ALBERT

Note: Zugl.: Greifswald, Univ., Diss., 2005

Note: Contents 1. Introduction 1.1 Historical Background 1.2 Some Examples of Spectral Methods 1.2.1 A Fourier Galerkin Method for the Wave Equation 1.2.2 A Chebyshev Collocation Method for the Heat Equation 1.2.3 A Legendre Galerkin with Numerical Integration (G-NI) Method for the Advection-Diffusion-Reaction Equation 1.2.4 A Legendre Tau Method for the Poisson Equation 1.2.5 Basic Aspects of Galerkin, Collocation, G-NI and Tau Methods 1.3 Three-Dimensional Applications in Fluids: A Look Ahead 2. Polynomial Approximation 2.1 The Fourier System 2.1.1 The Continuous Fourier Expansion 2.1.2 The Discrete Fourier Expansion 2.1.3 Differentiation 2.1.4 The Gibbs Phenomenon 2.2 Orthogonal Polynomials in (−1, 1) 2.2.1 Sturm-Liouville Problems 2.2.2 Orthogonal Systems of Polynomials 2.2.3 Gauss-Type Quadratures and Discrete Polynomial Transforms 2.3 Legendre Polynomials 2.3.1 Basic Formulas 2.3.2 Differentiation 2.3.3 Orthogonality, Diagonalization and Localization 2.4 Chebyshev Polynomials 2.4.1 Basic Formulas 2.4.2 Differentiation 2.5 Jacobi Polynomials 2.6 Approximation in Unbounded Domains 2.6.1 Laguerre Polynomials and Laguerre Functions 2.6.2 Hermite Polynomials and Hermite Functions 2.7 Mappings for Unbounded Domains 2.7.1 Semi-Infinite Intervals 2.7.2 The Real Line 2.8 Tensor-Product Expansions 2.8.1 Multidimensional Mapping 2.9 Expansions on Triangles and Related Domains 2.9.1 Collapsed Coordinates and Warped Tensor-Product Expansions 2.9.2 Non-Tensor-Product Expansions 2.9.3 Mappings 3. Basic Approaches to Constructing Spectral Methods 3.1 Burgers Equation 3.2 Strong and Weak Formulations of Differential Equations 3.3 Spectral Approximation of the Burgers Equation 3.3.1 Fourier Galerkin 3.3.2 Fourier Collocation 3.3.3 Chebyshev Tau 3.3.4 Chebyshev Collocation 3.3.5 Legendre G-NI 3.4 Convolution Sums 3.4.1 Transform Methods and Pseudospectral Methods 3.4.2 Aliasing Removal by Padding or Truncation 3.4.3 Aliasing Removal by Phase Shifts 3.4.4 Aliasing Removal for Orthogonal Polynomials 3.5 Relation Between Collocation, G-NI and Pseudospectral Methods 3.6 Conservation Forms 3.7 Scalar Hyperbolic Problems 3.7.1 Enforcement of Boundary Conditions 3.7.2 Numerical Examples 3.8 Matrix Construction for Galerkin and G-NI Methods 3.8.1 Matrix Elements 3.8.2 An Example of Algebraic Equivalence between G-NI and Collocation Methods 3.9 Polar Coordinates 3.10 Aliasing Effects 4. Algebraic Systems and Solution Techniques 4.1 Ad-hoc Direct Methods 4.1.1 Fourier Approximations 4.1.2 Chebyshev Tau Approximations 4.1.3 Galerkin Approximations 4.1.4 Schur Decomposition and Matrix Diagonalization 4.2 Direct Methods 4.2.1 Tensor Products of Matrices 4.2.2 Multidimensional Stiffness and Mass Matrices 4.2.3 Gaussian Elimination Techniques 4.3 Eigen-Analysis of Spectral Derivative Matrices 4.3.1 Second-Derivative Matrices 4.3.2 First-Derivative Matrices 4.3.3 Advection-Diffusion Matrices 4.4 Preconditioning 4.4.1 Fundamentals of Iterative Methods for Spectral Discretizations 4.4.2 Low-Order Preconditioning of Model Spectral Operators in One Dimension 4.4.3 Low-Order Preconditioning in Several Dimensions 4.4.4 Spectral Preconditioning 4.5 Descent and Krylov Iterative Methods for Spectral Equations 4.5.1 Multidimensional Matrix-Vector Multiplication 4.5.2 Iterative Methods 4.6 Spectral Multigrid Methods 4.6.1 One-Dimensional Fourier Multigrid Model Problem 4.6.2 General Spectral Multigrid Methods 4.7 Numerical Examples of Direct and Iterative Methods 4.7.1 Fourier Collocation Discretizations 4.7.2 Chebyshev Collocation Discretizations 4.7.3 Legendre G-NI Discretizations 4.7.4 Preconditioners for Legendre G-NI Matrices 4.8 Interlude 5. Polynomial Approximation Theory 