- Table View
- List View
Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics
by Kai Hormann N. SukumarIn Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics, eminent computer graphics and computational mechanics researchers provide a state-of-the-art overview of generalized barycentric coordinates. Commonly used in cutting-edge applications such as mesh parametrization, image warping, mesh deformation, and finite as well as boundary element methods, the theory of barycentric coordinates is also fundamental for use in animation and in simulating the deformation of solid continua. Generalized Barycentric Coordinates is divided into three sections, with five chapters each, covering the theoretical background, as well as their use in computer graphics and computational mechanics. A vivid 16-page insert helps illustrating the stunning applications of this fascinating research area. <P><P>Key Features: <li>Provides an overview of the many different types of barycentric coordinates and their properties. <li>Discusses diverse applications of barycentric coordinates in computer graphics and computational mechanics. <li>The first book-length treatment on this topic
Generalized Cauchy-Riemann Systems with a Singular Point
by Zafar D UsmanovA theory of generalized Cauchy-Riemann systems with polar singularities of order not less than one is presented and its application to study of infinitesimal bending of surfaces having positive curvature and an isolated flat point is given. The book contains results of investigations obtained by the author and his collaborators.
Generalized Connectivity of Graphs
by Xueliang Li Yaping MaoNoteworthy results, proof techniques, open problems and conjectures in generalized (edge-) connectivity are discussed in this book. Both theoretical and practical analyses for generalized (edge-) connectivity of graphs are provided. Topics covered in this book include: generalized (edge-) connectivity of graph classes, algorithms, computational complexity, sharp bounds, Nordhaus-Gaddum-type results, maximum generalized local connectivity, extremal problems, random graphs, multigraphs, relations with the Steiner tree packing problem and generalizations of connectivity. This book enables graduate students to understand and master a segment of graph theory and combinatorial optimization. Researchers in graph theory, combinatorics, combinatorial optimization, probability, computer science, discrete algorithms, complexity analysis, network design, and the information transferring models will find this book useful in their studies.
Generalized Dynamics of Soft-Matter Quasicrystals: Mathematical Models, Solutions and Applications (Springer Series in Materials Science #260)
by Tian-You Fan Wenge Yang Hui Cheng Xiao-Hong SunThis book highlights the mathematical models and solutions of the generalized dynamics of soft-matter quasicrystals (SMQ) and introduces possible applications of the theory and methods. Based on the theory of quasiperiodic symmetry and symmetry breaking, the book treats the dynamics of individual quasicrystal systems by reducing them to nonlinear partial differential equations and then provides methods for solving the initial-boundary value problems in these equations. The solutions obtained demonstrate the distribution, deformation and motion of SMQ and determine the stress, velocity and displacement fields. The interactions between phonons, phasons and fluid phonons are discussed in some fundamental materials samples. The reader benefits from a detailed comparison of the mathematical solutions for both solid and soft-matter quasicrystals, gaining a deeper understanding of the universal properties of SMQ. The second edition covers the latest research progress on quasicrystals in topics such as thermodynamic stability, three-dimensional problems and solutions, rupture theory, and the photonic band-gap and its applications. These novel chapters make the book an even more useful and comprehensive reference guide for researchers in condensed matter physics, chemistry and materials sciences.
Generalized Estimating Equations
by Joseph M. Hilbe James W. HardinGeneralized Estimating Equations, Second Edition updates the best-selling previous edition, which has been the standard text on the subject since it was published a decade ago. Combining theory and application, the text provides readers with a comprehensive discussion of GEE and related models. Numerous examples are employed throughout the text, al
The Generalized Fourier Series Method: Bending of Elastic Plates (Developments in Mathematics #65)
by Christian Constanda Dale DotyThis book explains in detail the generalized Fourier series technique for the approximate solution of a mathematical model governed by a linear elliptic partial differential equation or system with constant coefficients. The power, sophistication, and adaptability of the method are illustrated in application to the theory of plates with transverse shear deformation, chosen because of its complexity and special features. In a clear and accessible style, the authors show how the building blocks of the method are developed, and comment on the advantages of this procedure over other numerical approaches. An extensive discussion of the computational algorithms is presented, which encompasses their structure, operation, and accuracy in relation to several appropriately selected examples of classical boundary value problems in both finite and infinite domains. The systematic description of the technique, complemented by explanations of the use of the underlying software, will help the readers create their own codes to find approximate solutions to other similar models. The work is aimed at a diverse readership, including advanced undergraduates, graduate students, general scientific researchers, and engineers.The book strikes a good balance between the theoretical results and the use of appropriate numerical applications. The first chapter gives a detailed presentation of the differential equations of the mathematical model, and of the associated boundary value problems with Dirichlet, Neumann, and Robin conditions. The second chapter presents the fundamentals of generalized Fourier series, and some appropriate techniques for orthonormalizing a complete set of functions in a Hilbert space. Each of the remaining six chapters deals with one of the combinations of domain-type (interior or exterior) and nature of the prescribed conditions on the boundary. The appendices are designed to give insight into some of the computational issues that arise from the use of the numerical methods described in the book.Readers may also want to reference the authors’ other books Mathematical Methods for Elastic Plates, ISBN: 978-1-4471-6433-3 and Boundary Integral Equation Methods and Numerical Solutions: Thin Plates on an Elastic Foundation, ISBN: 978-3-319-26307-6.
