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The Secret Life of Equations: The 50 Greatest Equations and How They Work
by Richard CochraneDiscover the 50 equations that have led to incredible discoveries, ground-breaking technology and have shaped our understanding of the world.From much heralded classics, like Zeno's Dichotomy and Pythagoras's Theorem, to The Schrödinger Wave Equation and Google PageRank, each equation is broken down and explained in a unique, illustrated way, so that you understand what it's about; what it's good for; its history, detail and related equations.Behind every important scientific discovery there is an equation. They are far from baffling, and now you too can understand their power and beauty!
Semantics, Logics, and Calculi
by Christian W. Probst Chris Hankin René Rydhof HansenThis Festschrift volume is published in honorof Hanne Riis Nielson and Flemming Nielson on the occasion of their 60thbirthdays in 2014 and 2015, respectively. The papers included in this volumedeal with the wide area of calculi, semantics, and analysis. The book features contributions fromcolleagues, who have worked together with Hanne and Flemming through theirscientific life and are dedicated to them and to their work. The papers werepresented at a colloquium at the Technical University of Denmark in January2016.
Séminaire de Probabilités XLVIII
by Catherine Donati-Martin Antoine Lejay Alain RouaultIn addition to its further exploration of the subject of peacocks, introduced in recent Séminaires de Probabilités, this volume continues the series' focus on current research themes in traditional topics such as stochastic calculus, filtrations and random matrices. Also included are some particularly interesting articles involving harmonic measures, random fields and loop soups. The featured contributors are Mathias Beiglböck, Martin Huesmann and Florian Stebegg, Nicolas Juillet, Gilles Pags, Dai Taguchi, Alexis Devulder, Mátyás Barczy and Peter Kern, I. Bailleul, Jürgen Angst and Camille Tardif, Nicolas Privault, Anita Behme, Alexander Lindner and Makoto Maejima, Cédric Lecouvey and Kilian Raschel, Christophe Profeta and Thomas Simon, O. Khorunzhiy and Songzi Li, Franck Maunoury, Stéphane Laurent, Anna Aksamit and Libo Li, David Applebaum, and Wendelin Werner.
Seminal Contributions to Modelling and Simulation
by Khalid Al-Begain Andrzej BargielaMarking the 30th anniversary of the European Conference on Modelling and Simulation (ECMS), this inspirational text/reference reviews significant advances in the field of modelling and simulation, as well as key applications of simulation in other disciplines. The broad-ranging volume presents contributions from a varied selection of distinguished experts chosen from high-impact keynote speakers and best paper winners from the conference, including a Nobel Prize recipient, and the first president of the European Council for Modelling and Simulation (also abbreviated to ECMS). This authoritative book will be of great value to all researchers working in the field of modelling and simulation, in addition to scientists from other disciplines who make use of modelling and simulation approaches in their work.
Semiotics in Mathematics Education
by Norma Presmeg Luis Radford Wolff-Michael Roth Gert KadunzThis volume discusses semiotics in mathematics education as an activity with a formal sign system, in which each sign represents something else. Theories presented by Saussure, Peirce, Vygotsky and other writers on semiotics are summarized in their relevance to the teaching and learning of mathematics. The significance of signs for mathematics education lies in their ubiquitous use in every branch of mathematics. Such use involves seeing the general in the particular, a process that is not always clear to learners. Therefore, in several traditional frameworks, semiotics has the potential to serve as a powerful conceptual lens in investigating diverse topics in mathematics education research. Topics that are implicated include (but are not limited to): the birth of signs; embodiment, gestures and artifacts; segmentation and communicative fields; cultural mediation; social semiotics; linguistic theories; chains of signification; semiotic bundles; relationships among various sign systems; intersubjectivity; diagrammatic and inferential reasoning; and semiotics as the focus of innovative learning and teaching materials.
