With applications in quantum field theory, general relativity and elementary particle physics, this four-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This third volume covers supersymmetry, including detailed coverage of conformal supersymmetry in four and some higher dimensions, furthermore quantum superalgebras are also considered. Contents Lie superalgebras Conformal supersymmetry in 4D Examples of conformal supersymmetry for D > 4 Quantum superalgebras

This book presents essential studies and applications in the context of sliding mode control, highlighting the latest findings from interdisciplinary theoretical studies, ranging from computational algorithm development to representative applications. Readers will learn how to easily tailor the techniques to accommodate their ad hoc applications. To make the content as accessible as possible, the book employs a clear route in each paper, moving from background to motivation, to quantitative development (equations), and lastly to case studies/illustrations/tutorials (simulations, experiences, curves, tables, etc.). Though primarily intended for graduate students, professors and researchers from related fields, the book will also benefit engineers and scientists from industry.

This book contains papers presented at the 2014 MICCAI Workshop on Computational Diffusion MRI, CDMRI'14. Detailing new computational methods applied to diffusion magnetic resonance imaging data, it offers readers a snapshot of the current state of the art and covers a wide range of topics from fundamental theoretical work on mathematical modeling to the development and evaluation of robust algorithms and applications in neuroscientific studies and clinical practice. Inside, readers will find information on brain network analysis, mathematical modeling for clinical applications, tissue microstructure imaging, super-resolution methods, signal reconstruction, visualization, and more. Contributions include both careful mathematical derivations and a large number of rich full-color visualizations. Computational techniques are key to the continued success and development of diffusion MRI and to its widespread transfer into the clinic. This volume will offer a valuable starting point for anyone interested in learning computational diffusion MRI. It also offers new perspectives and insights on current research challenges for those currently in the field. The book will be of interest to researchers and practitioners in computer science, MR physics, and applied mathematics.

This book - specifically developed as a novel textbook on elementary classical mechanics - shows how analytical and numerical methods can be seamlessly integrated to solve physics problems. This approach allows students to solve more advanced and applied problems at an earlier stage and equips them to deal with real-world examples well beyond the typical special cases treated in standard textbooks. Another advantage of this approach is that students are brought closer to the way physics is actually discovered and applied, as they are introduced right from the start to a more exploratory way of understanding phenomena and of developing their physical concepts. While not a requirement, it is advantageous for the reader to have some prior knowledge of scientific programming with a scripting-type language. This edition of the book uses Matlab, and a chapter devoted to the basics of scientific programming with Matlab is included. A parallel edition using Python instead of Matlab is also available. Last but not least, each chapter is accompanied by an extensive set of course-tested exercises and solutions.

Evolutionary algorithms constitute a class of well-known algorithms, which are designed based on the Darwinian theory of evolution and Mendelian theory of heritage. They are partly based on random and partly based on deterministic principles. Due to this nature, it is challenging to predict and control its performance in solving complex nonlinear problems. Recently, the study of evolutionary dynamics is focused not only on the traditional investigations but also on the understanding and analyzing new principles, with the intention of controlling and utilizing their properties and performances toward more effective real-world applications. In this book, based on many years of intensive research of the authors, is proposing novel ideas about advancing evolutionary dynamics towards new phenomena including many new topics, even the dynamics of equivalent social networks. In fact, it includes more advanced complex networks and incorporates them with the CMLs (coupled map lattices), which are usually used for spatiotemporal complex systems simulation and analysis, based on the observation that chaos in CML can be controlled, so does evolution dynamics. All the chapter authors are, to the best of our knowledge, originators of the ideas mentioned above and researchers on evolutionary algorithms and chaotic dynamics as well as complex networks, who will provide benefits to the readers regarding modern scientific research on related subjects.

