ALBERT

Note: In kyrillischer Schrift , Zusammenfassungen in englischer Sprache

Note: In kyrillischer Schrift

Note: Soderžanie: Predislovie. - Osnovnye rezul'taty 25-letnego issledovanija Antarktiki / N. A. Kornilov. - Poljarnaja klimatologija na službe narodnogo chozjajstva / A. I. Voskresenskij, G. U. Karimova, L. S. Petrov. - Sostojanie i perspektivy okeanologičeskogo obespečenija narodnogo chozjajstva v Arktike / N. V. Mustafin, E. N. Dvorkin. - Sostojanie i perspektivy gidrochimičeskich issledovanij dlja obsluživanija naučnych i chozjajstvennych učreždenij Arktiki / V. P. Rusanov. - Obespečenie ledovoj informaciej ledokol'no-transportnych sudov v Arktike / V. E. Borodačev, A. V. Bušuev, A. A. Kirillov. - Izučenie prirodnych uslovij dlja obespečenija tranzitnogo plavanija po Severnomu Morskomu Puti / A. Ja. Buzuev, V. B. Fedjakov. - Ispol'zovanie novych metodov v monitoringe termičeskogo režima Arktiki / I. B. Eserkepova, K. M. Lugina, N. A. Speranskaja, R. L. Kagan, I. P. Smirnova, V. V. Subbotin. - Izučenie vysokich sloev atmosfery v Arktike, Antarktike, i nad Mirovym okeanom s pomošč'ju meteoraket / G. A. Kokin, K. E. Speranskij, S. S. Gajgerov. - Optičeskie svojstva atmosfery nad Atlantičeskim okeanom / E. E. Artemkin, S. I. Avdjušin, A. E. Mikirov. - Voprosy soveršenstvovanija sinoptičeskogo obespečenija sudochodstva i rybopromyslovych rabot v Južnom okeane / L. Ju. Ryžakov. - Radiolokacionnye issledovanija oblakov v različnych rajonach Mirovogo okeana / A. I. Korotov, A. E. Mjagkov, A. B. Ščupjackij. - Osnovnye itogi i perspektivy naučnych issledovanij Severozemel'skogo gljaciologičeskogo stacionara AANII "Kupol Vavilova" / L. S. Govorucha. - Nekotorye rezul'taty issledovanij po programme Meždunarodnogo antarktičeskogo gljaciologičeskogo proekta (MAGP) / V. G. Aver'janov. - Prilivnye javlenija vo l'dach Severnogo Ledovitogo okeana (po kosmičeskim dannym) / V. V. Bogorodskij, M. G. Nazirov. - Nekotorye čerty prostranstvennoj struktury ledjanogo pokrova arktičeskich morej v svjazi s turbulentnym treniem i geostrofičeskim zachvatom prilivnoj volny / M. G. Nazirov, V. G. Trofimova. - Primenenie model'nych naturnych ėksperimentov pri izučenii vzaimodejstvija nefteproduktov s okeanom i atmosferoj / V. V. Izmajlov, V. S. Račkov. - Neftjanye uglevodorody v vodach mirovogo okeana i metody bor'by s nimi / M. P. Nestepova, I. A. Nemirovskaja, O. S. Močalova. - Osnovnye rezul'taty issledovanij vozmožnych izmenenij gidrometeorologičeskich uslovij severnych morej pod vlijaniem vodochozjajstvennych meroprijatij / V. A. Potanin, A. A. Dement'ev. - Issledovanie struktury gidrofizičeskich polej v central'noj časti Arktičeskogo bassejna / L. I. Zubkov, A. V. Gusev, P. V. Bogorodskij. - Ispol'zovanie infrakrasnych (IK) aėrokosmičeskich nabljudenij Arktičeskich morej v navigacii i pri rešenii drugich narodnochozjajstvennych zadač / A. I. Paramonov, V. A. Čebotareva. - Set' avtomatičeskich magnitografov po proektu "Geografičeskij poligon v Antarktide" dlja izučenija okolozemnogo kosmičeskogo prostranstva / A. N. Zajcev, G. A. Timofeev, V. O. Papitašvili. - Prognozirovanie chodkosti sudov vo l'dach / V. I. Kašteljan, D. D. Maksutov, O. V. Faddeev. , In kyrill. Schr.

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

Note: Contents: Preface. - New introduction. - I. Introductory. - II. From Hobart to South Victoria Land. - III. Life in South Victoria Land. - IV. Cut off from all the world. - V. The winter in Victoria Land. - VI. Sledge Journey in winter. - VII. Among the penguins. - VIII. Return of the Southern Cross. - IX. Farthest south. - X. Towards civilization. - Appendix I. Appendix II.