Generalized Fractional Order Differential Equations Arising in Physical Models
by Santanu Ray Subhadarshan SahooThis book analyzes the various semi-analytical and analytical methods for finding approximate and exact solutions of fractional order partial differential equations. It explores approximate and exact solutions obtained by various analytical methods for fractional order partial differential equations arising in physical models.
Generalized Functions and Partial Differential Equations (Dover Books on Mathematics)
by Avner FriedmanThis self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research.Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography.
Generalized Hyperbolic Secant Distributions
by Matthias J. FischerAmong the symmetrical distributions with an infinite domain, the most popular alternative to the normal variant is the logistic distribution as well as the Laplace or the double exponential distribution, which was first introduced in 1774. Occasionally, the Cauchy distribution is also used. Surprisingly, the hyperbolic secant distribution has led a charmed life, although Manoukian and Nadeau had already stated in 1988 that ". . . the hyperbolic-secant distribution . . . has not received sufficient attention in the published literature and may be useful for students and practitioners. " During the last few years, however, several generalizations of the hyperbolic secant distribution have become popular in the context of financial return data because of its excellent fit. Nearly all of them are summarized within this Springer Brief.
Generalized Inverses: Theory and Computations (Developments in Mathematics #53)
by Sanzheng Qiao Yimin Wei Guorong WangThis book begins with the fundamentals of the generalized inverses, then moves to more advanced topics.It presents a theoretical study of the generalization of Cramer's rule, determinant representations of the generalized inverses, reverse order law of the generalized inverses of a matrix product, structures of the generalized inverses of structured matrices, parallel computation of the generalized inverses, perturbation analysis of the generalized inverses, an algorithmic study of the computational methods for the full-rank factorization of a generalized inverse, generalized singular value decomposition, imbedding method, finite method, generalized inverses of polynomial matrices, and generalized inverses of linear operators. This book is intended for researchers, postdocs, and graduate students in the area of the generalized inverses with an undergraduate-level understanding of linear algebra.
Generalized, Linear, and Mixed Models (Wiley Series in Probability and Statistics #651)
by Charles E. McCulloch Shayle R. Searle John M. NeuhausAn accessible and self-contained introduction to statistical models-now in a modernized new edition Generalized, Linear, and Mixed Models, Second Edition provides an up-to-date treatment of the essential techniques for developing and applying a wide variety of statistical models. The book presents thorough and unified coverage of the theory behind generalized, linear, and mixed models and highlights their similarities and differences in various construction, application, and computational aspects. A clear introduction to the basic ideas of fixed effects models, random effects models, and mixed models is maintained throughout, and each chapter illustrates how these models are applicable in a wide array of contexts. In addition, a discussion of general methods for the analysis of such models is presented with an emphasis on the method of maximum likelihood for the estimation of parameters. The authors also provide comprehensive coverage of the latest statistical models for correlated, non-normally distributed data. Thoroughly updated to reflect the latest developments in the field, the Second Edition features: A new chapter that covers omitted covariates, incorrect random effects distribution, correlation of covariates and random effects, and robust variance estimation A new chapter that treats shared random effects models, latent class models, and properties of models A revised chapter on longitudinal data, which now includes a discussion of generalized linear models, modern advances in longitudinal data analysis, and the use between and within covariate decompositions Expanded coverage of marginal versus conditional models Numerous new and updated examples With its accessible style and wealth of illustrative exercises, Generalized, Linear, and Mixed Models, Second Edition is an ideal book for courses on generalized linear and mixed models at the upper-undergraduate and beginning-graduate levels. It also serves as a valuable reference for applied statisticians, industrial practitioners, and researchers.
Generalized Linear Mixed Models: Modern Concepts, Methods and Applications (Chapman & Hall/CRC Texts in Statistical Science)
by Walter W. StroupWith numerous examples using SAS PROC GLIMMIX, this text presents an introduction to linear modeling using the generalized linear mixed model as an overarching conceptual framework. For readers new to linear models, the book helps them see the big picture. It shows how linear models fit with the rest of the core statistics curriculum and points out the major issues that statistical modelers must consider.