In this thesis, quantum estimation theory is applied to investigate uncertainty relations between error and disturbance in quantum measurement. The author argues that the best solution for clarifying the attainable bound of the error and disturbance is to invoke the estimation process from the measurement outcomes such as signals from a photodetector in a quantum optical system. The error and disturbance in terms of the Fisher information content have been successfully formulated and provide the upper bound of the accuracy of the estimation. Moreover, the attainable bound of the error and disturbance in quantum measurement has been derived. The obtained bound is determined for the first time by the quantum fluctuations and correlation functions of the observables, which characterize the non-classical fluctuation of the observables. The result provides the upper bound of our knowledge obtained by quantum measurements. The method developed in this thesis will be applied to a broad class of problems related to quantum measurement to build a next-generation clock standard and to successfully detect gravitational waves.

The methods considered in the 7th conference on "Finite Volumes for Complex Applications" (Berlin, June 2014) have properties which offer distinct advantages for a number of applications. The second volume of the proceedings covers reviewed contributions reporting successful applications in the fields of fluid dynamics, magnetohydrodynamics, structural analysis, nuclear physics, semiconductor theory and other topics.

The finite volume method in its various forms is a space discretization technique for partial differential equations based on the fundamental physical principle of conservation. Recent decades have brought significant success in the theoretical understanding of the method. Many finite volume methods preserve further qualitative or asymptotic properties, including maximum principles, dissipativity, monotone decay of free energy, and asymptotic stability. Due to these properties, finite volume methods belong to the wider class of compatible discretization methods, which preserve qualitative properties of continuous problems at the discrete level. This structural approach to the discretization of partial differential equations becomes particularly important for multiphysics and multiscale applications.

Researchers, PhD and masters level students in numerical analysis, scientific computing and related fields such as partial differential equations will find this volume useful, as will engineers working in numerical modeling and simulations.

Strong pulsed magnetic fields are important for several fields in physics and engineering, such as power generation and accelerator facilities. Basic aspects of the generation of strong and superstrong pulsed magnetic fields technique are given, including the physics and hydrodynamics of the conductors interacting with the field as well as an account of the significant progress in generation of strong magnetic fields using the magnetic accumulation technique. Results of computer simulations as well as a survey of available field technology are completing the volume.

This monograph is devoted to the nonperturbative dynamics in the Standard Model (SM), the basic theory of allfundamental interactions in nature except gravity. The Standard Model is divided into two parts: the quantum chromodynamics (QCD) and the electro-weak theory (EWT) are well-defined renormalizable theories in which the perturbation theory is valid. However, for the adequate description of the real physics nonperturbative effects are inevitable. This book describes how these nonperturbative effects may be obtained in the framework of spontaneous generation of effective interactions. The well-known example of such effective interaction is provided by the famous Nambu-Jona-Lasinio effective interaction. Also a spontaneous generation of this interaction in the framework of QCD is described and applied to the method for other effective interactions in QCD and EWT. The method is based on N.N. Bogoliubov's conception of compensation equations. As a result we then describe the principal features of the Standard Model, e.g. Higgs sector, and significant nonperturbative effects including recent results obtained at LHC and TEVATRON.

This thesis focuses on the study and characterization of entanglement and nonlocal correlations constrained under symmetries. It includes original results as well as detailed methods and explanations for a number of different threads of research: positive partial transpose (PPT) entanglement in the symmetric states; a novel, experimentally friendly method to detect nonlocal correlations in many-body systems; the non-equivalence between entanglement and nonlocality; and elemental monogamies of correlations. Entanglement and nonlocal correlations constitute two fundamental resources for quantum information processing, as they allow novel tasks that are otherwise impossible in a classical scenario. However, their elusive characterization is still a central problem in quantum information theory. The main reason why such a fundamental issue remains a formidable challenge lies in the exponential growth in complexity of the Hilbert space as well as the space of multipartite correlations. Physical systems of interest, on the other hand, display symmetries that can be exploited to reduce this complexity, opening the possibility that some of these questions become tractable for such systems.

