ALBERT

Note: In kyrill. Schr.

Note: In kyrill. Schr. - Mit engl. Zsfassung

Note: In kyrillischer Schrift

Note: Inhaltsverzeichnis = Contents = Soderžanie Die Flagge der Heimat = The flag of the motherland = Flag rodiny Arktis = Arctic = Arktika Die Drift geht weiter = Drift-ice research continues = Drejf prodolžaetsja Eisbezwinger = Ice fighters = Ledovye bojcy Auf fernen Inseln = On distant islands = Na dalekich ostrovach Antarktis = Antarctic = Antarktida Der sechste Erdteil = The sixth continent = Šestoj kontinent Polarflieger = Polar region pilots = Poljarnye letčiki Der Kältepol = The pole of cold = Poljus choloda Spuren im Schnee = Tracks on the snow = Sledy na snegu , Text in russischer, englischer und deutscher Sprache

Note: In kyrillischer Schrift

Note: Contents: Preface / G. A. Llano. - Welcoming Remarks / W. S. Benninghoff. - The Third Symposium in Historical Perspective / G. A. Knox. - Sir George E. R. Deacon: An Appreciation / K. J. Bertrand. - The Southern Ocean: History of Exploration / Sir George E. R. Deacon. - The Symposium. - Part I: The Structure and Function of Antarctic Marine Phytoplankton Ecosystems. - The Antarctic Marine Ecosystem / Joel W. Hedgpeth. - Primary Production and the Factors Controlling Phytoplankton Growth in the Southern Ocean / O. Holm-Hansen, S. Z. El-Sayed, G. A. Franceschini, and R. L. Cuhel. - Phytoplankton Biomass and Productivity in the Subtropical Convergence Area and Shelves of the Western Indian Subantarctic Islands / Jacqueline Plancke. - Sea Ice Habitats of Signy Island (South Orkneys) and Their Primary Productivity / Terence M. Whitaker. - Dissolved Oxygen and pH Increases by Primary Production in the Surface Water of Arthur Harbor, Antarctica, 1970-1971 / S. V. Shabica, J. W. Hedgpeth, and P. K. Park. - Heterotrophic Activity of Microorganisms in Antarctic Waters / R. Y. Morita, R. P. Griffiths, and S. S. Hayasaka. - Vitamins in the South Polar Seas: Distribution and Significance of Dissolved and Particulate Vitamin B12, Thiamine, and Biotin in the Southern Indian Ocean / A. F. Caducei and R. L. Cuhel. - Discussion. - Part II: The Structure and Function of Antarctic Marine Benthic Ecosystems. - Adaptations within the Antarctic Marine Benthic Ecosystem / Patrick M. Arnaud. - Bacterial Sulfur and Nitrogen Cycles in Sedimentary Deposits of "Fjord Bossière" (Kerguelen Archipelago) / D. Delille. - Antarctic Soft-Bottom, Macrobenthic Community Adaptations to a Cold, Stable, Highly Productive, Glacially Affected Environment / Michael D. Richardson and Joel W. Hedgpeth. - Ecological Adaptations by Antarctic Poikilotherms to the Polar Marine Environment / Martin G. White. - Scoloplos marginatus mcleani: Life Cycle and Adaptations to the Antarctic Benthic Environment / P. Hardy. - Benthic Bionomy of the Continental Shelf of the Kerguelen Archipelago, Macrofauna 2, Diversity of Benthic Annelid Population in a Fjord Close to the Morbihan Gulf / D. Desbruyeres. - Seasonal Variations in the Structure of Populations of Antarctic Polynoids and the Part Played by Polychaetes in the Biocenoses of the Arctic and Antarctic / V. G. Averincev. - Benthic Bionomy of the Continental Shelf of the Kerguelen Islands: Quantitative Data on the Echinoderms of the Morbihan Gulf / Alain Guille. - Seasonal Alterations in Coastal Communities in the Davis Sea / E. N. Gruzov. - First Investigations on the Density of Soft Bottom Meiofauna in Morbihan Bay (Kerguelen Islands) / J. Soyer and F. de Bovee. - Foods and Feeding Characteristics of Antarctic Asteroids and Ophiuroids / John H. Dearborn. - Analysis of the Gigantism and Dwarfness of Antarctic and Subantarctic Gammaridean Amphipoda / Claude De Broyer. - The Breeding Biology of Chorismus antarcticus (Pfeffer) and Notocrangon antarcticus (Pfeffer) (Crustacea, Decapoda) and Its Bearing on the Problems of the Impoverished Antarctic Decapod Fauna / J. Garrey H. Maxwell. - A Preliminary Investigation of the Lipids of Chorismus antarcticus (Pfeffer) (Crustacea, Decapoda) at South Georgia / Andrew Clarke. - Some Additions to Schemes of the Vertical Zonation of Marine Bottom Fauna / A. P. Andriashev. - Quantitative Studies on the Soft-Bottom Macrobenthic Animal Communities of Shallow Antarctic Bays / V. A. Gallardo, J. G. Castillo, M. A. Retamal, A. Yáñez, H. l. Moyano, and J. G. Hermosilla. - Discussion. - Part Ill: Adaptations