Separably Injective Banach Spaces
by Antonio Avilés Félix Cabello Sánchez Jesús M.F. Castillo Manuel González Yolanda MorenoThis monograph contains a detailed exposition of the up-to-date theory of separably injective spaces: new and old results are put into perspective with concrete examples (such as l∞/c0 and C(K) spaces, where K is a finite height compact space or an F-space, ultrapowers of L∞ spaces and spaces of universal disposition). It is no exaggeration to say that the theory of separably injective Banach spaces is strikingly different from that of injective spaces. For instance, separably injective Banach spaces are not necessarily isometric to, or complemented subspaces of, spaces of continuous functions on a compact space. Moreover, in contrast to the scarcity of examples and general results concerning injective spaces, we know of many different types of separably injective spaces and there is a rich theory around them. The monograph is completed with a preparatory chapter on injective spaces, a chapter on higher cardinal versions of separable injectivity and a lively discussion of open problems and further lines of research.
Sequential Learning and Decision-Making in Wireless Resource Management
by Rong Zheng Cunqing HuaThis book lays out the theoretical foundation of the so-called multi-armed bandit (MAB) problems and puts it in the context of resource management in wireless networks. Part I of the book presents the formulations, algorithms and performance of three forms of MAB problems, namely, stochastic, Markov and adversarial. Covering all three forms of MAB problems makes this book unique in the field. Part II of the book provides detailed discussions of representative applications of the sequential learning framework in cognitive radio networks, wireless LANs and wireless mesh networks. Both individuals in industry and those in the wireless research community will benefit from this comprehensive and timely treatment of these topics. Advanced-level students studying communications engineering and networks will also find the content valuable and accessible.
Service Network Design of Bike Sharing Systems
by Patrick VogelThis monograph presents a tactical planning approach for service network design in metropolitan areas. Designing the service network requires the suitable aggregation of demand data as well as the anticipation of operational relocation decisions. To this end, an integrated approach of data analysis and mathematical optimization is introduced. The book also includes a case study based on real-world data to demonstrate the benefit of the proposed service network design approach. The target audience comprises primarily research experts in the field of traffic engineering, but the book may also be beneficial for graduate students.
Set Theory: A First Course (Cambridge Mathematical Textbooks Ser.)
by Daniel W. CunninghamSet theory is a rich and beautiful subject whose fundamental concepts permeate virtually every branch of mathematics. One could say that set theory is a unifying theory for mathematics, since nearly all mathematical concepts and results can be formalized within set theory. This textbook is meant for an upper undergraduate course in set theory. In this text, the fundamentals of abstract sets, including relations, functions, the natural numbers, order, cardinality, transfinite recursion, the axiom of choice, ordinal numbers, and cardinal numbers, are developed within the framework of axiomatic set theory. The reader will need to be comfortable reading and writing mathematical proofs. The proofs in this textbook are rigorous, clear, and complete, while remaining accessible to undergraduates who are new to upper-level mathematics. Exercises are included at the end of each section in a chapter, with useful suggestions for the more challenging exercises.
The Seven Pillars of Statistical Wisdom
by Stephen M. StiglerWhat gives statistics its unity as a science? Stephen Stigler sets forth the seven foundational ideas of statistics--a scientific discipline related to but distinct from mathematics and computer science and one which often seems counterintuitive. His original account will fascinate the interested layperson and engage the professional statistician.
Several Real Variables
by Shmuel KantorovitzThis undergraduate textbook is based on lectures given bythe author on the differential and integral calculus of functions of severalreal variables. The book has a modern approach and includes topics such as: *The p-norms on vector space and theirequivalence *The Weierstrass and Stone-Weierstrassapproximation theorems *The differential as a linear functional;Jacobians, Hessians, and Taylor's theorem in several variables *The Implicit Function Theorem for a system ofequations, proved via Banach's Fixed Point Theorem *Applications to Ordinary Differential Equations *Line integrals and an introduction to surfaceintegrals This book features numerous examples, detailed proofs, aswell as exercises at the end of sections. Many of the exercises have detailedsolutions, making the book suitable for self-study. Several Real Variables will be useful for undergraduatestudents in mathematics who have completed first courses in linear algebra andanalysis of one real variable.
