Algebraic Methods in Physics

Self-Similarities and Invariant Densities for Model Sets. - Model Sets and Self-Similarities. - Averaging Operators and Invariant Densities. - Further Remarks. - Outlook. - References. - Symmetry Operations in the Brain: Music and Reasoning. - Trion Model. - Music Enhances Spatial-Temporal Reasoning. - References. - Lie Modules of Bounded Multiplicities. - Simple L Modules with Finite-Dimensional Weight Spaces. - Completely Pointed Modules. - Completely Pointed Modules Tensored with Finite-Dimensional Modules. - References. - Moving Frames and Coframes. - References. - The Fibonacci-Deformed Harmonic Oscillator. - About Strictly Increasing Sequences of Positive Numbers. - Quantum Algebra Associated with the Spectrum ? = xn. - The ?-Natural Spectrum. - The Fibonacci Deformation of Weyl Algebra. - Coherent States and Some Special Functions. - References. - Continuous and Discrete Linearizable Systems: The Riccati Saga. - Brief Review of the Continuous Gambier Equation. - Discrete Analog of the Gambier Equation Revisited. - Discrete Projective and Matrix Riccati Equations. - Discrete Conformai Riccati Equations. - Conclusions and Outlook. - References. - Superintegrability on Two-Dimensional Complex Euclidean Space. - Potential V5. - Potential V6. - Potential V7. - References. - Hydrodynamic Systems and the Higher-Dimensional Laplace Transformations of Cartan Submanifolds. - Hydrodynamic Systems Rich in Conservation Laws. - Applications of the Higher-Dimensional Laplace Transformation to Hydrodynamic Systems that are Rich in Conservation Laws. - References. - Branching Rules and Weight Multiplicities for Simple and Affine Lie Algebras. - Simple and Affine Lie Algebras. - Branching Rules for Simple Lie Algebras. - Young Diagrams and Branching Rules. - Weight Multiplicities of Simple Lie Algebras. - Young Tableauxand Weight Multiplicities. - Branching Rule Multiplicities for the Restriction from Affine to Simple Lie Algebras. - Branching Rules Derived from Characters. - Weight Multiplicities of Affine Lie Algebras. - References. - Conditions for the Existence of Higher Symmetries and Nonlinear Evolutionary Equations on the Lattice. - Construction of the Classifying Conditions. - The Toda Lattice Class. - References. - Complete Description of the Voronoï Cell of the Lie Algebra An Weight Lattice. On the Bounds for the Number of d-Faces of the n-Dimensional Voronoï Cells. - The Expression of the Bounds Nd(n) Obtained by Voronoï. - Detailed Description of the Voronoï Cells of the A Lattices. - The New Explicit Expression of Bounds Nd(n). - Expression of Nd(n) as Multiple of a Stirling Number of Second Kind. - Final Remarks. - References. - The Relativistic Oscillator and the Mass Spectra of Baryons. - The System of Three Relativistic Scalar Particles with Oscillator Interactions. - An Approach to the Spinorial Relativistic Three-Body System. - References. - Seiberg-Witten Theory Without Tears. - N = 2 Supersymmetry. - N = 2 Superaction. - Textbook Properties. - Spontaneous Symmetry-Breaking. - Holomorphy and Duality. - Perturbative and Nonperturbative F (A). - Preliminaries. - Fuchsian Maps. - The Schwarzian Derivatives. - SW Choice. - Correctness. - Uniqueness. - References. - Bargmann Representation for Some Deformed Harmonic Oscillators with Non-Fock Representation. - Representations. - Toward a Bargmann Representation. - The q-Oscillator. - Generalization of the Previous Example. - Deformed Algebra Associated to a Given Weight function. - Bargmann Representations Corresponding to Different ?. - The Case of an Annulus. - Conclusion. - References. - The Vector-Coherent-State Inducing Construction forClebsch-Gordan Coefficients. - Induced Representations of su(4). - SU(4) Clebsch-Gordan Coefficients. - Summary. - References. - Highest-Weight Representations of Borcherds Algebras. - Borcherds Algebras. - Cartan Subalgebra of an Affine Kac-Moody Algebra. - Adding Energy and Number Operators to the Cartan Subalgebra. - Conclusions. - References. - Graded Contractions of Lie Algebras of Physical Interest. - Notion of Graded Contractions. - Physical Applications. - References. Language: English