in Antarctic Vertebrates (Physiology). - Mechanisms of Cold Adaptation in Polar Marine Animals / Bruce L. Umminger. - The Significance of Vertebrates in the Antarctic Marine Ecosystem / Richard M. Laws. - The Role of Glycoprotein Antifreezes in the Survival of Antarctic Fishes / Arthur L. DeVries and Yuan Lin. - New Cytological, Biochemical, and Physiological Data on the Colorless Blood of the Channichthyidae (Pisces, Teleosteans, Perciformes) / J. C. Hureau, J. M. Fine, M. Marneux, and D. Petit. - Respiratory and Circulatory Adaptations to the Absence of Hemoglobin in Chaenichthyid Fishes / Edvard A. Hemmingsen and Everett L. Douglas. - Thermo- and Osmoregulatory Responses Induced by Heating and Cooling the Rostral Brainstem of the Adelie Penguin / H. T. Hammel, J. E. Maggert, E. Simon, L. Crawshaw, and R. Kaul. - Body Temperature Regulation of the Emperor Penguin (Aptenodytes forsteri G.) During Physiological Fasting / Yvon Le Maho, Philippe Delclitte, and René Groscolas. - Cardiovascular Adaptations of the Giant Petrel, Macronectes giganteus, to the Antarctic Environment / David E. Murrish and Charles L. Guard. - Temperature Regulation in the Newborn Weddell Seal, Leptonychotes weddelli / R. Elsner, D. D. Hammond, D. M. Denison, and R. Wyburn. - Discussion. - Part IV: Adaptations in Antarctic Vertebrates (Ecology). - Evolution Within Pelagic Ecosystems: Aspects of the Distribution and Evolution of the Family Myctophidae / Richard F. McGinnis. - Aspects of the Diet of the Antarctic Silverfish, Pleuragramma antarcticum / H. H. DeWitt and T. L. Hopkins. - The Bacterial Microflora in the Digestive Tracts of Penguins and Fishes from the Kerguelen Islands / R. Lesel and J. P. Menet. - The Rockhopper Penguin (Eudyptes chrysocome moseleyi), of Saint Paul and New Amsterdam Islands / T. Duroselle and B. Tollu. - Adaptive Significance of the Reoccupation Period of the Adelie Penguin / E. B. Spurr. - Interactions Between South Polar Skuas and Adelie Penguins / Dietland Müller-Schwarze and Christine Müller-Schwarze. - Comparative Feeding Ecology of the Giant Petrels Macronectes giganteus (Gmelin) and M. halli (Mathews) / G. W. Johnstone. - Feeding Methods in Seabirds: A Comparison of Polar and Tropical Nesting Communities in the Eastern Pacific Ocean / David G. Ainley. - Adaptations of Arctic Terns and Antarctic Terns Within Antarctic Ecosystems / D. F. Parmelee. - Distribution and Abundance of Seals in the Pack Ice of the Pacific Sector of the Southern Ocean / James R. Gilbert and Albert W. Erickson. - Adaptations of Weddell and Ringed Seals to Exploit the Polar Fast Ice Habitat in the Absence or Presence of Surface Predators / Ian Stirling. - Food Consumption of Seals in the Antarctic Pack Ice / Torger Øritsland. - The Leopard Seal (Hydrurga leptonyx) at Palmer Station, Antarctica / R. J. Hofman, R. A. Reichle, D. B. Siniff, and D. Müller-Schwarze. - Distribution of Toothed Whales in the Antarctic Ocean / Masaharu Nishiwaki. - Discussion. - Part V: The Structure and Function of Antarctic Freshwater Ecosystems. - Antarctic Freshwater Ecosystems: Review and Synthesis / Ronald B. Heywood. - Production and Periodicity of Antarctic Freshwater Phytoplankton / J. J. Light. - Studies on Some Saline Lakes of the Vestfold Hills, Antarctica / K. R. Kerry, D. R. Grace, R. Williams, and H. R. Burton. - Nitrogen and Phosphorus Availability to Plankton: and Benthic Communities in Lake Bonney, Southern Victoria Land, Antarctica / Robert C. Hoehn, Bruce C. Parker, Richard D. Fortner, Barron L. Weand, James A. Craft, Larry S. Lane, Robert W. Stavros, Harold G. Sugg, Jr., and Jeffrey T. Whitehurst. - Changes in Dissolved Organic Matter, Photosynthetic Production, and Microbial Community Composition in Lake Bonney, Southern Victoria Land, Antarctica / Bruce C. Parker, Robert C. Hoehn, Robert A. Paterson, James A. Craft, Larry S. Lane, Robert W. Stavros, Harold G. Sugg, Jr., Jeffrey T. Whitehurst, Richard D. Fortner, and Barron L. Weand. - Discussion. - Part VI: The Structure and Function of Antarctic Terrestrial Ecosystems. - Climatic Relationships in Antarctic and Northern Hemisphere Populations of a Cosmopolitan Moss, Bryum argenteum Hedw. / R. E. Longton and Marjorie A. Maclver. - The Growth of Mosses in Two Contrasting Communities in the Maritime Antarctic: Measurement and Pre , Includes some contributions in French

