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Wavelets: A Primer
by Christian BlatterThe Wavelet Transform has stimulated research that is unparalleled since the invention of the Fast Fourier Transform and has opened new avenues of applications in signal processing, image compression, radiology, cardiology, and many other areas. This book grew out of a short course for mathematics students at the ETH in Zurich; it provides a solid mathematical foundation for the broad range of applications enjoyed by the wavelet transform. Numerous illustrations and fully worked out examples enhance the book.
Wavelets: A Student Guide
by Peter NickolasThis text offers an excellent introduction to the mathematical theory of wavelets for senior undergraduate students. Despite the fact that this theory is intrinsically advanced, the author's elementary approach makes it accessible at the undergraduate level. Beginning with thorough accounts of inner product spaces and Hilbert spaces, the book then shifts its focus to wavelets specifically, starting with the Haar wavelet, broadening to wavelets in general, and culminating in the construction of the Daubechies wavelets. All of this is done using only elementary methods, bypassing the use of the Fourier integral transform. Arguments using the Fourier transform are introduced in the final chapter, and this less elementary approach is used to outline a second and quite different construction of the Daubechies wavelets. The main text of the book is supplemented by more than 200 exercises ranging in difficulty and complexity.
Wavelets: Mathematics and Applications (Studies In Advanced Mathematics Ser.)
by John J. Benedetto; Michael W. FrazierWavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis.The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.
Waves in Continuous Media (Lecture Notes in Geosystems Mathematics and Computing)
by S. L. Gavrilyuk N.I. Makarenko S.V. SukhininStarting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and conservation laws for quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations. Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids. The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations.
Waves in Flows (Advances in Mathematical Fluid Mechanics)
by Giovanni P. Galdi Tomáš Bodnár Šárka NečasováThis volume offers an overview of the area of waves in fluids and the role they play in the mathematical analysis and numerical simulation of fluid flows. Based on lectures given at the summer school “Waves in Flows”, held in Prague from August 27-31, 2018, chapters are written by renowned experts in their respective fields. Featuring an accessible and flexible presentation, readers will be motivated to broaden their perspectives on the interconnectedness of mathematics and physics. A wide range of topics are presented, working from mathematical modelling to environmental, biomedical, and industrial applications. Specific topics covered include:Equatorial wave–current interactionsWater–wave problemsGravity wave propagationFlow–acoustic interactions Waves in Flows will appeal to graduate students and researchers in both mathematics and physics. Because of the applications presented, it will also be of interest to engineers working on environmental and industrial issues.
Waves in Flows: The 2018 Prague-Sum Workshop Lectures (Advances in Mathematical Fluid Mechanics)
by Giovanni P. Galdi Tomáš Bodnár Šárka NečasováThis volume explores a range of recent advances in mathematical fluid mechanics, covering theoretical topics and numerical methods. Chapters are based on the lectures given at a workshop in the summer school Waves in Flows, held in Prague from August 27-31, 2018. A broad overview of cutting edge research is presented, with a focus on mathematical modeling and numerical simulations. Readers will find a thorough analysis of numerous state-of-the-art developments presented by leading experts in their respective fields. Specific topics covered include:ChemorepulsionCompressible Navier-Stokes systemsNewtonian fluidsFluid-structure interactions Waves in Flows: The 2018 Prague-Sum Workshop Lectures will appeal to post-doctoral students and scientists whose work involves fluid mechanics.
Waves in an Impossible Sea: How Everyday Life Emerges from the Cosmic Ocean
by Matt StrasslerA theoretical physicist takes readers on an awe-inspiring journey—found in "no other book" (Science)—to discover how the universe generates everything from nothing at all: "If you want to know what's really going on in the realms of relativity and particle physics, read this book" (Sean Carroll, author of The Biggest Ideas in the Universe). In Waves in an Impossible Sea, physicist Matt Strassler tells a startling tale of elementary particles, human experience, and empty space. He begins with a simple mystery of motion. When we drive at highway speeds with the windows down, the wind beats against our faces. Yet our planet hurtles through the cosmos at 150 miles per second, and we feel nothing of it. How can our voyage be so tranquil when, as Einstein discovered, matter warps space, and space deflects matter? The answer, Strassler reveals, is that empty space is a sea, albeit a paradoxically strange one. Much like water and air, it ripples in various ways, and we ourselves, made from its ripples, can move through space as effortlessly as waves crossing an ocean. Deftly weaving together daily experience and fundamental physics—the musical universe, the enigmatic quantum, cosmic fields, and the Higgs boson—Strassler shows us how all things, familiar and unfamiliar, emerge from what seems like nothing at all. Accessible and profound, Waves in an Impossible Sea is the ultimate guide to our place in the universe.
