Note: Intro -- Foreword -- Preface -- Contents -- 1 Introduction -- Part I Dynamics -- 2 Deterministic Dynamical Systems -- 2.1 Introduction -- 2.2 States and Their Time Evolution -- 2.3 Discrete Systems and Iterative Maps -- 2.4 Continuous Systems and ODEs -- 2.5 Continuous Systems and PDEs -- 2.6 Observables and Parameters -- 2.7 Invariant Sets and Orbits -- 2.8 Summary -- References -- 3 Linear and Integrable Systems -- 3.1 Introduction -- 3.2 Vector Spaces -- 3.3 Linear Dynamical Systems -- 3.4 Eigenanalysis -- 3.5 Nonlinear Interactions -- 3.6 Integrable Systems -- 3.7 The KAM Theorem -- 3.8 Dimensions of Dynamical Systems -- 3.9 Summary -- References -- 4 Stability and Long-Time Behavior -- 4.1 Introduction -- 4.2 Topology -- 4.3 Stability -- 4.4 Linear Stability of Fixed Points -- 4.5 Liapunov Function -- 4.6 Poincaré Maps -- 4.7 Linear Stability of Periodic Orbits -- 4.8 Sensitivity to Initial Conditions -- 4.9 Limiting Sets and Attractors -- 4.10 State Space Portrait -- 4.11 Ingredients of Chaos -- 4.12 Bifurcations -- 4.13 Summary -- References -- 5 Ergodic Theory -- 5.1 Introduction -- 5.2 The Evolution of Volumes -- 5.3 Measure Spaces -- 5.4 Invariant Measure -- 5.5 Poincaré Recurrence Theorem -- 5.6 Time Averages -- 5.7 Ergodic Measures -- 5.8 Ergodic System -- 5.9 Mixing and Exact Systems -- 5.10 Shift Map -- 5.11 Summary -- References -- 6 Numerical Algorithms -- 6.1 Introduction -- 6.2 Round-Off Error -- 6.3 Truncation Errors -- 6.4 Stability -- 6.5 Numerical Diffusion and Dispersion -- 6.6 Conservation Laws -- 6.7 Spectral and Finite Element Models -- 6.8 Summary -- Reference -- Part II Probability -- 7 Probability Theory -- 7.1 Introduction -- 7.2 Probability Spaces -- 7.3 Conditional Probabilities and Statistical Independence -- 7.4 Random Variables and Their Distributions -- 7.5 Expectation Values -- 7.6 Moments. , 7.7 Bi- and Multivariate Random Variables -- 7.8 Some Probability Distributions -- 7.9 Convergence of Sequences of Random Variables -- 7.10 Weak and Strong Law of Large Numbers -- 7.11 Central Limit Theorem -- 7.12 Extreme Value Theory -- 7.13 Summary -- Reference -- 8 Discrete-Time Stochastic Processes -- 8.1 Introduction -- 8.2 The Canonical Probability Space -- 8.3 Discrete Stochastic Processes -- 8.4 Independent Chains -- 8.5 Markov Chains -- 8.6 The Markov Operator -- 8.7 Asymptotic Behavior -- 8.8 Random Walks -- 8.9 Summary -- 9 Continuous-Time Stochastic Processes -- 9.1 Introduction -- 9.2 Separable Modifications -- 9.3 Markov Processes -- 9.4 Master Equation -- 9.5 Fokker-Planck Equation -- 9.6 The Wiener Process -- 9.7 Gaussian White Noise -- 9.8 Summary -- References -- 10 Information Entropy -- 10.1 Introduction -- 10.2 Information Content -- 10.3 Entropy of a Discrete Random Variable -- 10.4 Entropy of Bi- and Multivariate Random Variables -- 10.5 Asymptotic Equipartition Theorem -- 10.6 Entropy of Continuous Random Variables -- 10.7 Coarse-Graining and Smoothing -- 10.8 The Principle of Maximum Entropy -- 10.9 Summary -- References -- Part III Probability in Dynamical Evolution -- 11 Time Evolution of Broadened Initial States -- 11.1 Introduction -- 11.2 Broadened Versus Pure Initial States -- 11.3 Frobenius-Perron Operator -- 11.4 Liouville Equation -- 11.5 Stationary Densities -- 11.6 Convergence Toward Stationary Densities -- 11.7 Behavior of the Entropy -- 11.8 Summary -- References -- 12 Stochastic Processes Generated by Observables -- 12.1 Introduction -- 12.2 Relation Between Stochastic Processes and Dynamical Systems -- 12.3 Coarse-Graining -- 12.4 Elimination of Variables -- 12.5 Adiabatic Elimination of Fast Variables -- 12.6 Summary -- Reference -- 13 Stochastic Dynamical Systems -- 13.1 Introduction. , 13.2 Autoregressive Processes -- 13.3 Multiplicative Processes -- 13.4 Langevin Equation -- 13.5 Stochastic Differential Equations -- 13.6 Summary -- References -- Part IV Probability in Scientific Reasoning -- 14 Interpretations of Probability -- 14.1 Introduction -- 14.2 The Physicalist's Interpretation -- 14.3 The Frequentist's Interpretation -- 14.4 The Logicist's Interpretation -- 14.5 The Subjectivist's Interpretation -- 14.6 The Utilitarian Approach -- 14.7 Summary -- References -- 15 Parameter Estimation and Hypothesis Testing -- 15.1 Introduction -- 15.2 Sampling -- 15.3 Estimator Versus Estimate -- 15.4 Interpretation of Estimates -- 15.5 Maximum Likelihood Estimators -- 15.6 Mean Square Error -- 15.7 Minimizing Risk -- 15.8 Hypothesis Testing -- 15.9 Type I and II Errors -- 15.10 Likelihood Ratio Tests -- 15.11 Summary -- 16 Bayesian Inferences -- 16.1 Introduction -- 16.2 Bayes Theorem -- 16.3 The Bayesian Paradigm -- 16.4 Bayesian Estimators -- 16.5 Bayesian Hypothesis Testing -- 16.6 Comparison of Frequentist and Bayesian Approach -- 16.7 Choice of Prior -- 16.8 Statistical Inference -- 16.9 Decisions -- 16.10 Data Assimilation -- 16.11 Summary -- References -- Part V Probability in Physics -- 17 Equilibrium Statistical Mechanics -- 17.1 Introduction -- 17.2 Thermostatics -- 17.3 Implications of PME -- 17.4 The Micro-canonical Ensemble -- 17.5 Quantum-Mechanical Corrections -- 17.6 The Canonical Ensemble -- 17.7 Macro-Variables -- 17.8 The Thermodynamic Limit -- 17.9 The Ideal Gas of Particles -- 17.10 Summary -- References -- 18 Non-equilibrium Statistical Mechanics -- 18.1 Introduction -- 18.2 Fluid Dynamics -- 18.3 The Continuum Limit of a N-particle System -- 18.4 Average of a N-particle System -- 18.5 Applying PME -- 18.6 Summary -- References -- 19 Foundational Issues of Statistical Mechanics -- 19.1 Introduction. , 19.2 The Arrow of Time Versus Time-Reversible Systems -- 19.3 Entropy -- 19.4 Dynamical Constraints -- 19.5 Irreversibility and Microscopic Dynamics -- 19.6 Ensemble -- 19.7 Summary -- References -- 20 Quantum Mechanics -- 20.1 Introduction -- 20.2 The Pragmatic Rules -- 20.3 Pure States -- 20.4 Mixed States -- 20.5 Entangled States -- 20.6 Quantum Probability -- 20.7 Classical Versus Quantum Logic -- 20.8 The Foundational Issues -- 20.9 Summary -- References -- Appendix A Classical Mechanics -- A.1 Newtonian dynamics -- A.2 Hamilton's principle -- A.3 Hamiltonian Dynamics -- A.4 Harmonic Oscillator -- Appendix B Thermostatics -- B.1 Thermodynamic Variables and Processes -- B.2 First Law of Thermodynamics -- B.3 Second Law of Thermodynamics -- B.4 Thermodynamic Potentials -- B.5 Thermodynamic Limit -- Appendix C Fluid Dynamics -- C.1 Irreversible