Note: In kyrillischer Schrift

Note: Contents: Preface. - Chapter 1 Hydrological knowledge of Asia and used materials. - Chapter 2 Method of study. - Chapter 3 Distribution of water balance elements on territory of Asia. - Chapter 4 Water balance zonal features of Asia. - Chapter 5 Water resources of Asia. - Abstract. - References. - Supplement. , In kyrill. Schr.

Note: Contents 1. An Introduction to Mountain Effects 2. The Flow over Hills and the Generation of Mountain Waves 2.1 Buoyancy Forces 2.2 The Theory of Two- Dimensional Mountain Waves 2.3 Observations of Mountain Waves 2.4 The Three-Dimensional Flow over Isolated Hills 2.5 Large-Amplitude Mountains and Blocking 2.6 The Observed Barrier Effect of Mountains-The Fohn and Bora 2. 7 The Influence of the Boundary Layer on Mountain Flows 2.8 Slope Winds and Mountain and Valley Winds 3. The Flow near Mesoscale and Synoptic-Scale Mountains 3.1 Quasi-geostrophic Flow over a Mountain 3.2 The Effect of Inertia on the Flow over Mesoscale Mountains 3.3 Theories of Lee Cyclogenesis 4. Orographic Control of Precipitation 4.1 Observations of Rainfall Distribution 4.2 The Mechanism of Upslope Rain 4.3 The Redistribution of Rainfall by Small Hills 4.4 Orographic-Convective Precipitation 5. Planetary-Scale Mountain Waves 5.1 A Vertically Integrated Model of Topographically Forced Planetary Waves 5.2 The Vertical Structure of Planetary Waves on a ,8-Plane between Bounding Latitudes 5.3 Models of Stationary Planetary Waves Allowing Meridional Propagation and Lateral Variation in the Background Wind References

