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Fixed point results for Fractal generation of complex polynomials involving Sine function via Non-standard iterations

Hengxiao Qi, Muhammad Tanveer, Waqas Nazeer, Yu-Ming Chu
2020 IEEE Access  
This paper demonstrates some fixed point results for a sine function (i.e. sin(z n ) + c) via non-standard iterations (i.e. Mann, Ishikawa and Noor iterations etc.).  ...  Noor, CR and SP iterations) have same escape radii for any complex polynomial, so we use these results for S, CR and SP iterations also to apply for the generation of Julia and Mandelbrot sets with sin  ...  :Fixed point results for Fractal generation of complex polynomials involving Sine function via Non-standard iterations This work is licensed under a Creative Commons Attribution 4.0 License.  ... 
doi:10.1109/access.2020.3018090 fatcat:e3ftf7bk2fdivkswxdnkhaifv4

Old wine in fractal bottles I: Orthogonal expansions on self-referential spaces via fractal transformations

Christoph Bandt, Michael Barnsley, Markus Hegland, Andrew Vince
2016 Chaos, Solitons & Fractals  
The key idea is to use fractal transformations to provide unitary transformations between Hilbert spaces defined on attractors of iterated function systems.  ...  dense set of points, yet have good approximation properties.  ...  We thank Louisa Barnsley for her help with this paper.  ... 
doi:10.1016/j.chaos.2016.07.007 fatcat:mhl3yj2xqfajjjecdmpi72evsq

Image Cryptography Based On A Second-Order QRT Difference Equation

Agus Sutrisno, Aang Nuryaman, Muslim Ansori, Ahmad Faisol
2022 International journal of mathematical, engineering and management sciences  
For the digital text and image security algorithms, we developed the pseudo code algorithm implemented in Mathematica®.  ...  The use of mathematical concepts of mapping in cryptography provides advantages in securing text or image data. The qualitative properties of mapping can preserve data that is kept confidential.  ...  La Zakaria for the valuable discussion.  ... 
doi:10.33889/ijmems.2022.7.3.027 fatcat:nckijkjwkbf3fj4jmxcce54lcu

Characterization of a New Potential Family of Organic-Like Pattern-Generating Dynamical Systems

David M. Marciel
2019 SN Computer Science  
The study of these new systems could help in finding unexpected alternatives to the representation of the patterns generated by the mechanisms of segmentation and bioluminescence, especially in invertebrates  ...  The aforementioned new broad family of discrete-time dynamical systems and a new type of fractal structure are formulated.  ...  of the (bottom-left) Ctenophora (Sea Walnut) (Wikimedia [22] ) and (bottom-right) Mnemiopsis leidyi (Wikimedia [23] ) zooplanktons, obtained from the subfamily (10)  ... 
doi:10.1007/s42979-019-0028-6 fatcat:5247kidjgbbkjit2tjv4kzodsa

On the Beta Transformation [article]

Linas Vepstas
2018 arXiv   pre-print
The eigenvalues of the transfer operator seem to lie on a circle of radius 1/β in the complex plane.  ...  The spectrum appears to be the limit of a dense set of quasi-cyclotomic polynomials, the positive real roots of which include the Golden and silver ratios, the Pisot numbers, the n-bonnaci (tribonacci,  ...  Clearly, x = 1/2β n is such a fixed point: after n + 1 iterations of eqn Transfer operators The discovery and study of invariant measures, as well as of decaying states can be approached via the transfer  ... 
arXiv:1812.10593v1 fatcat:g2bbu3lk4rdpjek5xwa6wc3n6u

On non-extensive statistics, chaos and fractal strings

C. Castro
2005 Physica A: Statistical Mechanics and its Applications  
Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics.  ...  Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics (with a non-additive q-entropy) of an ensemble of fractal strings and  ...  of Mathematical Sciences ( Madras ) where this work was completed.  ... 
doi:10.1016/j.physa.2004.08.037 fatcat:ushtk4evuzffhj53qylibd4axm

Asymmetric collapse by dissolution or melting in a uniform flow

Chris H. Rycroft, Martin Z. Bazant
2016 Proceedings of the Royal Society A  
The structure of the non-analytic function is examined for three different test cases, and a practical approach to determine the collapse point using a generalized Newton--Raphson root-finding algorithm  ...  The simulations reveal a surprising exact relationship whereby the collapse point is the root of a non-analytic function given in terms of the flow velocity and the Laurent series coefficients describing  ...  As is typical for Newton-Raphson iterations of complex functions, the plot has a fractal structure, with large basins of attraction surrounding each root.  ... 
doi:10.1098/rspa.2015.0531 pmid:26997890 pmcid:PMC4786035 fatcat:jqpwitxwezhmncvtynjbdevns4

Theory of Deep Learning III: explaining the non-overfitting puzzle [article]

