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Spherical Harmonics and Approximations on the Unit Sphere: An Introduction

These notes provide an introduction to the theory of spherical harmonics in an arbitrary dimension as well as an overview of classical and recent results on some aspects of the approximation of functions by spherical polynomials and numerical integration over the unit sphere. The notes are intended for graduate students in the mathematical sciences and researchers who are interested in solving problems involving partial differential and integral equations on the unit sphere, especially on the unit sphere in three-dimensional Euclidean space. Some related work for approximation on the unit disk in the plane is also briefly discussed, with results being generalizable to the unit ball in more dimensions.

Spherical Models

Well-illustrated, practical approach to creating star-faced spherical forms that can serve as basic structures for geodesic domes. Complete instructions for making models from circular bands of paper with just a ruler and compass. Discusses tessellation, or tiling, and how to make spherical models of the semiregular solids and concludes with a discussion of the relationship of polyhedra to geodesic domes and directions for building models of domes. ". . . very pleasant reading." -- Science. 1979 edition.

Spherical Radial Basis Functions, Theory and Applications

This book is the first to be devoted to the theory and applications of spherical (radial) basis functions (SBFs), which is rapidly emerging as one of the most promising techniques for solving problems where approximations are needed on the surface of a sphere. The aim of the book is to provide enough theoretical and practical details for the reader to be able to implement the SBF methods to solve real world problems. The authors stress the close connection between the theory of SBFs and that of the more well-known family of radial basis functions (RBFs), which are well-established tools for solving approximation theory problems on more general domains. The unique solvability of the SBF interpolation method for data fitting problems is established and an in-depth investigation of its accuracy is provided. Two chapters are devoted to partial differential equations (PDEs). One deals with the practical implementation of an SBF-based solution to an elliptic PDE and another which describes an SBF approach for solving a parabolic time-dependent PDE, complete with error analysis. The theory developed is illuminated with numerical experiments throughout. Spherical Radial Basis Functions, Theory and Applications will be of interest to graduate students and researchers in mathematics and related fields such as the geophysical sciences and statistics.

Spheroidal Wave Functions

Intended to facilitate the use and calculation of spheroidal wave functions, this applications-oriented text features a detailed and unified account of the properties of these functions. Addressed to applied mathematicians, mathematical physicists, and mathematical engineers, it presents tables that provide a convenient means for handling wave problems in spheroidal coordinates.Topics include separation of the scalar wave equation in spheroidal coordinates, angle and radial functions, integral representations and relations, and expansions in spherical Bessel function products. Additional subjects include recurrence relations of Whittaker type, asymptotic expansions for large values of c, and vector wave functions. The text concludes with an appendix, references, and tables of numerical values.

Spiel, Zufall und Kommerz: Theorie und Praxis des Spiels um Geld zwischen Mathematik, Recht und Realität

Das Spiel mit dem Glück Von Brett- und Kartenspielen über Glücksspielautomaten bis hin zu Lotterien und Wettbüros – dieses Buch ist ebenso breit angelegt wie die Welt des Spiels und zeigt, was all diesen Spielen gemeinsam ist und wie sie wirklich funktionieren. Dabei geht um den Vergleich diverser Spielsysteme anhand wertneutraler Merkmale insbesondere zum Unterschied von Glücks- und Geschicklichkeitsspielen. Wo regieren der Zufall und der Kommerz, wo die Geschicklichkeit? Wie greifen sie ineinander, und welchen rechtlichen Regelungen unterliegt das kommerzielle Spiel? Was macht den besonderen Reiz der Pokerspiele aus? Viele Beispiele zeichnen historische Entwicklungen nach, Zusammenhänge und Gesetze der Wahrscheinlichkeitstheorie werden anschaulich erklärt und lange Spielfolgen bis zum „Point of no return“ bildlich dargestellt. Thomas Bronder räumt außerdem mit vielen Irrtümern, ungenauen Begriffsvorstellungen und Missverständnissen auf, etwa zu Chancengleichheit, Verlusttempo und Auszahlquoten. Vom erfolgreichen Buchmachen über erfolglose Gewinnsysteme bis zu Schneeballsystemen, Falschspiel, Betrug und Manipulation wird kein Thema ausgelassen. So liegt hiermit nun eine kleine „Bibel“ des Spiels um Geld vor, die nicht nur für Spieler, Journalisten und Juristen interessant ist.Die zweite Auflage enthält viele Ergänzungen und Korrekturen mit einem umfangreichen Sachwortverzeichnis zum Nachschlagen. Sie teilt Nullsummenspiele in fünf Klassen ein, beschreibt Besonderheiten beim Pokern und geht auf die Probleme mit Online-Glücksspielen im Internet ein.