Generalized Linear Mixed Models: Modern Concepts, Methods and Applications (Chapman & Hall/CRC Texts in Statistical Science)
by Walter W. Stroup Marina Ptukhina Julie GaraiGeneralized Linear Mixed Models: Modern Concepts, Methods, and Applications (2nd edition) presents an updated introduction to linear modeling using the generalized linear mixed model (GLMM) as the overarching conceptual framework. For students new to statistical modeling, this book helps them see the big picture – linear modeling as broadly understood and its intimate connection with statistical design and mathematical statistics. For readers experienced in statistical practice, but new to GLMMs, the book provides a comprehensive introduction to GLMM methodology and its underlying theory.Unlike textbooks that focus on classical linear models or generalized linear models or mixed models, this book covers all of the above as members of a unified GLMM family of linear models. In addition to essential theory and methodology, this book features a rich collection of examples using SAS® software to illustrate GLMM practice. This second edition is updated to reflect lessons learned and experience gained regarding best practices and modeling choices faced by GLMM practitioners. New to this edition are two chapters focusing on Bayesian methods for GLMMs.Key Features:• Most statistical modeling books cover classical linear models or advanced generalized and mixed models; this book covers all members of the GLMM family – classical and advanced models.• Incorporates lessons learned from experience and on-going research to provide up-to-date examples of best practices.• Illustrates connections between statistical design and modeling: guidelines for translating study design into appropriate model and in-depth illustrations of how to implement these guidelines; use of GLMM methods to improve planning and design.• Discusses the difference between marginal and conditional models, differences in the inference space they are intended to address and when each type of model is appropriate.• In addition to likelihood-based frequentist estimation and inference, provides a brief introduction to Bayesian methods for GLMMs.Walt Stroup is an Emeritus Professor of Statistics. He served on the University of Nebraska statistics faculty for over 40 years, specializing in statistical modeling and statistical design. He is a Fellow of the American Statistical Association, winner of the University of Nebraska Outstanding Teaching and Innovative Curriculum Award and author or co-author of three books on mixed models and their extensions.Marina Ptukhina (Pa-too-he-nuh), PhD, is an Associate Professor of Statistics at Whitman College. She is interested in statistical modeling, design and analysis of research studies and their applications. Her research includes applications of statistics to economics, biostatistics and statistical education. Ptukhina earned a PhD in Statistics from the University of Nebraska-Lincoln, a Master of Science degree in Mathematics from Texas Tech University and a Specialist degree in Management from The National Technical University "Kharkiv Polytechnic Institute."Julie Garai, PhD, is a Data Scientist at Loop. She earned her PhD in Statistics from the University of Nebraska-Lincoln and a bachelor’s degree in Mathematics and Spanish from Doane College. Dr Garai actively collaborates with statisticians, psychologists, ecologists, forest scientists, software engineers, and business leaders in academia and industry. In her spare time, she enjoys leisurely walks with her dogs, dance parties with her children, and playing the trombone.
Generalized Linear Mixed Models with Applications in Agriculture and Biology
by Josafhat Salinas Ruíz Osval Antonio Montesinos López Gabriela Hernández Ramírez Jose Crossa HiriartThis open access book offers an introduction to mixed generalized linear models with applications to the biological sciences, basically approached from an applications perspective, without neglecting the rigor of the theory. For this reason, the theory that supports each of the studied methods is addressed and later - through examples - its application is illustrated. In addition, some of the assumptions and shortcomings of linear statistical models in general are also discussed. An alternative to analyse non-normal distributed response variables is the use of generalized linear models (GLM) to describe the response data with an exponential family distribution that perfectly fits the real response. Extending this idea to models with random effects allows the use of Generalized Linear Mixed Models (GLMMs). The use of these complex models was not computationally feasible until the recent past, when computational advances and improvements to statistical analysis programs allowed users to easily, quickly, and accurately apply GLMM to data sets. GLMMs have attracted considerable attention in recent years. The word "Generalized" refers to non-normal distributions for the response variable and the word "Mixed" refers to random effects, in addition to the fixed effects typical of analysis of variance (or regression). With the development of modern statistical packages such as Statistical Analysis System (SAS), R, ASReml, among others, a wide variety of statistical analyzes are available to a wider audience. However, to be able to handle and master more sophisticated models requires proper training and great responsibility on the part of the practitioner to understand how these advanced tools work. GMLM is an analysis methodology used in agriculture and biology that can accommodate complex correlation structures and types of response variables.
