Atjaunināt sīkdatņu piekrišanu

Fractal Patterns in Nonlinear Dynamics and Applications [Hardback]

(University Putra Malaysia), , , (Sivanath Sastri College, Kolkata, India)
  • Formāts: Hardback, 206 pages, height x width: 234x156 mm, weight: 503 g, 8 Tables, black and white; 16 Line drawings, color; 31 Line drawings, black and white; 9 Halftones, black and white; 16 Illustrations, color; 40 Illustrations, black and white
  • Izdošanas datums: 05-Dec-2019
  • Izdevniecība: CRC Press Inc
  • ISBN-10: 1498741355
  • ISBN-13: 9781498741354
Citas grāmatas par šo tēmu:
  • Hardback
  • Cena: 178,26 €
  • Grāmatu piegādes laiks ir 3-4 nedēļas, ja grāmata ir uz vietas izdevniecības noliktavā. Ja izdevējam nepieciešams publicēt jaunu tirāžu, grāmatas piegāde var aizkavēties.
  • Daudzums:
  • Ielikt grozā
  • Piegādes laiks - 4-6 nedēļas
  • Pievienot vēlmju sarakstam
Fractal Patterns in Nonlinear Dynamics and ApplicationsPalielināt
  • Formāts: Hardback, 206 pages, height x width: 234x156 mm, weight: 503 g, 8 Tables, black and white; 16 Line drawings, color; 31 Line drawings, black and white; 9 Halftones, black and white; 16 Illustrations, color; 40 Illustrations, black and white
  • Izdošanas datums: 05-Dec-2019
  • Izdevniecība: CRC Press Inc
  • ISBN-10: 1498741355
  • ISBN-13: 9781498741354
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781498741354.html
Keywords:

The aim of this book is to describe the essence of fractals and multifractals dynamics in the applications of bioscience and engineering, bioinformatics, and financial time series. To reach these aims, the book will cover the basic idea, history, structure, methodology and analysis of fractals, the relationship between fractals and nonlinear dynamics, the applications of fractal and multifractal analysis in biomedical science, and how fractal signals and images are modelled by Iterated Function system. Illustrations and practical applications are given throughout the text to provide clear interpretations and explanations of various complex fractal objects and fractal modelling.

