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Spectral Measures and Dynamics: Typical Behaviors (Latin American Mathematics Series)
by César R. de Oliveira Moacir Aloisio Silas L. CarvalhoThis book convenes and deepens generic results about spectral measures, many of them available so far in scattered literature. It starts with classic topics such as Wiener lemma, Strichartz inequality, and the basics of fractal dimensions of measures, progressing to more advanced material, some of them developed by the own authors.A fundamental concept to the mathematical theory of quantum mechanics, the spectral measure relates to the components of the quantum state concerning the energy levels of the Hamiltonian operator and, on the other hand, to the dynamics of such state. However, these correspondences are not immediate, with many nuances and subtleties discovered in recent years.A valuable example of such subtleties is found in the so-called “Wonderland theorem” first published by B. Simon in 1995. It shows that, for some metric space of self-adjoint operators, the set of operators whose spectral measures are singular continuous is a generic set (which, for some, is exotic). Recent works have revealed that, on top of singular continuity, there are other generic properties of spectral measures. These properties are usually associated with a number of different notions of generalized dimensions, upper and lower dimensions, with dynamical implications in quantum mechanics, ergodicity of dynamical systems, and evolution semigroups. All this opens ways to new and instigating avenues of research.Graduate students with a specific interest in the spectral properties of spectral measure are the primary target audience for this work, while researchers benefit from a selection of important results, many of them presented in the book format for the first time.
Spectral Methods in Chemistry and Physics
by Bernard ShizgalThis book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed. The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations. The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials. The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared. MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.
Spectral Methods in Geodesy and Geophysics
by Christopher JekeliThe text develops the principal aspects of applied Fourier analysis and methodology with the main goal to inculcate a different way of perceiving global and regional geodetic and geophysical data, namely from the perspective of the frequency, or spectral, domain rather than the spatial domain. The word "methods" in the title is meant to convey that the transformation of a geophysical signal into the spectral domain can be applied for purposes of analysis as well as rapid computation. The text is written for graduate students; however, Chapters 1 through 4 and parts of 5 can also benefit undergraduates who have a solid and fluent knowledge of integral and differential calculus, have some statistical background, and are not uncomfortable with complex numbers. Concepts are developed by starting from the one-dimensional domain and working up to the spherical domain, which is part of every chapter. Many concepts are illustrated graphically with actual geophysical data primarily from signals of gravity, magnetism, and topography.
Spectral Mixture for Remote Sensing: Linear Model and Applications (Springer Remote Sensing/Photogrammetry)
by Yosio Edemir Shimabukuro Flávio Jorge PonzoniThis book explains in a didactic way the basic concepts of spectral mixing, digital numbers and orbital sensors, and then presents the linear modelling technique of spectral mixing and the generation of fractional images. In addition to presenting a theoretical basis for spectral mixing, the book provides examples of practical applications such as projects for estimating and monitoring deforested areas in the Amazon. In its seven chapters, the book offers remote sensing techniques to understand the main concepts, methods, and limitations of spectral mixing for digital image processing. Chapter 1 addresses the basic concepts of spectral mixing, while chapters 2 and 3 discuss digital numbers and orbital sensors such as MODIS and Landsat MSS. Chapter 4 details the linear spectral mixing model, and chapter 5 talks about how to use this technique to create fraction images. Chapter 6 offers remote sensing applications of fraction images in deforestation monitoring, burned-area mapping, selective logging detection, and land-use/land-cover mapping. Chapter 7 gives some concluding thoughts on spectral mixing, and considers future uses in environmental remote sensing. This book will be of interest to students, teachers, and researchers using remote sensing for Earth observation and environmental modelling.