This book shows cognitive scientists in training how mathematics, computer science and science can be usefully and seamlessly intertwined. It is a follow-up to the first two volumes on mathematics for cognitive scientists, and includes the mathematics and computational tools needed to understand how to compute the terms in the Fourier series expansions that solve the cable equation. The latter is derived from first principles by going back to cellular biology and the relevant biophysics. A detailed discussion of ion movement through cellular membranes, and an explanation of how the equations that govern such ion movement leading to the standard transient cable equation are included. There are also solutions for the cable model using separation of variables, as well an explanation of why Fourier series converge and a description of the implementation of MatLab tools to compute the solutions. Finally, the standard Hodgkin - Huxley model is developed for an excitable neuron and is solved using MatLab.

The Dirac equation is of fundamental importance for relativistic quantum mechanics and quantum electrodynamics. In relativistic quantum mechanics, the Dirac equation is referred to as one-particle wave equation of motion for electron in an external electromagnetic field. In quantum electrodynamics, exact solutions of this equation are needed to treat the interaction between the electron and the external field exactly. In this monograph, all propagators of a particle, i.e., the various Green's functions, are constructed in a certain way by using exact solutions of the Dirac equation.

Dynamical System Synchronization (DSS) meticulously presents for the first time the theory of dynamical systems synchronization based on the local singularity theory of discontinuous dynamical systems. The book details the sufficient and necessary conditions for dynamical systems synchronizations, through extensive mathematical expression. Techniques for engineering implementation of DSS are clearly presented compared with the existing techniques.

By focusing on the mostly used variational methods, this monograph aspires to give a unified description and comparison of various ways of constructing conserved quantities for perturbations and to study symmetries in general relativity and modified theories of gravity. The main emphasis lies on the field-theoretical covariant formulation of perturbations, the canonical Noether approach and the Belinfante procedure of symmetrisation. The general formalism is applied to build the gauge-invariant cosmological perturbation theory, conserved currents and superpotentials to describe physically important solutions of gravity theories. Meticulous attention is given to the construction of conserved quantities in asymptotically-flat spacetimes as well as in asymptotically constant curvature spacetimes such as the Anti-de Sitter space. Significant part of the book can be used in graduate courses on conservation laws in general relativity. THE SERIES: DE GRUYTER STUDIES IN MATHEMATICAL PHYSICS The series is devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply, and develop further, with sufficient rigor, mathematical methods to given problems in physics. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

This proceedings records the 31st International Colloquium on Group Theoretical Methods in Physics ("Group 31"). Plenary-invited articles propose new approaches to the moduli spaces in gauge theories (V. Pestun, 2016 Weyl Prize Awardee), the phenomenology of neutrinos in non-commutative space-time, the use of Hardy spaces in quantum physics, contradictions in the use of statistical methods on complex systems, and alternative models of supersymmetry. This volume's survey articles broaden the colloquia's scope out into Majorana neutrino behavior, the dynamics of radiating charges, statistical pattern recognition of amino acids, and a variety of applications of gauge theory, among others. This year's proceedings further honors Bertram Kostant (2016 Wigner Medalist), as well as S.T. Ali and L. Boyle, for their life-long contributions to the math and physics communities. The aim of the ICGTMP is to provide a forum for physicists, mathematicians, and scientists of related disciplines who develop or apply methods in group theory to share their research. The 31st ICGTMP was held in Rio de Janeiro, Brazil, from June 19th to June 25th, 2016. This was the first time that a colloquium of the prestigious and traditional ICGTMP series (which started in 1972 in Marseille, France) took place in South America. (The history of the colloquia can be found at http://icgtmp.blogs.uva.es/)

In How Language Informs Mathematics Dirk Damsma shows how Hegel's and Marx's systematic dialectical analysis of mathematical and economic language helps us understand the structure and nature of mathematical and capitalist systems. More importantly, Damsma shows how knowledge of the latter can inform model assumptions and help improve models. His book provides a blueprint for an approach to economic model building that does away with arbitrarily chosen assumptions and is sensitive to the institutional structures of capitalism. In light of the failure of mainstream economics to understand systemic failures like the financial crisis and given the arbitrary character of most assumptions in mainstream models, such an approach is desperately needed.

