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Happy Pi Day to You! All About Measuring Circles (The Cat in the Hat's Learning Library)
by Bonnie WorthLaugh and learn with fun facts about the history of pi, measurements, theorems, and more—all told in Dr. Seuss&’s beloved rhyming style and starring the Cat in the Hat! &“It is all about circles and measuring fun. So put on your Pi Hats! Let&’s start, everyone!&” The Cat in the Hat&’s Learning Library series combines beloved characters, engaging rhymes, and Seussian illustrations to introduce children to non-fiction topics from the real world! Go on an adventure with the Cat in the Hat and learn: how to measure and draw circleshow pi is a number so long that it never endshow Ancient Egyptians used pi to help build the pyramidsand much more!Perfect for story time and for the youngest readers, Happy Pi Day to You! All About Measuring Circles also includes an index, glossary, and suggestions for further learning. Look for more books in the Cat in the Hat&’s Learning Library series!High? Low? Where Did It Go? All About Animal CamouflageIs a Camel a Mammal? All About MammalsThe 100 Hats of the Cat in the Hat: A Celebration of the 100th Day of SchoolA Great Day for Pup: All About Wild BabiesWould You Rather Be a Pollywog? All About Pond LifeI Can Name 50 Trees Today! All About TreesFine Feathered Friends: All About BirdsMy, Oh My--A Butterfly! All About ButterfliesOh Say Can You Seed? All About Flowering PlantsInside Your Outside! All About the Human BodyIce is Nice! All About the North and South Poles
Haptic Interaction with Deformable Objects
by Guido BöttcherThe focus from most Virtual Reality (VR) systems lies mainly on the visual immersion of the user. But the emphasis only on the visual perception is insufficient for some applications as the user is limited in his interactions within the VR. Therefore the textbook presents the principles and theoretical background to develop a VR system that is able to create a link between physical simulations and haptic rendering which requires update rates of 1\,kHz for the force feedback. Special attention is given to the modeling and computation of contact forces in a two-finger grasp of textiles. Addressing further the perception of small scale surface properties like roughness, novel algorithms are presented that are not only able to consider the highly dynamic behaviour of textiles but also capable of computing the small forces needed for the tactile rendering at the contact point. Final analysis of the entire VR system is being made showing the problems and the solutions found in the work
The Harary Index of a Graph
by Kexiang Xu Kinkar Ch. Das Nenad TrinajstićThis is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems. This book is dedicated to Professor Frank Harary (1921--2005), the grandmaster of graph theory and its applications. It has be written by experts in the field of graph theory and its applications. For a connected graph G, as an important distance-based topological index, the Harary index H(G) is defined as the sum of the reciprocals of the distance between any two unordered vertices of the graph G. In this book, the authors report on the newest results on the Harary index of a graph. These results mainly concern external graphs with respect to the Harary index; the relations to other topological indices; its properties and applications to pure graph theory and chemical graph theory; and two significant variants, i. e. , additively and multiplicatively weighted Harary indices. In the last chapter, we present a number of open problems related to the Harary index. As such, the book will not only be of interest to graph researchers, but to mathematical chemists as well.
Harcourt Math: Reteach Workbook (Grade #4)
by HarcourtThis Reteach Workbook for Grade 4 contains: Understand Whole Numbers and Operations, Time, Data, and Graphing, Multiplication and Division Facts, Multiply By 1- and 2-Digit Numbers, Divide By 1- and 2-Digit Divisors, Geometry and Algebra, Fractions and Probability, Measurement and Decimals, Perimeter, Area, and Volume, etc.
Harcourt Math: Practice Workbook (Grade #3)
by Harcourt School PublishersA Grade 3 Math practice book.
Harcourt Math: Practice Workbook (Grade Two)
by Harcourt School PublishersThe math practice workbook for grade two deals with numbers and operations, digit addition and subtraction, money, time and data, geometry and patterns, and measurements and fractions.
Harcourt Math: Practice Workbook (Grade #4)
by Harcourt School PublishersA grade four mathematics book.
Harcourt Math: Practice Workbook (Grade #5)
by Harcourt School PublishersWrite and solve an equation for each problem. Explain what the variable represents.
