Series: Springer Texts in Statistics
2009, Approx. 495 p., Hardcover
ISBN: 978-0-387-09607-0
Due: December 2008
A Modern Approach to Regression with R focuses on tools and techniques for building regression models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to base inferences or conclusions only on valid models.
The regression output and plots that appear throughout the book have been generated using R. On the book website you will find the R code used in each example in the text. You will also find SAS-code and STATA-code to produce the equivalent output on the book website. Primers containing expanded explanations of R, SAS and STATA and their use in this book are also available on the book website.
The book contains a number of new real data sets from applications ranging from rating restaurants, rating wines, predicting newspaper circulation and magazine revenue, comparing the performance of NFL kickers, and comparing finalists in the Miss America pageant across states.
One of the aspects of the book that sets it apart from many other regression books is that complete details are provided for each example. The book is aimed at first year graduate students in statistics and could also be used for a senior undergraduate class.
Simon Sheather is Professor and Head of the Department of Statistics at Texas A&M University. Professor Sheather’s research interests are in the fields of flexible regression methods and nonparametric and robust statistics. He is a Fellow of the American Statistical Association and listed on ISIHighlyCited.com.
Transforming a model with AR(1) errors into a model with iid errors. -
A general approach to transforming GLS into LS. - Case Study. * Exercises.
- Mixed Models. - Random effects. - Maximum likelihood and restricted maximum
likelihood. - Residuals in mixed models. - Models with covariance structures
which vary over time. - Modeling the conditional mean. * Exercises. - Appendix:
nonparametric smoothing.
Series: Lecture Notes in Mathematics , Vol. 1961
2009, Approx. 160 p., Softcover
ISBN: 978-3-540-85798-3
Due: December 3, 2008
Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and the short-term, "who goes where" optimization are considered. These models can also be adapted for the optimization of other types of networks, such as telecommunications, pipeline or drainage networks. In the monograph we study the most general problem settings, namely, when neither the shape nor even the topology of the network to be constructed is known a priori.
1 Introduction.- 2 Problem setting.- 3 Optimal connected networks.- 4 Relaxed problem and existence of solutions.- 5 Topological properties of optimal sets.- 6 Optimal sets and geodesics in the two y dimensional case.- Appendix A The mass transportation problem.- Appendix B Some tools from Geometric Measure Theory.
Series: Springer Monographs in Mathematics
2009, Approx. 370 p., Hardcover
ISBN: 978-0-387-84896-9
Due: January 2009
Based on recent research by the author and his graduate students, this text describes novel variational formulations and resolutions of a large class of partial differential equations and evolutions, many of which are not amenable to the methods of the classical calculus of variations. While it contains many new results, the general and unifying framework of the approach, its versatility in solving a disparate set of equations, and its reliance on basic functional analytic principles, makes it suitable for an intermediate level graduate course. The applications, however, require a fair knowledge of classical analysis and PDEs which is needed to make judicious choices of function spaces where the self-dual variational principles need to be applied. It is the author's hope that this material will become standard for all graduate students interested in convexity methods for PDEs.
Preface.- Introduction.- Legendre-Fenchel Duality on Phase Space.- Self-dual Lagrangians on Phase Space.- Skew-adjoint Operators and Self-dual Lagrangians.- Self-dual Vector Fields and Their Calculus.- Variational Principles for Completely Self-dual Functionals.- Semigroups of Contractions Associated to Self-dual Lagrangians.- Iteration of Self-dual Lagrangians and Multiparameter Evolutions.- Direct Sum of Completely Self-dual Functionals.- Semilinear Evolution with Self-dual Boundary Conditions.- The Class of Antisymmetric Hamiltonians.- Variational Principles for Self-dual Functionals and First Applications.- The Role of the Co-Hamiltonian in Self-dual Variational Problems.- Direct Sum of Self-dual Functionals and Hamiltonian Systems.- Superposition of Interacting Self-dual Functionals.- Hamiltonian Systems of Partial Differential Equations.- The Self-dual Palais-Smale Condition for Noncoercive Functionals.- Navier-Stokes and other Self-dual Nonlinear Evolutions.- References.-
Series: CMS Books in Mathematics
2009, Approx. 515 p. 20 illus., Hardcover
ISBN: 978-0-387-84922-5
Due: January 2009
Pell's equation is a very simple, yet fundamental Diophantine equation which is believed to have been known to mathematicians for over 2000 years. Because of its popularity, the Pell equation is often discussed in textbooks and recreational books concerning elementary number theory, but usually not in much depth. This book provides a modern and deeper approach to the problem of solving the Pell equation. The main component of this will be computational techniques, but in the process of deriving these it will be necessary to develop the corresponding theory.
One objective of this book is to provide a less intimidating introduction for senior undergraduates and others with the same level of preparedness to the delights of algebraic number theory through the medium of a mathematical object that has fascinated people since the time of Archimedes. To achieve this, this work is made accessible to anyone with some knowledge of elementary number theory and abstract algebra. Many references and notes are provided for those who wish to follow up on various topics, and the authors also describe some rather surprising applications to cryptography.
Preface.- Introduction.- Early History of the Pell Equation.- Continued Fractions.- Quadratic Number Fields.- Ideals and Continued Fractions.- Quadratic Number Fields.- Ideals and Continued Fractions.- Some Special Pell Equations.- The Ideal Class Group.- The Analytic Class Number Formula.- Some Additional Analytic Results.- Some Computational Techniques.- (f, p) Representations of O-ideals.- Compact Representations.- The Subexponential Method.- Applications to Cryptography.- Unconditional Verification of the Regulator and the Class Number.- Principal Ideal Testing in O.- Conclusion.- Appendix.- References.- Index.
Series: Universitext
2009, Approx. 265 p., Softcover
ISBN: 978-0-387-84898-3
Due: January 2009
-Includes a nice selection of topics
-Contains a large selection of non-standard exercises
-Accessible presentation of key tools in harmonic and fourier analysis
The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The authors then proceed to use the linear Schrodinger equation to describe properties enjoyed by general dispersive equations. This information is then used to treat local and global well-posedness for the semi-linear Schrodinger equations. The end of each chapter contains recent developments and open problems, as well as exercises.
Preface.- The Fourier Transform.- Interpolation of Operators: A Multiplier Theorem.- Sobolev Spaces and Pseudo-differential Operators.- The Linear Schrodinger Equation.- The Nonlinear Schrodinger Equation, Local theory.- Asymptotic Behavior for NLS Equation.- Korteweg-de Vries Equation.- Asymptotic Behavior of Solutions for the k-gKdV Equations.- Other Nonlinear Dispersive Models.- General Quasilinear Schrodinger Equation.- Appendix.- References.- Index.-