Note: Contents: Foreword. - Introduction. - Information concerning the Taxonomic Arrangement and the Origin of the Material Examined. - Notes on Keys and Descriptions. - Glossary. - List of Abbreviations. - Key to the Genera. - Cyperus. - Eriophorum. - Scirpus. - Blysmus. - Eleocharis. - Trichophorum. - Schoenus. - Cladium. - Rhynchospora. - Kobresia. - Carex. - References. - Index of Used Specimens. - Index of Species. - Explanation of Plates. - Plates 1—39. - Fold up Map of Simple Systematical Plane Shapes and Colour Chart.

Note: Contents: Introduction. - Information concerning the Taxonomic Arrangement and the Material Examined. - Notes on Keys and Descriptions. - Glossary. - List of Abbreviations. - Salicaceae. - Myricaceae. - Corylaceae. - Betulaceae. - Fagaceae. - Ulmaceae. - Cannabaceae. - Urticaceae. - Santalaceae. - Loranthaceae. - Polygonaceae. - Chenopodioneae. - Amaranthaceae. - Portulacaceae. - Caryophyllaceace. - Nymphaeaceae. - Ceratophyllaceae. - Ranunculaceae. - Paeoniaceae. - Berberidaceae. - Aristolochiaceae. - Papaveraceae. - Cruciferae. - References. - Index of Taxa. - Plates. - Simple Symmetrical Plane Shapes.

Note: CONTENTS: Foreword. - Introduction. - SESSION I - ATMOSPHERIC GENERAL CIRCULATION MODELS AND CLIMATE SIMULATIONS. - Large-scale climate modelling and small-scale physical processes / J. Smagorinsky. - Simulation of climate by general circulation models with hydrologic cycles / S. Manabe. - Current parameterizations of land-surface processes in atmospheric general circulation models / D. J. Carson. - The sensitivity of numerically simulated climates to land surface conditions / Y. Mintz. - SESSION II - THE MICROPHYSICAL PROCESSES OF MOMENTUM, HEAT AND WATER TRANSFERS ACROSS AND NEAR THE SURFACE OF THE LAND. - Vertical flux of moisture and heat at a bare soil surface / W. H. Brutsaert. - The vertical fluxes of heat and moisture at a vegetated land surface / L. J. Fritschen. - Vertical flux of heat and moisture in snow and ice / M. Kuhn. - SESSION III - MESOSCALE PARAMETERIZATIONS OF THE TRANSFER PROCESSES. - Parameterization of hydrologic processes / J. C. I. Dooge. - Dynamic hydro-thermal balances at macroscale / P. S. Eagleson. - SESSION IV - LAND SURFACE GLOBAL DATA SETS. - Use of regional and global soils data for climate modelling/ M. J. Gardiner. - Land surface processes: Vegetation / A. Perrier. - Data on snow cover and glaciers for the global climatic models / V. M. Kotliakov and A. N. Krenke. - The shortwave albedo and the surface emissivity / K. Ya. Kondratyev, V. I. Korzov, V. V. Mukhenberg and L. N. Dyachenko. - Water balance / A. Baumgartner. - SESSION V - ACQUISITION OF LAND SURFACE DATA. - Possibilities for remote sensing of surface characteristics / K. I. Itten.

