Fractal Functions Dimensions And Signal Analysis

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Fractal Functions Dimensions And Signal Analysis

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Author : Santo Banerjee
language : en
Publisher: Springer Nature
Release Date : 2020-12-14

Fractal Functions Dimensions And Signal Analysis written by Santo Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-14 with Science categories.

This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.

Fractal Functions Dimensions And Signal Analysis Fractal Functions Chapter 3 Fractional Calculus And Generalized Fractal Functions

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Author : Santo Banerjee
language : en
Publisher:
Release Date : 2021

Fractal Functions Dimensions And Signal Analysis Fractal Functions Chapter 3 Fractional Calculus And Generalized Fractal Functions written by Santo Banerjee and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

This book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.

Frontiers Of Fractal Analysis

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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2022-07-07

Frontiers Of Fractal Analysis written by Santo Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-07 with Mathematics categories.

The history of describing natural objects using geometry is as old as the advent of science itself, in which traditional shapes are the basis of our intuitive understanding of geometry. However, nature is not restricted to such Euclidean objects which are only characterized typically by integer dimensions. Hence, the conventional geometric approach cannot meet the requirements of solving or analysing nonlinear problems which are related with natural phenomena, therefore, the fractal theory has been born, which aims to understand complexity and provide an innovative way to recognize irregularity and complex systems. Although the concepts of fractal geometry have found wide applications in many forefront areas of science, engineering and societal issues, they also have interesting implications of a more practical nature for the older classical areas of science. Since its discovery, there has been a surge of research activities in using this powerful concept in almost every branch of scientific disciplines to gain deep insights into many unresolved problems. This book includes eight chapters which focus on gathering cutting-edge research and proposing application of fractals features in both traditional scientific disciplines and in applied fields.

Interplay Of Fractals And Complexity In Mathematical Modelling And Physical Patterns

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Author : Santo Banerjee
language : en
Publisher: Springer Nature
Release Date : 2025-03-07

Interplay Of Fractals And Complexity In Mathematical Modelling And Physical Patterns written by Santo Banerjee and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-03-07 with Science categories.

This book presents selected, peer-reviewed contributions from the International Symposium on Mathematical Analysis of Fractals and Dynamical Systems—2023 (ISMAFDS - 2023), held at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Tamil Nadu in India during August 24-25, 2023. It offers readers an array of captivating connections between fractal theory and nonlinear dynamics across various physics sub-domains and mathematical modeling. Fractal geometry has been developed to describe irregular natural objects that defy characterization using Euclidean geometry. Fractal techniques, such as fractal dimension and fractal functions, prove effective in mathematically modeling real-world phenomena and forecasting future consequences. The impact of fractal theory on physical sciences is widely recognized, as natural phenomena frequently exhibit fractal structures. These new concepts revolutionize our understanding of the large-scale properties of matter distribution in the universe. The book aims to familiarize readers with recent developments in common fractal patterns found in statistical physics, quantum physics, and plasma physics. Furthermore, it highlights the relationship between fractals and nonlinear dynamics through innovative approaches in mathematical modeling. This publication caters to professionals in mathematics, physics, and computer science, and also serves as a helpful resource for non-specialists seeking to comprehend fractal and nonlinear dynamics concepts. It offers valuable applications for researchers in both pure and applied backgrounds of physics and engineering.

Advances In Electronics And Electron Physics

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Author :
language : en
Publisher: Academic Press
Release Date : 1994-05-18

Advances In Electronics And Electron Physics written by and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-05-18 with Computers categories.

Advances in Electronics and Electron Physics

Fractal Signatures In The Dynamics Of An Epidemiology

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Author : Santo Banerjee
language : en
Publisher: CRC Press
Release Date : 2023-12-01

Fractal Signatures In The Dynamics Of An Epidemiology written by Santo Banerjee and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-01 with Science categories.