Spieltheorie: Theorie und Verfahren zur Lösung von Nash- und verallgemeinerten Nash-Gleichgewichtsproblemen (Mathematik Kompakt)

Das Buch gibt eine Einführung in einige zentrale Konzepte der (mathematischen) Spieltheorie und legt seinen Fokus dabei auf die Lösung von Nash- und verallgemeinerten Nash-Gleichgewichtsproblemen. Die meisten Probleme der Spieltheorie lassen sich nicht von Hand lösen; stattdessen ist man auf geeignete numerische Verfahren angewiesen, mit deren Hilfe zumindest eine Näherungslösung berechnet werden kann. Einen Schwerpunkt dieses Buches bilden daher eine ganze Reihe von Methoden meist neueren Datums, die hier erstmals in Buchform präsentiert werden und zur numerischen Lösung von Nash- und verallgemeinerten Nash-Gleichgewichtsproblemen verwendet werden können. Aber auch Existenz- und Eindeutigkeitssätze sowie Zwei-Personen-Spiele werden ausführlich diskutiert. Darüber hinaus werden in eigenen Abschnitten die benötigten mathematischen Grundlagen zur Verfügung gestellt. Dazu gehören Aussagen über konvexe und monotone Funktionen sowie Optimalitätsbedingungen aus der restringierten Optimierung.

Spiking Neural P Systems: Theory, Applications and Implementations

Spiking neural P systems represent a significant advancement in the field of membrane computing, drawing inspiration from the communication patterns observed in neurons. Since their inception in 2006, these distributed and parallel neural-like computing models have gained popularity and emerged as important tools within the membrane computing area. As a key branch of the third generation of artificial neural networks, a fascinating research area of artificial intelligence, spiking neural P systems offer a captivating blend of theoretical elegance and practical utility. Their efficiency, Turing completeness, and real-life application characteristics, including interpretability and suitability for large-scale problems, have positioned them at the forefront of contemporary research in membrane computing and artificial intelligence. This state-of-the-art reference work is organized into three parts comprising twelve chapters. It thoroughly investigates the theoretical foundations, real-life applications, and implementations of spiking neural P systems. From fundamental principles to computational power and complexity, the theoretical aspects are explored, laying the groundwork for understanding their practical applications. Real-life applications span a diverse range of domains, including complex optimization, classification, fault diagnosis, medical image processing, information fusion, cryptography, and robot control. Additionally, the book discusses several software and hardware implementations that provide valuable insights into the practical deployment of spiking neural P systems. As the rapid development of spiking neural P systems continues to unfold, there is an increasing demand for a systematic and comprehensive summary of their capabilities and applications. This work serves as an invaluable resource for researchers, scholars, and practitioners interested in the theoretical underpinnings, algorithms, and practical implementation of artificial intelligence and membrane computing.

Spillovers to Emerging Equity Markets: An Econometric Assessment

A report from the International Monetary Fund.

Spin: From Basic Symmetries to Quantum Optimal Control

This monograph is a fundamental reference for scientists and engineers who encounter spin processes in their work. The author, Ilya Kuprov, derives the concept of spin from basic symmetries and gives an overview of theoretical and computational aspects of spin dynamics: from Dirac equation and spin Hamiltonian, through coherent evolution and relaxation theories, to quantum optimal control, and all the way to practical implementation advice for parallel computers.