Note: In kyrillischer Schrift

Note: Inhaltsverzeichnis Summary, Rezjume 1. Einleitung 2. Das Bewegungsverhalten von Eismassen, seine Untersuchung und Modellierung 2.1. Zum Modellbegriff 2.2. Typische Eismassen und ihr Bewegungsverhalten 2.2.1. Zur Theorie der Eisbewegung 2.2.2. Gletscher 2.2.3. Schelfeis und Eiskappe 2.3. Die Ermittlung von Eisbewegungen durch geodätische Verfahren 2.3.1. Die Vorplanung der Messungen 2.3.2. Die Durchführung der Messungen 2.3.3. Reduktion der Beobachtungen 2.3.4. Berechnung der Eisbewegungen 2.4. Das trendbehaftete vektorielle Zufallsfeld - Modell zur Beschreibung des Geschwindigkeitsfeldes einer Eismasse - in der Theorie stochastischer Prozesse 2.4.1. Definition des Vektorfeldes 2.4.2. Das Geschwindigkeitsfeld einer Eismasse - trendbehaftetes vektorielles Zufallsfeld 2.4.3. Definition eines vektoriellen Zufallsfeldes 2.4.4. Wahrscheinlichkeitsdichte und Verteilungsfunktion 2.4.5. Die Momente und die Korrelationsfunktionen 2.4.6. Vektorielle Zufallsfelder mit Hormalverteilungsgesetz 2.4.7. Homogene und isotrope vektorielle Zufallsfelder 2.4.8. Das Ergodenproblem 3. Das Konzept der Kollokation und seine Anwendung auf die Bearbeitung von Eisbewegungsmessungen 3.1. Zur Theorie der Kollokation 3.1.1. Das Kollokationsmodell von Moritz [40] 3.1.2. Nichtlineare Prädiktion nach Grafarend [12] 3.1.3. Kollokation von Vektorgrößen 3.2. Analyse und Bearbeitung des Datenmaterials 3.2.1. Die Trendbestimmung 3.2.2. Die Analyse des Zufallsfeldes 3.3. Das Kollokationsmodell bei der Bearbeitung von Eisbewegungsmessungen 3.3.1. Zuordnung und Interpretation der Größen 3.3.2. Zur zeitlichen Variation des Geschwindigkeitsfeldes einer Eismasse 3.3.3. Kollokation mit den ursprünglichen reduzierten Beobachtungen 4. Praktische Untersuchungen 4.1. Geschwindigkeitsquerprofile des Fedtschenko-Gletschers (Pamir) 4.2. Geschwindigkeitslängsprofil des Kongsvegen-Gletschers (Spitzbergen) 4.3. Geschwindigkeitslängsprofil des Hays-Gletschers (Antarktika) 4.4. Geschwindigkeitsquerprofil des Ross-Schelfeises (Antarktika) 4.5. Vergleich mit früheren Untersuchungen zur Abschätzung von Geschwindigkeitskorrelationen natürlicher Eismassen 5. Zusammenfassung 6. Literaturverzeichnis , Zusammenfassung in englischer und russischer Sprache

Note: In kyrillischer Schrift

Note: In kyrillischer Schrift

Note: Enthaltene Kapitel sind: Chapter 1 Laminar and turbulent flows Chapter 3 Reynolds equations and the semiempirical theories of turbulence Chapter 4 Turbulence in a thermally stratified medium