The recent COVID-19 pandemic threw the world into complete chaos with its rapid and devastating spread. Scientists are still trying to obtain a better understanding of the patterns of COVID-19 and trying to get a deeper understanding of mutant strains and their pathogenicity by performing genomic sequences of more samples. Fractal-based analysis provides its unique forecasting policy to reduce the spread of COVID-19, and in general, of any outbreaks. The book presents fractal and multifractal models of COVID-19 and reviews the impact of the pandemic including epidemiology, genome organization, transmission cycle, and control strategies based on mathematical models towards developing an immune intervention. Also, it covers non-clinical aspects such as economic development with graphical illustrations, meeting the needs of onlookers outside the sector who desire additional information on the epidemic. The fractal signatures describe the fractal textures in the patterns of Coronavirus. Studies on the epidemiology of COVID-19 in relation with the fractals and fractal functions serve to exhibit its irregular chaotic nature. Moreover, the book with its wide coverage on the Hurst exponent analysis and the fractal dimension estimation, greatly aids in measuring the epidemiology.

Proceedings Of The 2nd International Conference On Nonlinear Dynamics And Applications Icnda 2024 Volume 2

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Author : Asit Saha
language : en
Publisher: Springer Nature
Release Date : 2024-10-10

Proceedings Of The 2nd International Conference On Nonlinear Dynamics And Applications Icnda 2024 Volume 2 written by Asit Saha and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-10 with Science categories.

This book covers the latest advancements and applications of nonlinear dynamics in various fields of science and engineering, presenting a curated selection of peer-reviewed contributions at the 2nd International Conference on Nonlinear Dynamics and Applications (ICNDA 2024) at Sikkim Manipal Institute of Technology (SMIT). Organized by the Department of Mathematics, SMIT, SMU, this international conference provides a platform for scientists, researchers, and inventors to share their findings and exchange ideas in the ever-evolving field of nonlinear dynamics. This book comprises three volumes. Volume 2 focuses on chaos, complexity, and fractals in dynamical systems. It covers topics such as novel methods for solving population balance models; analysis of fractal structures and nonlinear partial differential equations; dynamics of disease therapy and cytokine interactions; stability and behavior of predator-prey and ecological systems; fluid dynamics and heat transfer in nanofluids; and numerical and analytical approaches to material and structural optimization

Information Technology In Bio And Medical Informatics Itbam 2010

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Author : Sami Khuri
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-18

Information Technology In Bio And Medical Informatics Itbam 2010 written by Sami Khuri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-18 with Computers categories.

This book constitutes the thoroughly refereed proceedings of the First International Conference on InformationTechnology in Bio- and Medical Informatics, held in Bilbao, Spain, in September 2010. The 14 selected long papers and 8 selected short papers are divided in the following groups:Workflow management and database; Decision support and data management in biomedicine; Medical data modelling and information retrieval; Data mining in bioinformatics; Knowledge representation and data management in bioinformatics; Biological data and signal processing.

Fractal Geometry And Stochastics V

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Author : Christoph Bandt
language : en
Publisher: Birkhäuser
Release Date : 2015-07-08

Fractal Geometry And Stochastics V written by Christoph Bandt and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-08 with Mathematics categories.

This book collects significant contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five topical sections: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. Each part starts with a state-of-the-art survey followed by papers covering a specific aspect of the topic. The authors are leading world experts and present their topics comprehensibly and attractively. Both newcomers and specialists in the field will benefit from this book.

Musical Signal Processing

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Author : Curtis Roads
language : en
Publisher: Routledge
Release Date : 2013-12-19

Musical Signal Processing written by Curtis Roads and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-19 with Music categories.

Compiled by an international array of musical and technical specialists, this book deals with some of the most important topics in modern musical signal processing. Beginning with basic concepts, and leading to advanced applications, it covers such essential areas as sound synthesis (including detailed studies of physical modelling and granular synthesis) ,control signal synthesis, sound transformation (including convolution), analysis/resynthesis (phase vocodor, wavelets, analysis by chaotic functions), object-oriented and artificial intelligence representations, musical interfaces and the integration of signal processing techniques in concert performance.