Fluid Dynamics -- C.2 Navier-Stokes and Euler Equations -- C.3 Eulerian Versus Lagrangian Description -- C.4 Variational Principles for Perfect Fluids -- Appendix D Some Proofs and Explicit Calculations -- D.1 Derivation of the Lorenz Equations -- D.2 Inverse Scattering Transform of the KdV Equation -- D.3 Adiabatic Elimination of Fast Variables -- D.4 Balance Equations -- D.5 Reduced Densities -- Appendix E Mathematical Tools, Conventions, and Notation -- E.1 Sets -- E.2 Functions -- E.3 Groups -- E.4 Vector Spaces -- E.5 Normed Spaces -- E.6 Metric Spaces -- E.7 Limits -- E.8 Linear Operators -- E.9 Matrix Notation -- E.10 Dirac Notation -- E.11 Eigenvectors and Eigenvalues -- E.12 Topological Sets -- E.13 Measure Spaces -- E.14 Two Important Inequalities -- E.15 Permutations and Combinations -- E.16 Calculus of Variation -- E.17 Legendre Transformation -- E.18 Classical Propositional Logic -- E.19 Fourier Transforms and Series -- E.20 Jacobian. , E.21 Stirling's Formula -- References -- Index.

Note: Intro -- Preface -- Contents -- List of Contributors -- Editors' Biography -- Part I Introduction -- 1 Bayesian Nonparametric Models -- 1.1 Nonparametric Bayesian Inference in Biostatistics and Bioinformatics -- 1.2 Dirichlet Process -- 1.2.1 DP Mixture -- 1.2.2 Generalizations of the DP -- 1.3 Dependent Dirichlet Process -- 1.3.1 Variations of the DDP -- 1.4 Polya Tree -- 1.5 Gaussian Process -- 1.6 Conclusion -- References -- 2 Bayesian Nonparametric Biostatistics -- 2.1 Introduction -- 2.1.1 Organization of this Chapter -- 2.2 Comments on the DPM and MPT -- 2.3 Longitudinal Data: Semiparametric Autoregressive Modeling -- 2.3.1 The Semiparametric Model -- 2.3.2 Model Specification for Hormone Data -- 2.4 Survival Data: Nonparametric and Semiparametric Modeling -- 2.4.1 Nonparametric and Semiparametric Survival Regression: A Selective Historical Perspective -- 2.4.2 Semiparametric Models for Survival Data with Time-Dependent Covariates -- 2.4.3 A Nonparametric Survival Regression Model -- 2.5 Joint Modeling of Longitudinal and Survival Data -- 2.5.1 Medfly Data Analysis -- 2.6 Medical Diagnostic Data -- 2.6.1 ROC Regression -- 2.6.2 A Semiparametric ROC Regression Model in the Absence of a Gold Standard Test -- 2.6.3 Joint Longitudinal Diagnostic Outcome Modeling and Analysis -- 2.7 Final Remarks -- References -- Part II Genomics and Proteomics -- 3 Bayesian Shape Clustering -- 3.1 Introduction -- 3.2 Methodology -- 3.2.1 Inner Product Matrix Using Elastic Shape Analysis -- 3.2.2 Likelihood Specification for the Inner Product Matrix -- 3.2.3 Priors and Hyperpriors -- 3.2.3.1 Hyperpriors -- 3.2.3.2 Posterior Computation and Final Selection of Clusters -- 3.3 Experimental Results -- 3.3.1 Synthetic Examples -- 3.3.2 Clustering Real Protein Sequences -- References -- 4 Estimating Latent Cell Subpopulations with Bayesian Feature Allocation Models. , 4.1 Introduction -- 4.1.1 Biological and Statistical Background -- 4.1.2 Bayesian Feature Allocation Models for Tumor Heterogeneity -- 4.1.3 Existing Methods -- 4.2 Probability Model -- 4.2.1 Models on SNVs Alone -- 4.2.1.1 The Finite IBP -- 4.2.2 Linked Models on SNVs and CNVs -- 4.2.2.1 Representing CNV (L) and SNV (Z) -- 4.2.2.2 Sampling Model and Prior -- 4.2.2.3 The Categorical Indian Buffet Process -- 4.2.3 Posterior Simulation -- 4.3 Simulation -- 4.4 Lung Cancer Data -- 4.5 Conclusions -- References -- 5 Species Sampling Priors for Modeling Dependence: An Application to the Detection of Chromosomal Aberrations -- 5.1 Introduction -- 5.2 Species Sampling Sequences: Basics and Extensions -- 5.3 A Beta-GOS Hierarchical Model -- 5.3.1 MCMC Posterior Sampling -- 5.4 A Comparison with Hidden Semi-Markov Models -- 5.5 Application to the Analysis of Array CGH Data -- 5.6 Final Remarks -- References -- 6 Modeling the Association Between Clusters of SNPs and Disease Responses -- 6.1 Introduction -- 6.2 Clustering Through Bayesian Nonparametric Models -- 6.3 Application to SNPs: Data Description and Model Specification -- 6.3.1 SNP Data for Beginners -- 6.3.2 Cluster Model Specification -- 6.3.3 Association Study Between SNP Clusters and Disease -- 6.4 Application to SNPs: Bayesian Inference -- 6.5 Conclusions -- References -- 7 Bayesian Inference on Population Structure: From Parametricto Nonparametric Modeling -- 7.1 Introduction -- 7.2 Parametric Modeling -- 7.2.1 Models with and Without Admixture -- 7.2.2 Extensions: Linked Loci and Correlated Allele Frequencies -- 7.3 Nonparametric Modeling -- 7.3.1 Models with and Without Admixture -- 7.3.2 The MCMC Algorithm -- 7.4 Discussion and Concluding Remarks -- References -- 8 Bayesian Approaches for Large Biological Networks -- 8.1 Introduction -- 8.2 Introduction to Graphical Models. , 8.2.1 Undirected Graphical Models -- 8.2.1.1 Bayesian Estimation of Undirected Graphical Models -- 8.2.2 Directed Graphical Models -- 8.2.2.1 Bayesian Estimation of Gaussian DAG Models -- 8.3 Bayesian Nonlinear Model Selection for Gene Regulatory Networks -- 8.3.1 Model -- 8.3.2 Application to GBM Data -- 8.4 Efficient Approaches for Undirected Networks -- 8.4.1 Inference on Directed Graphical Models Via Regression Modeling -- 8.4.2 An Undirected Graphical Model Analysis of GBM Data -- 8.5 Discussion -- References -- 9 Nonparametric Variable Selection, Clustering and Predictionfor Large Biological Datasets -- 9.1 Introduction -- 9.2 Model Construction -- 9.2.1 Modeling the Covariates and Latent Clusters -- 9.2.2 Modeling the Predictor Choices and Regression Outcomes -- 9.3 Posterior Inference -- 9.3.1 Covariate-to-Cluster Allocation -- 9.3.2 Latent Vectors and Indicators -- 9.3.3 Cluster Predictors and Cluster Representatives -- 9.3.4 Predictions -- 9.4 Application to Gene Expression Data in Multiple Myeloma -- 9.5 Conclusions -- References -- Part III Survival Analysis -- 10 Markov Processes in Survival Analysis -- 10.1 Introduction -- 10.2 Markov Processes -- 10.2.1 Discrete Time Processes -- 10.2.2 Lévy-Driven Processes -- 10.2.3 From Discrete to Continuous Time Processes -- 10.3 Nonparametric Priors -- 10.3.1 Survival Models -- 10.3.2 Survival Regression Models -- 10.3.3 Cure Rate Models -- 10.3.4 Multivariate Models -- 10.4 Numerical Illustrations -- 10.4.1 Example 1 -- 10.4.2 Example 2 -- 10.4.3 Example 3 -- References -- 11 Bayesian Spatial Survival Models -- 11.1 Introduction -- 11.2 A Selection of Nonparametric Priors -- 11.2.1 Gamma Process -- 