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Crossed products. --- Group rings. --- Galois theory. --- Crossed products --- Galois theory --- Group rings --- 512.54 --- Group theory --- Rings (Algebra) --- Equations, Theory of --- Number theory --- Cross products --- Products, Crossed --- Associative rings --- 512.54 Groups. Group theory --- Groups. Group theory --- Ordered algebraic structures

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For the analysis and optimization of the picosecond pulsed terahertz radiation generated by electron storage rings or other pulsed sources, ultra-fast detectors are required which are able to resolve picosecond dynamic processes directly in the time domain. In this book, a new direct terahertz detector technology based on the high-temperature superconductor YBa2Cu3O7-x has been developed which opens new routes in the analysis of picosecond time-domain processes with a wide dynamic range.

terahertz detector --- picosecond temporal resolution --- high-temperature superconductivity --- synchrotron radiation --- electron storage rings

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Topological algebras --- Topological algebras. --- Algebras, Topological --- topological-algebraic structures --- topological dynamics --- topological semigroups --- noncommutative probability --- fuzzy topological algebras --- Functional analysis --- Linear topological spaces --- Rings (Algebra) --- Calculus

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This open access textbook welcomes students into the fundamental theory of measure, integration, and real analysis. Focusing on an accessible approach, Axler lays the foundations for further study by promoting a deep understanding of key results. Content is carefully curated to suit a single course, or two-semester sequence of courses, creating a versatile entry point for graduate studies in all areas of pure and applied mathematics. Motivated by a brief review of Riemann integration and its deficiencies, the text begins by immersing students in the concepts of measure and integration. Lebesgue measure and abstract measures are developed together, with each providing key insight into the main ideas of the other approach. Lebesgue integration links into results such as the Lebesgue Differentiation Theorem. The development of products of abstract measures leads to Lebesgue measure on Rn. Chapters on Banach spaces, Lp spaces, and Hilbert spaces showcase major results such as the Hahn–Banach Theorem, Hölder’s Inequality, and the Riesz Representation Theorem. An in-depth study of linear maps on Hilbert spaces culminates in the Spectral Theorem and Singular Value Decomposition for compact operators, with an optional interlude in real and complex measures. Building on the Hilbert space material, a chapter on Fourier analysis provides an invaluable introduction to Fourier series and the Fourier transform. The final chapter offers a taste of probability. Extensively class tested at multiple universities and written by an award-winning mathematical expositor, Measure, Integration & Real Analysis is an ideal resource for students at the start of their journey into graduate mathematics. A prerequisite of elementary undergraduate real analysis is assumed; students and instructors looking to reinforce these ideas will appreciate the electronic Supplement for Measure, Integration & Real Analysis that is freely available online.

Integral calculus & equations --- Measure theory. --- Measure and Integration. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Mathematics --- Measure theory

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This course-tested text is an ideal starting point for engineers and physicists entering the field of particle accelerators. The fundamentals are comprehensively introduced, derivations of essential results are provided, and a consistent notation style used throughout the book allows readers to quickly familiarize themselves with the field, providing a solid theoretical basis for further studies.   Emphasis is placed on the essential features of the longitudinal motion of charged particle beams, together with the corresponding RF generation and power amplification devices for synchrotron and storage ring systems. In particular, electrical engineering aspects such as closed-loop control of system components are discussed.   The book also offers a valuable resource for graduate students in physics, electronics engineering, or mathematics looking for an introductory and self-contained text on accelerator physics.

Physics. --- Particle Acceleration and Detection, Beam Physics. --- Microwaves, RF and Optical Engineering. --- Measurement Science and Instrumentation. --- Nanoscale Science and Technology. --- Mathematical Applications in the Physical Sciences. --- Particle acceleration. --- Microwaves. --- Physique --- Particules (Physique nucléaire) --- Micro-ondes --- Accélération --- Physics --- Physical Sciences & Mathematics --- Nuclear Physics --- Particle accelerators. --- Synchrotrons. --- Storage rings. --- Particle storage rings --- Synchrotron --- Accelerators, Particle --- Atom smashers --- Charged particle accelerators --- Mathematical physics. --- Nanoscale science. --- Nanoscience. --- Nanostructures. --- Physical measurements. --- Measurement. --- Optical engineering. --- Particle accelerators --- Nuclear physics --- Accelerator mass spectrometry --- Instruments --- Hertzian waves --- Electric waves --- Electromagnetic waves --- Geomagnetic micropulsations --- Radio waves --- Shortwave radio --- Particles (Nuclear physics) --- Acceleration (Mechanics) --- Acceleration --- Measurement   . --- Physical mathematics --- Nanoscience --- Nano science --- Nanoscale science --- Nanosciences --- Science --- Measuring --- Mensuration --- Mathematics --- Technology --- Metrology --- Physical measurements --- Measurements, Physical --- Mathematical physics --- Measurement --- Mechanical engineering --- Closed-loop Control --- Longitudinal Beam Dynamics --- Low-Level RF (LLRF) Systems --- Particle Accelerator Technology --- RF Accelerating Cavities and Power Amplification --- Radio Frequency Systems --- Synchrotrons