LEADER 05741nam 2200685 a 450 001 9910458120603321 005 20200520144314.0 010 $a1-281-91891-1 010 $a9786611918910 010 $a981-270-976-2 035 $a(CKB)1000000000399360 035 $a(EBL)1679512 035 $a(OCoLC)879074277 035 $a(SSID)ssj0000269434 035 $a(PQKBManifestationID)11240979 035 $a(PQKBTitleCode)TC0000269434 035 $a(PQKBWorkID)10243712 035 $a(PQKB)11553964 035 $a(MiAaPQ)EBC1679512 035 $a(WSP)00006497 035 $a(Au-PeEL)EBL1679512 035 $a(CaPaEBR)ebr10255992 035 $a(CaONFJC)MIL191891 035 $a(EXLCZ)991000000000399360 100 $a20070419d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aWavelet and wave analysis as applied to materials with micro or nanostructure$b[electronic resource] /$fCarlo Cattani, Jeremiah Rushchitsky 210 $aHackensack, NJ $cWorld Scientific Pub. Co.$dc2007 215 $a1 online resource (473 p.) 225 1 $aSeries on advances in mathematics for applied sciences ;$vv. 74 300 $aDescription based upon print version of record. 311 $a981-270-784-0 320 $aIncludes bibliographical references (p. 443-454) and index. 327 $aContents; Preface; 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 327 $a2.4.3 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 327 $a2.9.2 Synthesis: transition from the coarse scale to the fine scale2.10 Wavelet Families; 2.10.1 Haar wavelet; 2.10.2 Stro?mberg wavelet; 2.10.3 Gabor wavelet; 2.10.4 Daubechies-Jaffard-Journe? 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-Lemarie? wavelet; 2.11 Integral Wavelet Transform 327 $a2.11.1 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 327 $a3.4 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 327 $a3.8 Computer Modelling Data on Micro- and Nanocomposites 330 $a This seminal book unites three different areas of modern science: the micromechanics and nanomechanics of composite materials; wavelet analysis as applied to physical problems; and the propagation of a new type of solitary wave in composite materials, nonlinear waves. Each of the three areas is described in a simple and understandable form, focusing on the many perspectives of the links among the three. All of the techniques and procedures are described here in the clearest and most open form, enabling the reader to quickly learn and use them when faced with the new and more advanced problem 410 0$aSeries on advances in mathematics for applied sciences ;$vv. 74. 606 $aWavelets (Mathematics) 606 $aNanostructures$xMathematics 608 $aElectronic books. 615 0$aWavelets (Mathematics) 615 0$aNanostructures$xMathematics. 676 $a620.1/18015152433 700 $aCattani$b Carlo$f1954-$0512688 701 $aRushchit?skii?$b I?A. I?A$g(I?Arema I?Aroslavovich)$0996608 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910458120603321 996 $aWavelet and wave analysis as applied to materials with micro or nanostructure$92284998 997 $aUNINA