11.2.2 B-Splines and Bernstein Polynomials -- 11.2.3 Dirichlet Process Mixture Model -- 11.2.4 Polya Tree -- 11.3 Survival Models -- 11.3.1 Proportional Hazards -- 11.3.2 Accelerated Failure Time. , 11.3.2.1 Linear Dependent Dirichlet Process -- 11.3.2.2 Linear Dependent Tailfree Process -- 11.3.3 Proportional Odds -- 11.3.4 Other Semiparametric Models -- 11.4 Spatial Dependence -- 11.4.1 Spatial Frailty Modeling -- 11.4.1.1 Point-Referenced Data Modeling -- 11.4.1.2 Areal Data Modeling -- 11.4.1.3 Related Literature -- 11.4.2 Spatial Copula Modeling -- 11.4.3 Other Spatial Dependence Modelings -- 11.5 Illustrations -- 11.5.1 SEER Cancer Data -- 11.5.2 Leukemia Data -- 11.6 Concluding Remarks -- References -- 12 Fully Nonparametric Regression Modelling of Misclassified Censored Time-to-Event Data -- 12.1 Introduction -- 12.2 Commonly Used Continuous Time-to-Event Regression Models -- 12.2.1 The Proportional Hazards Model -- 12.2.2 The Accelerated Failure Time Model -- 12.2.3 Other Models and Extensions -- 12.3 A Nonparametric Model with Misclassification and Censoring -- 12.3.1 The Misclassification Model -- 12.3.2 The Underlying Time-to-Event Model -- 12.3.3 The Implied Statistical Model -- 12.4 The Computational Implementation -- 12.4.1 The Full Conditional for the Unobserved Time-to-Events -- 12.4.2 The Full Conditional for the Misclassification Parameters -- 12.5 Illustrations -- 12.5.1 Simulated Data -- 12.5.2 The Signal Tandmobiel® Data -- 12.6 Concluding Remarks -- References -- Part IV Random Functions and Response Surfaces -- 13 Neuronal Spike Train Analysis Using Gaussian Process Models -- 13.1 Introduction -- 13.2 Gaussian Process Models -- 13.3 Gaussian Process Model of Firing Rates -- 13.4 Detecting Synchrony Among Multiple Spike Trains -- 13.4.1 Computation -- 13.4.2 Results for Experimental Data -- 13.5 Future Directions -- 13.5.1 Multivariate GPs -- 13.5.2 Dynamic Networks -- 13.5.3 Community Detection -- References -- 14 Bayesian Analysis of Curves Shape Variation Through Registration and Regression -- 14.1 Introduction. , 14.2 Phase Variability and Curve Registration -- 14.3 Bayesian Hierarchical Curve Registration -- 14.3.1 Hierarchical Model -- 14.3.2 Penalized Regression Splines Representation of Random Functionals -- 14.3.3 Inference for Hierarchical Curve Registration Models -- 14.3.4 Case Studies in Bayesian Curve Registration -- 14.4 Regression Models for Timing and Amplitude of Functional Features -- 14.4.1 Generalized Curve Registration Models -- 14.4.2 Amplitude and Phase Regression -- 14.4.3 Growth Velocities and Drug Concentrations Revisited -- 14.5 Joint Functional Regression and Registration -- 14.5.1 Functional Regression and Mixed Models -- 14.5.2 Functional Mixed Registration -- 14.5.3 Functional Mixed Registration of Growth Velocities and Drug Concentrations -- 14.6 Differential Expression and Gene Profile Similarities -- 14.6.1 A Functional Mixture Model for Differential Expression -- 14.6.2 Posterior Measures of Profile Similarities -- 14.6.3 A Case Study of Time-Course Gene Expression Analysis -- 14.7 Concluding Remarks -- References -- 15 Biomarker-Driven Adaptive Design -- 15.1 Introduction -- 15.2 Bayesian CART Models -- 