Spinning Strings and Correlation Functions in the AdS/CFT Correspondence (Springer Theses)

This book addresses several aspects of the integrable structure of the AdS/CFT correspondence. In particular it presents computations made on both sides of the AdS/CFT correspondence, at weak and at strong coupling. On the string theory side of the correspondence, the book focuses on the evaluation of the energy spectrum of closed string solutions moving in some deformed backgrounds that preserve integrability. On the gauge theory side, it explores various formal problems arising in the computation of two and three-point functions by means of the Algebraic Bethe Ansatz and the Quantum Inverse Scattering method. The book features numerous results on integrability in the context of the AdS/CFT correspondence. Self-contained and pedagogical, it includes general discussions and detailed presentations on the use of integrable systems techniques and their applications.

Spinors in Four-Dimensional Spaces

Without using the customary Clifford algebras frequently studied in connection with the representations of orthogonal groups, this book gives an elementary introduction to the two-component spinor formalism for four-dimensional spaces with any signature. Some of the useful applications of four-dimensional spinors, such as Yang-Mills theory, are derived in detail using illustrative examples. Spinors in Four-Dimensional Spaces is aimed at graduate students and researchers in mathematical and theoretical physics interested in the applications of the two-component spinor formalism in any four-dimensional vector space or Riemannian manifold with a definite or indefinite metric tensor. This systematic and self-contained book is suitable as a seminar text, a reference book, and a self-study guide.

Spintronics-Based Neuromorphic Computing (Springer Tracts in Electrical and Electronics Engineering)

The book discusses almost all aspects of spintronics-based neuromorphic computing, starting from a very basic level, and will be of interest to both spintronics and neuromorphic computing communities. The chapters also cover most simulation and experimental studies reported recently by researchers worldwide on this topic. The book includes an introductory chapter on nanomagnetism and spin physics and another on neural network algorithms (covering both the machine-learning and neuroscience aspects of these algorithms). These introductory chapters will help the readers build their background and truly appreciate the recent research results on spintronics-based neuromorphic computing, presented in the later chapters of the book. Various numerical simulation exercises are also provided in the book.

Spirals, Helical Lines, and Spiral-Like Figures: Mathematical Playfulness in Two and Three Dimensions

In this book you will discover the mathematical patterns and regularities of various spirals, helixes and spiral-like figures. Their geometric aspects and connections are presented in a visually appealing way and are supplemented as best as possible with analytical aspects and representations. Using examples from technology and nature, you will learn about round, square, golden and spherical spirals and examine their curvature behavior and other exciting properties. The examples are arranged thematically and the book has a modular structure so that the individual chapters can be read largely independently of each other. It is therefore a valuable resource for students, pupils, (prospective) teachers, those interested in mathematics and those who want to become one.Additional animations are available with the SN More Media app: simply download the SN More Media app free of charge, scan an image or a link with the play button and immediately play the animation on your smartphone or tablet.The translation was done with the help of artificial intelligence. A subsequent human revision was done primarily in terms of content.

Splash!: Modeling and Measurement Applications for Young Learners in Grades K-1

Splash! is a mathematics unit for high-ability learners in kindergarten and first grade focusing on concepts related to linear measurement, the creativity elements of fluency and flexibility, and the overarching, interdisciplinary concept of models. The unit consists of 13 lessons centered on the idea of designing a community pool. Students examine the question of why we measure, the importance of accuracy in measurement, and the various units and tools of measurement. The unit presents a hands-on, constructivist approach, allowing children to build their knowledge base and their skills as they explore mathematical ideas through play and planned investigations. Students are involved in creative and critical thinking, problem solving, process skill development, and communication.Grades K-1

Splash!

It's hard to keep up with the goings-on at Ann Jonas's pond. What fun young readers will have keeping track! Cat. Dog. Frog. Fish. Who went in and who jumped out? Here is a counting book as fresh as a spring-fed pond.