Note: Contents: Preface. - List of Symbols Commonly Used in the Text. - Acknowledgements. - 1 Introduction. - 2 Properties of Sea Water Relevant to Physical Oceanography. - Introduction. - Density. - Measurement of density, temperature and salinity. - Relative density, sigma-t and specific volume. - Tables for density and specific volume as functions of temperature, salinity and pressure. - Sources of data. - 3 The Basic Physical Laws Used in Oceanography and Classifications of Forces and Motions in the Sea. - Basic laws. - Classification of forces and motion. - 4 The Equation of Continuity of Volume. - The concept of continuity of volume. - The derivation of the equation of continuity of volume. - An application of the equation of continuity. - 5 Stability and Double Diffusion. - Static stabiIity. - Criterion for static stability (E). - Numerical values for stability. - Double diffusion. - Dynamic stability. - 6 The Equation of Motion in Oceanography. - The form of the equation of motion. - Obtaining solutions to the equations, including boundary conditions. - The derivation of the terms in the equation of motion. - The pressure term. - Transforming from axes fixed in space to axes fixed in the rotating earth. - Gravitation and gravity. - The Coriolis terms. - Other accelerations. - Coordinate systems. - 7 The Role of the Non-Linear Terms in the Equations of Motion. - The non-linear terms in the equation of motion. - The friction term for the instantaneous velocity. - What is the source of the difficulty?. - Scaling and the Reynolds Number. - Reynolds stresses. - Equations for the mean or average motion. - Reynolds stresses and eddy viscosity. - Scaling the equations of motion. - Dynamic stabiIity. - The effect of density variations on dynamic stability. - Effects of rotation. - 8 Currents Without Friction: Geostrophic Flow. - Hydrostatic equiIibrium. - Inertial flow. - GeopotentiaI. - Geopotential surfaces and isobaric surfaces. - The geostrophic equation. - Why worry about the geostrophic equation?. - The geostrophic method for calculating relative velocities. - An example of the calculation of a geostrophic velocity profile. - An alternative derivation of the geostrophic equation. - The 'thermal wind' equations. - Absolute velocities. - Relations between isobaric and level surfaces. - Relations between isobaric and isopycnal surfaces. - Comments on the geostrophic equation. - Justification for using the geostrophic approach to obtain the speeds of strong currents. - 9 Currents With Friction. - Wind-driven circulations - introduction. - Nansen's qualitative argument. - The equations of motion with friction included. - Ekman's solution to the equations of motion with friction present. - Comments on the above experimental observations. - Transport and upwelling. - Upwelling or downwelling away from boundaries. - Bottom friction and shallow water effects. - Limitations of the Ekman theory. - Sverdrup's solution for the wind-driven circulation. - Orders of magnitude of the terms. - Application of the Sverdrup equation. - The general form of the Sverdrup equation. - The mass transport stream function. - Westward intensification - Stommel's contribution. - The planetary wind field. - Munk's solution. - Comments on Munk's solution. - Vorticity. - Relative vorticity. - Planetary vorticity. - Absolute vorticity. - Potential vorticity. - Westward intensification of ocean currents explained using conservation of potential vorticity. - Equatorial undercurrents. - The boundary layer approach. - The use of the boundary layer approach to obtain a solution to Munk's equation. - A simple inertial theory by Stommel. - 10 Thermohaline Effects. - The deep circulation. - Equations for salt and temperature (heat) conservation. - Equations for the average salinity and temperature. - Reynolds fluxes and eddy diffusivity. - Thermoclines and the thermohaline circulation. - The mixed layer of the ocean. - 11 Numerical Models. - Introduction. - Numerical methods. - General approach to numerical modelling of ocean circulations. - Descriptions of some models of individual oceans. - O'Brien's two-dimensional wind-driven model of the North Pacific. - Cox's model of the Indian Ocean. - Holland and Hirschmann's model of the Atlantic Ocean. - Two models of the circulation of the world ocean. - Models of mesoscale eddies. - Comments on the numerical model solutions. - 12 Waves. - Introduction. - Some general characteristics of waves. - Small amplitude waves. - Orbital motion of the water particles. - Refraction and breaking in shallow water; diffraction. - The generation of waves. - Measurement of waves. - ReaI waves. - Wave generation by the wind; semi-empirical relations. - Energy of waves. - Tsunamis or seismic sea waves. - Internal waves. - Effects of rotation. - Modified gravity waves. - Kelvin waves. - Planetary or Rossby waves. - Topographic effects. - 13 Tides. - Introduction. - Tide-producing forces. - Components of the tide-producing forces. - Ocean responses to the tide-producing forces - tidaI theories. - The practical approach to tide prediction. - The measurement of tides. - Types of tides. - Tidal currents. - Tides in bays-resonance. - Storm surges. - 14 Some Presently Active and Future Work. - APPENDIX I Mathematical Review with Some Elementary Fluid Mechanics. - Introduction. - Scalars and vectors. - Derivatives. - The individual or total derivative. - Integrals. - Fields. - Descriptions of fluid flow. - Convergences and divergences. - Hydrostatic pressure. - Slope effects. - CompressibiIity. - Centripetal and centrifugal forces. - APPENDIX 2 Units Used in Physical Oceanography. - Introduction. - Base units. - Derived and temporary units. - Units used in dynamic oceanography and some numerical values. - SUGGESTIONS FOR FURTHER READING AND FOR REFERENCE. - INDEX.