15.3 The Model -- 15.4 SUBA Design -- 15.4.1 Design -- 15.4.2 Posterior Inference on the Partition -- 15.5 Example -- 15.5.1 Simulation Setup -- 15.5.2 Comparison -- 15.5.3 Simulation Results -- 15.5.4 Report on Partition -- 15.6 Conclusion and Discussion -- References -- 16 Bayesian Nonparametric Approaches for ROC Curve Inference -- 16.1 Introduction -- 16.2 ROC Curves -- 16.3 Modeling Approaches for the No Covariate Case -- 16.3.1 DPM Models -- 16.3.2 Bayesian Bootstrap -- 16.4 Modeling Approaches for the Covariate Case -- 16.5 Illustration -- 16.6 Concluding Remarks -- References -- Part V Spatial Data -- 17 Spatial Bayesian Nonparametric Methods -- 17.1 Introduction. , 17.2 Bayesian Non-parametric Priors for a Covariance Function.

Note: Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 Introduction -- 2 Equilibrium thermodynamics of sea water -- 2.1 Salinity -- 2.2 Equilibrium thermodynamics of a two-component system -- 2.3 Potential temperature and density -- 2.4 Equation of state -- 2.5 Spiciness -- 2.6 Specific heat -- 2.7 Latent heat -- 2.8 Boiling and freezing temperature -- 2.9 Chemical potentials -- 2.10 Measured quantities -- 2.11 Mixing -- 3 Balance equations -- 3.1 Continuum hypothesis -- 3.2 Conservation equations -- 3.3 Conservation of salt and water -- 3.4 Momentum balance -- 3.5 Momentum balance in a rotating frame of reference -- 3.6 Angular momentum balance -- 3.7 Energy balance -- 3.8 Radiation -- 3.9 Continuity of fluxes -- 4 Molecular flux laws -- 4.1 Entropy production -- 4.2 Flux laws -- 4.3 Molecular diffusion coefficients -- 4.4 Entropy production and energy conversion -- 4.5 Boundary conditions -- 5 The gravitational potential -- 5.1 Poisson equation -- 5.2 The geoid -- 5.3 The spherical approximation -- 5.4 Particle motion in gravitational field -- 5.5 The tidal potential -- 6 The basic equations -- 6.1 The pressure and temperature equations -- 6.2 The complete set of basic equations -- 6.3 Tracers -- 6.4 Theorems -- 6.5 Thermodynamic equilibrium -- 6.6 Mechanical equilibrium -- 6.7 Neutral directions -- 7 Dynamic impact of the equation of state -- 7.1 Two-component fluids -- 7.2 One-component fluids -- 7.3 Homentropic fluids -- 7.4 Incompressible fluids -- 7.5 Homogeneous fluids -- 8 Free wave solutions on a sphere -- 8.1 Linearized equations of motion -- 8.2 Separation of variables -- 8.3 The vertical eigenvalue problem -- 8.4 The horizontal eigenvalue problem -- 8.5 Short-wave solutions -- 8.6 Classification of waves -- 9 Asymptotic expansions -- 9.1 General method -- 9.2 Adiabatic elimination of fast variables. , 9.3 Stochastic forcing -- 10 Reynolds decomposition -- 10.1 Reynolds decomposition -- 10.2 Reynolds equations -- 10.3 Eddy fluxes -- 10.4 Background and reference state -- 10.5 Boundary layers -- 11 Boussinesq approximation -- 11.1 Anelastic approximation -- 11.2 Additional approximations -- 11.3 Equations -- 11.4 Theorems -- 11.5 Dynamical significance of two-component structure -- 12 Large-scale motions -- 12.1 Reynolds average of Boussinesq equations -- 12.2 Parametrization of eddy fluxes -- 12.3 Boundary conditions -- 12.4 Boussinesq equations in spherical coordinates -- 13 Primitive equations -- 13.1 Shallow water