# krainaksiazek small perturbation theory 20107003

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### Algebraic Methods in Nonlinear Perturbation Theory Springer, Berlin

**Książki / Literatura obcojęzyczna**

This book will be of interest for everybody working on perturbation theory in differential equations. The book requires only a standard mathematical background for engineers and does not require reference to the special literature. Topics which are covered include: matrix perturbation theory; systems of ordinary differential equations with small parameter; reconstruction and equations in partial derivatives. Boundary problems are not discussed in this volume. The reader will find many examples throughout the book.

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### Classical Mechanics Dover Publications

**Książki / Literatura obcojęzyczna**

Chapter 1. Kinematics of Particles 1. Introduction 2. Definition and Description of Particles 3. Velocity 4. Acceleration 5. Special Coordinate Systems 6. Vector Algebra 7. Kinematics and Measurement Exercises Chapter 2. The Laws of Motion 8. Mass 9. Momentum and Force 10. Kinetic Energy 11. Potential Energy 12. Conservation of Energy 13. Angular Momentum 14. Rigid Body Rotating about a Fixed Point 15. A Theorem on Quadratic Functions 16. Inertial and Gravitational Masses Exercises Chapter 3. Conservative Systems with One Degree of Freedom 17. The Oscillator 18. The Plan Pendulum 19. Child-Langmuir Law Exercises Chapter 4. Two-Particle Systems 20. Introduction 21. Reduced Mass 22. Relative Kinetic Energy 23. Laboratory and Center-of-Mass Systems 24. Central Motion Exercises Chapter 5. Time-Dependent Forces and Nonconservative Motion 25. Introduction 26. The Inverted Pedulum 27. Rocket Motion 28. Atmospheric Drag 29. The Poynting-Robertson Effect 30. The Damped Oscillator Exercises Chapter 6. Lagrange's Equations of Motion 31. Derivation of Lagrange's Equations 32. The Lagrangian Function 33. The Jacobian Integral 34. Momentum Integrals 35. Charged Particle in an Electromagnetic Field Exercises Chapter 7. Applications of Lagrange's Equations 36. Orbits under a Central Force 37. Kepler Motion 38. Rutherford Scattering 39. The Spherical Pendulum 40. Larmor's Theorem 41. The Cylindrical Magnetron Exercises Chapter 8. Small Oscillations 42. Oscillations of a Natural System 43. Systems with Few Degrees of Freedom 44. "The Stretched String, Discrete Masses" 45. Reduction of the Number of Degrees of Freedom 46. Laplace Transforms and Dissipative Systems Exercises Chapter 9. Rigid Bodies 47. Displacements of a Rigid Body 48. Euler's Angles 49. Kinematics of Rotation 50. The Momental Ellipsoid 51. The Free Rotator 52. Euler's Equations of Motion Exercises Chapter 10. Hamiltonian Theory 53. Hamilton's Equations 54. Hamilton's Equations in Various Coordinate Systems 55. Charged Particle in an Electromagnetic Field 56. The Virial Theorem 57. Variational Principles 58. Contact Transformations 59. Alternative Forms of Contact Transformations 60. Alternative Forms of the Equations of Motion Exercises Chapter 11. The Hamilton-Jacobi Method 61. The Hamilton-Jacobi Equation 62. Action and Angle Variables-Periodic Systems 63. Separable Mulitply-Periodic Systems 64. Applications Exercises Chapter 12. Infinitesimal Contact Transformations 65. Transformation Theory of Classical Dynamics 66. Poisson Brackets 67. Jacobi's Identity 68. Poisson Brackets in Quantum Mechanics Exercises Chapter 13. Further Development of Transformation Theory 69. Notation 70. Integral Invariants and Liouville's Theorem 71. Lagrange Brackets 72. Change of Independent Variable 73. Extended Contact Transformations 74. Perturbation Theroy 75. Stationary State Perturbation Theory 76. Time-Dependent Perturbation Theory 77. Quasi Coordinates and Quasi Momenta Exercises Chapter 14. Special Applications 78. Noncentral Forces 79. Spin Motion 80. Variational Principles in Rocket Motion 81. The Boltzmann and Navier-Stokes Equations Chapter 15. Continuous Media and Fields 82. The Stretched String 83. Energy-Momentum Relations 84. Three-Dimensional Media and Fields 85. Hamiltonian Form of Field Theory Exercises Chapter 16. Introduction to Special Relativity Theory 86. Introduction 87. Space-Time and Lorentz Transformation 88. The Motion of a Free Particle 89. Charged Particle in an Electromagnetic Field 90. Hamiltonian Formulation of the Equations of Motion 91. Transformation Theory and the Lorentz Group 92. Thomas Precession Exercises Chapter 17. The Orbits of Particles in High Energy Accelerators 93. Introduction 94. Equilibrium Orbits 95. Betatron Oscillations 96. Weak Focusing Accelerators 97. Strong Focusing Accelerators 98. Acceleration and Synchrotron Oscillations Appendix I Riemannian Geometry Appendix II Linear Vector Spaces Appendix III Group Theory and Molecular Vibrations Apendix IV Quaternions and Pauli Spin Matrices Index