Spectral Multi-Detector Computed Tomography: Data Acquisition, Image Formation, Quality Assessment and Contrast Enhancement (Series in Medical Physics and Biomedical Engineering)
by Xiangyang TangX-ray computed tomography (CT) has been one of the most popular diagnostic imaging modalities for decades in the clinic for saving patients’ lives or improving their quality of life. This book is an introductory one-stop shop for technological and clinical topics in multi-detector computed tomography (MDCT). Starting with MDCT’s fundamentals in physics and mathematics, the book provides an in-depth introduction to its system architecture and imaging chain, signal detection via energy-integration and photon-counting mechanisms, clinical application-driven scan modes and protocols, analytic and iterative image reconstruction solutions, and spectral imaging – the latest technological advancement in MDCT. The book extends its coverage on image quality assessment under the theory of signal detection and statistical decision. In recognition of its clinical relevance for conspicuity enhancement in angiographic and parenchymal imaging applications, the book features a chapter dedicated to the fundamental (chemical, physical and physicochemical) properties and clinical administration of iodinated contrast agent. The book ends with an outlook of the contrast agents that are novel in material and delivery, and their synergy with spectral MDCT to elevate CT’s contrast resolution in cardiovascular, neurovascular and oncologic applications. This book will be an invaluable reference for researchers, engineers, radiological physicians and technologists, and graduate and senior undergraduate students. Features Provides an accessible introduction to the subject Up to date with the latest advances in emerging technologies and procedures Provides a historical overview of CT technology Xiangyang Tang, PhD, is an imaging scientist with extensive research and development experience in industry (GE Healthcare), academia (Emory University School of Medicine) and the clinic (Emory Healthcare). With a focus on computed tomography, Tang has been working in the field of medical imaging for more than 20 years. He is a professor of radiology and imaging sciences at Emory University School of Medicine, Fellow of SPIE (International Society for Optics and Photonics) and Fellow of AAPM (American Association of Physicists in Medicine). Along with the publication of more than 200 papers in leading scientific journals and conferences, his contributions to the scientific community include serving as associate editor for a number of prestigious journals, in addition to working on the scientific committees of leading conferences and panels for numerous federal and foundational study sections.
Spectral Techniques In Proteomics
by Daniel S. SemFacilitating the innovation, development, and application of new spectroscopic methods in proteomics, Spectral Techniques in Proteomics provides a broad overview of the spectroscopic toolbox that can be used, either with proteome or sub-proteome mixtures or with individual/purified proteins studied in parallel. It gives a modest overview of
Spectral Theory and Mathematical Physics: STMP 2018, Santiago, Chile (Latin American Mathematics Series #254)
by Georgi Raikov Pablo Miranda Nicolas PopoffThis proceedings volume contains peer-reviewed, selected papers and surveys presented at the conference Spectral Theory and Mathematical Physics (STMP) 2018 which was held in Santiago, Chile, at the Pontifical Catholic University of Chile in December 2018. The original works gathered in this volume reveal the state of the art in the area and reflect the intense cooperation between young researchers in spectral theoryand mathematical physics and established specialists in this field. The list of topics covered includes: eigenvalues and resonances for quantum Hamiltonians; spectral shift function and quantum scattering; spectral properties of random operators; magnetic quantum Hamiltonians; microlocal analysis and its applications in mathematical physics. This volume can be of interest both to senior researchers and graduate students pursuing new research topics in Mathematical Physics.
Spectral Theory and Quantum Mechanics
by Valter MorettiThis book pursues the accurate study of the mathematical foundations of Quantum Theories. It may be considered an introductory text on linear functional analysis with a focus on Hilbert spaces. Specific attention is given to spectral theory features that are relevant in physics. Having left the physical phenomenology in the background, it is the formal and logical aspects of the theory that are privileged. Another not lesser purpose is to collect in one place a number of useful rigorous statements on the mathematical structure of Quantum Mechanics, including some elementary, yet fundamental, results on the Algebraic Formulation of Quantum Theories. In the attempt to reach out to Master's or PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book should benefit established researchers to organise and present the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly.
Spectral Theory and Quantum Mechanics (Universitext)
by Mathieu LewinThis textbook presents the spectral theory of self-adjoint operators on Hilbert space and its applications in quantum mechanics. Based on a course taught by the author in Paris, the book not only covers the mathematical theory but also provides its physical interpretation, offering an accessible introduction to quantum mechanics for students with a background in mathematics. The presentation incorporates numerous physical examples to illustrate the abstract theory. The final two chapters present recent findings on Schrödinger’s equation for systems of particles. While primarily designed for graduate courses, the book can also serve as a valuable introduction to the subject for more advanced readers. It requires no prior knowledge of physics, assuming only a graduate-level understanding of mathematical analysis from the reader.
Spectral Theory of Guided Waves
by A.S Silbergleit Y KopilevichSpectral Theory of Guided Waves represents a distillation of the authors' (and others) efforts over several years to rigorously discuss many of the properties of guided waves. The bulk of the book deals with the properties of eigenwaves of regular waveguiding systems and relates these to a variety of physical situations and applications to illustrate their generality. The book also includes considerable discussion of the basic properties of normal waves with quadratic operator pencils. Unique in its coverage of these subjects, the book will be of interest to engineers, applied mathematicians, and physicists with a working knowledge of functional analysis and spectral theory.