Sharpening Your Advanced SAS Skills
by Sunil GuptaSharpening Your Advanced SAS Skills presents sophisticated SAS programming techniques, procedures, and tools, such as Proc SQL, hash tables, and SAS Macro programming, for any industry. Drawing on his more than 20 years' experience of SAS programming in the pharmaceutical industry, the author provides a unique approach that empowers both advanced p
Sheaves and functions modulo p: lectures on the Woods Hole trace formula
by Lenny TaelmanThe Woods Hole trace formula is a Lefschetz fixed-point theorem for coherent cohomology on algebraic varieties. It leads to a version of the sheaves-functions dictionary of Deligne, relating characteristic-p-valued functions on the rational points of varieties over finite fields to coherent modules equipped with a Frobenius structure. This book begins with a short introduction to the homological theory of crystals of Böckle and Pink with the aim of introducing the sheaves-functions dictionary as quickly as possible, illustrated with elementary examples and classical applications. Subsequently, the theory and results are expanded to include infinite coefficients, L-functions, and applications to special values of Goss L-functions and zeta functions. Based on lectures given at the Morningside Center in Beijing in 2013, this book serves as both an introduction to the Woods Hole trace formula and the sheaves-functions dictionary, and to some advanced applications on characteristic p zeta values.
A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions (Lecture Notes in Physics #919)
by János K. Asbóth László Oroszlány András PályiThis course-based primer provides newcomers to the field with a concise introduction to some of the core topics in the emerging field of topological insulators. The aim is to provide a basic understanding of edge states, bulk topological invariants, and of the bulk--boundary correspondence with as simple mathematical tools as possible. The present approach uses noninteracting lattice models of topological insulators, building gradually on these to arrive from the simplest one-dimensional case (the Su-Schrieffer-Heeger model for polyacetylene) to two-dimensional time-reversal invariant topological insulators (the Bernevig-Hughes-Zhang model for HgTe). In each case the discussion of simple toy models is followed by the formulation of the general arguments regarding topological insulators. The only prerequisite for the reader is a working knowledge in quantum mechanics, the relevant solid state physics background is provided as part of this self-contained text, which is complemented by end-of-chapter problems.
The Short-Run Approach to Long-Run Equilibrium in Competitive Markets
by Anthony Horsley Andrew J. WrobelThe authors present a new formal framework for finding the long-run competitive market equilibrium through short-run equilibria by exploiting the operating policies and plant valuations. This "short-run approach" develops ideas of Boiteux and Koopmans. Applied to the peak-load pricing of electricity generated by thermal, hydro and pumped-storage plants, it gives a sound and practical method of valuing the fixed assets--in this case, the river flows and the geological sites suitable for reservoirs. Its main mathematical basis is the producer's short-run profit maximization programme and its dual; their solutions have relatively simple forms that can greatly ease the fixed-point problem of solving for the general equilibrium. Since the optimal values (profit and cost functions) are usually nondifferentiable--this is so when there are joint costs of production such as capacity constraints--nonsmooth calculus is employed to resolve long-standing discrepancies between textbook theory and industrial reality by giving subdifferential extensions of basic results of microeconomics, including the Wong-Viner Envelope Theorem.
