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Author Cattani, Carlo, 1954-
Title Wavelet and wave analysis as applied to materials with micro or nanostructure / Carlo Cattani, Jeremiah Rushchitsky.
Imprint Hackensack, NJ : World Scientific Pub. Co., [2007]

Series Series on advances in mathematics for applied sciences ; v. 74
Series on advances in mathematics for applied sciences ; v. 74.
Subject Wavelets (Mathematics)
Nanostructures -- Mathematics.
Alt Name Rushchit︠s︡kiĭ, I︠A︡. I︠A︡. (I︠A︡rema I︠A︡roslavovich)
Description 1 online resource (x, 458 pages) : illustrations.
Bibliography Note Includes bibliographical references (pages 443-454) and index.
Contents Preface; Contents; 1. Introduction; 2. Wavelet Analysis; 2.1 Wavelet and Wavelet Analysis. Preliminary Notion; 2.1.1 The space L 2 (R); 2.1.2 The spaces L p (R) (p = 1); 2.1.3 The Hardy spaces H p (R) (p = 1); 2.1.4 The sketch scheme of wavelet analysis; 2.2 Rademacher, Walsh and Haar Functions; 2.2.1 System of Rademacher functions; 2.2.2 System of Walsh functions; 2.2.3 System of Haar functions; 2.3 Integral Fourier Transform. Heisenberg Uncertainty Principle; 2.4 Window Transform. Resolution; 2.4.1 Examples of window functions; 2.4.2 Properties of the window Fourier transform.
2.4.3 Discretization and discrete window Fourier transform2.5 Bases. Orthogonal Bases. Biorthogonal Bases; 2.6 Frames. Conditional and Unconditional Bases; 2.6.1 Wojtaszczyk's definition of unconditional basis (1997); 2.6.2 Meyer's definition of unconditional basis (1997); 2.6.3 Donoho's definition of unconditional basis (1993); 2.6.4 Definition of conditional basis; 2.7 Multiresolution Analysis; 2.8 Decomposition of the Space L 2 (R); 2.9 Discrete Wavelet Transform. Analysis and Synthesis; 2.9.1 Analysis: transition from the fine scale to the coarse scale.
2.9.2 Synthesis: transition from the coarse scale to the fine scale2.10 Wavelet Families; 2.10.1 Haar wavelet; 2.10.2 Strömberg wavelet; 2.10.3 Gabor wavelet; 2.10.4 Daubechies-Jaffard-Journé wavelet; 2.10.5 Gabor-Malvar wavelet; 2.10.6 Daubechies wavelet; 2.10.7 Grossmann-Morlet wavelet; 2.10.8 Mexican hat wavelet; 2.10.9 Coifman wavelet -- coiflet; 2.10.10 Malvar-Meyer-Coifman wavelet; 2.10.11 Shannon wavelet or sinc-wavelet; 2.10.12 Cohen-Daubechies-Feauveau wavelet; 2.10.13 Geronimo-Hardin-Massopust wavelet; 2.10.14 Battle-Lemarié wavelet; 2.11 Integral Wavelet Transform.
2.11.1 Definition of the wavelet transform2.11.2 Fourier transform of the wavelet; 2.11.3 The property of resolution; 2.11.4 Complex-value wavelets and their properties; 2.11.5 The main properties of wavelet transform; 2.11.6 Discretization of the wavelet transform; 2.11.7 Orthogonal wavelets; 2.11.8 Dyadic wavelets and dyadic wavelet transform; 2.11.9 Equation of the function (signal) energy balance; 3. Materials with Micro- or Nanostructure; 3.1 Macro-, Meso-, Micro-, and Nanomechanics; 3.2 Main Physical Properties of Materials; 3.3 Thermodynamical Theory of Material Continua.
3.4 Composite Materials3.5 Classical Model of Macroscopic (Effective) Moduli; 3.6 Other Microstructural Models; 3.6.1 Bolotin model of energy continualization; 3.6.2 Achenbach-Hermann model of effective stiffness; 3.6.3 Models of effective stiffness of high orders; 3.6.4 Asymptotic models of high orders; 3.6.5 Drumheller-Bedford lattice microstructural models; 3.6.6 Mindlin microstructural theory; 3.6.7 Eringen microstructural model. Eringen-Maugin model; 3.6.8 Pobedrya microstructural theory; 3.7 Structural Model of Elastic Mixtures; 3.7.1 Viscoelastic mixtures; 3.7.2 Piezoelastic mixtures.
Summary This seminal book unites three different areas of modern science: the micromechanics and nanomechanics of composite materials; wavelet analysis as applied to physical problems; and the propagation of a new type of solitary wave in composite materials, nonlinear waves. Each of the three areas is described in a simple and understandable form, focusing on the many perspectives of the links among the three. All of the techniques and procedures are described here in the clearest and most open form, enabling the reader to quickly learn and use them when faced with the new and more advanced problems.
Note Print version record.
ISBN 9789812709769 (electronic bk.)
9812709762 (electronic bk.)
9789812707840 (hardcover ; alk. paper)
9812707840 (hardcover ; alk. paper)
OCLC # 646769046
Additional Format Print version: Cattani, Carlo, 1954- Wavelet and wave analysis as applied to materials with micro or nanostructure. Hackensack, NJ : World Scientific Pub. Co., ©2007 (DLC) 2007016752