Spectral Theory of Localized Resonances and Applications
by Hongyu Liu Youjun DengThis book is devoted to the spectral theory of localized resonances including surface plasmon/polariton resonances, atypical resonances, anomalous localized resonances and interior transmission resonances. Those resonance phenomena arise in different physical contexts, but share similar features. They form the fundamental basis for many cutting-edge technologies and applications including invisibility cloaking and super-resolution imaging. The book presents a systematic and comprehensive treatment on these resonance phenomena and the associated applications in a unified manner from a mathematical and spectral perspective, covering acoustic, electromagnetic and elastic wave scattering.The book can serve as a handy reference book for researchers in this field and it can also serve as a textbook or an inspiring source for postgraduate students who are interested in entering this field.
Spectral Theory of Nonautonomous Dynamical Systems and Applications
by Thai Son DoanThe main challenge in the study of nonautonomous phenomena is to understand the very complicated dynamical behaviour both as a scientific and mathematical problem. The theory of nonautonomous dynamical systems has experienced a renewed and steadily growing interest in the last twenty years, stimulated also by synergetic effects of disciplines which have developed relatively independent for some time such as topological skew product, random dynamical systems, finite-time dynamics and control systems. The book provides new insights in many aspects of the qualitative theory of nonautonomous dynamical systems including the spectral theory, the linearization theory, the bifurcation theory. The book first introduces several important spectral theorem for nonautonomous differential equations including the Lyapunov spectrum, Sacker-Sell spectrum and finite-time spectrum. The author also establishes the smooth linearization and partial linearization for nonautonomous differential equations in application part. Then the second part recalls the multiplicative ergodic theorem for random dynamical systems and discusses several explicit formulas in computing the Lyapunov spectrum for random dynamical systems generated by linear stochastic differential equations and random difference equations with random delay. In the end, the Pitchfork bifurcation and Hopf bifurcation with additive noise are investigated in terms of change of the sign of Lyapunov exponents and loss of topological equivalence. This book might be appealing to researchers and graduate students in the field of dynamical systems, stochastic differential equations, ergodic theory.
Spectral and Dynamical Stability of Nonlinear Waves
by Keith Promislow Todd KapitulaThis book unifies the dynamical systems and functional analysis approaches to the linear and nonlinear stability of waves. It synthesizes fundamental ideas of the past 20+ years of research, carefully balancing theory and application. The book isolates and methodically develops key ideas by working through illustrative examples that are subsequently synthesized into general principles. Many of the seminal examples of stability theory, including orbital stability of the KdV solitary wave, and asymptotic stability of viscous shocks for scalar conservation laws, are treated in a textbook fashion for the first time. It presents spectral theory from a dynamical systems and functional analytic point of view, including essential and absolute spectra, and develops general nonlinear stability results for dissipative and Hamiltonian systems. The structure of the linear eigenvalue problem for Hamiltonian systems is carefully developed, including the Krein signature and related stability indices. The Evans function for the detection of point spectra is carefully developed through a series of frameworks of increasing complexity. Applications of the Evans function to the Orientation index, edge bifurcations, and large domain limits are developed through illustrative examples. The book is intended for first or second year graduate students in mathematics, or those with equivalent mathematical maturity. It is highly illustrated and there are many exercises scattered throughout the text that highlight and emphasize the key concepts. Upon completion of the book, the reader will be in an excellent position to understand and contribute to current research in nonlinear stability.
Spectral and Imaging Cytometry: Methods and Protocols (Methods in Molecular Biology #2635)
by Natasha S. Barteneva Ivan A. VorobjevThis second edition volume expands on the previous edition with discussions on the latest approaches used in the spectral cytometry field. Beginning with a brief history of spectral cytometry development, this book continues with a section addressing new protocols in different areas of imaging cytometry based on the unique technology of Imagestream and also introduces FlowCam – cytometer with capabilities of analyzing phytoplankton and zooplankton. Written for the highly successful Methods in Molecular Biology series, chapters include brief introductions to their respective topics, complete lists of the materials and reagents necessary, and reproducible laboratory protocols with tips on troubleshooting and recommendations.Cutting-edge and thorough, Spectral and Imaging Flow Cytometry: Methods and Protocols, Second Edition is a valuable resources for beginners and professionals interested in learning more about this developing field. Chapters 1, 2, and 5 are available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Spectral and Shape Analysis in Medical Imaging
by Martin Reuter Christian Wachinger Hervé LombaertThis book constitutes the refereed post-conference proceedings of the First International Workshop on Spectral and Shape Analysis in Medical Imaging, SeSAMI 2016, held in conjunction with MICCAI 2016, in Athens, Greece, in October 2016. The 10 submitted full papers presented in this volume were carefully reviewed. The papers reflect the following topics: spectral methods; longitudinal methods; and shape methods.
