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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 Theory: Basic Concepts and Applications (Graduate Texts in Mathematics #284)
by David BorthwickThis textbook offers a concise introduction to spectral theory, designed for newcomers to functional analysis. Curating the content carefully, the author builds to a proof of the spectral theorem in the early part of the book. Subsequent chapters illustrate a variety of application areas, exploring key examples in detail. Readers looking to delve further into specialized topics will find ample references to classic and recent literature. Beginning with a brief introduction to functional analysis, the text focuses on unbounded operators and separable Hilbert spaces as the essential tools needed for the subsequent theory. A thorough discussion of the concepts of spectrum and resolvent follows, leading to a complete proof of the spectral theorem for unbounded self-adjoint operators. Applications of spectral theory to differential operators comprise the remaining four chapters. These chapters introduce the Dirichlet Laplacian operator, Schrödinger operators, operators on graphs, and the spectral theory of Riemannian manifolds. Spectral Theory offers a uniquely accessible introduction to ideas that invite further study in any number of different directions. A background in real and complex analysis is assumed; the author presents the requisite tools from functional analysis within the text. This introductory treatment would suit a functional analysis course intended as a pathway to linear PDE theory. Independent later chapters allow for flexibility in selecting applications to suit specific interests within a one-semester course.
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 High Order Methods for Partial Differential Equations ICOSAHOM 2016
by Jan S. Hesthaven Marco L. Bittencourt Ney A. DumontThis book features a selection of high-quality papers chosen from the best presentations at the International Conference on Spectral and High-Order Methods (2016), offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM 2012
by Jan S. Hesthaven Mejdi Azaïez Henda El FekihThe book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2012), and provides an overview of the depth and breath of the activities within this important research area. The carefully reviewed selection of the papers will provide the reader with a snapshot of state-of-the-art and help initiate new research directions through the extensive bibliography.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014
by Jan S. Hesthaven Robert M. Kirby Martin BerzinsThe book contains a selection of high quality papers, chosen among the best presentations during the International Conference on Spectral and High-Order Methods (2014), and provides an overview of the depth and breadth of the activities within this important research area. The carefully reviewed selection of papers will provide the reader with a snapshot of the state-of-the-art and help initiate new research directions through the extensive biography.
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018: Selected Papers from the ICOSAHOM Conference, London, UK, July 9-13, 2018 (Lecture Notes in Computational Science and Engineering #134)
by Christoph Schwab Spencer J. Sherwin David Moxey Joaquim Peiró Peter E. VincentThis open access book features a selection of high-quality papers from the presentations at the International Conference on Spectral and High-Order Methods 2018, offering an overview of the depth and breadth of the activities within this important research area. The carefully reviewed papers provide a snapshot of the state of the art, while the extensive bibliography helps initiate new research directions.
Spectral and Scattering Theory for Second Order Partial Differential Operators (Chapman & Hall/CRC Monographs and Research Notes in Mathematics)
by Kiyoshi MochizukiThe book is intended for students of graduate and postgraduate level, researchers in mathematical sciences as well as those who want to apply the spectral theory of second order differential operators in exterior domains to their own field. In the first half of this book, the classical results of spectral and scattering theory: the selfadjointness, essential spectrum, absolute continuity of the continuous spectrum, spectral representations, short-range and long-range scattering are summarized. In the second half, recent results: scattering of Schrodinger operators on a star graph, uniform resolvent estimates, smoothing properties and Strichartz estimates, and some applications are discussed.
Spectral and Scattering Theory: Proceedings Of The Taniguchi International Workshop
by Mitsuru Ikawa"This useful volume, based on the Taniguchi International Workshop held recently in Sanda, Hyogo, Japan, discusses current problems and offers the mostup-to-date methods for research in spectral and scattering theory."
Spectrum 8th Grade Math Workbook: Focused Practice for Math Mastery (Spectrum Series)
by Spectrum8th Grade Math Workbook for kids ages 13-14 <p> Support your child’s educational journey with the Spectrum grade 8 math workbook that teaches essential math skills to eighth graders. <p><p> Spectrum’s 8th grade math workbook is a great way for eighth graders to learn essential math skills such as learning Pythagorean Theorem, geometry, rational and irrational numbers, and more through a variety of problem-solving activities that are both fun AND educational! <p><p> Why You’ll Love This Math Book <p> Engaging and educational math for 8th grade students. “Using and rewriting exponents”, “solving word problems”, and “linear equations” are a few of the fun activities that incorporate math in everyday settings to help inspire learning. <p> Testing progress along the way. Pretests, posttests, a mid-test, final test, and an answer key are included in the 8th grade math workbook to help track your child’s progress along the way before moving on to new and exciting math lessons. <p><p> About Spectrum <p> For more than 20 years, Spectrum has provided solutions for parents who want to help their children get ahead, and for teachers who want their students to meet and exceed set learning goals—providing workbooks that are a great resource for both homeschooling and classroom curriculum.