Tomaso Poggio, Kenji Kawaguchi, Qianli Liao, Brando Miranda, Lorenzo Rosasco, Xavier Boix, Jack Hidary, Hrushikesh Mhaskar
2018 arXiv   pre-print
This property holds for loss functions such as the logistic and cross-entropy loss independently of the initial conditions.  ...  Gradient descent enforces a form of implicit regularization controlled by the number of iterations, and asymptotically converges to the minimum norm solution for appropriate initial conditions of gradient  ...  CBMM acknowledges the support of NVIDIA Corporation with the donation of the DGX-1 used in part for this research. HNM is supported in part by ARO Grant W911NF-15-1-0385  ... 
arXiv:1801.00173v2 fatcat:gt6wixwtzbgvpmzokcicbg3koe

Discerning non-autonomous dynamics

Philip T. Clemson, Aneta Stefanovska
2014 Physics reports  
Here we review current methods for the analysis of non-autonomous dynamics including those for extracting properties of interactions and the direction of couplings.  ...  However, while a complex structure can be relatively safely broken down into the minutest parts, and technology is now delving into nanoscales, the function of complex systems requires a completely different  ...  We also thank Victor Efimov, Kimitoshi Kono, Denis Konstantinov and Masamitsu Watanabe for providing data presented in the example applications.  ... 
doi:10.1016/j.physrep.2014.04.001 fatcat:flbv6stq5ne2pap4exvge3f6i4

Synthetic Data in Quantitative Scanning Probe Microscopy

David Nečas, Petr Klapetek
2021 Nanomaterials  
In this paper we review methods used for their generation and the applications of synthetic data in scanning probe microscopy, focusing on their principles, performance, and applicability.  ...  Synthetic data are of increasing importance in nanometrology. They can be used for development of data processing methods, analysis of uncertainties and estimation of various measurement artefacts.  ...  Subtraction of polynomials has no effect in the limit of infinitely large flat rough surfaces for any fixed polynomial degree.  ... 
doi:10.3390/nano11071746 doaj:b1e1bde8620f4376bb757baf672420e2 fatcat:ilhmlzzejrbkddoj2dmdyuw5r4

Mathematical Modelling of COVID-19 and Solving Riemann Hypothesis, Polignac's and Twin Prime Conjectures Using Novel Fic-Fac Ratio With Manifestations of Chaos-Fractal Phenomena

John Y. C. Ting
2020 Journal of Mathematics Research  
this Sieve result in primary spin-o s from first key step consisting of providing proof for Riemann hypothesis (and explaining closely related two types of Gram points), and second key step consisting  ...  These problems are literally ”complex systems” containing well-defined Incompletely Predictable entities such as nontrivial zeros and two types of Gram points in Riemann zeta function (or its  ...  Examples: Mandelbrot set, Julia set, Burning Ship fractal and Lyapunov fractal. Iterated function systems -These have a (deterministic) fixed geometric replacement rule.  ... 
doi:10.5539/jmr.v12n6p1 fatcat:kvamqswn4bawjl5upomcjlnql4

Complex Systems, Emergence, and Multiscale Analysis: A Tutorial and Brief Survey

Jianbo Gao, Bo Xu
2021 Applied Sciences  
With the rapidly accumulating big data in almost every branch of science, engineering, and society, a golden age for the study of complex systems and emergence has arisen.  ...  The latter are very useful for finding key parameters characterizing the evolution of a dynamical system, including malfunctioning of the system.  ...  The authors also thank Bin Liu for preparing Figure 3 and Zhenzhen Wang for preparing Figure 6 . Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/app11125736 fatcat:eq2wc3bevrgtpgei5fdt655gea

Quantum Complexity as Hydrodynamics [article]

Pablo Basteiro, Johanna Erdmenger, Pascal Fries, Florian Goth, Ioannis Matthaiakakis, René Meyer
2022 arXiv   pre-print
For large N, our cost function captures two essential properties of holographic complexity measures: ergodicity and conjugate points.  ...  To achieve this, we introduce a basis of non-commutative plane waves for the 𝔰𝔲(N) algebra and define a metric with polynomial penalty factors.  ...  decomposition for the Cosine and Sine functions.  ... 
arXiv:2109.01152v2 fatcat:bmb4dln4vvb55prnos5dzoe2aa

An Overview of Complex Fractal Dimensions: From Fractal Strings to Fractal Drums, and Back [article]

Michel L. Lapidus
2018 arXiv   pre-print
Our main goal in this long survey article is to provide an overview of the theory of complex fractal dimensions and of the associated geometric or fractal zeta functions, first in the case of fractal strings  ...  Special attention is paid to discussing a variety of examples illustrating the general theory rather than to providing complete statements of the results and their proofs, for which we refer to the author's  ...  I wish to thank all of my wonderful collaborators over the past twenty five to thirty years on many aspects of the theory of complex fractal dimensions and its various extensions or related topics, including  ... 
arXiv:1803.10399v2 fatcat:eq2c2ggihnfatf2hiej2sd7z5i

Data-adaptive wavelets and multi-scale singular-spectrum analysis

Pascal Yiou, Didier Sornette, Michael Ghil
2000 Physica D : Non-linear phenomena  
approximately to successive derivatives of the first mother wavelet in standard wavelet analysis.  ...  We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic and geophysical time series.  ...  Constructive comments from two anonymous referees helped to improve the presentation; they resulted in particular in the addition of Appendix B.  ... 
doi:10.1016/s0167-2789(00)00045-2 fatcat:c5wez3ejcjadnhwuxsdwoym2du
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