Research Catalog

Title

Wavelet and wave analysis as applied to materials with micro or nanostructure / Carlo Cattani, Jeremiah Rushchitsky.

Author

Cattani, Carlo, 1954-

Publication

Hackensack, NJ : World Scientific Pub. Co., [2007], ©2007.

Items in the Library & Off-site

Holdings

Details

Additional Authors

Rushchit︠s︡kiĭ, I︠A︡. I︠A︡. (I︠A︡rema I︠A︡roslavovich)

Description

x, 458 pages : illustrations; 24 cm.

Series Statement

Series on advances in mathematics for applied sciences ; v. 74

Uniform Title

Series on advances in mathematics for applied sciences ; v. 74.

Subjects

• Wavelets (Mathematics)
• Nanostructures > Mathematics

Bibliography (note)

• Includes bibliographical references (p. 443-454) and index.

Contents

1. Introduction -- 2. Wavelet Analysis -- 2.1. Wavelet and Wavelet Analysis. Preliminary Notion -- 2.2. Rademacher, Walsh and Haar Functions -- 2.3. Integral Fourier Transform. Heisenberg Uncertainty Principle -- 2.4. Window Transform. Resolution -- 2.5. Bases. Orthogonal Bases. Biorthogonal Bases -- 2.6. Frames. Conditional and Unconditional Bases -- 2.7. Multiresolution Analysis -- 2.8. Decomposition of the Space L[superscript 2](R) -- 2.9. Discrete Wavelet Transform. Analysis and Synthesis -- 2.10. Wavelet Families -- 2.11. Integral Wavelet Transform -- 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 Materials -- 3.5. Classical Model of Macroscopic (Effective) Moduli -- 3.6. Other Microstructural Models -- 3.7. Structural Model of Elastic Mixtures -- 3.8. Computer Modelling Data on Micro- and Nanocomposites -- 4. Waves in Materials -- 4.1. Waves Around the World -- 4.2. Analysis of Waves in Linearly Deformed Elastic Materials -- 4.3. Analysis of Waves in Nonlinearly Deformed Elastic Materials -- 4.4. Nonlinear Wave Equations -- 4.5. Comparison of Murnaghan and Signorini Approaches -- 5. Simple and Solitary Waves in Materials -- 5.1. Simple (Riemann) Waves -- 5.2. Solitary Elastic Waves in Composite Materials -- 5.3. New Hierarchy of Elastic Waves in Materials -- 6. Solitary Waves and Elastic Wavelets -- 6.1. Elastic Wavelets -- 6.2. The Link between the Trough Length and the Characteristic Length -- 6.3. Initial Profiles as Chebyshev-Hermite and Whittaker Functions -- 6.4. Some Features of the Elastic Wavelets -- 6.5. Solitary Waves in Mechanical Experiments -- 6.6. Ability of Wavelets in Detecting the Profile Features.

ISBN

• 9789812707840 (hardcover : alk. paper)
• 9812707840 (hardcover : alk. paper)

LCCN

2007016752

OCLC

• ocn123485620
• 123485620
• SCSB-5383309

Owning Institutions

Columbia University Libraries