approximation -- 13.2 Primitive equations in height coordinates -- 13.3 Vorticity equations -- 13.4 Rigid lid approximation -- 13.5 Homogeneous ocean -- 14 Representation of vertical structure -- 14.1 Decomposition into barotropic and baroclinic flow components -- 14.2 Generalized vertical coordinates -- 14.3 Isopycnal coordinates -- 14.4 Sigma-coordinates -- 14.5 Layer models -- 14.6 Projection onto normal modes -- 15 Ekman layers -- 15.1 Ekman number -- 15.2 Boundary layer theory -- 15.3 Ekman transport -- 15.4 Ekman pumping -- 15.5 Laminar Ekman layers -- 15.6 Modification of kinematic boundary condition -- 16 Planetary geostrophic flows -- 16.1 The geostrophic approximation -- 16.2 The barotropic problem -- 16.3 The barotropic general circulation -- 16.4 The baroclinic problem -- 17 Tidal equations -- 17.1 Laplace tidal equations -- 17.2 Tidal loading and self-gravitation -- 18 Medium-scale motions -- 18.1 Geometric approximations -- 18.2 Background stratification -- 19 Quasi-geostrophic flows -- 19.1 Scaling of the density equation -- 19.2 Perturbation expansion -- 19.3 Quasi-geostrophic potential vorticity equation -- 19.4 Boundary conditions -- 19.5 Conservation laws -- 19.6 Diffusion and forcing -- 19.7 Layer representation. , 20 Motions on the f-plane -- 20.1 Equations of motion -- 20.2 Vorticity equations -- 20.3 Nonlinear internal waves -- 20.4 Two-dimensional flows in a vertical plane -- 20.5 Two-dimensional flows in a horizontal plane -- 21 Small-scale motions -- 21.1 Equations -- 21.2 The temperature-salinity mode -- 22 Sound waves -- 22.1 Sound speed -- 22.2 The acoustic wave equation -- 22.3 Ray equations -- 22.4 Helmholtz equation -- Appendix A Equilibrium thermodynamics -- A.1 Thermodynamic variables -- A.2 Thermodynamic processes -- A.3 Thermodynamic potentials -- A.4 Thermodynamic relations -- A.5 Extremal principles -- A.6 Thermodynamic inequalities -- A.7 Mixing -- A.8 Phase transitions -- A.9 Ideal gas -- Appendix B Vector and tensor analysis -- B.1 Scalars, vectors, and tensors -- B.2 Calculus -- B.3 Two-dimensional fields -- B.4 Differential geometry -- B.5 Reynolds transport theorem -- B.6 Isotropic and axisymmetric tensors -- Appendix C Orthogonal curvilinear coordinate systems -- C.1 Curvilinear coordinate systems -- C.2 Common differential operators -- C.3 Spherical coordinates -- C.4 Pseudo-spherical coordinates -- C.5 Two-dimensional spherical coordinates -- Appendix D Kinematics of fluid motion -- D.1 Lagrangian description -- D.2 Displacement gradient tensor -- D.3 Eulerian description -- D.4 Velocity gradient tensor -- D.5 Classification and representations of velocity fields -- Classes of velocity fields -- Representation of velocity fields -- D.6 Global description -- D.7 Conservative tracers -- Appendix E Kinematics of waves -- E.1 Elementary propagating waves -- E.2 Standing waves -- E.3 Geometric optics -- Appendix F Conventions and notation -- F.1 Conventions -- F.2 Notation -- Latin symbols -- Greek symbols -- Sub- and superscripts -- References -- Index.

Note: Elektronisch verfübar unter: http://www.soest.hawaii.edu/PubServices/AhaHulikoa.html

Note: Kiel, Univ., Diss., 1975

Note: Includes bibliographical references and index