Spectral, Photon Counting Computed Tomography: Technology and Applications (Devices, Circuits, and Systems)
by Krzysztof Iniewski Katsuyuki Taguchi Ira BlevisSpectral, Photon Counting Computed Tomography is a comprehensive cover of the latest developments in the most prevalent imaging modality (x-ray computed tomography (CT)) in its latest incarnation: Spectral, Dual-Energy, and Photon Counting CT. Disadvantages of the conventional single-energy technique used by CT technology are that different materials cannot be distinguished and that the noise is larger. To address these problems, a novel spectral CT concept has been proposed. Spectral Dual-Energy CT (DE-CT) acquires two sets of spectral data, and Spectral Photon Counting CT (PC-CT) detects energy of x-ray photons to reveal additional material information of objects by using novel energy-sensitive, photon-counting detectors. The K-edge imaging may be a gateway for functional or molecular CT. The book covers detectors and electronics, image reconstruction methods, image quality assessments, a simulation tool, nanoparticle contrast agents, and clinical applications for spectral CT.
Spectrally Resolved Detector Arrays for Multiplexed Biomedical Fluorescence Imaging (Springer Theses)
by Anna Siri LuthmanThis book describes the design, development, characterisation and application of two novel fluorescence imaging instruments based on spectrally resolved detector arrays (SRDAs). The simplest SRDA is the standard colour camera, which integrates a Bayer filter array of red, green and blue colour filters to replicate the colour sensing capability of the human eye. The SRDAs used in this book contain many more colours, ranging from 16 to over 100 colour channels. Using these compact, robust and low-cost detectors for biomedical applications opens new avenues of exploration that were not possible before, in particular, the use of spectral imaging in endoscopy. The work presented shows for the first time that not only can this new type of camera be used for fluorescence imaging, but also that it is able to resolve signals from up to 7 different dyes – a level of multiplexing not previously achieved in tissue with such compact and robust equipment. Furthermore, it reports the application of a bimodal endoscope performing both reflectance and fluorescence imaging using these cameras in an ex vivo pig oesophagus model.
Spectrophotometric Determination of Palladium & Platinum: Methods & Reagents
by Ajay Kumar GoswamiThis versatile resource consolidates available methods for the spectrophotometric determination of palladium and platinum and serves as a practical ready-to-use guide for those researching palladium and platinum and for those working in the field of medicinal metal complexes of the two metals. The beauty of spectrophotometric methods lies in their simplicity, convenience, and easy operability, not to mention their cost-effectiveness. They can be automated easily and are thus the most affordable methods for the below reasons: Address analysts from all areas of industry, research labs and postgraduate students of analytical or medicinal chemistry as well as material science Detail all recently developed methods for palladium and platinum determination using spectrophotometry in a single source. Organized so that anyone interested in a particular method using a specific reagent can go directly to those details Facilitates the development of better methods for specific conditions of a sample
Spectroscopic Ellipsometry for Photovoltaics: Volume 1: Fundamental Principles and Solar Cell Characterization (Springer Series in Optical Sciences #212)
by Hiroyuki Fujiwara Robert W. CollinsThis book provides a basic understanding of spectroscopic ellipsometry, with a focus on characterization methods of a broad range of solar cell materials/devices, from traditional solar cell materials (Si, CuInGaSe2, and CdTe) to more advanced emerging materials (Cu2ZnSnSe4, organics, and hybrid perovskites), fulfilling a critical need in the photovoltaic community.The book describes optical constants of a variety of semiconductor light absorbers, transparent conductive oxides and metals that are vital for the interpretation of solar cell characteristics and device simulations. It is divided into four parts: fundamental principles of ellipsometry; characterization of solar cell materials/structures; ellipsometry applications including optical simulations of solar cell devices and online monitoring of film processing; and the optical constants of solar cell component layers.