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### Mathematical Foundations of the State Lumping of Large Systems Springer Netherlands

**Książki / Literatura obcojęzyczna**

This volume is devoted to theoretical results which formalize the concept of state lumping: the transformation of evolutions of systems having a complex (large) phase space to those having a simpler (small) phase space. The theory of phase lumping has aspects in common with averaging methods, projection formalism, stiff systems of differential equations, and other asymptotic theorems. Numerous examples are presented in this book from the theory and applications of random processes, and statistical and quantum mechanics which illustrate the potential capabilities of the theory developed. The volume contains seven chapters. Chapter 1 presents an exposition of the basic notions of the theory of linear operators. Chapter 2 discusses aspects of the theory of semigroups of operators and Markov processes which have relevance to what follows. In Chapters 3--5, invertibly reducible operators perturbed on the spectrum are investigated, and the theory of singularly perturbed semigroups of operators is developed assuming that the perturbation is subordinated to the perturbed operator. The case of arbitrary perturbation is also considered, and the results are presented in the form of limit theorems and asymptotic expansions. Chapters 6 and 7 describe various applications of the method of phase lumping to Markov and semi-Markov processes, dynamical systems, quantum mechanics, etc. The applications discussed are by no means exhaustive and this book points the way to many more fruitful applications in various other areas. For researchers whose work involves functional analysis, semigroup theory, Markov processes and probability theory.

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### Sedimentology Books LLC, Reference Series

**Książki / Literatura obcojęzyczna**

Source: Wikipedia. Pages: 146. Chapters: Clay, Dune, Sediment, Desert varnish, Floodplain, River delta, Silt, Gravel, Braided river, Diagenesis, Giant current ripples, Sediment transport, Touchet Formation, Laterite, Soil liquefaction, Clastic rock, Roddon, Foreland basin, Contourite, Sieve analysis, Cross-bedding, Regolith, List of important publications in geology, Angoumian, Aeolian processes, Sedimentary structures, Carbonate platform, Saprolite, Point bar, Back-arc basin, Alluvial fan, Carbonate hardgrounds, Soil gradation, Bioturbation, Siltation, Beach evolution, Avulsion, Manning formula, Geological unit, Turbidite, Molasse basin, Varve, Consolidation, Hummocky cross-stratification, Dish structure, Sedimentary basin, Glaciogenic Reservoir Analogue Studies Project, Antidune, Diluvium, Rhythmite, Load cast, Cyclic sediments, Fluvial, Jet, Roundness, Badlands, Modern recession of beaches, Box corer, Wave-formed ripple, National Center for Earth-surface Dynamics, Flysch, Biorhexistasy, Palaeochannel, Seismite, Marine regression, Kasha-Katuwe Tent Rocks National Monument, Saar-Nahe Basin, Zechstein, Marine transgression, Unified Soil Classification System, Eluvium, Exner equation, Aggradation, Lamination, Omarolluk, Alluvium, Shields parameter, Imbrication, Vitrinite, Paleocurrent, Miogeocline, Pebble, Pediment, Society for Sedimentary Geology, Cementation, Sedimentary basin analysis, Bed load, Tar pit, Deposition, Sand volcano, Degradation, Cyclothems, Thermal history modelling, Illuvium, Conodont Alteration Index, Shear velocity, Sedimentary depositional environment, Abrasion, Culm Measures, Basin modelling, Connate fluids, Forearc, Rouse number, River morphology, Graded bedding, Colluvium, Perturbation, Maturity, Wax Lake Delta, Braid bar, Pull apart basin, Bouma sequence, Cutans, ZTR index, Mouth bar, Pockmark, Clastic wedge, Bed material load, Back-stripping, Progradation, Alginite, Matrix-supported rock, Detritus, Foreset bed, Shrink-swell capacity, Neomorphism, Alluvial river, Retrogradation, River channel migration, Subaqueous fan, Allochem, Diamicton, Terrigenous sediment, Gelifluction, Key bed, Upper plane bed, Wackestone, Kankar, Authigenic, Suspended load, Leaching, Lower shoreface, Micritisation, Isopach map, Terrace Crossing, Backswamp, Lens, Tempestite, Lacustrine delta, Wash load, Lower plane bed, Sand sheet, Slide, Paludal, Lithotope. Excerpt: Giant current ripples are active channel topographic forms up to 20 m high, which develop within near-talweg areas of the main outflow valleys crated by glacial lake outburst floods. Giant current ripple marks are morphologic and genetic macroanalogues of small current ripples formed in sandy stream sediments. The giant current ripple marks are important depositional forms in diluvial plain and mountain scablands. J Harlen Bretz in 1949.The history of the scabland studies has two distinct stages: the "old" one that began with the first works by J Harlen Bretz and Joseph Pardee in North America and lasted until the end of the 20th century that was crowned with the discovery of giant current ripple marks in Eurasia, and a "new" one. The latter is associated with heated debates concerning the genesis of the relief under study and which involved a lot of Russian geologists, geomorphologists and geographers. The discussion about the origin of the giant ripples dealt at least to a certain extent with every aspect of the diluvial theory, from the genesis of the lakes themselves, their...

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t1=0.038, t2=0, t3=0, t4=0, t=0.038