Harcourt Math: Level 5 (Harcourt School Publishers Math Ser.)
by Harcourt School Publishers StaffThe authors of Harcourt Math want you to enjoy learning math and to feel confident that you can do it. We invite you to share your math book with family members. Take them on a guided tour through your book!
Harcourt Math (Grade #6)
by Evan M. MaletskyThe authors of Harcourt Math want you to be a good mathematician, but most of all we want you to enjoy learning math and feel confident that you can do it. We invite you to share your book with family members. Take them on a guided tour through your book!
Harcourt Math (California Edition)
by Harcourt School PublishersThis book makes a student enjoy learning math and to feel confident that he CAN DO. The unit lessons of the book contain: Understand Numbers and Operations, Data, Graphing, and Time, Multiplication and Division Facts, Multiply by 1- and 2-Digit Numbers, Divide by 1- and 2-Digit Divisors, Fractions and Decimals, Measurement, Algebra, and Graphing, Geometry, and Probability.
Hard X-Ray Imaging of Solar Flares
by Michele Piana A. Gordon Emslie Anna Maria Massone Brian R. DennisThe idea for this text emerged over several years as the authors participated in research projects related to analysis of data from NASA's RHESSI Small Explorer mission. The data produced over the operational lifetime of this mission inspired many investigations related to a specific science question: the when, where, and how of electron acceleration during solar flares in the stressed magnetic environment of the active Sun.A vital key to unlocking this science problem is the ability to produce high-quality images of hard X-rays produced by bremsstrahlung radiation from electrons accelerated during a solar flare. The only practical way to do this within the technological and budgetary limitations of the RHESSI era was to opt for indirect modalities in which imaging information is encoded as a set of two-dimensional spatial Fourier components. Radio astronomers had employed Fourier imaging for many years. However, differently than for radio astronomy, X-ray images produced by RHESSI had to be constructed from a very limited number of sparsely distributed and very noisy Fourier components. Further, Fourier imaging is hardly intuitive, and extensive validation of the methods was necessary to ensure that they produced images with sufficient accuracy and fidelity for scientific applications.This book summarizes the results of this development of imaging techniques specifically designed for this form of data. It covers a set of published works that span over two decades, during which various imaging methods were introduced, validated, and applied to observations. Also considering that a new Fourier-based telescope, STIX, is now entering its nominal phase on-board the ESA Solar Orbiter, it became more and more apparent to the authors that it would be a good idea to put together a compendium of these imaging methods and their applications. Hence the book you are now reading.
The Hardy Space H1 with Non-doubling Measures and Their Applications
by Dachun Yang Dongyong Yang Guoen HuThe present book offers an essential but accessible introduction to the discoveries first made in the 1990s that the doubling condition is superfluous for most results for function spaces and the boundedness of operators. It shows the methods behind these discoveries, their consequences and some of their applications. It also provides detailed and comprehensive arguments, many typical and easy-to-follow examples, and interesting unsolved problems. The theory of the Hardy space is a fundamental tool for Fourier analysis, with applications for and connections to complex analysis, partial differential equations, functional analysis and geometrical analysis. It also extends to settings where the doubling condition of the underlying measures may fail.
Hardy Spaces: Elements Of Advanced Analysis (Cambridge Studies in Advanced Mathematics #179)
by Nikolaï NikolskiThe theory of Hardy spaces is a cornerstone of modern analysis. It combines techniques from functional analysis, the theory of analytic functions and Lesbesgue integration to create a powerful tool for many applications, pure and applied, from signal processing and Fourier analysis to maximum modulus principles and the Riemann zeta function. This book, aimed at beginning graduate students, introduces and develops the classical results on Hardy spaces and applies them to fundamental concrete problems in analysis. The results are illustrated with numerous solved exercises that also introduce subsidiary topics and recent developments. The reader's understanding of the current state of the field, as well as its history, are further aided by engaging accounts of important contributors and by the surveys of recent advances (with commented reference lists) that end each chapter. Such broad coverage makes this book the ideal source on Hardy spaces.
