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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.
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.
This volume is the first of two containing selected papers from the
International Conference on Advances in Mathematical Sciences,
Vellore, India, December 2017 - Volume I. This meeting brought
together researchers from around the world to share their work,
with the aim of promoting collaboration as a means of solving
various problems in modern science and engineering. The authors of
each chapter present a research problem, techniques suitable for
solving it, and a discussion of the results obtained. These volumes
will be of interest to both theoretical- and application-oriented
individuals in academia and industry. Papers in Volume I are
dedicated to active and open areas of research in algebra,
analysis, operations research, and statistics, and those of Volume
II consider differential equations, fluid mechanics, and graph
theory.
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