ALBERT

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.

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.: Bremen, Univ., Diss., 2005

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

Note: CONTENTS Abstract Preface Introduction Equipment Data collection and reduction Data analysis and interpretation Point penetration resistance and material properties Lithologic and temperature profiles Casing penetration resistance Applications Shallow foundations Deep foundations Foundations in permafrost Correlations with laboratory tests Conclusions Selected bibliography Appendix A: Description of penetrometer and test procedures Appendix B: Point resistance and skin friction data

Note: CONTENT Abstract Preface Introduction Ice accretion parameters Physics of ice accretion Interaction between water droplets and flow field Time dependence in droplet trajectories Thermodynamic processes at the surface of the object Time dependence in the thermodynamics Time dependence of lesser order Numerical ice accretion model Major subroutines Options for droplet size variations Option for the helicopter rotor case Results Conclusions and future studies Literature cited Appendix A: Computer program

Note: CONTENTS Abstract Preface Introduction Test sites and ice cover properties Beam testing Results Discussion Conclusions Literature cited

Note: CONTENTS Abstract Preface Nomenclature Introduction Segregation freezing Analysis Heat conduction in the nascent ice layer Water flow in the unfrozen soil Heat transfer in the unfrozen soil Energy balance at the segregation-freezing front Numerical computation Literature cited Appendix A. Essence of Portnov’s method Appendix B. Frost-heaving without air available

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 Introduction Site description Background and objectives Project history Approach General Aircraft imagery and sensor data LANDSAT imagery Ground truth data Results and discussion Remote sensing techniques Conventional techniques Comparison of results Conclusions Advantages and disadvantages Applications Recommendations Literature cited

Note: In kyrill. Schr. - Legende russ. u. engl.

Note: CONTENTS Abstract Preface Introduction The protected membrane roof Winter construction considerations Construction costs Conclusion

Note: CONTENTS Abstract Preface Foreword Introduction Terminology Forces on individual cutters Torque force and tool force Forces on the rotor axis Tractive thrust and down thrust Alternative tool force formulations Vehicle traction Power/weight ratio Weight and balance Force, torque, speed and power Specific energy Efficiency and performance index Power density Power requirements for ejection of cuttings Hydrodynamic resistance in underwater cutting

Note: Contents Preface 1 Data Analysis in Earth Sciences 1.1 Introduction 1.2 Collecting Data 1.3 Types of Data 1.4 Methods of Data Analysis Recommended Reading 2 Introduction to MATLAB 2.1 MATLAB in Earth Sciences 2.2 Getting Started 2.3 The Syntax 2.4 Data Storage 2.5 Data Handling 2.6 Scripts and Functions 2.7 Basic Visualization Tools Recommended Reading 3 Univariate Statistics 3.1 Introduction 3.2 Empirical Distributions Measures of Central Tendency Measures of Dispersion 3.3 Example of Empirical Distributions 3.4 Theoretical Distributions Uniform Distribution Binomial or Bernoulli Distribution Poisson Distribution Normal or Gaussian Distribution Logarithmic Normal or Log-Normal Distribution Student's t Distribution Fisher's F Distribution Χ2 or Chi-Squared Distribution 3.5 Example ofTheoretical Distributions 3.6 Thet-Test 3.7 TheF-Test 3.8 The Χ2-Test Recommended Reading 4 Bivariate Statistics 4.1 Introduction 4.2 Pearson's Correlation Coefficient 4.3 Classical Linear Regression Analysis and Prediction 4.4 Analyzing the Residuals 4.5 Bootstrap Estimates of the Regression Coefficients 4.6 Jackknife Estimates of the Regression Coefficients 4.7 Cross Validation 4.8 Reduced Major Axis Regression 4.9 Curvilinear Regression Recommended Reading 5 Time-Series Analysis 5.1 Introduction 5.2 Generating Signals 5.3 Blackman-Tukey Autospectral Analysis 5.4 Blackman-Tukey Crossspectral Analysis 5.5 Interpolating and Analyzing Unevenly-Spaced Data 5.6 Evolutionary Blackman-Tukey Powerspectrum 5.7 Lomb-Scargle Powerspectrum 5.8 Wavelet Powerspectrum 5.9 Nonlinear Time-Series Analysis (by N. Marwarn) Phase Space Portrait Recurrence Plots Recommended Reading 6 Signal Processing 6.1 Introduction 6.2 Generating Signals 6.3 Linear Time-Invariant Systems 6.4 Convolution and Filtering 6.5 Comparing Functions for Filtering Data Series 6.6 Recursive and Nonrecursive Filters 6.7 Impulse Response 6.8 Frequency Response 6.9 Filter Design 6.10 Adaptive Filtering Recommended Reading 7 Spatial Data 7.1 Types of Spatial Data 7.2 The GSHHS Shoreline Data Set 7.3 The 2-Minute Gridded Global Elevation Data ETOPO2 7.4 The 30-Arc Seconds Elevation Model GTOPO30 7.5 The Shuttle Radar Topography Mission SRTM 7.6 Gridding and Contouring Background 7.7 Gridding Example 7.8 Comparison of Methods and Potential Artifacts 7.9 Statistics of Point Distributions Test for Uniform Distribution Test for Random Distribution Test for Clustering 7.10 Analysis of Digital Elevation Models (by R. Gebbers) 7.11 Geostatistics and Kriging (by R. Gebbers) Theorical Background Preceding Analysis Variography with the Classical Variogram Kriging Discussion of Kriging Recommended Reading 8 Image Processing 8.1 Introduction 8.2 Datastorage 8.3 Importing, Processing and Exporting Images 8.4 Importing, Processing and Exporting Satellite Images 8.5 Georeferencing Satellite Images 8.6 Digitizing from the Screen Recommended Reading 9 Multivariate Statistics 9.1 Introduction 9.2 Principal Component Analysis 9.3 Independent Component Analysis (by N. Marwan) 9.4 Cluster Analysis Recommended Reading 10 Statistics on Directional Data 10.1 Introduction 10.2 Graphical Representation 10.3 Empirical Distributions 10.4 Theoretical Distributions 10.5 Test for Randomness of Directional Data 10.6 Test for the Significance of a Mean Direction 10.7 Test for the Difference of Two Sets of Directions Recommended Reading General Index

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 Introduction Sea ice characteristics Ridging intensity Arctic terrain characteristics databank Digital terrain maps Digital laser profiles Standard terrain tapes Mobility analysis Terrestrial and coastal characteristics Northern Alaska Interior Alaska Arctic USSR Northern Canada and Greenland Climatological characteristics General features Surface winds Temperatures Precipitation and visibility Electromagnetic/optical propagation Ecological effects of SEV operations SK-5 tests Simulated SEV tests Conclusions Literature cited Additional CRREL SEV Bibliography