Topological Aspects of Four-Manifolds -- The Theory of Donaldson Invariants -- The Theory of Seiberg-Witten Invariants -- Supersymmetry in Four Dimensions -- Topological Quantum Field Theories in Four Dimensions -- The Mathai-Quillen Formalism -- The Seiberg-Witten Solution of N = 2 SUSY Yang-Mills Theory -- The u-plane Integral -- Some Applications of the u-plane Integral -- Further Developmen…
The intriguing mechanism of spontaneous symmetry breaking is a powerful innovative idea at the basis of most of the recent developments in theoretical physics, from statistical mechanics to many-body theory to elementary particles theory; for infinitely extended systems a symmetric Hamiltonian can account for non symmetric behaviours, giving rise to non symmetric realizations of a physical syst…
Why Symmetry? -- J-Pairing Interractions of Fermions in a Single-J Shell -- Supersymmetry in Nuclei -- The Relativistic Many Body Problem in Quantum Mechanics -- Gauge Invariance and the E1 Sum Rule in Nuclei -- The Heisenberg Group in Classical and Quantum Information Transmission -- Quantum Field Theory of Particle Mixing and Oscillations -- Two-Photon Interactions in Cavity QED -- Low-Dimens…
KdV-Class Solitons -- Generalized KdV Equations. NLS and DNLS Equations -- Classic Two- and Three-Dimensional KP Models and Their Applications -- Generalized Two- and Three-Dimensional Models and Their Applications -- Appendices.This book is devoted to one of the most interesting and rapidly developing areas of modern nonlinear physics and mathematics - the theoretical, analytical and advanced …
The Role of Mathematics in Physical Sciences — Interdisciplinary and Philosophical Aspects -- Mathematics and Physics: Reflecting on the Historical Role of Mathematics -- Oliver Heaviside’s “Dinner” -- Quantum Physics and Mathematical Debates Concerning the Problem of the Ontological Priority between Continuous Quantity and Discrete Quantity -- John von Neumann on Mathematical and Axiom…
Tutorial: Introductory Material -- Quantum Annealing: Basics and Applications -- Other Optimizations.Quantum annealing employs quantum fluctuations in frustrated systems or networks to anneal the system down to its ground state, or more generally to its so-called minimum cost state. Often this procedure turns out to be more effective, in multivariable optimization problems, than its classical c…
Equations with One Dependent Function -- Systems of Equations -- Method of the Degenerate Hodograph -- Method of Differential Constraints -- Invariant and Partially Invariant Solutions -- Symmetries of Equations with Nonlocal Operators -- Symbolic Computer Calculations.Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Each so…
Neural Networks: An Overview -- Modeling with Neural Networks: Principles and Model Design Methodology -- Modeling Metholodgy: Dimension Reduction and Resampling Methods -- Neural Identification of Controlled Dynamical Systems and Recurrent Networks -- Closed-Loop Control Learning -- Discrimination -- Self-Organizing Maps and Unsupervised Classification -- Neural Networks without Training for O…
Dirac Monopole -- Magnetic Monopole in Classical Theory -- The Electron-Monopole System:Quantum-Mechanical Interaction -- Topological Roots of the Abelian Monopole -- Abelian Monopole: Relativistic Quantum Theory -- Monopole in Non-Abelian Gauge Theories -- ’t Hooft-Polyakov Monopole -- Multimonopole Configurations -- SU(2) Monopole in Quantum Theory -- Monopoles Beyond SU(2) Group -- Monopol…
Information and telecommunication systems for emergency management -- High Performance Computing in Engineering and Science -- Completely splitting method for the Navier-Stokes problem -- Methods of shock wave calculation -- Distributed and collaborative visualization of simulation results -- Safety problems of technical objects -- Direct numerical simulations of shock-boundary layer interactio…