Mathematics and Its Applications

1. Collective Excitations in Quasi-Periodical Molecular Structures.- 1. Crisis in Bioenergetics.- 2. Alpha-Helical Structure of Proteins.- 3. Collective Excitations in a Single Chain of Peptide Groups.- 4. Excitons in Molecular a Chain.- 5. Solitons in Molecular a Chain.- 6. Solitons in Real ?-Helical Molecules.- 2. Some Phenomena with Participation of Molecular Solitons.- 7. Solitons and Molecular Mechanism for Muscle Contraction.- 8. Solitons and the Molecular Mechanism of the Effect of Radiation on Cells.- 9. A Possible Mechanism for General Anesthesia.- 10. Intracellular Dynamics and Solitons.- 3. Excitation of Solitons in One-Dimensional Systems.- 11. Time-Dependent Evolution of Initial Excitation.- 12. Initial Excitation in the Form of a Hyperbolic Secant.- 13. Initial Excitation in the Form of a Rectangular Impulse.- 4. Dynamical Properties of Solitons.- 14. Free Solitons.- 15. Soliton Motion with Friction.- 16. Soliton Motion Affected by External Inhomogeneous Fields.- 5. Solitons in Molecular Systems with Nonlinear Intermolecular Interactions.- 17. The Equation of Soliton Motion for General Intermolecular Interaction.- 18. Cubic Anharmonicity.- 19. Quartic Anharmonicity.- 20. Repulsive Core Potential.- 6. Super-Sound Acoustic Solitons.- 21. Solitons in Toda Nonlinear Lattices.- 22. Acoustic Solitons in Molecular Chain with Cubic Anharmonicity.- 23. Acoustic Solitons in Molecular Chain with Quartic Anharmonicity.- 24. The Capture of an Excess Electron by Supersound Acoustic Solitons.- 25. Supersound Solitons in Nonlinear Quasi-One-Dimensional Molecular Structures.- 7 The Theory of Electron Transfer by Solitons.- 26. The Donor-Acceptor Model of Electron Transfer by Protein Molecules.- 26.1. Pairing of Two Excess Electrons in a One-Dimensional Molecular Chain.- 27. The Interaction of an Electron with Nondipole Optical Phonons.- 8 Space-Periodic Excitations in Nonlinear Systems.- 28. Mobile Periodical Excitations in One-Dimensional Systems.- 28.1. First Type of Periodic Excitations.- 28.2. Second Type of Periodic Excitations.- 29. Elementary Data on Jacobian Elliptic Functions.- 30. Periodic Solutions of the Nonlinear Schrodinger Equation. Cnoidal Waves.- 30.1. Cnoidal Waves of the First Kind.- 30.2. Cnoidal Waves of the Second Kind.- 30.3. Solutions of the Nonlinear Schrodinger Equation with a Negative Nonlinearity Parameter.- 31. Periodic Solutions for Some Quasiparticles in a Quasi-One-Dimensional Molecular Chain.- 31.1. Superconductivity of Organic Crystals.- 32. Autolocalized Periodic Thickening of Particles Described by a Complex Field with Inertialess Self-Interaction.- 32.1. First Type of Autolocalized Solutions: Attractive Forces.- 32.2. Second Type of Autolocalized Solutions: Attractive Forces.- 32.3. Repulsive Forces.- 32.4. Autolocalized Excitations in Closed Molecular Chains.- 9 The Quantum Theory of Quasiparticle Motion in a Molecular Chain Taking into Account Thermal Vibrations.- 33. Equations for the Stationary States of a Quasiparticle in a One-Dimensional Chain within a Thermostat.- 34. Nonlocalized Stationary States of a Quasiparticle.- 35. Smooth Autolocalized State-Single Soliton.- 36. Solutions Describing the Movement of Periodically Arranged Quasiparticles.- 37. Strong Quasiparticle Autolocalization.- 37.1. Chains with Narrow Energy Bands.- 37.2. Chains with Broad Energetic Bands.- 38. Radiation Excitation of Optical Solitons in Crystalline Acetanilide.- 38.1. Optical Solitons in Crystalline Acetanilide.- 38.2. Absorption of Radiation Resulting from the Creation of Optical Solitons.- 38.3. Acoustic Solitons in an ACN Crystal.- 10 The Nonlinear Sine-Gordon Equation.- 39. Canonic Form of the Sine-Gordon Equation.- 40. Single-Phase Solutions of the Sine-Gordon Equation.- 40.1. Magnetic-Type Wave Solutions.- 40.2. Electric-Type Wave Solutions.- 41. The Solution of the Sine-Gordon Equation by the Method of Separation of Variables.- 41.1. Single-Phase Solutions.- 41.2. Double-Phase Solutions.- 41.3. Standing Waves.- 42. Josephson Tunnelling Effect in Superconductors.- 43. The Dynamics of Dislocations in Crystals.- 44. Bloch Wave Motion.- 45. The Propagation of Ultrashort Optical Pulses.- 11 Conformational Excitations in One-Dimensional Molecular Systems.- 46. Quasi-One-Dimensional Systems Undergoing Structural Phase Transitions.- 46.1. Order-Disorder Transitions.- 46.2. Displacive Transitions.- 12 Solitons and Proton Motion in Hydrogen-Bonded Molecular Structures.- 47. A Model of Proton Conductivity: Basic Equations.- 48. Proton Motion Neglecting the Interaction between Sublattices.- 49. Proton Motion Taking into Account the Interaction between Sublattice Displacements.- 50. The Motion of Orientational Defects in Chains of Water Molecules.- 50.1. The Motion of Orientational Defects in an Electric Field.- 50.2. The Interaction of Orientational Bjerrum Defects.- 51. The Migration of Protons in Near-Surface Layers of Water.- 51.1. Proton Pumps in Cellular Membranes.- 51.2. The Role of Structuralized Water in Cartilage Tissues.- 13 Three-Dimensional Solitons (Polarons) in Ionic Crystals.- 52. The Landau and Pekar Concepts of Autolocalization of the Electron in Ionic Crystal.- 52.1. Adiabatic Theory of Pekar's Polaron.- 53. Generalized Theory of Polarons.- 53.1. The Direct Variational Principle.- 53.2. Energy and Wave Function of a Slow Polaron.- 14 The Generation of Solitons and Bisolitons.- 54. The Generation of a Soliton at the Boundary of a Soft Molecular Chain.- 54.1. The Dependence of Wave Functions. Soliton Generation.- 54.2. Bisoliton Generation.- 15 Nonlinear Bisolitonic Mechanism of High-Tc Superconductivity.- 55. Discovery of High-Tc Superconductors and their Basic Properties.- 56. The Basis of the Bisoliton Model of High-Tc Superconductivity.- 56.1. Isolated Bisolitons in a Quasi-One-Dimensional Chain.- 56.2. Bose Condensation of Bisolitons.- 56.3. Stability of the Bisoliton Condensate and Critical Superconducting Currents.- 56.4. Small and Medium Quasiparticle Densities in a Chain.- 56.5. The Generation of Bisolitons at the Boundary of a Metal with Superconductors.- 56.6. Direct Measurements of Energy Gap in Superconductors.