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Fixed point results for Fractal generation of complex polynomials involving Sine function via Non-standard iterations
2020
IEEE Access
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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
2016
Chaos, Solitons & Fractals
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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
2022
International journal of mathematical, engineering and management sciences
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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
2019
SN Computer Science
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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]
2018
arXiv
pre-print
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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
2005
Physica A: Statistical Mechanics and its Applications
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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
2016
Proceedings of the Royal Society A
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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]
2018
arXiv
pre-print
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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
2014
Physics reports
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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
2021
Nanomaterials
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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
2020
Journal of Mathematics Research
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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
2021
Applied Sciences
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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]
2022
arXiv
pre-print
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2021 pre-print arXiv:2109.01152v1 fatcat:akeckqj55zhdjmbdz4n7djicg4
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]
2018
arXiv
pre-print
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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
2000
Physica D : Non-linear phenomena
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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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