Note: In kyrillischer Schrift

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

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

Note: CONTENTS: Preface / Claude R. Duguay and Alain Pietroniro. - Introduction / Claude R. Duguay and Alain Pietroniro. - Remote Sensing of Snow Cover / Dieter Scherer, Dorothy K. Hall, Volker Hochschild, Max König, Jan-Gunnar Winther, Claude R. Duguay, Frédérique Pivot, Christian Mätzler, Frank Rau, Klaus Seidel, Rune Solberg, and Anne E. Walker. - Remote Sensing of Glaciers and Ice Sheets / Jan-Gunnar Winther, Robert Bindschadler, Max König, and Dieter Scherer. - Ice Characteristics and Processes, and Remote Sensing of Frozen Rivers and Lakes / Martin O. Jeffries, Kim Morris, and Nickolai Kozlenko. - Satellite Remote Sensing of Permafrost and Seasonally Frozen Ground / Claude R. Duguay, Tingjun Zhang, David W. Leverington, and Vladimir E. Romanovsky. - Remote Sensing of Surface Water and Soil Moisture / Alain Pietroniro, Jessika Töyrä, Robert Leconte, and Geoff Kite. - Evaporation/Evapotranspiration Estimates With Remote Sensing / Raoul Granger and Normand Bussières. - Appendix: Acronyms. - Subject Index.

Note: Ersch. unregelmäßig , Beiträge teilweise in Englisch

Note: Ch. 1. Structure and development of a plant : an overview -- ch. 2. The protoplast : plasma membrane, nucleus, and cytoplasmic organelles -- ch. 3. The protoplast : endomembrane system, secretory pathways, cytoskeleton, and stored compounds -- ch. 4. Cell wall -- ch. 5. Meristems and differentiation -- ch. 6. Apical meristems -- ch. 7. Parenchyma and collenchyma -- ch. 8. Sclerenchyma -- ch. 9. Epidermis -- ch. 10. Xylem : cell types and developmental aspects -- ch. 11. Xylem : secondary xylem and variations in wood structure -- ch. 12. Vascular cambium -- ch. 13. Phloem : cell types and developmental aspects -- ch. 14. Phloem : secondary phloem and variations in its structure -- ch. 15. Periderm -- ch. 16. External secretory structures -- ch. 17. Internal secretory structures.

Note: In kyrill. Schr.

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

Note: Zugl.: Bremen, Univ., Diss., 2006

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: In kyrillischer Schrift