Generalized Linear Models: A Unified Approach (Quantitative Applications in the Social Sciences #134)
by Professor Jeff Gill Michelle TorresGeneralized Linear Models: A Unified Approach provides an introduction to and overview of GLMs, with each chapter carefully laying the groundwork for the next. Authors Jeff Gill and Michelle Torres provide examples using real data from multiple fields in the social sciences such as psychology, education, economics, and political science, including data on voting intentions in the 2016 U.S. Republican presidential primaries. The Second Edition also strengthens material on the exponential family form, including a new discussion on the multinomial distribution; adds more information on how to interpret results and make inferences in the chapter on estimation procedures; and has a new section on extensions to generalized linear models.
Generalized Linear Models: A Unified Approach (Quantitative Applications in the Social Sciences #134)
by Professor Jeff Gill Michelle TorresGeneralized Linear Models: A Unified Approach provides an introduction to and overview of GLMs, with each chapter carefully laying the groundwork for the next. Authors Jeff Gill and Michelle Torres provide examples using real data from multiple fields in the social sciences such as psychology, education, economics, and political science, including data on voting intentions in the 2016 U.S. Republican presidential primaries. The Second Edition also strengthens material on the exponential family form, including a new discussion on the multinomial distribution; adds more information on how to interpret results and make inferences in the chapter on estimation procedures; and has a new section on extensions to generalized linear models.
Generalized Linear Models (Chapman & Hall/CRC Monographs on Statistics and Applied Probability #37)
by P. McCullaghThe success of the first edition of Generalized Linear Models led to the updated Second Edition, which continues to provide a definitive unified, treatment of methods for the analysis of diverse types of data. Today, it remains popular for its clarity, richness of content and direct relevance to agricultural, biological, health, engineering, and ot
Generalized Linear Models for Bounded and Limited Quantitative Variables (Quantitative Applications in the Social Sciences #181)
by Professor Michael Smithson Dr. Yiyun ShouThis book introduces researchers and students to the concepts and generalized linear models for analyzing quantitative random variables that have one or more bounds. Examples of bounded variables include the percentage of a population eligible to vote (bounded from 0 to 100), or reaction time in milliseconds (bounded below by 0). The human sciences deal in many variables that are bounded. Ignoring bounds can result in misestimation and improper statistical inference. Michael Smithson and Yiyun Shou's book brings together material on the analysis of limited and bounded variables that is scattered across the literature in several disciplines, and presents it in a style that is both more accessible and up-to-date. The authors provide worked examples in each chapter using real datasets from a variety of disciplines. The software used for the examples include R, SAS, and Stata. The data, software code, and detailed explanations of the example models are available on an accompanying website.
Generalized Linear Models for Bounded and Limited Quantitative Variables (Quantitative Applications in the Social Sciences #181)
by Professor Michael Smithson Dr. Yiyun ShouThis book introduces researchers and students to the concepts and generalized linear models for analyzing quantitative random variables that have one or more bounds. Examples of bounded variables include the percentage of a population eligible to vote (bounded from 0 to 100), or reaction time in milliseconds (bounded below by 0). The human sciences deal in many variables that are bounded. Ignoring bounds can result in misestimation and improper statistical inference. Michael Smithson and Yiyun Shou's book brings together material on the analysis of limited and bounded variables that is scattered across the literature in several disciplines, and presents it in a style that is both more accessible and up-to-date. The authors provide worked examples in each chapter using real datasets from a variety of disciplines. The software used for the examples include R, SAS, and Stata. The data, software code, and detailed explanations of the example models are available on an accompanying website.
Generalized Linear Models for Insurance Data
by Piet De Jong Gillian Z. HellerThis is the only book actuaries need to understand generalized linear models (GLMs) for insurance applications. GLMs are used in the insurance industry to support critical decisions. Until now, no text has introduced GLMs in this context or addressed the problems specific to insurance data. Using insurance data sets, this practical, rigorous book treats GLMs, covers all standard exponential family distributions, extends the methodology to correlated data structures, and discusses recent developments which go beyond the GLM. The issues in the book are specific to insurance data, such as model selection in the presence of large data sets and the handling of varying exposure times. Exercises and data-based practicals help readers to consolidate their skills, with solutions and data sets given on the companion website. Although the book is package-independent, SAS code and output examples feature in an appendix and on the website. In addition, R code and output for all the examples are provided on the website.