Preface v
Symbols xi
1 Scaling, Scale-invariance and Self-similarity
1(30)
1.1 Dimensions of physical quantity
4(1)
1.2 Buckingham Pi-theorem
5(3)
1.3 Examples to illustrate the significance of n-theorem
8(3)
1.4 Similarity
11(2)
1.5 Self-similarity
13(3)
1.6 Dynamic scaling
16(2)
1.7 Scale-invariance: Homogeneous function
18(3)
1.7.1 Scale invariance: Generalized homogeneous functions
20(1)
1.7.2 Dimension functions are scale-invariant
21(1)
1.8 Power-law distribution
21(10)
1.8.1 Examples of power-law distributions
22(1)
1.8.1.1 Euclidean geometry
22(1)
1.8.1.2 First return probability
23(5)
1.8.2 Extensive numerical simulation to verify powerlaw first return probability
28(3)
2 Fractals
31(38)
2.1 Introduction
31(2)
2.2 Euclidean geometry
33(2)
2.3 Fractals
35(10)
2.3.1 Recursive Cantor set
37(3)
2.3.2 Von Koch curve
40(2)
2.3.3 Sierpinski gasket
42(3)
2.4 Space of fractal
45(13)
2.4.1 Complete metric space
45(4)
2.4.2 Banach contraction mapping
49(2)
2.4.3 Completeness of the fractal space
51(7)
2.5 Construction of deterministic fractals
58(11)
2.5.1 Iterated function system
58(11)
3 Stochastic Fractal
69(28)
3.1 Introduction
69(1)
3.2 A brief description of stochastic process
70(1)
3.3 Dyadic Cantor Set (DCS): Random fractal
71(2)
3.4 Kinetic dyadic Cantor set
73(4)
3.5 Stochastic dyadic Cantor set
77(4)
3.6 Numerical simulation
81(4)
3.7 Stochastic fractal in aggregation with stochastic self-replication
85(10)
3.8 Discussion and summary
95(2)
4 Multifractality
97(32)
4.1 Introduction
97(2)
4.2 The Legendre transformation
99(2)
4.3 Theory of multifractality
101(4)
4.3.0.1 Properties of the mass exponent τ(q)
102(2)
4.3.1 Legendre transformation of τs(q): f(α) spectrum
104(1)
4.3.1.1 Physical significance of α and f(α)
105(1)
4.4 Multifractal formalism in fractal
105(5)
4.4.1 Deterministic multifractal
107(3)
4.5 Cut and paste model on Sierpinski carpet
110(5)
4.6 Stochastic multifractal
115(1)
4.7 Weighted planar stochastic lattice model
115(1)
4.8 Algorithm of the weighted planar stochastic lattice (WPSL)
116(3)
4.9 Geometric properties of WPSL
119(5)
4.9.0.1 Multifractal analysis to stochastic Sierpinski carpet
120(2)
4.9.0.2 Legendre transformation of the mass exponent τs(q): The f(α) spectrum
122(2)
4.10 Multifractal formalism in kinetic square lattice
124(5)
4.10.1 Discussions
126(3)
5 Fractal and Multifractal in Stochastic Time Series
129(24)
5.1 Introduction
129(1)
5.2 Concept of scaling law, monofractal and multifractal time series
130(3)
5.3 Stationary and non-stationary time series
133(2)
5.4 Fluctuation analysis on monofractal stationary and non-stationary time series
135(9)
5.4.1 Autocorrelation function
135(1)
5.4.2 Fourier based spectrum analysis
135(1)
5.4.3 Hurst exponent
136(3)
5.4.4 Fluctuation analysis (FA)
139(1)
5.4.5 Detrended fluctuation analysis
140(4)
5.5 Fluctuation analysis on stationary and non-stationary multifractal time series
144(6)
5.5.1 Wavelet transform modulus maxima
144(1)
5.5.2 Multifractal detrended fluctuation analysis
145(5)
5.6 Discussion
150(3)
6 Application in Image Processing
153(30)
6.1 Introduction
153(3)
6.1.1 Digital image
153(1)
6.1.2 Digital image processing
154(1)
6.1.3 Image segmentation
155(1)
6.2 Generalized fractal dimensions
156(6)
6.2.1 Monofractal dimensions
156(2)
6.2.2 Box dimension of image
158(2)
6.2.3 Multifractal dimension
160(2)
6.3 Image thresholding
162(2)
6.3.1 Multifractal dimensions: A threshold measure
162(2)
6.4 Performance analysis
164(2)
6.4.1 Evaluation measure for quantitative analysis
164(1)
6.4.2 Human visual perception
164(2)
6.5 Medical image processing
166(2)
6.6 Mid-sagittal plane detection
168(15)
6.6.1 Description of experimental MRI data
171(1)
6.6.2 Performance evaluation metrics
171(1)
6.6.3 Results and discussions
172(9)
6.6.4 Conclusion
181(2)
References 183(8)
Index 191
Santo Banerjee was a senior research associate in the Department of Mathematics, Politecnico di Torino, Italy from 2009-2011. He is now working in the Institute for Mathematical Research, University Putra Malaysia (UPM), and is also a founder member of the Malaysia-Italy Centre of Excellence in Mathematical Science, UPM, Malaysia. His research is mainly concerned with Nonlinear Dynamics, Chaos, Complexity and Secure Communication. He is a Managing Editor of The European Physical Journal Plus.

M K Hassan obtained a PhD from Brunel University, Uxbridge, London in 1997. He was a Humboldt research fellow from 2000-2001 and worked at Potsdam University, Germany. He is a senior professor in the Department of Physics, Dhaka University, Bangladesh currently. His primary research interests consist of problems which are far from equilibrium. In particular, he is involved in the study of a number of non-equilibrium phenomena, including theory of percolation under phase transition and critical phenomena, complex network theory, worked rigorously on stochastic fractals and multifractals, complex network theory, kinetics of aggregation and fragmentation, monolayer growth by deposition, nucleation and growth processes. The concept of symmetry, order, scaling, similarity and self-similarity, dynamic and finite-size scaling, fractal, multifractal, power-law, data-collapse, etc. have been the key tools of his research.

Sayan Mukherjee is working as Assistant Professor of Mathematics at Sivanath Shastri College, University of Calcutta, India. He has authored about 40 scientific papers in reputed journals and proceedings of the conferences and book chapters. His research interests include nonlinear time series analysis, biomedical and music signals, complexity analysis.

A Gowrisankar received his PhD (2017) degrees in Mathematics from the Gandhigram Rural Institute (Deemed to be University), Tamil Nadu, India. Further, he got institute postdoctoral fellowship from Indian Institute of Technology Guwahati, India. At present, he working as Assistant Professor in the Department of Mathematics, Vellore Institute of Technology, Vellore, India. His broad area of research includes fractal analysis, image processing and fractional calculus of fractal functions.