5.1 Fourier Approximation 5.1.1 Inverse Inequalities for Trigonometric Polynomials 5.1.2 Estimates for the Truncation and Best Approximation Errors 5.1.3 Estimates for the Interpolation Error 5.2 Sturm-Liouville Expansions 5.2.1 Regular Sturm-Liouville Problems 5.2.2 Singular Sturm-Liouville Problems 5.3 Discrete Norms 5.4 Legendre Approximations 5.4.1 Inverse Inequalities for Algebraic Polynomials 5.4.2 Estimates for the Truncation and Best Approximation Errors 5.4.3 Estimates for the Interpolation Error 5.4.4 Scaled Estimates 5.5 Chebyshev Approximations 5.5.1 Inverse Inequalities for Polynomials 5.5.2 Estimates for the Truncation and Best Approximation Errors 5.5.3 Estimates for the Interpolation Error 5.6 Proofs of Some Approximation Results 5.7 Other Polynomial Approximations 5.7.1 Jacobi Polynomials 5.7.2 Laguerre and Hermite Polynomials 5.8 Approximation in Cartesian-Product Domains 5.8.1 Fourier Approximations 5.8.2 Legendre Approximations 5.8.3 Mapped Operators and Scaled Estimates 5.8.4 Chebyshev and Other Jacobi Approximations 5.8.5 Blended Trigonometric and Algebraic Approximations 5.9 Approximation in Triangles and Related Domains 6. Theory of Stability and Convergence 6.1 Three Elementary Examples Revisited 6.1.1 A Fourier Galerkin Method for the Wave Equation 6.1.2 A Chebyshev Collocation Method for the Heat Equation 6.1.3 A Legendre Tau Method for the Poisson Equation 6.2 Towards a General Theory 6.3 General Formulation of Spectral Approximations to Linear Steady Problems 6.4 Galerkin, Collocation, G-NI and Tau Methods 6.4.1 Galerkin Methods 6.4.2 Collocation Methods 6.4.3 G-NI Methods 6.4.4 Tau Methods 6.5 General Formulation of Spectral Approximations to Linear Evolution Problems 6.5.1 Conditions for Stability and Convergence: The Parabolic Case 6.5.2 Conditions for Stability and Convergence: The Hyperbolic Case 6.6 The Error Equation 7. Analysis of Model Boundary-Value Problems 7.1 The Poisson Equation 7.1.1 Legendre Methods 7.1.2 Chebyshev Methods 7.1.3 Other Boundary-Value Problems 7.2 Singularly Perturbed Elliptic Equations 7.2.1 Stabilization of Spectral Methods 7.3 The Eigenvalues of Some Spectral Operators 7.3.1 The Discrete Eigenvalues for Lu = −uxx 7.3.2 The Discrete Eigenvalues for Lu = −νuxx + βux 7.3.3 The Discrete Eigenvalues for Lu = ux 7.4 The Preconditioning of Spectral Operators 7.5 The Heat Equation 7.6 Linear Hyperbolic Equations 7.6.1 Periodic Boundary Conditions 7.6.2 Nonperiodic Boundary Conditions 7.6.3 The Resolution of the Gibbs Phenomenon 7.6.4 Spectral Accuracy for Non-Smooth Solutions 7.7 Scalar Conservation Laws 7.8 The Steady Burgers Equation Appendix A. Basic Mathematical Concepts A.1 Hilbert and Banach Spaces A.2 The Cauchy-Schwarz Inequality A.3 Linear Operators Between Banach Spaces A.4 The Fr´echet Derivative of an Operator A.5 The Lax-Milgram Theorem A.6 Dense Subspace of a Normed Space A.7 The Spaces Cm(Ω), m ≥ 0 A.8 Functions of Bounded Variation and the Riemann(-Stieltjes) Integral A.9 The Lebesgue Integral and Lp-Spaces A.10 Infinitely Differentiable Functions and Distributions A.11 Sobolev Spaces and Sobolev Norms A.12 The Sobolev Inequality A.13 The Poincar´e Inequality A.14 The Hardy Inequality A.15 The Gronwall Lemma Appendix B. Fast Fourier Transforms Appendix C. Iterative Methods for Linear Systems C.1 A Gentle Approach to Iterative Methods C.2 Descent Methods for Symmetric Problems C.3 Krylov Methods for Nonsymmetric Problems Appendix D. Time Discretizations D.1 Notation and Stability Definitions D.2 Standard ODE Methods D.2.1 Leap Frog Method D.2.2 Adams-Bashforth Methods D.2.3 Adams-Moulton Methods D.2.4 Backwards-Difference Formulas D.2.5 Runge-Kutta Methods D.3 Integrating Factors D.4 Low-Storage Schemes References Index