Generalized Linear Models With Examples in R (Springer Texts in Statistics)
by Peter K. Dunn Gordon K. SmythThis textbook presents an introduction to multiple linear regression, providing real-world data sets and practice problems. A practical working knowledge of applied statistical practice is developed through the use of these data sets and numerous case studies. The authors include a set of practice problems both at the end of each chapter and at the end of the book. Each example in the text is cross-referenced with the relevant data set, so that readers can load the data and follow the analysis in their own R sessions. The balance between theory and practice is evident in the list of problems, which vary in difficulty and purpose.This book is designed with teaching and learning in mind, featuring chapter introductions and summaries, exercises, short answers, and simple, clear examples. Focusing on the connections between generalized linear models (GLMs) and linear regression, the book also references advanced topics and tools that have not typically been included in introductions to GLMs to date, such as Tweedie family distributions with power variance functions, saddlepoint approximations, likelihood score tests, modified profile likelihood, and randomized quantile residuals. In addition, the authors introduce the new R code package, GLMsData, created specifically for this book. Generalized Linear Models with Examples in R balances theory with practice, making it ideal for both introductory and graduate-level students who have a basic knowledge of matrix algebra, calculus, and statistics.
Generalized Locally Toeplitz Sequences: Theory and Applications
by Carlo Garoni Stefano Serra-CapizzanoBased on their research experience, the authors propose a reference textbook in two volumes on the theory of generalized locally Toeplitz sequences and their applications. This first volume focuses on the univariate version of the theory and the related applications in the unidimensional setting, while the second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications. This book systematically develops the theory of generalized locally Toeplitz (GLT) sequences and presents some of its main applications, with a particular focus on the numerical discretization of differential equations (DEs). It is the first book to address the relatively new field of GLT sequences, which occur in numerous scientific applications and are especially dominant in the context of DE discretizations. Written for applied mathematicians, engineers, physicists, and scientists who (perhaps unknowingly) encounter GLT sequences in their research, it is also of interest to those working in the fields of Fourier and functional analysis, spectral analysis of DE discretization matrices, matrix analysis, measure and operator theory, numerical analysis and linear algebra. Further, it can be used as a textbook for a graduate or advanced undergraduate course in numerical analysis.
Generalized Locally Toeplitz Sequences: Volume I
by Carlo Garoni Stefano Serra-CapizzanoBased on the authors’ research experience, this two-volume reference textbook focuses on the theory of generalized locally Toeplitz sequences and its applications. The first volume discusses the univariate version of the theory and the related applications in the unidimensional setting, while this second volume, which addresses the multivariate case, is mainly devoted to concrete PDE applications. This book systematically develops the multivariate version of the theory of generalized locally Toeplitz (GLT) sequences and presents some of its main applications to the numerical discretization of partial differential equations (PDEs). Written for applied mathematicians, engineers, physicists, and scientists who (perhaps unknowingly) encounter GLT sequences in their research, it is also of interest to those working in the fields of Fourier and functional analysis, spectral analysis of PDE discretization matrices, matrix analysis, numerical analysis, linear and multilinear algebra. Further, it can be used as a textbook for graduate or advanced undergraduate courses in numerical analysis.
Generalized Measure Theory
by Zhenyuan Wang George J. KlirGeneralized Measure Theory examines the relatively new mathematical area of generalized measure theory. The exposition unfolds systematically, beginning with preliminaries and new concepts, followed by a detailed treatment of important new results regarding various types of nonadditive measures and the associated integration theory. The latter involves several types of integrals: Sugeno integrals, Choquet integrals, pan-integrals, and lower and upper integrals. All of the topics are motivated by numerous examples, culminating in a final chapter on applications of generalized measure theory. Some key features of the book include: many exercises at the end of each chapter along with relevant historical and bibliographical notes, an extensive bibliography, and name and subject indices. The work is suitable for a classroom setting at the graduate level in courses or seminars in applied mathematics, computer science, engineering, and some areas of science. A sound background in mathematical analysis is required. Since the book contains many original results by the authors, it will also appeal to researchers working in the emerging area of generalized measure theory.
Generalized Metric Spaces and Mappings
by Shou Lin Ziqiu YunThe idea of mutual classification of spaces and mappings is one of the main research directions of point set topology. In a systematical way, this book discusses the basic theory of generalized metric spaces by using the mapping method, and summarizes the most important research achievements, particularly those from Chinese scholars, in the theory of spaces and mappings since the 1960s. This book has three chapters, two appendices and a list of more than 400 references. The chapters are "The origin of generalized metric spaces", "Mappings on metric spaces" and "Classes of generalized metric spaces". Graduates or senior undergraduates in mathematics major can use this book as their text to study the theory of generalized metric spaces. Researchers in this field can also use this book as a valuable reference.