| List of Figures |
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xv | |
| Preface |
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xvii | |
| Authors |
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xix | |
| Chapter 1 Introduction |
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1 | (26) |
| Chapter 2 General Technique |
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27 | (24) |
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2.1 General Proper Space Definition-Eigenvector Problem for Perturbations over a Homogeneous Ground State |
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27 | (24) |
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2.1.1 General 1+1 D Problem. Linear Evolution in Homogeneous Case |
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27 | (3) |
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2.1.2 Transition to X-Representation |
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30 | (2) |
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2.1.3 Boundary Regime Propagation |
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32 | (5) |
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2.1.4 On Weak Nonlinearity Account Problems |
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37 | (3) |
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2.1.5 Weakly Inhomogeneous Ground State. Hyperbolic Equation |
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40 | (1) |
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2.1.6 Weak Inhomogeneity. Directed Waves |
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41 | (2) |
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2.1.7 Link to Spectral Theorem |
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43 | (8) |
| Chapter 3 One-Dimensional Problem in Hydrodynamics |
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51 | (24) |
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3.1 On the Hydro-Thermodynamic Relations for Quasi-Isentropic Processes |
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51 | (5) |
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3.2 Thermoconducting Flow of an Uniform Newtonian Gas. Modes, Projectors and Dynamic Equations. Acoustic Heating |
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56 | (6) |
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56 | (3) |
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3.2.2 Fluids Different from Ideal Gases |
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59 | (3) |
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3.3 Non-Newtonian Fluids. |
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62 | (2) |
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3.4 Acoustics of a Fluid Which Is Affected by Constant Mass Force |
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64 | (11) |
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3.4.1 Isothermal Atmosphere 1D Dynamics |
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64 | (3) |
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3.4.2 Examples of Projecting: Decomposition of the Total Field of Exclusively Entropy or Acoustic Parts and Energy Release with Mass Injection |
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67 | (2) |
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3.4.3 Dynamics of the Short-Scale Waves |
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69 | (6) |
| Chapter 4 Coupling of Sound with Vorticity: Acoustic Streaming |
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75 | (8) |
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4.1 3D Hydrodynamics and Vortex Mode |
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75 | (2) |
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77 | (3) |
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4.3 Examples of Acoustic Streaming: Weakly Difracting Beam and Stationary Waveform |
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80 | (3) |
| Chapter 5 Projecting in Flows with Relaxation: Effects of Sound in Acoustically Active Fluids |
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83 | (48) |
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5.1 Vibrationally Relaxing Gases |
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83 | (17) |
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5.2 Chemically Reacting Gases |
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100 | (8) |
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5.2.1 Remarks on the Thermal Self-Focusing of Sound |
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106 | (2) |
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5.3 The Nonlinear Effects of Sound in a Liquid with Relaxation Losses |
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108 | (6) |
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5.4 On the Nonlinear Effects of Magnetoacoustic Perturbations in a Perfectly Conducting Viscous and Thermoconducting Gas |
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114 | (17) |
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5.4.1 On the Nonlinear Interactions in a Plasma with Finite Electrical Conductivity |
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123 | (8) |
| Chapter 6 Boundary Layer Problem: Acoustic and Tollmienn-Schlichting Waves |
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131 | (16) |
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131 | (2) |
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6.2 Basic Equations for Compressible Fluid |
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133 | (1) |
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134 | (1) |
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6.4 The Tollmienn-Schlichting Mode |
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135 | (1) |
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136 | (1) |
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6.6 Peculiarities of Non-Commutative Projecting in the Inhomogeneous Linear Problem |
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137 | (2) |
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6.7 Nonlinear Flow: Coupled Dynamic Equations |
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139 | (2) |
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6.8 Resonance Interaction of Acoustic and T-S Modes |
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141 | (6) |
| Chapter 7 1D Electrodynamics |
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147 | (36) |
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7.1 Cauchy Problem for 1D Electrodynamics. Polarized Hybrid Fields |
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147 | (6) |
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7.1.1 The Problem Formulation Outline |
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147 | (1) |
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7.1.2 On Dynamical Projection Method Application: Cauchy Problem |
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148 | (2) |
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7.1.3 The Effect of a Cumulative Part of Interaction |
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150 | (1) |
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7.1.4 Dispersion Account, an Example |
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151 | (2) |
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7.2 General Dynamics Equations, SPE System |
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153 | (2) |
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7.2.1 The Shafer-Wayne (SPE) and Generalizations |
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154 | (1) |
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7.2.2 Discussion and Conclusions |
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154 | (1) |
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7.3 Boundary Regime Propagation in 1D Electrodynamics |
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155 | (12) |
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7.3.1 Statement of Problem |
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155 | (2) |
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7.3.2 Operators of Dielectric Permittivity and Magnetic Permeability |
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157 | (2) |
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7.3.3 Inverse Dielectric and Magnetic Operators |
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159 | (1) |
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7.3.4 Projecting Operators in 1D Electrodynamics with Unique Polarization: Boundary Regime Propagation |
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160 | (3) |
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7.3.5 On Integral Kernels Details |
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163 | (2) |
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7.3.6 Polarized Hybrid Fields. Equations for Left and Right Waves |
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165 | (2) |
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167 | (7) |
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167 | (1) |