Note: Zugl.: München,Univ. der Bundeswehr, Diss., 2005

Note: Erscheinungsjahr in Vorlageform:c 1971

Note: Contents Preface Part I Anatomy of a cyclone 1 Anatomy of a cyclone 1.1 A 'typical' extra-tropical cyclone 1.2 Describing the atmosphere 1.3 Air masses and fronts 1.4 The structure of a typical extra-tropical cyclone Review questions 2 Mathematical methods in fluid dynamics 2.1 Scalars and vectors 2.2 The algebra of vectors 2.3 Scalar and vector fields 2.4 Coordinate systems on the Earth 2.5 Gradients of vectors 2.6 Line and surface integrals 2.7 Eulerian and Lagrangian frames of reference 2.8 Advection Review questions 3 Properties of fluids 3.1 Solids, liquids, and gases 3.2 Thermodynamic properties of air 3.3 Composition of the atmosphere 3.4 Static stability 3.5 The continuum hypothesis 3.6 Practical assumptions 3.7 Continuity equation Review questions 4 Fundamental forces 4.1 Newton's second law: F=ma 4.2 Body, surface, and line forces 4.3 Forces in an inertial reference frame 4.4 Forces in a rotating reference frame 4.5 The Navier-Stokes equations Review questions 5 Scale analysis 5.1 Dimensional homogeneity 5.2 Scales 5.3 Non-dimensional parameters 5.4 Scale analysis 5.5 The geostrophic approximation Review questions 6 Simple steady motion 6.1 Natural coordinate system 6.2 Balanced flow 6.3 The Boussinesq approximation 6.4 The thermal wind 6.5 Departures from balance Review questions 7 Circulation and vorticity 7.1 Circulation 7.2 Vorticity 7.3 Conservation of potential vorticity 7.4 An introduction to the vorticity equation Review questions 8 Simple wave motions 8.1 Properties of waves 8.2 Perturbation analysis 8.3 Planetary waves Review questions 9 Extra-tropical weather systems 9.1 Fronts 9.2 Frontal cyclones 9.3 Baroclinic instability Review questions Part II Atmospheric phenomena 10 Boundary layers 10.1 Turbulence 10.2 Reynolds decomposition 10.3 Generation of turbulence 10.4 Closure assumptions Review questions 11 Clouds and severe weather 11.1 Moist processes in the atmosphere 11.2 Air mass thunderstorms 11.3 Multi-cell thunderstorms 11.4 Supercell thunderstorms and tornadoes 11.5 Mesoscale convective systems Review questions 12 Tropical weather 12.1 Scales of motion 12.2 Atmospheric oscillations 12.3 Tropical cyclones Review questions 13 Mountain weather 13.1 Internal gravity waves 13.2 Flow over mountains 13.3 Downslope windstorms Review questions 14 Polar weather 14.1 Katabatic winds 14.2 Barrier winds 14.3 Polar lows Review questions 15 Epilogue: the general circulation 15.1 Fueled by the Sun 15.2 Radiative-convective equilibrium 15.3 The zonal mean circulation 15.4 The angular momentum budget 15.5 The energy cycle Appendix A - symbols Appendix Β - constants and units Bibliography Index