A Signal Theoretic Introduction to Random Processes
by Roy M. HowardA fresh introduction to random processes utilizing signal theory By incorporating a signal theory basis, A Signal Theoretic Introduction to Random Processes presents a unique introduction to random processes with an emphasis on the important random phenomena encountered in the electronic and communications engineering field. The strong mathematical and signal theory basis provides clarity and precision in the statement of results. The book also features: A coherent account of the mathematical fundamentals and signal theory that underpin the presented material Unique, in-depth coverage of material not typically found in introductory books Emphasis on modeling and notation that facilitates development of random process theory Coverage of the prototypical random phenomena encountered in electrical engineering Detailed proofs of results A related website with solutions to the problems found at the end of each chapter A Signal Theoretic Introduction to Random Processes is a useful textbook for upper-undergraduate and graduate-level courses in applied mathematics as well as electrical and communications engineering departments. The book is also an excellent reference for research engineers and scientists who need to characterize random phenomena in their research. provides details the prototypical random processes that are fundamental to electrical, electronic, and communication engineering. Consequently, chapter 7-10 coverage includes details of the characterization of random phenomena from an engineering perspective: probability mass function/probability density function evolution, autocorrelation function, and power spectral density. Chapter 11 features an introduction to order statistics, which provides the background for a discussion of the Poisson point random process in Chapter 12. Chapter 13 introduces birth-death random processes and then Chapter 14 provides an introduction to first passage time theory.
Simple Statistical Tests for Geography
by Danny McCarrollThis book is aimed directly at students of geography, particularly those who lack confidence in manipulating numbers. The aim is not to teach the mathematics behind statistical tests, but to focus on the logic, so that students can choose the most appropriate tests, apply them in the most convenient way and make sense of the results. Introductory chapters explain how to use statistical methods and then the tests are arranged according to the type of data that they require. Diagrams are used to guide students toward the most appropriate tests. The focus is on nonparametric methods that make very few assumptions and are appropriate for the kinds of data that many students will collect. Parametric methods, including Student’s t-tests, correlation and regression are also covered. Although aimed directly at geography students at senior undergraduate and graduate level, this book provides an accessible introduction to a wide range of statistical methods and will be of value to students and researchers in allied disciplines including Earth and environmental science, and the social sciences.
Simulation-Driven Modeling and Optimization
by Slawomir Koziel Leifur Leifsson Xin-She YangThis edited volume is devoted to the now-ubiquitous use of computational models across most disciplines of engineering and science, led by a trio of world-renowned researchers in the field. Focused on recent advances of modeling and optimization techniques aimed at handling computationally-expensive engineering problems involving simulation models, this book will be an invaluable resource for specialists (engineers, researchers, graduate students) working in areas as diverse as electrical engineering, mechanical and structural engineering, civil engineering, industrial engineering, hydrodynamics, aerospace engineering, microwave and antenna engineering, ocean science and climate modeling, and the automotive industry, where design processes are heavily based on CPU-heavy computer simulations. Various techniques, such as knowledge-based optimization, adjoint sensitivity techniques, and fast replacement models (to name just a few) are explored in-depth along with an array of the latest techniques to optimize the efficiency of the simulation-driven design process. High-fidelity simulation models allow for accurate evaluations of the devices and systems, which is critical in the design process, especially to avoid costly prototyping stages. Despite this and other advantages, the use of simulation tools in the design process is quite challenging due to associated high computational cost. The steady increase of available computational resources does not always translate into the shortening of the design cycle because of the growing demand for higher accuracy and necessity to simulate larger and more complex systems. For this reason, automated simulation-driven design--while highly desirable--is difficult when using conventional numerical optimization routines which normally require a large number of system simulations, each one already expensive.
Simulation Modeling and Arena (Wiley Series In Modeling And Simulation Ser.)