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7.4.2 Theory of Initial Disturbance Propagation, Cauchy Problem Formulation |
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168 | (1) |
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7.4.3 The Projection Method for the Cauchy Problem |
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169 | (3) |
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7.4.4 Nonlinearity Account, Interaction of Polarized Waves: General Relations |
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172 | (2) |
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7.5 Comparison of Results Obtained with the Multiple Scale Method |
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174 | (2) |
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7.6 Projection Method for Boundary Regime Propagation |
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176 | (7) |
| Chapter 8 Metamaterials |
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183 | (42) |
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8.1 Statement of Problem for Metamaterials |
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183 | (4) |
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8.1.1 Two Words on Metamaterials |
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183 | (1) |
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8.1.2 Maxwell's Equations. Operators of Dielectric Permittivity and Magnetic Permeability |
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183 | (3) |
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8.1.3 Boundary Regime Problem |
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186 | (1) |
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8.2 Dynamic Projecting Operators |
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187 | (2) |
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8.3 Separated Equations and Definitions for Hybrid Waves |
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189 | (2) |
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191 | (1) |
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8.5 General Equations of 1D Wave Propagation in a Metamaterial That Is Described by the Lossless Drude Model |
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192 | (2) |
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8.6 Kerr Nonlinearity Account for Lossless Drude Metamaterials |
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194 | (6) |
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8.6.1 Equations of Interaction of Left and Right Waves with Kerr Effect |
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194 | (1) |
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8.6.2 Stationary Solution |
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195 | (5) |
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8.7 Statement of Problem for Waves with Two Polarizations |
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200 | (3) |
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8.7.1 Maxwell's Equations. Boundary Regime Problem |
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200 | (3) |
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8.8 Dynamic Projecting Operators |
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203 | (4) |
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8.9 Separated Equations and Definition for Left and Right Waves |
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207 | (2) |
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8.10 General Nonlinearity Account |
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209 | (2) |
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8.11 Kerr Nonlinearity Account for Lossless Drude Metamaterials |
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211 | (2) |
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8.11.1 Equations of Interaction of the Waves via Kerr Effect |
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211 | (2) |
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213 | (7) |
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8.12.1 Linear Wave Packets for the Right Waves |
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213 | (1) |
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8.12.2 Unidirectional Wavetrains Interaction |
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214 | (4) |
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8.12.3 Coupled Nonlinear Schrodinger Equations |
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218 | (2) |
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8.13 Stationary Solutions of SPE System for Unidirectional Waves |
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220 | (5) |
| Chapter 9 Waves in Waveguides |
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225 | (36) |
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9.1 Electromagnetic Waves in Metal Rectangular Waveguide Filled with a Material: Projecting Operators Method |
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225 | (8) |
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9.1.1 Maxwell's Equations for a Waveguide. Boundary Conditions |
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225 | (1) |
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9.1.2 The Transversal Waveguide Modes Evolution |
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226 | (7) |
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233 | (1) |
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9.3 Polarizations and Directed Modes in Rectangular Waveguides |
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233 | (1) |
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9.4 Cylindrical Dielectric Waveguides |
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233 | (7) |
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9.4.1 On Transversal Fiber Modes |
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233 | (1) |
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9.4.2 A Formulation and Solution of Linear Problem, a Step to Dynamic Projecting Procedure |
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234 | (1) |
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9.4.3 Transition to Bessel Functions Basis |
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235 | (5) |
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9.5 Dynamical Projecting Operators |
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240 | (6) |
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9.5.1 z-Evolution System and Transition to w-Domain |
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240 | (5) |
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9.5.2 Projection Operators in Time Domain. Dispersion Account |
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245 | (1) |
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9.6 Including Nonlinearity |
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246 | (10) |
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9.6.1 Application of Projection Operators |
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254 | (2) |
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256 | (5) |
| Chapter 10 Waves in 3D Space |
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261 | (14) |
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261 | (1) |
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10.2 Basic Equations and Starting Points |
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262 | (2) |
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10.3 Determination of Operator Eigenvalues, Eigenvectors and Projecting Operators for a Full System of Maxwell's Equations |
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264 | (5) |
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10.3.1 Projection by Operator P1 Application |
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266 | (1) |
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10.3.2 Projection with Operator P2 |
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267 | (1) |
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10.3.3 Results for Other Projector Operator |
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267 | (2) |
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10.4 The Case of the Linear Dependence of Electromagnetic Induction on the Electric Field and the Magnetic Induction on the Magnetic Field |
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269 | (3) |
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10.4.1 Projection Operators |
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270 | (2) |
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10.5 Examples with a Symmetry Account |
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272 | (1) |
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10.5.1 Spherical Geometry |
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272 | (1) |
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10.5.2 Quasi-One-Dimensional Geometry |
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272 | (1) |
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273 | (2) |
| Index |
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275 | |
Lisainfo e-raamatute kohta