Spectrum MathWorkbook, Grade 3
by Spectrum<p>The Spectrum Math Workbook for third grade features 160 pages of focused instruction and progressive practice to help students stay ahead in math and enhance problem-solving skills. <p>This standards-based workbook provides systematic and thought-provoking practice designed to increase in complexity for the following content areas: adding and subtracting to four-digit numbers, multiplying and dividing, fractions, perimeter and area, and graphs and line plots. With easy-to-follow instructions, tests, and an included answer key, parents and teachers can accurately monitor students’ progress. <p>The best-selling Spectrum series is a favorite of parents and teachers because it’s carefully designed to be both effective and engaging––the perfect building blocks for a lifetime of learning.</p>
Speculation, Trading, and Bubbles
by Joseph E. Stiglitz Patrick Bolton Kenneth J. Arrow Sanford J. Grossman José A. ScheinkmanThe history of financial markets is full of moments in which asset prices inflate far beyond their intrinsic value. These events are commonly called bubbles, and in this book, José A. Scheinkman and other top economists offer new explanations for this phenomenon.Scheinkman discusses some stylized facts concerning bubbles, such as high trading volume and the coincidence between bubbles' implosion and increases in supply, and he develops a model for bubbles based on differences in beliefs among investors that explains these observations. Sandy Grossman and Patrick Bolton offer commentaries on Scheinkman's work, investigating factors that contribute to bubbles, such as excessive leverage, overconfidence, mania, and panic in speculative markets. Kenneth J. Arrow and Joseph E. Stiglitz add introductory material contextualizing Scheinkman's findings.
Speculation, Trading, and Bubbles (Kenneth J. Arrow Lecture Series)
by José A. ScheinkmanAs long as there have been financial markets, there have been bubbles—those moments in which asset prices inflate far beyond their intrinsic value, often with ruinous results. Yet economists are slow to agree on the underlying forces behind these events. In this book José A. Scheinkman offers new insight into the mystery of bubbles. Noting some general characteristics of bubbles—such as the rise in trading volume and the coincidence between increases in supply and bubble implosions—Scheinkman offers a model, based on differences in beliefs among investors, that explains these observations. Other top economists also offer their own thoughts on the issue: Sanford J. Grossman and Patrick Bolton expand on Scheinkman's discussion by looking at factors that contribute to bubbles—such as excessive leverage, overconfidence, mania, and panic in speculative markets—and Kenneth J. Arrow and Joseph E. Stiglitz contextualize Scheinkman's findings.
Speech Enhancement in the STFT Domain
by Jacob Benesty Jingdong Chen Emanuël A.P. HabetsThis work addresses this problem in the short-time Fourier transform (STFT) domain. We divide the general problem into five basic categories depending on the number of microphones being used and whether the interframe or interband correlation is considered. The first category deals with the single-channel problem where STFT coefficients at different frames and frequency bands are assumed to be independent. In this case, the noise reduction filter in each frequency band is basically a real gain. Since a gain does not improve the signal-to-noise ratio (SNR) for any given subband and frame, the noise reduction is basically achieved by liftering the subbands and frames that are less noisy while weighing down on those that are more noisy. The second category also concerns the single-channel problem. The difference is that now the interframe correlation is taken into account and a filter is applied in each subband instead of just a gain. The advantage of using the interframe correlation is that we can improve not only the long-time fullband SNR, but the frame-wise subband SNR as well. The third and fourth classes discuss the problem of multichannel noise reduction in the STFT domain with and without interframe correlation, respectively. In the last category, we consider the interband correlation in the design of the noise reduction filters. We illustrate the basic principle for the single-channel case as an example, while this concept can be generalized to other scenarios. In all categories, we propose different optimization cost functions from which we derive the optimal filters and we also define the performance measures that help analyzing them.