Note: CONTENTS Page Abstract Preface Conversion factors: U.S. customary to metric (SI) units of measurement Background Objectives Profiling system Approach Profiling method Data reduction and interpretation Results Conclusions Recommendations Literature cited Appendix A. Comparison of ground and aerial data

Note: CONTENTS Abstract Preface List of symbols Introduction I. Initiation of ice jams by partial surface obstructions A. Introductory remarks B. Experimental apparatus and procedure C. Dimensional analysis D. Presentation of results and discussion ΙΙ. Thickness of ice jams due to accumulation and transport of ice floes A. Introductory remarks B. Experimental apparatus and procedures C. Presentation of results E. Conclusion III. Compressive strength of floating fragmented ice covers A. Introductory remarks B. Experimental setup and procedure C. Presentation of results and discussion D. Conclusions Literature cited Appendix A: Experimental results on ice jam initiation Appendix B: Effect of surface tension on submergence velocity of ice floes Appendix C: Experimental results for ice jam thickness study Appendix D: Experimental results on compressive strength of fragmented ice cover

Note: CONTENTS Abstract Preface Conversion factors: US, customary to metric (SI) units of measurement Introduction Infrared camera Core samples State House State House Annex State Library Legislative Office Building Public Health Complex Highway Garage Fish and Game Offlces Supreme Court John O. Morton Building Department of Health and Welfare Laboratory Economics of roof reinsulation Conclusions and recommendations Literature cited

Note: CONTENTS Abstract Preface Conversion factors: U.S. customary to metric units of measurements Introduction The freezing proeess Icing observations Geographical distribution of icing and contributing meteorological conditions Extreme icing conditions Extremes of icc accumulation Prediction of icing occurrences Prediction of icing intensity and rate Control methods Measurement of icing rate Conclusions and recommendations Literature cited Appendix A. Maps of icing occurrence and rate Appendix B. Data for computing ship icing rates Appendix C. Estimation of ice accumulation

Note: CONTENTS Page Abstract Preface Introduction Low slope roof problems and repair costs Protected membrane roofs and materials Installations of protected membrane roofs Performance evaluation Test program Effectiveness Thermal efficiency Heat balance Internal cooling due to rain Moisture absorption and thermal conductivity of insulations Durability and life expectancy Fire resistance Patent considerations Costs of roofs Design considerations Proposed specifications Conclusions and recommendations Literature cited

Note: Contents Introduction The discovery Age of the island Island visit Other islands of grounded ice Discussion Literature cited

Note: Contents Abstract Preface Summary Conversion factors: U.S. customary to SI metric units Introduction Typical methods of constructing ice bridges Current knowledge Test program Objectives Equipment Procedure Data General Specific ice sheets Test results Conclusions Recommendations Literature cited

