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Wavelet and wave analysis as applied to materials with micro or nanostructure /
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 desc...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hackensack, NJ :
World Scientific Pub. Co.,
©2007.
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| Colección: | Series on advances in mathematics for applied sciences ;
v. 74. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.