Speech and Audio Processing: A MATLAB®-based Approach
by Ian Vince McloughlinWith this comprehensive and accessible introduction to the field, you will gain all the skills and knowledge needed to work with current and future audio, speech, and hearing processing technologies. Topics covered include mobile telephony, human-computer interfacing through speech, medical applications of speech and hearing technology, electronic music, audio compression and reproduction, big data audio systems and the analysis of sounds in the environment. All of this is supported by numerous practical illustrations, exercises, and hands-on MATLAB examples on topics as diverse as psychoacoustics (including some auditory illusions), voice changers, speech compression, signal analysis and visualisation, stereo processing, low-frequency ultrasonic scanning, and machine learning techniques for big data. With its pragmatic and application driven focus, and concise explanations, this is an essential resource for anyone who wants to rapidly gain a practical understanding of speech and audio processing and technology.
Speed Math for Kids: Helping Children Achieve Their Full Potential
by Bill HandleyPopular Australian author and inspirational teacher, Bill Handley, has developed and, over the years, refined methods of teaching mathematics and learning strategies that have achieved amazing results. His best-selling book, Speed Mathematics convinced readers that people who excel at maths use better strategies and are not necessarily more intelligent. This book contains additional methods and applications based on the strategies taught in Speed Mathematics that make the principles clearer, encourage creative thought, and are just plain fun. The book was written for young people but people of any age will enjoy it. The book has notes throughout for parents and teachers. By following his innovative approach you will have kids playing with numbers, performing lightning quick calculations and, most of all, having fun! Bill claims: 'If you are good at maths, people think you are intelligent. People will treat you like you are a genius. Your teachers and your friends will treat you differently. You will even think differently about yourself'. The emphasis in this book is on playing with mathematics. Enjoy it. Show off what you learn and make mathematics your favourite subject.
Speed Math for Kids: The Fast, Fun Way To Do Basic Calculations
by Bill HandleyLearn how to easily do quick mental math calculations Speed Math for Kids is your guide to becoming a math genius--even if you have struggled with math in the past. Believe it or not, you have the ability to perform lightning quick calculations that will astonish your friends, family, and teachers. You'll be able to master your multiplication tables in minutes, and learn basic number facts while doing it. While the other kids in class are still writing down the problems, you can be calling out the answers. Speed Math for Kids is all about playing with mathematics. This fun-filled book will teach you: How to multiply and divide large numbers in your head What you can do to make addition and subtraction easy Tricks for understanding fractions and decimals How to quickly check answers every time you make a calculation And much more If you're looking for a foolproof way to do multiplication, division, factoring estimating, and more, Speed Math for Kids is the book for you. With enough practice you'll go straight to the top of the class!
Speed Math: Simple Methods to Do Math Quickly in One’s Head (Idiot's Guides)
by Gaurav TekriwalDo math more quickly and with more confidence — with less reliance on paper, apps, and calculators. For people who automatically run to the nearest calculator, Idiot's Guides: Speed Math teaches tips, tricks, and straightforward methods to doing math at a fast — and accurate — rate. Practice examples easily illustrate how even the most math-shy person can better perform calculations.
Speed Mathematics Simplified (Dover Books on Mathematics)
by Edward StoddardThis entertaining, easy-to-follow book is ideal for anyone who works with numbers and wants to develop greater speed, ease, and accuracy in doing mathematical calculations. In an inspiring introduction, science writer Edward Stoddard offers important suggestions for mastering an entirely new system of figuring. Without having to discard acquired information about mathematical computation, students build on the knowledge they already have, "streamline" these techniques for rapid use and then combine them with classic shortcuts.Initially, readers learn to master a basic technique known as the Japanese "automatic" figuring method — the principle behind the abacus. This method enables users to multiply without carrying, divide with half the written work of long division, and mentally solve mathematical problems that usually require pencil and paper or a calculator. Additional chapters explain how to build speed in addition and subtraction, how to check for accuracy, master fractions, work quickly with decimals, handle percentages, and much more. A valuable asset for people in business who work with numbers on a variety of levels, this outstanding book will also appeal to students, teachers, and anyone looking for a reliable way to improve skill and speed in doing basic arithmetic.
Speed Mathematics: Secrets Skills For Quick Calculation
by Bill HandleyThis new, revised edition of the bestselling Speed Mathematics features new chapters on memorising numbers and general information, calculating statistics and compound interest, square roots, logarithms and easy trig calculations. Written so anyone can understand, this book teaches simple strategies that will enable readers to make lightning-quick calculations. People who excel at mathematics use better strategies than the rest of us; they are not necessarily more intelligent. With Speed Mathematics you'll discover methods to make maths easy and fun. This book is perfect for students, parents, teachers and anyone who enjoys working with figures and even those who are terrified of numbers!