Note: CONTENTS Introduction Experimental work SCR samples CAG samples CMS samples UAG samples SI samples Optical system Equipment Procedure Photographic work Large cracks and fissures Small damage to the surface Small damage to the buIk Results Damage as a function of the position x of the focal point; n(x) Damage as a function of the number of irradiations #; n(#) Damage as a function of crystallographic orientation ĉ; n (ĉ); p (ĉ) Damage as a function of surface structure Damage as a function of age A; n (A) Damage as a function of wavelength λ; p(λ) Systematic study of damage as a function of W, t, m and s; n(W, t, m, s) Analysis Fracture in ice Mechanisms for optically generated damage in transparent dielectrics Discussion of the results Summary and conclusions Literature cited

Note: CONTENTS Page Abstract Preface Introduction Definition of revegetation Definition of restoration Objectives Some revegetation considerations Site conditions Nutrient regime Plant adaptations Native species vs introduced species Methods Seedbed preparation Seeding methods Timing of seeding Seed mixes Fertilization Agronomic grasses and legumes Selection criteria Laboratory evaluation Field evaluation Effect of revegetation methods Site conditions Maintenance of herbaceous cover Introduced woody species Native species — succession Significance of disturbance Primary succession Secondary succession Herbaceous native species Selection Laboratory evaluation Field evaluation Effect of revegetation methods Woody native species Selection Laboratory evaluation Field evaluation Native species and agronomic species, in combination Recommendations for research Summary Bibliography Appendix: Species tested

Note: CONTENTS Abstract Preface Nomenclature Introduction Description of study Sample preparation Test equipment and procedure Discussion of results Stress-density relationship Stress-deformation relationship Summary and conclusions Microstructural examination of artifically compacted snow Analytical techniques Results and discussion Conclusions Literature cited Appendix: Photographs of oscilloscope traces

