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• An introduction to survival and event history analysis.- Stochastic processes in event history analysis.- Non-parametric analysis of survival and event history data.- Regression models.- Parametric counting process models.- Unobserved hererogeneity: The odd effects of frailty.- Multivariate frailty models.- Marginal and dynamic models for recurrent events and clustered survival data.- Causality.- First passage time models: Understanding the shape of the hazard rate.- Diffusion- and Levy process models for dynamic frailty.- Markov processes and the product-integral.- Vector-valued counting processes, martingales and stochastic integrals.- References.
• (source: Nielsen Book Data)

The aim of this book is to bridge the gap between standard textbook models and a range of models where the dynamic structure of the data manifests itself fully. The common denominator of such models is stochastic processes. The authors show how counting processes, martingales, and stochastic integrals fit very nicely with censored data. Beginning with standard analyses such as Kaplan-Meier plots and Cox regression, the presentation progresses to the additive hazard model and recurrent event data. Stochastic processes are also used as natural models for individual frailty; they allow sensible interpretations of a number of surprising artifacts seen in population data. The stochastic process framework is naturally connected to causality. The authors show how dynamic path analyses can incorporate many modern causality ideas in a framework that takes the time aspect seriously. To make the material accessible to the reader, a large number of practical examples, mainly from medicine, are developed in detail. Stochastic processes are introduced in an intuitive and non-technical manner. This book is aimed at investigators who use event history methods and want a better understanding of the statistical concepts. It is suitable as a textbook for graduate courses in statistics and biostatistics.
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This monograph is the first in world chemical literature that has the review, generalization and systematization of all the problems of physical chemistry or organic peroxides. The general information concerning organic peroxide classifications, and the methods of their synthesis is given. The properties of peroxide bond are briefly considered. The structure of organic peroxides is analyzed in detail. The features of NMR spectroscopy as well as vibration spectroscopy of peroxides of a various structure are considered. Experimental data on thermal decomposition of organic peroxides in the gas phase and in solution are generalized. The influence of high pressure and cage effect on thermal decomposition of peroxides is described. Further, the acid-catalyzed reaction of decomposition, synthesis and transformations of organic peroxides are considered. The theoretical approaches to determination of thermodynamic properties of organic peroxides are considered. In the appendix kinetic and thermodynamic parameters of the representative set of peroxides are described and the areas of their application are specified. The examples of synthesis of the large set of organic peroxides are given. This monograph is intended for scientists, engineers and technicians, PhDs and students specializing in organic, physical, or polymer chemistry, biochemistry and environmental research.
(source: Nielsen Book Data)

• Non-singular transformations General ergodic and spectral theorems Transformations with infinite invariant measures Markov maps Recurrent events and similarity of Markov shifts Inner functions Hyperbolic geodesic flows Cocycles and skew products Bibliography Index.
• (source: Nielsen Book Data)

Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. This book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behavior, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible 'ergodic behavior' is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.
(source: Nielsen Book Data)

• SIMULATED ANNEALING. Combinatorial Optimization. Simulated Annealing. Asymptotic Convergence. Finite-Time Approximation. Simulated Annealing in Practice. Parallel Simulated Annealing Algorithms. BOLTZMANN MACHINES. Neural Computing. Boltzmann Machines. Combinatorial Optimization and Boltzmann Machines. Classification and Boltzmann Machines. Learning and Boltzmann Machines. Appendix. Bibliography. Indices.
• (source: Nielsen Book Data)

Wiley-Interscience Series in Discrete Mathematics and Optimization Advisory Editors Ronald L. Graham Jan Karel Lenstra Robert E. Tarjan Discrete Mathematics and Optimization involves the study of finite structures. It is one of the fastest growing areas in mathematics today. The level and depth of recent advances in the area and the wide applicability of its evolving techniques point to the rapidity with which the field is moving from its beginnings to maturity and presage the ever-increasing interaction between it and computer science. The Series provides a broad coverage of discrete mathematics and optimization, ranging over such fields as combinatorics, graph theory, enumeration, mathematical programming and the analysis of algorithms, and including such topics as Ramsey theory, transversal theory, block designs, finite geometries, Polya theory, graph and matroid algorithms, network flows, polyhedral combinatorics and computational complexity. The Wiley - Interscience Series in Discrete Mathematics and Optimization will be a substantial part of the record of this extraordinary development. Recent titles in the Series: Search Problems Rudolf Ahlswede, University of Bielefeld, Federal Republic of Germany Ingo Wegener, Johann Wolfgang Goethe University, Frankfurt, Federal Republic of Germany The problems of search, exploration, discovery and identification are of key importance in a wide variety of applications. This book will be of great interest to all those concerned with searching, sorting, information processing, design of experiments and optimal allocation of resources. 1987 Introduction to Optimization E. M. L. Beale FRS, Scicon Ltd, Milton Keynes, and Imperial College, London This book is intended as an introduction to the many topics covered by the term optimization', with special emphasis on applications in industry. It is divided into three parts. The first part covers unconstrained optimization, the second describes the methods used to solve linear programming problems, and the third covers nonlinear programming, integer programming and dynamic programming. The book is intended for senior undergraduate and graduate students studying optimization as part of a course in mathematics, computer science or engineering. 1988.
(source: Nielsen Book Data)

• Preface.- Plane Geometry.- Transformations.- Symmetry.- Curves.- Solid Geometry.- Appendix.- References.- Index.
• (source: Nielsen Book Data)

This is a book on Euclidean geometry that covers the standard material in a completely new way, while also introducing a number of new topics that would be suitable as a junior-senior level undergraduate textbook. The author does not begin in the traditional manner with abstract geometric axioms. Instead, he assumes the real numbers, and begins his treatment by introducing such modern concepts as a metric space, vector space notation, and groups, and thus lays a rigorous basis for geometry, while at the same time giving the student tools that will be useful in other courses.
(source: Nielsen Book Data)