Speed Skating
by Katie Marsico Cecilia MindenSpeed skating is a great way to get in shape, and a great way to put your math skills to work. In speed skating, seconds can make all the difference. Understanding speeds and measurements can help keep you on pace and improve your times.
Speed, Data, and Ecosystems: Excelling in a Software-Driven World (Chapman & Hall/CRC Innovations in Software Engineering and Software Development Series)
by Jan BoschAs software R&D investment increases, the benefits from short feedback cycles using technologies such as continuous deployment, experimentation-based development, and multidisciplinary teams require a fundamentally different strategy and process. This book will cover the three overall challenges that companies are grappling with: speed, data and ecosystems. Speed deals with shortening the cycle time in R&D. Data deals with increasing the use of and benefit from the massive amounts of data that companies collect. Ecosystems address the transition of companies from being internally focused to being ecosystem oriented by analyzing what the company is uniquely good at and where it adds value.
Speeding-Up Radio-Frequency Integrated Circuit Sizing with Neural Networks (SpringerBriefs in Applied Sciences and Technology)
by Nuno C. Lourenço Ricardo M. Martins Nuno C. Horta João L. Domingues Pedro J. Vaz António P. GusmãoIn this book, innovative research using artificial neural networks (ANNs) is conducted to automate the sizing task of RF IC design, which is used in two different steps of the automatic design process. The advances in telecommunications, such as the 5th generation broadband or 5G for short, open doors to advances in areas such as health care, education, resource management, transportation, agriculture and many other areas. Consequently, there is high pressure in today’s market for significant communication rates, extensive bandwidths and ultralow-power consumption. This is where radiofrequency (RF) integrated circuits (ICs) come in hand, playing a crucial role. This demand stresses out the problem which resides in the remarkable difficulty of RF IC design in deep nanometric integration technologies due to their high complexity and stringent performances. Given the economic pressure for high quality yet cheap electronics and challenging time-to-market constraints, there is an urgent need for electronic design automation (EDA) tools to increase the RF designers’ productivity and improve the quality of resulting ICs. In the last years, the automatic sizing of RF IC blocks in deep nanometer technologies has moved toward process, voltage and temperature (PVT)-inclusive optimizations to ensure their robustness. Each sizing solution is exhaustively simulated in a set of PVT corners, thus pushing modern workstations’ capabilities to their limits. Standard ANNs applications usually exploit the model’s capability of describing a complex, harder to describe, relation between input and target data. For that purpose, ANNs are a mechanism to bypass the process of describing the complex underlying relations between data by feeding it a significant number of previously acquired input/output data pairs that the model attempts to copy. Here, and firstly, the ANNs disrupt from the most recent trials of replacing the simulator in the simulation-based sizing with a machine/deep learning model, by proposing two different ANNs, the first classifies the convergence of the circuit for nominal and PVT corners, and the second predicts the oscillating frequencies for each case. The convergence classifier (CCANN) and frequency guess predictor (FGPANN) are seamlessly integrated into the simulation-based sizing loop, accelerating the overall optimization process. Secondly, a PVT regressor that inputs the circuit’s sizing and the nominal performances to estimate the PVT corner performances via multiple parallel artificial neural networks is proposed. Two control phases prevent the optimization process from being misled by inaccurate performance estimates. As such, this book details the optimal description of the input/output data relation that should be fulfilled. The developed description is mainly reflected in two of the system’s characteristics, the shape of the input data and its incorporation in the sizing optimization loop. An optimal description of these components should be such that the model should produce output data that fulfills the desired relation for the given training data once fully trained. Additionally, the model should be capable of efficiently generalizing the acquired knowledge in newer examples, i.e., never-seen input circuit topologies.
Spektren, Garben, Schemata: Eine kurze Einführung (essentials)
by Jürgen JostDas essential führt in die wesentlichen Konzepte der modernen algebraischen Geometrie ein. Dabei werden zunächst algebraische Grundbegriffe wiederholt. Die algebraische Struktur eines kommutativen Ringes spiegelt sich in der Menge seiner Primideale wider. Diese Menge kann mit einer topologischen Struktur versehen werden; dies ist der Begriff des Spektrums, der also algebraische in topologische Daten übersetzt. Mithilfe des Begriffs der Garbe kann man aus dieser topologischen die algebraische Struktur zurückgewinnen. Dieses reichhaltige Wechselspiel wird im Begriff des Schemas erfasst. Dadurch kann man die grundlegenden Objekte der algebraischen Geometrie, Nullstellengebilde von Polynomen, algebraisch untersuchen und umgekehrt geometrische Methoden auf arithmetische Fragen anwenden.