Note: In kyrillischer Schrift

Note: In kyrillischer Schrift

Note: In kyrillischer Schrift

Note: In kyrillischer Schrift

Note: In kyrillischer Schrift

Note: Inhaltsverzeichnis: Vorwort. - 1. Zielsetzung und Ablauf der Heidelberg-Ellesmere Island-Expedition 1978 / D. Barsch und L. King. - 2. Das Borup-Fjord-Gebiet in N-Ellesmere Island, N. W. T., Kanada: Entdeckung und Begehung des Gebietes, vorhandene Karten und offizielle Namen / L. King. - 3. Geodätische und photogrammetrische Arbeiten an der Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada, im Rahmen der "Heidelberg-Ellesmere-Island-Expedition 1978" / G. Hell. - 4. Geologie, Tektonik und strukturelle Verzeichnung der geomorphologischen Großformen im Expeditionsgebiet Oobloyah Bay - Neil Peninsula, N-Ellesmere Island, N.W.T., Kanada / H. R. Völk. - 5. Witterungsverlauf im Oobloyah-Tal, N-Ellesmere Island, N.W.T., Kanada, vom 24. Juni bis zum 4. August 1978, ein statistischer Wertevergleich / W. A. Flügel. - 6. Das Sommerklima von N-Ellesmere Island, N.W.T., Kanada - eine Beurteilung von Stationswerten unter besonderer Berücksichtigung des Sommers 1978 / L. King. - 7. Zur Geomorphologie des Expeditionsgebietes Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada / D. Barsch. - 8. Studien zur gegenwärtigen Geomorphodynamik im Bereich der Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada / D. Barsch. - 9. Terassen, Flußarbeit und das Modell der exzessiven Talbildungszone im Expeditionsgebiet Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada / D. Barsch. - 10. Die Gletscher im Einzugsgebiet des Borup-Fjord, N-Ellesmere Island, N.W.T., Kanada / L. King. - 11. Gletschergeschichtliche Arbeiten im Gebiet zwischen Oobloyah Bay und Esayoo Bay, N-Ellesmere Island, N.W.T., Kanada / L. King. - 12. Glaziologische Beobachtungen an der Stirn des Weber-Gletschers, Borup-Fjord-Gebiet, N-Ellesmere Island, N.W.T., Kanada / D. Barsch, L. King und R. Mäusbacher. - 13. Jungquartäre Delta- und Flußentwicklung im glazialisostatischen Hebungsraum der Oobloyah Bay auf N-Ellesmere Island, N.W.T., Kanada / H. R. Völk. - 14. Hydrologische Studien zum Wasserhaushalt hocharktischer Einzugsgebiete im Bereich des Oobloyah-Tals, N-Ellesmere Island, N.W.T., Kanada / W. A. Flügel. - 15. Hydrochemische Untersuchungen von Niederschlägen, Bodenwasser, Seen und Flüssen im Oobloyah-Tal, N-Ellesmere Island, N.W.T., Kanada / W. A. Flügel. - 16. Geomorphologische Kartierung im Oobloyah-Tal, N-Ellesmere Island, N.W.T., Kanada / R. Mäusbacher. - 17. Gesteinstemperaturen und Insolationsverwitterung im hocharktischen Bereich, Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada / H. Eichler. - 18. Kleinformen der hocharktischen Verwitterung im Bereich der Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada - Formengenese und Prozesse / H. Eichler. - 19. Oberflächennahe Bodentemperaturmessungen in Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada / R. Mäusbacher. - 20. Recent iron ore deposition and heavy metal accumulation in Access Lake, Oobloyah Valley, northern Ellesmere Island, N.W.T., Canada / D. Barsch und G. Müller. - 21. Die Meereisentwicklung im Inneren des östlichen kanadischen Arktisarchipels und ihre Bedeutung für die Arbeiten der Heidelberg-Ellesmere Island-Expedition an der Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada / L. King. - 22. Gefäßpflanzen von Oobloyah Bay, N-Ellesmere Island, N.W.T., Kanada; eine kommentierte Pflanzenliste und phänologische Beobachtungen / R. Mäusbacher. - 23. The mosses of peat mounds, Oobloyah Bay, northern Ellesmere Island, N.W.T., Canada / L. King. - 24. Beobachtungen zu organischen Kleinformen im Oobloyah Tal, N-Ellesmere Island, N.W.T., Kanada / W. A. Flügel und R. Mäusbacher. - 25. Faunal notes of the Heidelberg Ellesmere Island Expedition 1978, Oobloyah Bay, northern Ellesmere Island, N.W.T., Canada / D. Barsch und L. King. - Anlage 1: Orthophotokarte 〈1 : 25 000〉 Oobloyah Bay. - Anlage 2: Geomorphologische Karte 〈1 : 25 000〉 Oobloyah Bay. - Anlage 3: Radiocarbondaten. - Anlage 4: Planung, Einkauf und Lagerung der Nahrungsmittel. , Beiträge teilweise in deutsch, teilweise in englisch

Note: Contents: Preface. - Introduction. - Chapter 1 Some of the physiographical peculiarities of the Kuznetsky Alatau and the morphology of recent glaciation of the ridge. - Chapter 2 Structure of glaciers of the Kuznetsky Alatau : Density of firn on névés and glaciers. - Chapter 3 Conditions for glacier existence in the Kuznetsky Alatau : oroclimatic basis for glaciation. - Chapter 4 Regime of glaciers of the Kuznetsky Alatau. - Conclusion. - Abstract. - Bibliography. , In kyrill. Schr. - Zsfassung in engl. Sprache.