Waves, Particles and Fields: Introducing Quantum Field Theory
by Anthony C. Fischer-CrippsChoice Outstanding Title, September 2020This book fills a gap in the middle ground between quantum mechanics of a single electron to the concept of a quantum field. In doing so, the book is divided into two parts; the first provides the necessary background to quantum theory extending from Planck’s formulation of black body radiation to Schrodinger’s equation; and the second part explores Dirac’s relativistic electron to quantum fields, finishing with an description of Feynman diagrams and their meaning. Much more than a popular account, yet not too heavy so as to be inaccessible, this book assumes no prior knowledge of quantum physics or field theory and provides the necessary foundations for readers to then progress to more advanced texts on quantum field theory. It will be of interest to undergraduate students in physics and mathematics, in addition to an interested, general audience.Features: Provides an extensive yet accessible background to the concepts Contains numerous, illustrative diagrams Presents in-depth explanations of difficult subjects
Way Out in the Desert
by Jennifer Ward T. J. MarshThis toe-tapping text will have you singing along with the lovable creatures of the desert in no time! Filled with vibrant illustrations of many of the charming plants and animals that call the Sonoran Desert home, Way Out in the Desert is a wonderful teaching tool that takes you on a trip down memory lane. If you remember singing Over in the Meadow as a child, now you can give your children their own memories of this timeless tune. So take a child on a trip where Way out in the desert having fun in the sun lived a mother horned toad and her little toady one...
Ways Out Of Social Isolation For Older People In The Context Of New Media: CONNECT-ED – A Project to Improve Social Participation
by Britta Thege Juliane Köchling-Farahwaran Sonja Börm Stephan DettmersThe book introduces the concept of encounter CONNECT-ED from the practice of working with the elderly to impart media skills and presents empirical data on the social participation and quality of life of the participants. The research results show the potential of the Internet for older people and open up perspectives for gender- and age-sensitive advanced training opportunities.
Ways of Thinking in STEM-based Problem Solving: Teaching and Learning in a New Era
by Lyn D. English Timothy LehmannTaking a future-oriented approach, this book addresses students’ ways of thinking in STEM-based problem solving. It provides a rich set of chapters that explore how we can advance important thinking skills in STEM education for K-12 students. STEM education is essential to understanding and solving many of the world’s major challenges. However, the kind of interdisciplinary modes of thinking required to tackle such unforeseen problems is lacking in most STEM education delivery. This book examines the various ways of thinking that can be applied to effective STEM-based problem solving across K-12 education. These include design and design-based thinking, systems thinking and modeling, critical thinking, innovative and adaptive thinking, intuition in problem solving, and computational and algorithmic thinking. Across the chapters, the authors’ interdisciplinary perspectives give further depth to understanding how students learn and apply their thinking to solve STEM-based problems. The book also provides guidance on how to assess ways of thinking in STEM education, to ensure educators can recognize students’ progress and development.Bringing together a team of international experts, this book is essential reading for pre-service teachers, teacher educators, and researchers in STEM education.
We Are Generation Z: How Identity, Attitudes, and Perspectives Are Shaping Our Future
by Vivek PanditA young author shares an insider’s perspective on what it means to be Generation Z—and what Generation Z means for the world.Born at the turn of the millennium, the members of Generation Z are no strangers to today’s fast-paced, hyperconnected world. They were born in the Digital Age. They grew up online. Their identities, attitudes, and perspectives have all been uniquely integrated with technology. Now, as they stand at the brink of adulthood, it’s time for the world to discover: Who is Generation Z?Vivek Pandit understands firsthand what it means to be a digital native, and he has a unique view of the road ahead. By exploring the forces that have shaped him and his peers, he gives insight into how they may go on to shape the world.Winner of the Moonbeam Children’s Book Award Gold Medal in the Youth Author (under 18) category
We Just Averaged over Two Trillion Cross-Country Growth Regressions
by Eduardo Ley Mark F.J. SteelA report from the International Monetary Fund.
We Reason & We Prove for ALL Mathematics: Building Students’ Critical Thinking, Grades 6-12 (Corwin Mathematics Series)
by Michael Steele Gabriel J. Stylianides Fran Arbaugh Margaret Peg Smith Justin D. BoyleSharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, this book transcends all mathematical content areas with a variety of activities for teachers that include Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.
We Reason & We Prove for ALL Mathematics: Building Students’ Critical Thinking, Grades 6-12 (Corwin Mathematics Series)
by Michael Steele Gabriel J. Stylianides Fran Arbaugh Margaret Peg Smith Justin D. BoyleSharpen concrete teaching strategies that empower students to reason-and-prove What does reasoning-and-proving instruction look like and how can teachers support students’ capacity to reason-and-prove? Designed as a learning tool for mathematics teachers in grades 6-12, this book transcends all mathematical content areas with a variety of activities for teachers that include Solving and discussing high-level mathematical tasks Analyzing narrative cases that make the relationship between teaching and learning salient Examining and interpreting student work Modifying curriculum materials and evaluating learning environments to better support students to reason-and-prove No other book tackles reasoning-and-proving with such breath, depth, and practical applicability.