Spline and Spline Wavelet Methods with Applications to Signal and Image Processing

This book presents various contributions of splines to signal and image processing from a unified perspective that is based on the Zak transform (ZT). It expands the methodology from periodic splines, which were presented in the first volume, to non-periodic splines. Together, these books provide a universal toolbox accompanied by MATLAB software for manipulating polynomial and discrete splines, spline-based wavelets, wavelet packets and wavelet frames for signal/ image processing applications. In this volume, we see that the ZT provides an integral representation of discrete and polynomial splines, which, to some extent, is similar to Fourier integral. The authors explore elements of spline theory and design, and consider different types of polynomial and discrete splines. They describe applications of spline-based wavelets to data compression. These splines are useful for real-time signal processing and, in particular, real-time wavelet and frame transforms. Further topics addressed in this volume include: "global" splines, such as interpolating, self-dual and smoothing, whose supports are infinite; the compactly supported quasi-interpolating and smoothing splines including quasi-interpolating splines on non-uniform grids; and cubic Hermite splines as a source for the design of multiwavelets and multiwavelet frames. Readers from various disciplines including engineering, computer science and mathematical information technology will find the descriptions of algorithms, applications and software in this book especially useful.

Spline Collocation Methods for Partial Differential Equations: With Applications in R

A comprehensive approach to numerical partial differential equations Spline Collocation Methods for Partial Differential Equations combines the collocation analysis of partial differential equations (PDEs) with the method of lines (MOL) in order to simplify the solution process. Using a series of example applications, the author delineates the main features of the approach in detail, including an established mathematical framework. The book also clearly demonstrates that spline collocation can offer a comprehensive method for numerical integration of PDEs when it is used with the MOL in which spatial (boundary value) derivatives are approximated with splines, including the boundary conditions. R, an open-source scientific programming system, is used throughout for programming the PDEs and numerical algorithms, and each section of code is clearly explained. As a result, readers gain a complete picture of the model and its computer implementation without having to fill in the details of the numerical analysis, algorithms, or programming. The presentation is not heavily mathematical, and in place of theorems and proofs, detailed example applications are provided. Appropriate for scientists, engineers, and applied mathematicians, Spline Collocation Methods for Partial Differential Equations: Introduces numerical methods by first presenting basic examples followed by more complicated applications Employs R to illustrate accurate and efficient solutions of the PDE models Presents spline collocation as a comprehensive approach to the numerical integration of PDEs and an effective alternative to other, well established methods Discusses how to reproduce and extend the presented numerical solutions Identifies the use of selected algorithms, such as the solution of nonlinear equations and banded or sparse matrix processing Features a companion website that provides the related R routines Spline Collocation Methods for Partial Differential Equations is a valuable reference and/or self-study guide for academics, researchers, and practitioners in applied mathematics and engineering, as well as for advanced undergraduates and graduate-level students.

Splines and PDEs: Cetraro, Italy 2017 (Lecture Notes in Mathematics #2219)

This book takes readers on a multi-perspective tour through state-of-the-art mathematical developments related to the numerical treatment of PDEs based on splines, and in particular isogeometric methods. A wide variety of research topics are covered, ranging from approximation theory to structured numerical linear algebra. More precisely, the book provides (i) a self-contained introduction to B-splines, with special focus on approximation and hierarchical refinement, (ii) a broad survey of numerical schemes for control problems based on B-splines and B-spline-type wavelets, (iii) an exhaustive description of methods for computing and analyzing the spectral distribution of discretization matrices, and (iv) a detailed overview of the mathematical and implementational aspects of isogeometric analysis. The text is the outcome of a C.I.M.E. summer school held in Cetraro (Italy), July 2017, featuring four prominent lecturers with different theoretical and application perspectives. The book may serve both as a reference and an entry point into further research.

Splines and Variational Methods (Dover Books on Mathematics)

One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text's first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.

Splitting Algorithms, Modern Operator Theory, and Applications

This book brings together research articles and state-of-the-art surveys in broad areas of optimization and numerical analysis with particular emphasis on algorithms. The discussion also focuses on advances in monotone operator theory and other topics from variational analysis and nonsmooth optimization, especially as they pertain to algorithms and concrete, implementable methods. The theory of monotone operators is a central framework for understanding and analyzing splitting algorithms. Topics discussed in the volume were presented at the interdisciplinary workshop titled Splitting Algorithms, Modern Operator Theory, and Applications held in Oaxaca, Mexico in September, 2017. Dedicated to Jonathan M. Borwein, one of the most versatile mathematicians in contemporary history, this compilation brings theory together with applications in novel and insightful ways.

