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Groups and Manifolds
Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.
Who Owns Outer Space?
Explores the environmental, safety, and security challenges facing humanity's rapid expansion into Space and proposes actionable solutions.
Global Identitarianism
Global Identitarianism is about the global spread of the new far-right ideology and social movement Identitarianism. Founded in France in 2003, Identitarianism has inspired a range of groups such as Generation Identity in Europe and the alt-right in America. It has been spread by a far-right constellation that includes white nationalist direct action groups, think tanks, ‘alternative media’ organizations, social media ‘celebrities’, and political candidates. This book explores the global reach of this contentious far-right social movement using examples from Europe, North America, Australia, and South America. It will be essential reading for scholars and activists alike with an interest in race relations, fascism, extremism, migration studies, and social movements.
Dynamical Systems and Geometric Mechanics
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.
Nonlinear Gaussian Filtering : Theory, Algorithms, and Applications
By restricting to Gaussian distributions, the optimal Bayesian filtering problem can be transformed into an algebraically simple form, which allows for computationally efficient algorithms. Three problem settings are discussed in this thesis: (1) filtering with Gaussians only, (2) Gaussian mixture filtering for strong nonlinearities, (3) Gaussian process filtering for purely data-driven scenarios. For each setting, efficient algorithms are derived and applied to real-world problems.
Explore Earth
A sky full of air, oceans made of water, and the presence of life are some of the things that set Earth apart from other planets. Learn what else makes Earth unique among the planets in our solar system! Access a downloadable 3D printer model from NASA via Page Plus QR codes.
Collective Effects in Condensed Matter Physics
This monograph offers a concise overview of the theoretical description of various collective phenomena in condensed matter physics. These effects include the basic electronic structure in solid state physics, lattice vibrations, superconductivity, light-matter interaction and more advanced topics such as martensitic transistions.
Irreducible Cartesian Tensors
This monograph covers the concept of cartesian tensors with the needs and interests of physicists, chemists and other physical scientists in mind. After introducing elementary tensor operations and rotations, spherical tensors, combinations of tensors are introduced, also covering Clebsch-Gordan coefficients. After this, readers from the physical sciences will find generalizations of the results to spinors and applications to quantum mechanics.