This book presents the state-of-the-art in various aspects of analysis and mining of online social networks. Within the broader context of online social networks, it focuses on important and upcoming topics of social network analysis and mining such as the latest in sentiment trends research and a variety of techniques for community detection and analysis. The book collects chapters that are expanded versions of the best papers presented at the IEEE/ACM International Conference on Advances in Social Networks Analysis and Mining (ASONAM'2015), which was held in Paris, France in August 2015. All papers have been peer reviewed and checked carefully for overlap with the literature. The book will appeal to students and researchers in social network analysis/mining and machine learning.

This thesis sheds important new light on the puzzling properties of Strontium Ruthenate. Using a sophisticated weak-coupling approach, exact within certain limits, it shows that proper treatment of spin-orbit and multi-band effects is crucial to the physics. Based on the results of these calculations, it resolves a crucial, long-standing puzzle in the field: It demonstrates why the experimentally observed time-reversal breaking is not incompatible with the observed lack of measurable edge currents. Lastly, the thesis makes predictions for the properties of the material under uniaxial strain, which are in good agreement with recent experiments -resolving the mystery of the so-called 3K phase, and suggesting the intriguing possibility that under strain the superconductor may become conventional.

This book introduces the fascinating world of plasmonics and physics at the nanoscale, with a focus on simulations and the theoretical aspects of optics and nanotechnology. A research field with numerous applications, plasmonics bridges the gap between the micrometer length scale of light and the secrets of the nanoworld. This is achieved by binding light to charge density oscillations of metallic nanostructures, so-called surface plasmons, which allow electromagnetic radiation to be focussed down to spots as small as a few nanometers. The book is a snapshot of recent and ongoing research and at the same time outlines our present understanding of the optical properties of metallic nanoparticles, ranging from the tunability of plasmonic resonances to the ultrafast dynamics of light-matter interaction. Beginning with a gentle introduction that highlights the basics of plasmonic interactions and plasmon imaging, the author then presents a suitable theoretical framework for the description of metallic nanostructures. This model based on this framework is first solved analytically for simple systems, and subsequently through numerical simulations for more general cases where, for example, surface roughness, nonlinear and nonlocal effects or metamaterials are investigated.

Systems with mechanical degrees of freedom containing unstable objects are analysed in this monograph and algorithms for their control are developed, discussed, and numerically tested. This is achieved by identifying unstable modes of motion and using all available resources to suppress them. By using this approach the region of states from which a stable regime can be reached is maximised. The systems discussed in this book are models for pendula and vehicles and find applications in mechatronics, robotics as well as in mechanical and automotive engineering.

This is the first book to systematically consider the modern aspects of chaotic dynamics of magnetic field lines and charged particles in magnetically confined fusion plasmas. The analytical models describing the generic features of equilibrium magnetic fields and magnetic perturbations in modern fusion devices are presented. It describes mathematical and physical aspects of onset of chaos, generic properties of the structure of stochastic magnetic fields, transport of charged particles in tokamaks induced by magnetic perturbations, new aspects of particle turbulent transport, etc. The presentation is based on the classical and new unique mathematical tools of Hamiltonian dynamics, like the action--angle formalism, classical perturbation theory, canonical transformations of variables, symplectic mappings, the Poincare-Melnikov integrals. They are extensively used for analytical studies as well as for numerical simulations of magnetic field lines, particle dynamics, their spatial structures and statistical properties. The numerous references to articles on the latest development in the area are provided. The book is intended for graduate students and researchers who interested in the modern problems of magnetic stochasticity in magnetically confined fusion plasmas. It is also useful for physicists and mathematicians interested in new methods of Hamiltonian dynamics and their applications.