Note: Peter Turner and Amanda Turner: Palaeomagnetic Applications in Hydrocarbon Exploration and Production: Introduction / Geological Society, London, Special Publications, 98:1-5, doi:10.1144/GSL.SP.1995.098.01.01 --- Magnetic Mineral Assemblages and Hydrocarbons --- Hans G. Machel: Magnetic mineral assemblages and magnetic contrasts in diagenetic environments — with implications for studies of palaeomagnetism, hydrocarbon migration and exploration / Geological Society, London, Special Publications, 98:9-29, doi:10.1144/GSL.SP.1995.098.01.02 --- Palaeomagnetic Properties of Hydrocarbon Reservoirs --- Hervé Perroud, Annick Chauvin, and Michel Rebelle: Hydrocarbon seepage dating through chemical remagnetization / Geological Society, London, Special Publications, 98:33-41, doi:10.1144/GSL.SP.1995.098.01.03 --- P. Turner, S. D. Burley, D. Rey, and J. Prosser: Burial history of the Penrith Sandstone (Lower Permian) deduced from the combined study of fluid inclusion and palaeomagnetic data / Geological Society, London, Special Publications, 98:43-78, doi:10.1144/GSL.SP.1995.098.01.04 --- Stuart A. Hall and Ian Evans: Palaeomagnetic and rock magnetic properties of hydrocarbon reservoir rocks from the Permian Basin, southeastern New Mexico, USA / Geological Society, London, Special Publications, 98:79-95, doi:10.1144/GSL.SP.1995.098.01.05 --- S. A. Johnson, P. Turner, A. Hartley, and D. Rey: Palaeomagnetic implications for the timing of hematite precipitation and remagnetization in the Carboniferous Barren Red Measures, UK southern North Sea / Geological Society, London, Special Publications, 98:97-117, doi:10.1144/GSL.SP.1995.098.01.06 --- Mark W. Hounslow, Barbara A. Maher, and Laurence Thistlewood: Magnetic mineralogy of sandstones from the Lunde Formation (late Triassic), northern North Sea, UK: origin of the palaeomagnetic signal / Geological Society, London, Special Publications, 98:119-147, doi:10.1144/GSL.SP.1995.098.01.07 --- Claus Beyer: Results from a palaeomagnetic investigation of the Brent Group sediments in wells 34/10–16 and 34/10–17 showing evidence for complete remagnetization of the sediment / Geological Society, London, Special Publications, 98:149-159, doi:10.1144/GSL.SP.1995.098.01.08 --- Magnetostratigraphic Applications --- Mark W. Hounslow, Barbara A. Maher, Laurence Thistlewood, and Kevin Dean: Magnetostratigraphic correlations in two cores from the late Triassic Lunde Formation, Beryl Field, northern North Sea, UK / Geological Society, London, Special Publications, 98:163-172, doi:10.1144/GSL.SP.1995.098.01.09 --- Kifaya N. Belkaaloul, Djafar M. Aissaoui, Michel Rebelle, and Gerard Sambet: Magnetostratigraphic correlations of the Jurassic carbonates from the Paris Basin: implications for petroleum exploration / Geological Society, London, Special Publications, 98:173-186, doi:10.1144/GSL.SP.1995.098.01.10 --- Eirik Hauger and Paul Van Veen: Application of magnetostratigraphy to Brent Group reservoir zonation in the Visund Field / Geological Society, London, Special Publications, 98:187-204, doi:10.1144/GSL.SP.1995.098.01.11 --- Gillian M. Turner and Ian D. Bryant: Application of a palaeomagnetic reversal stratigraphy to constrain well correlation and sequence stratigraphic interpretation of the Eocene C1 Sands, Maui Field, New Zealand / Geological Society, London, Special Publications, 98:205-221, doi:10.1144/GSL.SP.1995.098.01.12 --- R. Thompson and T. D. J. Cameron: Palaeomagnetic study of Cenozoic sediments in North Sea boreholes: an example of a magnetostratigraphic conundrum in a hydrocarbonproducing area / Geological Society, London, Special Publications, 98:223-236, doi:10.1144/GSL.SP.1995.098.01.13 --- Core Orientation and Susceptibility Logging --- T. C. Rolph, J. Shaw, T. R. Harper, and J. T. Hagan: Viscous remanent magnetization: a tool for orientation of drill cores / Geological Society, London, Special Publications, 98:239-243, doi:10.1144/GSL.SP.1995.098.01.14 --- E. A. Hailwood and F. Ding: Palaeomagnetic reorientation of cores and the magnetic fabric of hydrocarbon reservoir sands / Geological Society, London, Special Publications, 98:245-258, doi:10.1144/GSL.SP.1995.098.01.15 --- Reidar Løvlie and Paul Van Veen: Magnetic susceptibility of a 180 m sediment core: reliability of incremental sampling and evidence for a relationship between susceptibility and gamma activity / Geological Society, London, Special Publications, 98:259-266, doi:10.1144/GSL.SP.1995.098.01.16 --- H. Shi and D. H. Tarling: Magnetic field of a core barrel / Geological Society, London, Special Publications, 98:267-272, doi:10.1144/GSL.SP.1995.098.01.17 --- D. H. Tarling and H. Shi: Magnetic anisotropy of borehole core samples / Geological Society, London, Special Publications, 98:273-280, doi:10.1144/GSL.SP.1995.098.01.18 --- Structural Applications --- S. A. Stewart and K. C. Jackson: Palaeomagnetic analysis of fold closure growth and volumetrics / Geological Society, London, Special Publications, 98:283-295, doi:10.1144/GSL.SP.1995.098.01.19