Note: In kyrillischer Schrift

Note: In kyrillischer Schrift

Note: Inhaltsverzeichnis: Svojstva koėfficientov prelomlenija, zatuchania i koėfficienta propuskanija ionosfery na nizkich i sverchnizkich častotach = Свойства коэффициентов преломления, затухания и коэффициента пропускания ионосферы на низких и сверхнизких частотах = Die Eigenschaften des Brechungs- und Dämpfungskoeffizienten sowie des Durchlässigkeitskoeffizienten der Ionosphäre bei niedrigen und extrem niedrigen Frequenzen / D. S. Fligel' = Д. С. Флигель. - Scatter an Meteorspuren / L. Třiskova. - Radio-Echos von Meteorspuren und ihre Bedeutung für die Physik der Hochatmosphäre / P. Glöde. - Die Windsysteme in der unteren Ionosphäre nach Radiobeobachtungen im Langwellenbereich und nach Radarbeobachtungen an Meteoriten / K. Sprenger. - Ergebnisse und Aspekte von Messungen des atmosphärischen Funkstörpegels im Längstwellenbereich in verschiedenen Breiten / E. A. Lauter, B. Schäning. - Molnievye razrjady i rasprostranenie ėlektromagnitnych voln nizkoj i sverchnizkoj častoty nad zemnoj poverchnost'ju = Молниевые разряды и распространение электромагнитных волн низкой и сверхнизкой частоты над земной поверхностью = Blitzentladungen und die Ausbreitung elektromagnetischer Wellen niedriger und extrem niedriger Frequenzen über die Erdoberfläche / D. S. Fligel' = Д. С. Флигель. - Funkcija rasprostranenija i srednjaja fazovaja skorost' ėlektromagnitnych voln na sverchnizkich častotach = Функция распространения и средняя фазовая скорость электромагнитных волн на сверхнизких частотах = Die Ausbreitungsfunktion und die mittlere Phasengeschwindigkeit der elektromagnetischen Wellen extrem niedriger Frequenzen / G. A. Michailova = Г. А. Михайлова. - Weitere Untersuchungen über Sq und L / G. Fanselau.

Note: Kartenbeilage unter dem Titel: Indre Kongsfjorden (Vestspitsbergen) : Nordblatt 〈1 : 25 000〉 , Kartenbeilage unter dem Titel: Indre Kongsfjorden (Vestspitsbergen) : Südblatt 〈1 : 25 000〉 , Inhalt: Zur Karte "Indre Kongsfjorden (Vestspitsbergen) 1: 25 000" (W. Pillewizer) Zur Karte des Kongsvegen-Kronebre 1 : 50 000, (Westspitzbergen) (W. Pillewizer) Die Bewegung der Zunge des Blomstrandbre (Kongsfjord, Vestspitzbergen) (I. Militzer, U. Voigt) Block Movement of Glaciers (W. Pillewizer, U. Voigt) Errata zu Teil I

Note: Inhaltsverzeichnis: Einführungsvortrag zum Internationalen Ozonseminar / K. H. Grasnick. - On the accuracy of spectroscopic measurements of atmospheric ozone / G. M. B. Dobson. - Atmospheric ozone in Central and Southeast Europe during the IQSY / Rumen D. Bojkov. - Über Ozongehalt und stratosphärische Zirkulation im europäischen Raum bei spezieller Wetterlage / C. Busch. - Infra-red emission and atmospheric ozone / C. D. Walshaw. - Nekotorye rezul'taty issledovanij atmosfernogo ozona v SSSR v period MGSS = Некоторые результаты исследований атмосферного озона в СССР в период МГСС = Einige Ergebnisse der Untersuchung des atmosphärischen Ozons während des IQSY in der UdSSR / G. P. Guščin = Г. П. Гущин = G. P. Guschtschin. - Die stratosphärische Erwärmung über Mitteleuropa vom 8.-12- März 1965 / W. Hoebbel, K. H. Grasnick. - Einige Erscheinungen der unteren Ionosphäre und mögliche Kopplungen zu tieferen Atmosphärenschichten / G. Entzian. - Comparison between the vertical ozone distribution profiles obtained from Umkehr and ozonesonde data / Rumen D. Bojkov. - Entwicklungsstand der Ozonsondentechnik / D. Sonntag. - Opyty po usoveršenstvovaniju apparatury spektrofotometra dobsona i nekotorye techničeskie uslovija graduirovki optičeskich klinov = Опыты по усовершенствованию аппаратуры спектрофотометра добсона и некоторые технические условия градуировки оптических клинов = Versuche zur Vervollkommnung der Apparatur des Dobson-Spektrophotometers und einige technische Bedingungen der Eichung der optischen Keile / M. Gorski = М. Горски. - The analysis of the accuracy of measurements of the total ozone amount performed at Belsk - Poland / A. Dziewulska-Łosiowa. - Einige Verbesserungen zur Temperaturkonstanz innerhalb des Dobson-Spektrophotometers / K. H. Grasnick. - On isotopic mass transport from stratosphere to troposphere by baroclinic disturbances / M. Łękawska-Degórska. - Anschriften der Verfasser. , Beiträge teilweise in deutscher, teilweise in englischer, teilweise in russischer Sprache , Beiträge teilweise in kyrillischer Schrift

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

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

Note: In kyrill. Schr.

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