This book explores the rise of theoretical physics in 19th century Germany. The authors show how the junior second physicist in German universities over time became the theoretical physicist, of equal standing to the experimental physicist. Gustav Kirchhoff, Hermann von Helmholtz, and Max Planck are among the great German theoretical physicists whose work and career are examined in this book. Physics was then the only natural science in which theoretical work developed into a major teaching and research specialty in its own right. Readers will discover how German physicists arrived at a well-defined field of theoretical physics with well understood and generally accepted goals and needs. The authors explain the nature of the work of theoretical physics with many examples, taking care always to locate the research within the workplace. The book is a revised and shortened version of Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, a two-volume work by the same authors. This new edition represents a reformulation of the larger work. It retains what is most important in the original work, while including new material, sharpening discussions, and making the research more accessible to readers. It presents a thorough examination of a seminal era in physics.

This book contains four survey papers related to different topics in computational mechanics, in particular (1) novel discretization and solver techniques in mechanics and (2) inverse, control, and optimization problems in mechanics. These topics were considered in lectures, seminars, tutorials, and workshops at the Special Semester on Computational Mechanics held at the Johann Radon Institute for Computational and Applied Mathematics (RICAM), Linz, Austria, in December 2005.

This book is an elementary introduction to the basic concepts of financial mathematics with a central focus on discrete models and an aim to demonstrate simple but widely used financial derivatives for managing market risks. Only a basic knowledge of probability, real analysis, ordinary differential equations, linear algebra and some common sense are required to utilise this book. Financial mathematics is an application of advanced mathematical and statistical methods to financial management and markets, with a main objective to quantify and hedge risks. Since the book aims to present the basics of financial mathematics to the reader, only essential elements of probability and stochastic analysis are given to explain ideas on derivative pricing and hedging. To keep the reader intrigued and motivated, the book has a sandwich structure: Probability and stochastics are given on the spot, at places where mathematics can almost immediately be illustrated by an application to finance. The first part of the book introduces one of the main principles in finance - no arbitrage pricing.It also introduces main financial instruments such as forward and futures contracts, bonds and swaps, and options. This part is not mathematical. The second part deals with pricing and hedging of European- and American-type options in the discrete time setting. In addition, the concept of complete and incomplete markets is discussed. Elementary probability is briefly revised and discrete-time - discrete-space stochastic processes used in financial modelling are considered. The third part discusses stochastic analysis and introduces the Wiener process, Ito integrals, and stochastic differential equations. The main feature of this final part of the book is the famous Black - Scholes formula for pricing European options. Some guidance for further study of this exciting and rapidly changing subject is given in the last chapter. The book has approximately 100 exercises, for which most solutions have been provided.

The book "Computational Error and Complexity in Science and Engineering" pervades all the science and engineering disciplines where computation occurs. Scientific and engineering computation happens to be the interface between the mathematical model/problem and the real world application. One needs to obtain good quality numerical values for any real-world implementation. Just mathematical quantities symbols are of no use to engineers/technologists. Computational complexity of the numerical method to solve the mathematical model, also computed along with the solution, on the other hand, will tell us how much computation/computational effort has been spent to achieve that quality of result. Anyone who wants the specified physical problem to be solved has every right to know the quality of the solution as well as the resources spent for the solution. The computed error as well as the complexity provide the scientific convincing answer to these questions.
Specifically some of the disciplines in which the book will be readily useful are (i) Computational Mathematics, (ii) Applied Mathematics/Computational Engineering, Numerical and Computational Physics, Simulation and Modelling. Operations Research (both deterministic and stochastic), Computing Methodologies, Computer Applications, and Numerical Methods in Engineering.
Key Features:
- Describes precisely ready-to-use computational error and complexity
- Includes simple easy-to-grasp examples wherever necessary.
- Presents error and complexity in error-free, parallel, and probabilistic methods.
- Discusses deterministic and probabilistic methods with error and complexity.
- Points out the scope and limitation ofmathematical error-bounds.
- Provides a comprehensive up-to-date bibliography after each chapter.
- Describes precisely ready-to-use computational error and complexity
- Includes simple easy-to-grasp examples wherever necessary.
- Presents error and complexity in error-free, parallel, and probabilistic methods.
- Discusses deterministic and probabilistic methods with error and complexity.
- Points out the scope and limitation of mathematical error-bounds.
- Provides a comprehensive up-to-date bibliography after each chapter.