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Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)

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This third edition builds on the introduction of spectral analysis as a means of investigating wave propagation and transient oscillations in structures. Each chapter of the textbook has been revised, updated and augmented with new material, such as a modified treatment of the curved plate and cylinder problem that yields a relatively simple but accurate spectral analysis. Finite element methods are now integrated into the spectral analyses to gain further insights into the high-frequency problems. In addition, a completely new chapter has been added that deals with waves in periodic and discretized structures. Examples for phononic materials meta-materials as well as genuine atomic systems are given. Systematically develops and then applies the spectral methods to analyzing the dynamic responses; Examines spectral analysis of discrete and discretized structures; Explains spectral analysis as applied to metamaterials and nanostructures; Reinforces reader understanding with a combination of experimental and analytical results related to wave propagation in structures.

Mechanics. --- Mechanics, Applied. --- Vibration. --- Dynamical systems. --- Dynamics. --- Solid Mechanics. --- Vibration, Dynamical Systems, Control. --- Classical Mechanics. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Cycles --- Sound --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Wave-motion, Theory of. --- Spectral theory (Mathematics) --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Undulatory theory

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Spectral theory (Mathematics) --- Linear operators. --- Linear maps --- Maps, Linear --- Operators, Linear --- Operator theory --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Teoria espectral (Matemàtica) --- Operadors lineals --- Teoria d'operadors --- Operadors de Calderón-Zygmund --- Operadors autoadjunts --- Operadors de Toeplitz --- Anàlisi funcional --- Equacions en derivades parcials --- Successions espectrals (Matemàtica) --- Espais de Hilbert --- Operadors lineals.

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This book concerns issues related to biomathematics, medicine, or cybernetics as practiced by engineers. Considered population dynamics models are still in the interest of researchers, and even this interest is increasing, especially now in the time of SARS-CoV-2 coronavirus pandemic, when models are intensively studied in order to help predict its behaviour within human population. The structures of population dynamics models and practical methods of finding their solutions are discussed. Finally, the hypothesis of the existence of non-trivial ergodic properties of the model of erythropoietic response dynamics formulated by A. Lasota in the form of delay differential equation with unimodal feedback is analysed. The research can be compared with actual medical data, as well as shows that the structures of population models can reflect the dynamic structures of reality. .

Computers. --- Engineering mathematics. --- Computer science—Mathematics. --- Computer mathematics. --- Biomedical engineering. --- Theory of Computation. --- Engineering Mathematics. --- Mathematical Applications in Computer Science. --- Biomedical Engineering and Bioengineering. --- Clinical engineering --- Medical engineering --- Bioengineering --- Biophysics --- Engineering --- Medicine --- Computer mathematics --- Electronic data processing --- Mathematics --- Engineering analysis --- Mathematical analysis --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)

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This textbook provides a graduate-level introduction to the spectral theory of linear operators on Banach and Hilbert spaces, guiding readers through key components of spectral theory and its applications in quantum physics. Based on their extensive teaching experience, the authors present topics in a progressive manner so that each chapter builds on the ones preceding. Researchers and students alike will also appreciate the exploration of more advanced applications and research perspectives presented near the end of the book. Beginning with a brief introduction to the relationship between spectral theory and quantum physics, the authors go on to explore unbounded operators, analyzing closed, adjoint, and self-adjoint operators. Next, the spectrum of a closed operator is defined and the fundamental properties of Fredholm operators are introduced. The authors then develop the Grushin method to execute the spectral analysis of compact operators. The chapters that follow are devoted to examining Hille-Yoshida and Stone theorems, the spectral analysis of self-adjoint operators, and trace-class and Hilbert-Schmidt operators. The final chapter opens the discussion to several selected applications. Throughout this textbook, detailed proofs are given, and the statements are illustrated by a number of well-chosen examples. At the end, an appendix about foundational functional analysis theorems is provided to help the uninitiated reader. A Guide to Spectral Theory: Applications and Exercises is intended for graduate students taking an introductory course in spectral theory or operator theory. A background in linear functional analysis and partial differential equations is assumed; basic knowledge of bounded linear operators is useful but not required. PhD students and researchers will also find this volume to be of interest, particularly the research directions provided in later chapters.

Functional analysis. --- Mathematical analysis. --- Analysis (Mathematics). --- Mathematical physics. --- Functional Analysis. --- Analysis. --- Mathematical Physics. --- Physical mathematics --- Physics --- 517.1 Mathematical analysis --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Mathematics --- Spectral theory (Mathematics) --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Teoria espectral (Matemàtica) --- Anàlisi funcional --- Equacions en derivades parcials --- Successions espectrals (Matemàtica) --- Espais de Hilbert --- Differential equations. --- Differential Equations. --- 517.91 Differential equations --- Differential equations