronization time and higher life for the synchronizer in transmission, mathematical models aiming at synchronization time and synchronizer life were established separately based on Newton’s second law and adhesive wear theory, M-B fractal contact model. The evaluation function was constructed by ideal point method to establish a multi-objective parameter optimization model with the two objectives. …”
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Barrow holographic dark energy: a path to reconstructing f(R, T) gravity by P. S. Ens, A. F. Santos

“…We employ Barrow’s holographic dark energy model, derived from fractal surfaces of black holes, to investigate the reconstruction process. …”
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Numerical Characteristic of Gear System Attractor in Phase Space based on G-P Algorithm of Correlation Dimension by He Lin, Matthias Rätsch, Sanmin Wang, Guangshen Xu

“…The results show that the more complex of attractor structure generates the larger correlation dimension values, and causing strong vibration to the system, correlation dimension of chaotic attractor is between integer 1 and 2 with fractal characteristic.…”
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Bifurcation Analysis and Chaos Control in a Discrete-Time Predator-Prey System of Leslie Type with Simplified Holling Type IV Functional Response by S. M. Sohel Rana, Umme Kulsum

“…Furthermore, we compute numerically maximum Lyapunov exponents and fractal dimension to justify the chaotic behaviors of the system. …”
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Soliton outcomes and dynamical properties of the fractional Phi-4 equation by Md Mostafa, Mohammad Safi Ullah

“…Under the given parameters, 2D and 3D phase portraits, time series, return map, Lyapunov exponent, recurrence plot, strange attractor, bifurcation diagram, and fractal dimension plot are provided. These plots show the periodic, quasi-periodic, and chaotic nature of the suggested nonlinear problem. …”
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CHANNELING: SEARCH OF THE METAANTHROPOLOGIC MEAS-UREMENTS OF MIND BEING IN THE UNIVERSE (based on the World Wide Web) by Anatoly T. Tshedrin

“…In the development of channeling manifest fractal effects associated with the reproduction of their previous ideas about the history of ETI. …”
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Combined multi-scale characterization of pores in ultra-thick coal seams of Jurassic Xishanyao Formation, Tiaohu-Malang sags, Santanghu Basin by Yue CHEN, Qiqi LEI, Dongmin MA, Xin WANG, Xinggang WANG, Diefang HUANG, Gaoxiang RONG

“…For the 9-2 coal sample, the fractal dimensions of micropores and small pores are 2.53 and 2.63, respectively, indicating higher complexity and better permeability connectivity. …”
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CHANNELING: SEARCH OF THE METAANTHROPOLOGIC MEAS-UREMENTS OF MIND BEING IN THE UNIVERSE (based on the World Wide Web) by Anatoly T. Tshedrin

“…In the development of channeling manifest fractal effects associated with the reproduction of their previous ideas about the history of ETI. …”
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Can’t Help Lovin’:David Chidester’s Pop Culture Colonialism by Kathryn Lofton

“…West and Smith offer an opportunity to argue the connection between these two strands of scholarly observance, showing the fractal effects of colonialism in Africa on the preferences of pop culture consumption in America.The attraction to West’s unlikability is the other side of the easy adorationfor Jordan Smith: like those colonists who gave religion to those colonized subjects they dominated, pop consumers refuse to admit their intimate and needful connection to those idols who resist theircontrol. …”
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