Note: Contents Acknowledgments Chapter 1. Introduction 1.1 Discovery 1.2 General Introduction 1.3 Just for Fun — An Isotope Biography of Mr. Polychaete Chapter 2. Isotope Notation and Measurement Overview 2.1 The Necessary Minimum for Ecologists 2.2 Why Use the 5 Notation? 2.3 Why Is 8 a Good Substitute for % Heavy Isotope? 2.4 8 and the Ratio-of-Ratios 2.5 Chapter Summary Chapter 3. Using Stable Isotope Tracers Overview 3.1 Isotope Circulation in the Biosphere 3.2 Landscape Ecology and Isotope Maps 3.3 Community Ecology and Invasive Species in Food Webs 3.4 Life History Ecology and Animal Migrations 3.5 Plants, Microbes, and Scaling Up 3.6 Chapter Summary Chapter 4. Isotope Chi ("I Chi") Overview 4.1 Chocolate Isotopes 4.2 Oxygen in the Sea 4.3 Equations for Isotope Chi ("I Chi") 4.4 Building an I Chi Gain-Loss Model, Step by Step 4.5 Errors in I Chi Models 4.6 Exact Equations for I Chi Models 4.7 Cows in a Pasture 4.8 Chapter Summary Chapter 5. Mixing Overview 5.1 Isotope Mixing in Food Webs 5.2 Isotope Sourcery 5.3 Mixing Mechanics 5.4 Advanced Mixing Mechanics 5.5 Mixing Assumptions and Errors or the Art and Wisdom of Using Isotope Mixing Models 5.6 River Sulfate and Mass-Weighted Mixing 5.7 A Special Muddy Case and Mixing Through Time 5.8 The Qualquan Chronicles and Mixing Across Landscapes 5.9 Dietary Mixing, Turnover, and a Stable Isotope Clock 5.10 Chapter Summary Chapter 6. Isotope Additions Overview 6.1 Addition Addiction 6.2 The Golden Spike Award for Isotopes 6.3 Chapter Summary Chapter 7. Fractionation Overview 7.1 Fractionation Fundamentals 7.2 Isotopium and Fractionation in Closed Systems 7.3 A Strange and Routine Case 7.4 A Genuine Puzzle — Fractionation or Mixing? 7.5 Cracking the Closed Systems 7.6 Equilibrium Fractionation, Subtle Drama in the Cold 7.7 A Supply/Demand Model for Open System Fractionation 7.8 Open System Fractionation and Evolution of the Earth's Sulfur Cycle 7.9 Open System Legacies 7.10 Conducting Fractionation Experiments 7.11 Chapter Summary Chapter 8. Scanning the Future Overview 8.1 The Isotope Scanner 8.2 Mangrove Maude 8.3 The Beginner's Advantage—Imagine! 8.4 Chapter Summary Appendix. Important Isotope Equations and Useful Conversions Index Supplemental Electronic Materials on the Accompanying CD A. Chapter 1 Color Figures and Cartoon Problems B. Chapter 2 Color Figures and Cartoon Problems Technical Supplement 2A: Measuring Spiked Samples Technical Supplement 2B: Ion Corrections Technical Supplement 2C: The Ratio Notation and The Power of 1 C. Chapter 3 Color Figures and Cartoons Problems D. Chapter 4 Color Figures and Cartoons Problems I Chi Spreadsheets E. Chapters 5 Color Figures and Cartoons Problems I Chi Spreadsheets F. Chapter 6 Color Figure and Cartoon Problems I Chi Spreadsheet Technical Supplement 6A: How Much Isotope Should I Add? Technical Supplement 6B: Noisy Data and Data Analysis with Enriched Samples G. Chapter 7 Color Figures and Cartoons Problems I Chi Spreadsheets Technical Supplement 7A: A Chemist's View of Isotope Effects Technical Supplement 7B: Derivations of Closed System Isotope Equations H. Chapter 8 Color Figures and Cartoons Problems I. All Problems for Chapters 1-8 J. All Answers to Problems for Chapters 1-8 K. All Figures and Cartoons L. All I Chi Spreadsheets M. A Reading List

Note: Contents: 1. Introduction. 2. RC Filter. 3. General linear time invariant systems. 4. The seismometer. 5. The sampling process. 6. Analog-to-digital conversion. 7. From infinitely continuous to finite discrete. 8. The digital anti-alias filter. 9. Inverse and simulation filtering of digital seismograms. 10. The measurement of wavelet parameters from digital seismograms. References. Appendix: Solution to problems.