by Manuel D. RossettiEmphasizes a hands-on approach to learning statistical analysis and model building through the use of comprehensive examples, problems sets, and software applications With a unique blend of theory and applications, Simulation Modeling and Arena®, Second Edition integrates coverage of statistical analysis and model building to emphasize the importance of both topics in simulation. Featuring introductory coverage on how simulation works and why it matters, the Second Edition expands coverage on static simulation and the applications of spreadsheets to perform simulation. The new edition also introduces the use of the open source statistical package, R, for both performing statistical testing and fitting distributions. In addition, the models are presented in a clear and precise pseudo-code form, which aids in understanding and model communication. Simulation Modeling and Arena, Second Edition also features: Updated coverage of necessary statistical modeling concepts such as confidence interval construction, hypothesis testing, and parameter estimation Additional examples of the simulation clock within discrete event simulation modeling involving the mechanics of time advancement by hand simulation A guide to the Arena Run Controller, which features a debugging scenario New homework problems that cover a wider range of engineering applications in transportation, logistics, healthcare, and computer science A related website with an Instructor’s Solutions Manual, PowerPoint® slides, test bank questions, and data sets for each chapter Simulation Modeling and Arena, Second Edition is an ideal textbook for upper-undergraduate and graduate courses in modeling and simulation within statistics, mathematics, industrial and civil engineering, construction management, business, computer science, and other departments where simulation is practiced. The book is also an excellent reference for professionals interested in mathematical modeling, simulation, and Arena.
Singular Optics (Series in Optics and Optoelectronics)
by Gregory J. Gbur"This engagingly written text provides a useful pedagogical introduction to an extensive class of geometrical phenomena in the optics of polarization and phase, including simple explanations of much of the underlying mathematics." —Michael Berry, University of Bristol, UK "The author covers a vast number of topics in great detail, with a unifying mathematical treatment. It will be a useful reference for both beginners and experts…." —Enrique Galvez, Charles A. Dana Professor of Physics and Astronomy, Colgate University "a firm and comprehensive grounding both for those looking to acquaint themselves with the field and those of us that need reminding of the things we thought we knew, but hitherto did not understand: an essential point of reference." —Miles Padgett, Kelvin Chair of Natural Philosophy and Vice Principal (Research), University of Glasgow This book focuses on the various forms of wavefield singularities, including optical vortices and polarization singularities, as well as orbital angular momentum and associated applications. It highlights how an understanding of singular optics provides a completely different way to look at light. Whereas traditional optics focuses on the shape and structure of the non-zero portions of the wavefield, singular optics describes a wave’s properties from its null regions. The contents cover the three main areas of the field: the study of generic features of wavefields, determination of unusual properties of vortices and wavefields that contain singularities, and practical applications of vortices and other singularities.
Singularities and Computer Algebra
by Wolfram Decker Gerhard Pfister Mathias SchulzeThis book arose from a conference on "Singularities and Computer Algebra" which was held at the Pfalz-Akademie Lambrecht in June 2015 in honor of Gert-Martin Greuel's 70th birthday. This unique volume presents a collection of recent original research by some of the leading figures in singularity theory on a broad range of topics including topological and algebraic aspects, classification problems, deformation theory and resolution of singularities. At the same time, the articles highlight a variety of techniques, ranging from theoretical methods to practical tools from computer algebra. Greuel himself made major contributions to the development of both singularity theory and computer algebra. With Gerhard Pfister and Hans Sch#65533;nemann, he developed the computer algebra system SINGULAR, which has since become the computational tool of choice for many singularity theorists. The book addresses researchers whose work involves singularity theory and computer algebra from the PhD to expert level.