Hardy Spaces on Ahlfors-Regular Quasi Metric Spaces
by Ryan Alvarado Marius MitreaSystematically constructing an optimal theory, this monograph develops and explores several approaches to Hardy spaces in the setting of Alhlfors-regular quasi-metric spaces. The text is divided into two main parts, with the first part providing atomic, molecular, and grand maximal function characterizations of Hardy spaces and formulates sharp versions of basic analytical tools for quasi-metric spaces, such as a Lebesgue differentiation theorem with minimal demands on the underlying measure, a maximally smooth approximation to the identity and a Calderon-Zygmund decomposition for distributions. These results are of independent interest. The second part establishes very general criteria guaranteeing that a linear operator acts continuously from a Hardy space into a topological vector space, emphasizing the role of the action of the operator on atoms. Applications include the solvability of the Dirichlet problem for elliptic systems in the upper-half space with boundary data from Hardy spaces. The tools established in the first part are then used to develop a sharp theory of Besov and Triebel-Lizorkin spaces in Ahlfors-regular quasi-metric spaces. The monograph is largely self-contained and is intended for mathematicians, graduate students and professionals with a mathematical background who are interested in the interplay between analysis and geometry.
Hardy Type Inequalities on Time Scales
by Ravi P. Agarwal Donal O'Regan Samir H. SakerThe book is devoted to dynamic inequalities of Hardy type and extensions and generalizations via convexity on a time scale T. In particular, the book contains the time scale versions of classical Hardy type inequalities, Hardy and Littlewood type inequalities, Hardy-Knopp type inequalities via convexity, Copson type inequalities, Copson-Beesack type inequalities, Liendeler type inequalities, Levinson type inequalities and Pachpatte type inequalities, Bennett type inequalities, Chan type inequalities, and Hardy type inequalities with two different weight functions. These dynamic inequalities contain the classical continuous and discrete inequalities as special cases when T = R and T = N and can be extended to different types of inequalities on different time scales such as T = hN, h > 0, T = qN for q > 1, etc. In this book the authors followed the history and development of these inequalities. Each section in self-contained and one can see the relationship between the time scale versions of the inequalities and the classical ones. To the best of the authors' knowledge this is the first book devoted to Hardy-type inequalities and their extensions on time scales.
Harmonic Analysis and Applications: Mathematics And Applications (Studies In Advanced Mathematics Ser. #23)
by John J. BenedettoHarmonic analysis plays an essential role in understanding a host of engineering, mathematical, and scientific ideas. In Harmonic Analysis and Applications, the analysis and synthesis of functions in terms of harmonics is presented in such a way as to demonstrate the vitality, power, elegance, usefulness, and the intricacy and simplicity of the subject. This book is about classical harmonic analysis - a textbook suitable for students, and an essay and general reference suitable for mathematicians, physicists, and others who use harmonic analysis.Throughout the book, material is provided for an upper level undergraduate course in harmonic analysis and some of its applications. In addition, the advanced material in Harmonic Analysis and Applications is well-suited for graduate courses. The course is outlined in Prologue I. This course material is excellent, not only for students, but also for scientists, mathematicians, and engineers as a general reference. Chapter 1 covers the Fourier analysis of integrable and square integrable (finite energy) functions on R. Chapter 2 of the text covers distribution theory, emphasizing the theory's useful vantage point for dealing with problems and general concepts from engineering, physics, and mathematics. Chapter 3 deals with Fourier series, including the Fourier analysis of finite and infinite sequences, as well as functions defined on finite intervals. The mathematical presentation, insightful perspectives, and numerous well-chosen examples and exercises in Harmonic Analysis and Applications make this book well worth having in your collection.
Harmonic Analysis and Applications (Springer Optimization and Its Applications #168)
by Michael Th. RassiasThis edited volume presents state-of-the-art developments in various areas in which Harmonic Analysis is applied. Contributions cover a variety of different topics and problems treated such as structure and optimization in computational harmonic analysis, sampling and approximation in shift invariant subspaces of L2(ℝ), optimal rank one matrix decomposition, the Riemann Hypothesis, large sets avoiding rough patterns, Hardy Littlewood series, Navier–Stokes equations, sleep dynamics exploration and automatic annotation by combining modern harmonic analysis tools, harmonic functions in slabs and half-spaces, Andoni –Krauthgamer –Razenshteyn characterization of sketchable norms fails for sketchable metrics, random matrix theory, multiplicative completion of redundant systems in Hilbert and Banach function spaces. Efforts have been made to ensure that the content of the book constitutes a valuable resource for graduate students as well as senior researchers working on Harmonic Analysis and its various interconnections with related areas.