Spectroscopic Ellipsometry for Photovoltaics: Volume 2: Applications and Optical Data of Solar Cell Materials (Springer Series in Optical Sciences #214)
by Hiroyuki Fujiwara Robert W. CollinsSpectroscopic ellipsometry has been applied to a wide variety of material and device characterizations in solar cell research fields. In particular, device performance analyses using exact optical constants of component layers and direct analyses of complex solar cell structures are unique features of advanced ellipsometry methods. This second volume of Spectroscopic Ellipsometry for Photovoltaics presents various applications of the ellipsometry technique for device analyses, including optical/recombination loss analyses, real-time control and on-line monitoring of solar cell structures, and large-area structural mapping. Furthermore, this book describes the optical constants of 148 solar cell component layers, covering a broad range of materials from semiconductor light absorbers (inorganic, organic and hybrid perovskite semiconductors) to transparent conductive oxides and metals. The tabulated and completely parameterized optical constants described in this book are the most current resource that is vital for device simulations and solar cell structural analyses.
Spectroscopic Instrumentation
by Thomas Eversberg Klaus VollmannIn order to analyze the light of cosmic objects, particularly at extremely great distances, spectroscopy is the workhorse of astronomy. In the era of very large telescopes, long-term investigations are mainly performed with small professional instruments. Today they can be done using self-designed spectrographs and highly efficient CCD cameras, without the need for large financial investments. This book explains the basic principles of spectroscopy, including the fundamental optical constraints and all mathematical aspects needed to understand the working principles in detail. It covers the complete theoretical and practical design of standard and Echelle spectrographs. Readers are guided through all necessary calculations, enabling them to engage in spectrograph design. The book also examines data acquisition with CCD cameras and fiber optics, as well as the constraints of specific data reduction and possible sources of error. In closing it briefly highlights some main aspects of the research on massive stars and spectropolarimetry as an extension of spectroscopy. The book offers a comprehensive introduction to spectroscopy for students of physics and astronomy, as well as a valuable resource for amateur astronomers interested in learning the principles of spectroscopy and spectrograph design.
Spectroscopic Investigations of Hydrogen Bond Network Structures in Water Clusters
by Kenta MizuseThe properties and nature of water clusters studied with novel spectroscopic approaches are presented in this thesis. Following a general introduction on the chemistry of water and water clusters, detailed descriptions of the experiments and analyses are given. All the experimental results, including first size-selective spectra of large clusters consisting of 200 water molecules, are presented with corresponding analyses. Hitherto unidentified hydrogen bond network structures, dynamics, and reactivity of various water clusters have been characterized at the molecular level. The main targets of this book are physical chemists and chemical physicists who are interested in water chemistry or cluster chemistry.
Spectroscopic Membrane Probes: Volume 1
by Leslie M. LoewThe general picture we have of membranes and of the properties of the proteins imbedded in them, has, arguably emerged directly from probe studies over the past 20 years. This work is designed to make these techniques accessible to a board audience of cell biologists. The techniques discussed revolve primarily around the fluorescence of membrane probes, but applications of light absorption and Raman scattering are included. In addition to reviews of the major applications, most chapters include information on the required apparatus, experimental design, data analysis, and potential pit falls.
Spectroscopic Membrane Probes: Volume 2
by Leslie M. LoewThe optical spectra of molecular membrane probes can be interpreted terms of the structure, dynamics, and the physiological state of the membrane. The general picture we have of membranes and of the properties of the proteins imbedded in them, has, arguably, emerged directly from probe studies over the last 20 years. This work is designed to make these techniques accessible to a broad audience of cell biologist. The techniques discussed revolve primarily around the fluorescence of membrane probes, but applications of light absorption and Raman scattering are included. In addition to reviews of the major applications, most chapters include information on required apparatus, experimental design, data analysis, and potential pitfalls.
Spectroscopic Methods and Analyses
by Adrian H. Thomas Christopher Jones Barbara MulloyAlthough spectroscopic methods are of great use to biological scientists, many researchers lack a specialist's knowledge of these techniques. Spectroscopic Methods and Analyses provides hands-on information on these valuable research tools, emphasizing practical aspects, such as amounts and purity of required samples, limitations and advantages of the technique, and interpretation of the results, thus enabling every molecular biologist-either independently or with the help of a specialist-to evaluate the usefulness of a technique, to plan an original program, and to gain a realistic idea of the resources needed.An indispensable guide for all biochemists, cell and molecular biologists, pharmacologists, immunologists, pathologists, and neuroscientists.