Six Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design
by Benjamin DiLeonardo-ParkerGet Started with Tessellation FoldingSix Simple Twists: The Pleat Pattern Approach to Origami Tessellation Design explains the process of designing an origami pattern. It answers the questions "how is a tessellation folded" and "what are the further possibilities."The author introduces an innovative pleat pattern technique of origami design that is
Skipper Supreme: Buck Showalter and the Baltimore Orioles
by Todd Karpovich Jeff Seidel Jason La CanforaFor the first decade of the 21st century, the Baltimore Orioles were perpetual cellar dwellers, with losing seasons from 1998-2011-fourteen straight years. They were the worst team in baseball when two-time American League Manager of the Year Buck Showalter took over as manager in August 2010, but they went 34-23 in the last two months of the season, and that set the tone for everything to follow.Buck, along with Andy MacPhail (president of baseball operations) and Dan Duquette (general manager), worked hard to change things in Baltimore, and the results have shown. In 2012, the Orioles went 93-69 and reached the postseason for the first time since 1997. In 2013, they fell short of the playoffs, but they still hit the most homers in the majors. They also set a new record in errorless games and fewest errors in a season. In addition, the Orioles boasted three Gold Glove winners: third baseman Manny Machado, center fielder Adam Jones, and shortstop J.J. Hardy. In 2014, after winning the AL East, they swept the Tigers in the divisional series before losing to the red-hot Royals in the American League Championship.This book details the club’s miraculous turnaround under Buck. It discusses key signings like Nelson Cruz, the quiet effectiveness of Nick Markakis, Jones’s leadership, the struggles of Chris Davis, and several other story lines from Showalter’s tenure.Skyhorse Publishing, as well as our Sports Publishing imprint, are proud to publish a broad range of books for readers interested in sports-books about baseball, pro football, college football, pro and college basketball, hockey, or soccer, we have a book about your sport or your team.Whether you are a New York Yankees fan or hail from Red Sox nation; whether you are a die-hard Green Bay Packers or Dallas Cowboys fan; whether you root for the Kentucky Wildcats, Louisville Cardinals, UCLA Bruins, or Kansas Jayhawks; whether you route for the Boston Bruins, Toronto Maple Leafs, Montreal Canadiens, or Los Angeles Kings; we have a book for you. While not every title we publish becomes a New York Times bestseller or a national bestseller, we are committed to publishing books on subjects that are sometimes overlooked by other publishers and to authors whose work might not otherwise find a home.
Small Area Estimation and Microsimulation Modeling
by Azizur Rahman Ann HardingSmall Area Estimation and Microsimulation Modeling is the first practical handbook that comprehensively presents modern statistical SAE methods in the framework of ultramodern spatial microsimulation modeling while providing the novel approach of creating synthetic spatial microdata. Along with describing the necessary theories and their advantages and limitations, the authors illustrate the practical application of the techniques to a large number of substantive problems, including how to build up models, organize and link data, create synthetic microdata, conduct analyses, yield informative tables and graphs, and evaluate how the findings effectively support the decision making processes in government and non-government organizations. Features Covers both theoretical and applied aspects for real-world comparative research and regional statistics production Thoroughly explains how microsimulation modeling technology can be constructed using available datasets for reliable small area statistics Provides SAS codes that allow readers to utilize these latest technologies in their own work. This book is designed for advanced graduate students, academics, professionals and applied practitioners who are generally interested in small area estimation and/or microsimulation modeling and dealing with vital issues in social and behavioural sciences, applied economics and policy analysis, government and/or social statistics, health sciences, business, psychology, environmental and agriculture modeling, computational statistics and data simulation, spatial statistics, transport and urban planning, and geospatial modeling. Dr Azizur Rahman is a Senior Lecturer in Statistics and convenor of the Graduate Program in Applied Statistics at the Charles Sturt University, and an Adjunct Associate Professor of Public Health and Biostatistics at the University of Canberra. His research encompasses small area estimation, applied economics, microsimulation modeling, Bayesian inference and public health. He has more than 60 scholarly publications including two books. Dr. Rahman’s research is funded by the Australian Federal and State Governments, and he serves on a range of editorial boards including the International Journal of Microsimulation (IJM). Professor Ann Harding, AO is an Emeritus Professor of Applied Economics and Social Policy at the National Centre for Social and Economic Modelling (NATSEM) of the University of Canberra. She was the founder and inaugural Director of this world class Research Centre for more than sixteen years, and also a co-founder of the International Microsimulation Association (IMA) and served as the inaugural elected president of IMA from 2004 to 2011. She is a fellow of the Academy of the Social Sciences in Australia. She has more than 300 publications including several books in microsimulation modeling.