Weak and Measure-Valued Solutions to Evolutionary PDEs
by J. Necas J. Malek M. Rokyta M. RuzickaThis book provides a concise treatment of the theory of nonlinear evolutionary partial differential equations. It provides a rigorous analysis of non-Newtonian fluids, and outlines its results for applications in physics, biology, and mechanical engineering
Weakly Stationary Random Fields, Invariant Subspaces and Applications
by Vidyadhar S. Mandrekar David A. RedettThe first book to examine weakly stationary random fields and their connections with invariant subspaces (an area associated with functional analysis). It reviews current literature, presents central issues and most important results within the area. For advanced Ph.D. students, researchers, especially those conducting research on Gaussian theory.
Weakly Wandering Sequences in Ergodic Theory
by Stanley Eigen Arshag Hajian Yuji Ito Vidhu PrasadThe appearance of weakly wandering (ww) sets and sequences for ergodic transformations over half a century ago was an unexpected and surprising event. In time it was shown that ww and related sequences reflected significant and deep properties of ergodic transformations that preserve an infinite measure. This monograph studies in a systematic way the role of ww and related sequences in the classification of ergodic transformations preserving an infinite measure. Connections of these sequences to additive number theory and tilings of the integers are also discussed. The material presented is self-contained and accessible to graduate students. A basic knowledge of measure theory is adequate for the reader.
Wealth, Income Inequalities, and Demography
by Luigi PaganettoIn this book, leading experts take a long-term view of the trends and policies of most relevance in achieving the structural readjustment required by the current crisis, which for too long has been viewed merely as an economic recession. A wide variety of issues are addressed, including the implications of the massive movement of wealth from advanced countries to emerging ones and the increasing income inequality evident within many countries. Prospects for growth toward the mid-century and beyond are discussed, with consideration of lessons from the past and the impact of various constraints, including corruption. The policies and reforms required to restore economic dynamism within the EU and more generally, to foster the "Good Economy" are discussed, recognizing the need for measures to promote innovation, entrepreneurship, well-being and high levels of environmental performance. The book comprises a selection of contributions presented at the XXV Villa Mondragone International Economic Seminar. For the past quarter of a century, this seminar has brought together leading experts to engage in debates on pressing economic questions. This book, based on the most recent gathering, will be of interest to all who are concerned about the challenges to growth, well-being and social inclusion that will have to be confronted in the coming decades.
Weaponized Lies: How to Think Critically in the Post-Truth Era
by Daniel J. LevitinPreviously Published as A Field Guide to Lies We're surrounded by fringe theories, fake news, and pseudo-facts. These lies are getting repeated. New York Times bestselling author Daniel Levitin shows how to disarm these socially devastating inventions and get the American mind back on track. Here are the fundamental lessons in critical thinking that we need to know and share now. Investigating numerical misinformation, Daniel Levitin shows how mishandled statistics and graphs can give a grossly distorted perspective and lead us to terrible decisions. Wordy arguments on the other hand can easily be persuasive as they drift away from the facts in an appealing yet misguided way. The steps we can take to better evaluate news, advertisements, and reports are clearly detailed. Ultimately, Levitin turns to what underlies our ability to determine if something is true or false: the scientific method. He grapples with the limits of what we can and cannot know. Case studies are offered to demonstrate the applications of logical thinking to quite varied settings, spanning courtroom testimony, medical decision making, magic, modern physics, and conspiracy theories. This urgently needed book enables us to avoid the extremes of passive gullibility and cynical rejection. As Levitin attests: Truth matters. A post-truth era is an era of willful irrationality, reversing all the great advances humankind has made. Euphemisms like "fringe theories," "extreme views," "alt truth," and even "fake news" can literally be dangerous. Let's call lies what they are and catch those making them in the act.
Weaponized Lies: How to Think Critically in the Post-Truth Era
by Daniel J. LevitinIt's raining fringe theories, fake news, and pseudo-facts. These lies are getting repeated. New York Times bestselling author Daniel Levitin shows how to disarm these socially devastating inventions and get the American mind back on track. Here are the fundamental lessons in critical thinking (previously published as A Field Guide to Lies) that we need to know and share now. Investigating numerical misinformation, Daniel Levitin shows how mishandled statistics and graphs can give a grossly distorted perspective and lead us to terrible decisions. Wordy arguments on the other hand can easily be persuasive as they drift away from the facts in an appealing yet misguided way. The steps we can take to better evaluate news, advertisements, and reports are clearly detailed. Ultimately, Levitin turns to what underlies our ability to determine if something is true or false: the scientific method. He grapples with the limits of what we can and cannot know. Case studies are offered to demonstrate the applications of logical thinking to quite varied settings, spanning courtroom testimony, medical decision making, magic, modern physics, and conspiracy theories.This urgently needed book enables us to avoid the extremes of passive gullibility and cynical rejection. As Levitin attests: Truth matters. A post-truth era is an era of willful irrationality, reversing all the great advances humankind has made. Euphemisms like "fringe theories," "extreme views," "alt truth," and even "fake news" can literally be dangerous. Let's call lies what they are and catch those making them in the act.
Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy
by Cathy O'NeilLonglisted for the National Book AwardNew York Times BestsellerA former Wall Street quant sounds an alarm on the mathematical models that pervade modern life — and threaten to rip apart our social fabricWe live in the age of the algorithm. Increasingly, the decisions that affect our lives—where we go to school, whether we get a car loan, how much we pay for health insurance—are being made not by humans, but by mathematical models. In theory, this should lead to greater fairness: Everyone is judged according to the same rules, and bias is eliminated.But as Cathy O’Neil reveals in this urgent and necessary book, the opposite is true. The models being used today are opaque, unregulated, and uncontestable, even when they’re wrong. Most troubling, they reinforce discrimination: If a poor student can’t get a loan because a lending model deems him too risky (by virtue of his zip code), he’s then cut off from the kind of education that could pull him out of poverty, and a vicious spiral ensues. Models are propping up the lucky and punishing the downtrodden, creating a “toxic cocktail for democracy.” Welcome to the dark side of Big Data.Tracing the arc of a person’s life, O’Neil exposes the black box models that shape our future, both as individuals and as a society. These “weapons of math destruction” score teachers and students, sort résumés, grant (or deny) loans, evaluate workers, target voters, set parole, and monitor our health.O’Neil calls on modelers to take more responsibility for their algorithms and on policy makers to regulate their use. But in the end, it’s up to us to become more savvy about the models that govern our lives. This important book empowers us to ask the tough questions, uncover the truth, and demand change.— Longlist for National Book Award (Non-Fiction)— Goodreads, semi-finalist for the 2016 Goodreads Choice Awards (Science and Technology)— Kirkus, Best Books of 2016— New York Times, 100 Notable Books of 2016 (Non-Fiction)— The Guardian, Best Books of 2016— WBUR's "On Point," Best Books of 2016: Staff Picks— Boston Globe, Best Books of 2016, Non-Fiction
Wearing Gauss's Jersey
by Dean HathoutWearing Gauss's Jersey focuses on "Gauss problems," problems that can be very tedious and time consuming when tackled in a traditional, straightforward way but if approached in a more insightful fashion, can yield the solution much more easily and elegantly. The book shows how mathematical problem solving can be fun and how students can improve the
Weather Derivatives
by Achilleas D. Zapranis Antonis Alexandridis K.Weather derivatives are financial instruments that can be used by organizations or individuals as part of a risk management strategy to minimize risk associated with adverse or unexpected weather conditions. Just as traditional contingent claims, a weather derivative has an underlying measure, such as: rainfall, wind, snow or temperature. Nearly $1 trillion of the U.S. economy is directly exposed to weather-related risk. More precisely, almost 30% of the U.S. economy and 70% of U.S. companies are affected by weather. The purpose of this monograph is to conduct an in-depth analysis of financial products that are traded in the weather market. Presenting a pricing and modeling approach for weather derivatives written on various underlying weather variables will help students, researchers, and industry professionals accurately price weather derivatives, and will provide strategies for effectively hedging against weather-related risk. This book will link the mathematical aspects of the modeling procedure of weather variables to the financial markets and the pricing of weather derivatives. Very little has been published in the area of weather risk, and this volume will appeal to graduate-level students and researchers studying financial mathematics, risk management, or energy finance, in addition to investors and professionals within the financial services industry.
Weather Modeling and Forecasting of PV Systems Operation
by Viorel Badescu Eugenia Paulescu Paul Gravila Marius PaulescuIn the past decade, there has been a substantial increase of grid-feeding photovoltaic applications, thus raising the importance of solar electricity in the energy mix. This trend is expected to continue and may even increase. Apart from the high initial investment cost, the fluctuating nature of the solar resource raises particular insertion problems in electrical networks. Proper grid managing demands short- and long-time forecasting of solar power plant output. Weather modeling and forecasting of PV systems operation is focused on this issue. Models for predicting the state of the sky, nowcasting solar irradiance and forecasting solar irradiation are studied and exemplified. Statistical as well as artificial intelligence methods are described. The efficiency of photovoltaic converters is assessed for any weather conditions. Weather modeling and forecasting of PV systems operation is written for researchers, engineers, physicists and students interested in PV systems design and utilization.