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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.

Statistical physics. --- Computational complexity. --- System theory. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Complexity. --- Complex Systems. --- Systems, Theory of --- Systems science --- Science --- Complexity, Computational --- Electronic data processing --- Machine theory --- Physics --- Mathematical statistics --- Philosophy --- Statistical methods --- Interpolation. --- Approximation theory --- Numerical analysis

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This book provides a comprehensive overview of statistical descriptions of turbulent flows. Its main objectives are to point out why ordinary perturbative treatments of the Navier–Stokes equation have been rather futile, and to present recent advances in non-perturbative treatments, e.g., the instanton method and a stochastic interpretation of turbulent energy transfer. After a brief introduction to the basic equations of turbulent fluid motion, the book outlines a probabilistic treatment of the Navier–Stokes equation and chiefly focuses on the emergence of a multi-point hierarchy and the notion of the closure problem of turbulence. Furthermore, empirically observed multiscaling features and their impact on possible closure methods are discussed, and each is put into the context of its original field of use, e.g., the renormalization group method is addressed in relation to the theory of critical phenomena. The intended readership consists of physicists and engineers who want to get acquainted with the prevalent concepts and methods in this research area.

Computational complexity. --- Vibration. --- Dynamical systems. --- Dynamics. --- Statistical physics. --- Fluid mechanics. --- Fluids. --- Complexity. --- Vibration, Dynamical Systems, Control. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Engineering Fluid Dynamics. --- Fluid- and Aerodynamics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Cycles --- Sound --- Complexity, Computational --- Electronic data processing --- Machine theory --- Hydraulics --- Hydrostatics --- Permeability --- Hydromechanics --- Continuum mechanics --- Mathematical statistics --- Statistical methods --- Turbulence --- Mathematical models.

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This book provides an in-depth account of the fascinating but far from simple actions and processes that take place when a brass instrument is played. Written by three leading researchers in brass instrument acoustics who are also experienced brass players, it draws together the many recent advances in our understanding of the subtly interrelated factors shaping the musician's control of the instrument's sound. The reader is introduced to models of sound generation, propagation and radiation. In particular, the current understanding of the behaviour of the player's lips, the modes of vibration of the air column inside the instrument, and the radiation of sound from a brass instrument bell are explained. The functions of the mouthpiece and of mutes are discussed. Spectral enrichment arising from nonlinear propagation of the internal sound wave in loud playing is shown to be an important influence on the timbre of many types of brass instrument. The characteristics of brass instruments in contemporary use (including cornets, trumpets, french horns, trombones and tubas) are identified, and related to those of the great variety of instruments at earlier stages in the evolution of the brass family. This copiously illustrated book concludes with case studies of the recreation of ancient instruments and some of the current applications of electronics and information technology to brass instrument performance. While most of the material presented is accessible by a general readership, the topic of musical instrument modelling is developed at a mathematical level which makes it a useful academic resource for advanced teaching and research. Written by three internationally acknowledged experts in the acoustics and organology of brass instruments who are also experienced brass instrument players. Provides both an accessible introduction to brass instrument science and a review of recent research results and mathematical modeling techniques Represents the first monograph on the science underlying the design and performance of musical instruments of the brass family.

Acoustics. --- Acoustical engineering. --- Vibration. --- Dynamical systems. --- Dynamics. --- Statistical physics. --- Engineering Acoustics. --- Vibration, Dynamical Systems, Control. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Physics --- Mathematical statistics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Cycles --- Sound --- Acoustic engineering --- Sonic engineering --- Sonics --- Sound engineering --- Sound-waves --- Engineering --- Statistical methods --- Industrial applications --- Brass instruments --- Brasses (Musical instruments) --- Wind instruments

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The book offers a novel approach to the study of the complex dynamics of cities. It is based on (1) Synergetics as a science of cooperation and selforganization, (2) information theory including semantic and pragmatic aspects, and optimization principles, (3) a theory of steady state maintenance, and of (4) phase transition, i.e. qualitative changes of structure or behavior. From this novel theoretical vantage point, the book addresses particularly three issues that stand at the core of current discourse on cities: Urban Scaling, Smart Cities and City Planning. An important consequence of “the 21st century as the age of cities”, is that the study of cities currently attracts scientists from a variety of disciplines, ranging from physics, mathematics and computer science, through urban studies, architecture, planning and human geography, to economics, psychology, sociology, public administration and more. The book is thus likely to attract scholars, researchers and students of these research domains, of complexity theories of cities, as well as of general complexity theory. In addition, it is directed also to practitioners of urbanism, city planning and urban design.

Transportation engineering. --- Traffic engineering. --- Computational complexity. --- Statistical physics. --- Transportation Technology and Traffic Engineering. --- Complexity. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Physics --- Mathematical statistics --- Complexity, Computational --- Electronic data processing --- Machine theory --- Engineering, Traffic --- Road traffic --- Street traffic --- Traffic, City --- Traffic control --- Traffic regulation --- Urban traffic --- Highway engineering --- Transportation engineering --- Civil engineering --- Engineering --- Statistical methods

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This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.

Computers. --- Statistical physics. --- Dynamical systems. --- Theory of Computation. --- Applications of Nonlinear Dynamics and Chaos Theory. --- Complex Systems. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Mathematical statistics --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Statistical methods --- Attractors (Mathematics) --- Attracting sets (Mathematics) --- Attractors of a dynamical system --- Dynamical system, Attractors of --- Sets, Attracting (Mathematics) --- Differentiable dynamical systems --- Attractors (Mathematics).