Splitting The Herd: A Corral Of Odds And Evens

Splitting Methods in Communication, Imaging, Science, and Engineering

This book is about computational methods based on operator-splitting. The three editors, while all being applied mathematicians whose expertise include splitting methods, work in different application areas including computational mechanics, image processing, wireless communication, nonlinear optics (optical fibers), and so on. Therefore, the book will present very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas. ​

Splunk Certified Study Guide: Prepare for the User, Power User, and Enterprise Admin Certifications

Make your Splunk certification easier with this exam study guide that covers the User, Power User, and Enterprise Admin certifications. This book is divided into three parts. The first part focuses on the Splunk User and Power User certifications starting with how to install Splunk, Splunk Processing Language (SPL), field extraction, field aliases and macros, and Splunk tags. You will be able to make your own data model and prepare an advanced dashboard in Splunk.In the second part, you will explore the Splunk Admin certification. There will be in-depth coverage of Splunk licenses and user role management, and how to configure Splunk forwarders, indexer clustering, and the security policy of Splunk. You’ll also explore advanced data input options in Splunk as well as .conf file merging logic, btool, various attributes, stanza types, editing advanced data inputs through the .conf file, and various other types of .conf file in Splunk.The concluding part covers the advanced topics of the Splunk Admin certification. You will also learn to troubleshoot Splunk and to manage existing Splunk infrastructure. You will understand how to configure search head, multi-site indexer clustering, and search peers besides exploring how to troubleshoot Splunk Enterprise using the monitoring console and matrix.log. This part will also include search issues and configuration issues. You will learn to deploy an app through a deployment server on your client’s instance, create a server class, and carry out load balancing, socks proxy, and indexer discovery.By the end of the Splunk Certified Study Guide, you will have learned how to manage resources in Splunk and how to use REST API services for Splunk. This section also explains how to set up Splunk Enterprise on the AWS platform and some of the best practices to make them work efficiently together.The book offers multiple choice question tests for each part that will help you better prepare for the exam.What You Will LearnStudy to pass the Splunk User, Power User, and Admin certificate examsImplement and manage Splunk multi-site clusteringDesign, implement, and manage a complex Splunk Enterprise solutionMaster the roles of Splunk Admin and troubleshootingConfigure Splunk using AWSWho This Book Is For People looking to pass the User, Power User, and Enterprise Admin exams. It is also useful for Splunk administrators and support engineers for managing an existing deployment.

Sport Analytics: A data-driven approach to sport business and management

The increasing availability of data has transformed the way sports are played, promoted and managed. This is the first textbook to explain how the big data revolution is having a profound influence across the sport industry, demonstrating how sport managers and business professionals can use analytical techniques to improve their professional practice. While other sports analytics books have focused on player performance data, this book shows how analytics can be applied to every functional area of sport business, from marketing and event management to finance and legal services. Drawing on research that spans the entire sport industry, it explains how data is influencing the most important decisions, from ticket sales and human resources to risk management and facility operations. Each chapter contains real world examples, industry profiles and extended case studies which are complimented by a companion website full of useful learning resources. Sport Analytics: A data-driven approach to sport business and management is an essential text for all sport management students and an invaluable reference for any sport management professional involved in operational research.

Sport and Migration: Borders, Boundaries and Crossings

From Major League Baseball to English soccer’s Premier League, all successful contemporary professional sports leagues include a wide diversity of nationalities and ethnicities within their playing and coaching rosters. The international migration of sporting talent and labor, encouraged and facilitated by the social and economic undercurrents of globalization, mean that world sport is now an important case study for any student or researcher with an interest in international labor flows, economic migration, global demography or the interdependent world economy. In this dazzling collection of papers, leading international sport studies scholars chart the patterns, policies and personal experiences of labour migration within and around sport, and in doing so cast important new light both on the forces shaping modern sport and on the role that sport plays in shaping the world economy and global society. Presenting original case studies of sports from European and African soccer to Japanese baseball to rugby union in New Zealand, the book makes an important contribution to our understanding of a wide range of issues within contemporary social science, such as national identity politics, economic structure and organization, north-south relations, imperial legacies and gender relations. This book is invaluable reading for students and researchers working in sport studies, human geography, economics or international business.