On Topological Indices of Fractal and Cayley Tree Type Dendrimers by Muhammad Imran, Abdul Qudair Baig, Waqas Khalid

“…Furthermore, we give closed analytical results of these indices for fractal trees and Cayley trees.…”
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How to Calculate the Goodness-of-Fit of a Fractal Dimension by Fritz Albregtsen

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The Fractal Dimension of River Length Based on the Observed Data by Ni Zhihui, Wu Lichun, Wang Ming-hui, Yi Jing, Zeng Qiang

“…Although the phenomenon that strictly meets the constant dimension fractal form in the nature does not exist, fractal theory provides a new way and means for the study of complex natural phenomena. …”
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Fractal Tilings Based on Successive Adjacent Substitution Rule by Peichang Ouyang, Xiaosong Tang, Kwokwai Chung, Tao Yu

“…A fractal tiling or f-tiling is a tiling which possesses self-similarity and the boundary of which is a fractal. f-tilings have complicated structures and strong visual appeal. …”
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Synthesizing fractal images by means of shift dynamical systems by Jonas Valantinas, Rokas Valantinas, Tomas Žumbakis

“… In this paper, the adaptation problem of the time escape algorithm to the special class of fractal images (attractors of iterated function systems) and the necessary mathematical context are ana­lysed. …”
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Fractal Control and Synchronization of the Discrete Fractional SIRS Model by Miao Ouyang, Yongping Zhang, Jian Liu

“…The discrete SIRS models with the Caputo deltas sense and the theories of fractional calculus and fractal theory provide a reasonable and sensible perspective of studying infectious disease phenomenon. …”
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A New Model of Ultracapacitors Based on Fractal Fundamentals by Xiaodong Zhang, Yi Sun, Jia Song, Aijun Wu, Xiaoyan Cui

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Fractal Acoustic Metamaterials with Subwavelength and Broadband Sound Insulation by Yu Liu, Meng Chen, Wenshuai Xu, Tao Yang, Dongliang Pei, Heng Jiang, Yuren Wang

“…We construct new fractal acoustic metamaterials by coiling up space, which can allow subwavelength-scale and broadband sound insulation to be achieved. …”
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CPW-Fed Fractal Slot Antenna for UWB Application by Hou Zhang, Hai-Yang Xu, Bo Tian, Xian-Feng Zeng

“…A novel printed ultrawideband (UWB) CPW-fed Koch fractal slot antenna is proposed. The UWB bandwidth is largely enhanced by the three-iteration Koch fractal slot whose extrusive angle is 900 instead of 600 to obtain better convoluted shape and self-similarity. …”
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Analysis of a Fractal Boundary: The Graph of the Knopp Function by Mourad Ben Slimane, Clothilde Mélot

“…A usual classification tool to study a fractal interface is the computation of its fractal dimension. …”
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Ultra-Wideband Fractal Ring Antenna for Biomedical Applications by Ilyas Saleem, Umair Rafique, Shobit Agarwal, Hüseyin Şerif SAVCI, Syed Muzahir Abbas, Subhas Mukhopadhyay

“…In this paper, an efficient, coplanar waveguide (CPW)-fed printed circular ring fractal ultra-wideband (UWB) antenna is presented for biomedical applications. …”
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Surface Evaluation by Estimation of Fractal Dimension and Statistical Tools by Vlastimil Hotar, Petr Salac

“…The text presents application of fractal geometry (fractal dimension) for complex surface analysis in combination with standard roughness parameters (statistical tool).…”
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Fractal Statistical Study on the Strength of Jointed Rock Mass by Fangtao Li, Zhiping Hu, Xiang Ren, Jiakuan Ma, Xuexu An, Yunxin Zheng, Yonghui Zhang

“…In this study, two strength calculation models for rock mass joint rupture failure and shear slip failure are established according to different relative sizes and working conditions, and the effects of fractal dimension, water pressure, and number of cracks on the strength and failure probability of rock mass are analyzed. …”
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Fractal Characteristic of Rock Cutting Load Time Series by Hongxiang Jiang, Changlong Du, Songyong Liu, Kuidong Gao

“…A test-bed was developed to perform the rock cutting experiments under different cutting conditions. The fractal theory was adopted to investigate the fractal characteristic of cutting load time series and fragment size distribution in rock cutting. …”
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Novel Design of Electromagnetic Bandgap Using Fractal Geometry by Huynh Nguyen Bao Phuong, Dao Ngoc Chien, Tran Minh Tuan

“…A novel electromagnetic bandgap (EBG) structural design based on Fractal geometry is presented in this paper. These Fractals, which are the Sierpinski triangles, are arranged to repeat each 60° to produce the hexagonal unit cells. …”
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Quantum–Fractal–Fractional Operator in a Complex Domain by Adel A. Attiya, Rabha W. Ibrahim, Ali H. Hakami, Nak Eun Cho, Mansour F. Yassen

Subjects: “…fractal–fractional operator…”
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Slow Motion and Zoom in HD Digital Videos Using Fractals by Maurizio Murroni, Cristian Perra, Daniele D. Giusto

“…Purpose of this paper is to present an alternative technique combining fractals theory and wavelet decomposition to achieve spatial zoom and slow motion replay of HD digital color video sequences. …”
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Explicit Spectral Decimation for a Class of Self-Similar Fractals by Sergio A. Hernández, Federico Menéndez-Conde

“…The method of spectral decimation is applied to an infinite collection of self-similar fractals. The sets considered are a generalization of the Sierpinski Gasket to higher dimensions; they belong to the class of nested fractals and are thus very symmetric. …”
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Optimized Ultrawideband and Uniplanar Minkowski Fractal Branch Line Coupler by Mohammad Jahanbakht, Mohammad Tondro Aghmyoni

“…The non-Euclidean Minkowski fractal geometry is used in design, optimization, and fabrication of an ultrawideband (UWB) branch line coupler. …”
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Charaterisation of function spaces via mollification; fractal quantities for distributions by Hans Triebel

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