Harmonic Analysis and Integral Geometry (Chapman & Hall/CRC Research Notes in Mathematics Series)
by Massimo A PicardelloComprising a selection of expository and research papers, Harmonic Analysis and Integral Geometry grew from presentations offered at the July 1998 Summer University of Safi, Morocco-an annual, advanced research school and congress. This lively and very successful event drew the attendance of many top researchers, who offered both individual lecture
Harmonic Analysis and Partial Differential Equations: Proceedings of the Workshop in Abidjan, Côte d'Ivoire, May 22-26, 2023 (Applied and Numerical Harmonic Analysis)
by Justin Feuto Bérenger Akon KpataThis proceedings volume collects selected papers presented at the Harmonic Analysis and Applications Workshop held in Abidjan, Côte d'Ivoire from May 22-26, 2023. Chapters present surveys and recent research results from experts and cover a range of topics at the intersections of classical and abstract harmonic analysis, PDEs, and numerical analysis.
Harmonic Analysis and the Theory of Probability (Dover Books on Mathematics)
by Salomon BochnerNineteenth-century studies of harmonic analysis were closely linked with the work of Joseph Fourier on the theory of heat and with that of P. S. Laplace on probability. During the 1920s, the Fourier transform developed into one of the most effective tools of modern probabilistic research; conversely, the demands of the probability theory stimulated further research into harmonic analysis.Mathematician Salomon Bochner wrote a pair of landmark books on the subject in the 1930s and 40s. In this volume, originally published in 1955, he adopts a more probabilistic view and emphasizes stochastic processes and the interchange of stimuli between probability and analysis. Non-probabilistic topics include Fourier series and integrals in many variables; the Bochner integral; the transforms of Plancherel, Laplace, Poisson, and Mellin; applications to boundary value problems, to Dirichlet series, and to Bessel functions; and the theory of completely monotone functions.The primary significance of this text lies in the last two chapters, which offer a systematic presentation of an original concept developed by the author and partly by LeCam: Bochner's characteristic functional, a Fourier transform on a Euclidean-like space of infinitely many dimensions. The characteristic functional plays a role in stochastic processes similar to its relationship with numerical random variables, and thus constitutes an important part of progress in the theory of stochastic processes.
Harmonic Analysis on Exponential Solvable Lie Groups
by Hidenori Fujiwara Jean LudwigThis book is the first one that brings together recent results on the harmonic analysis of exponential solvable Lie groups. There still are many interesting open problems, and the book contributes to the future progress of this research field. As well, various related topics are presented to motivate young researchers. The orbit method invented by Kirillov is applied to study basic problems in the analysis on exponential solvable Lie groups. This method tells us that the unitary dual of these groups is realized as the space of their coadjoint orbits. This fact is established using the Mackey theory for induced representations, and that mechanism is explained first. One of the fundamental problems in the representation theory is the irreducible decomposition of induced or restricted representations. Therefore, these decompositions are studied in detail before proceeding to various related problems: the multiplicity formula, Plancherel formulas, intertwining operators, Frobenius reciprocity, and associated algebras of invariant differential operators. The main reasoning in the proof of the assertions made here is induction, and for this there are not many tools available. Thus a detailed analysis of the objects listed above is difficult even for exponential solvable Lie groups, and it is often assumed that G is nilpotent. To make the situation clearer and future development possible, many concrete examples are provided. Various topics presented in the nilpotent case still have to be studied for solvable Lie groups that are not nilpotent. They all present interesting and important but difficult problems, however, which should be addressed in the near future. Beyond the exponential case, holomorphically induced representations introduced by Auslander and Kostant are needed, and for that reason they are included in this book.