• Part I. Vectors: 1. Real vectors
• 2 Complex vectors
• Part II. Matrices: 3. Real matrices
• 4. Complex matrices
• Part III. Vector Spaces: 5. Complex and real vector spaces
• 6. Inner-product space
• 7. Hilbert space
• Part IV. Rank, Inverse, and Determinant: 8. Rank
• 9. Inverse
• 10. Determinant
• Part V. Partitioned Matrices: 11. Basic results and multiplication relations
• 12. Inverses
• 13. Determinants
• 14. Rank (in)equalities
• 15. The sweep operator
• Part VI. Systems of Equations: 16. Elementary matrices
• 17. Echelon matrices
• 18. Gaussian elimination
• 19. Homogeneous equations
• 20. Nonhomogeneous equations
• Part VII. Eigenvalues, Eigenvectors, and Factorizations: 21. Eigenvalues and eigenvectors
• 22. Symmetric matrices
• 23. Some results for triangular matrices
• 24. Schur's decomposition theorem and its consequences
• 25. Jordan's decomposition theorem
• 26. Jordan chains and generalized eigenvectors
• Part VIII. Positive (Semi)Definite and Idempotent Matrices: 27. Positive (semi)definite matrices
• 28. Partitioning and positive (semi)definite matrices
• 29. Idempotent matrices
• Part IX. Matrix Functions: 30. Simple functions
• 31. Jordan representation
• 32. Matrix-polynomial representation
• Part X. Kronecker Product, Vec-Operator, and Moore-Penrose Inverse: 33. The Kronecker product
• 34. The vec-operator
• 35. The Moore-Penrose inverse
• 36. Linear vector and matrix equations
• 37. The generalized inverse
• Part XI. Patterned Matrices, Commutation and Duplication Matrix: 38. The commutation matrix
• 39. The symmetrizer matrix
• 40. The vec-operator and the duplication matrix
• 41. Linear structures
• Part XII. Matrix Inequalities: 42. Cauchy-Schwarz type inequalities
• 43. Positive (semi)definite matrix inequalities
• 44. Inequalities derived from the Schur complement
• 45. Inequalities concerning eigenvalues
• Part XIII. Matrix calculus: 46. Basic properties of differentials
• 47. Scalar functions
• 48. Vector functions
• 49. Matrix functions
• 50. The inverse
• 51. Exponential and logarithm
• 52. The determinant
• 53. Jacobians
• 54. Sensitivity analysis in regression models
• 55. The Hessian matrix
• 56. Least squares and best linear unbiased estimation
• 57. Maximum likelihood estimation
• 58. Inequalities and equalities.
• (source: Nielsen Book Data)

Matrix Algebra is the first volume of the Econometric Exercises Series. It contains exercises relating to course material in matrix algebra that students are expected to know while enrolled in an (advanced) undergraduate or a postgraduate course in econometrics or statistics. The book contains a comprehensive collection of exercises, all with full answers. But the book is not just a collection of exercises; in fact, it is a textbook, though one that is organized in a completely different manner than the usual textbook. The volume can be used either as a self-contained course in matrix algebra or as a supplementary text.
(source: Nielsen Book Data)

• Preface to the series. Preface. Introduction. Chapters
• 1. Phenomenological theory of recombination.
• 2. Impurity centers.
• 3. Cascade capture by isolated attractive centers.
• 4. One-quantum transitions.
• 5. Experimental data on capture by attractive centers in Ge and Si.
• 6. Reciprocal influence of impurity centers.
• 7. Capture limited by diffusion.
• 8. Capture by repulsive centers.
• 9. Multiphonon capture and thermal emission.
• 10. Thermal emission and capture in an electric field.
• 11. Auger recombination.
• 12. Impurity Auger processes. Appendices. References. Author index. Subject index. Materials index. Cumulative index.
• (source: Nielsen Book Data)

In recent years, great progress has been made in the understanding of recombination processes controlling the number of excess free carriers in semiconductors under nonequilibrium conditions. As a result, it is now possible to give a comprehensive theoretical description of these processes. The authors have selected a number of experimental results which elucidate the underlying physical problems and enable a test of theoretical models. The following topics are dealt with: phenomenological theory of recombination, theoretical models of shallow and deep localized states, cascade model of carrier capture by impurity centers, capture restricted by diffusion, multiphonon processes, Auger processes, effect of electric field on capture and thermal emission of carriers.
(source: Nielsen Book Data)

• Part I. Foundations of Preference, Value, and Utility: 1. Preference, value, and utility
• 2. Foundations of expected utility
• 3. Some flawed methods of decision making
• Part II. Deterministic Decisions: 4. The order rule: preferences for deterministic consequences
• 5. Getting the attributes right
• 6. Preference functions for single attributes
• 7. Preference functions for multiple attributes
• 8. Additive preference functions
• 9. Valuing deterministic consequences - value functions
• Part III. Decisions with Uncertainty: Multi-attribute Utility Functions Using a Value Measure: 10. Single-attribute utility function
• 11. Multi-attribute utility functions using preference and value functions
• 12. Utility functions over additive preference or value functions
• Part IV. Decisions with Uncertainty: Properties of Single-Attribute Utility Functions: 13. The role of the utility function in valuing uncertain deals
• 14. The risk aversion function
• 15. Scale transformations applied to lottery outcomes
• 16. The invariant transformation of a utility function
• 17. Valuing changes in investment opportunities
• 18. One-switch utility functions
• 19. Utility transversality
• 20. Multi-attribute risk aversion
• Part V. Decisions with Uncertainty: Multi-attribute Utility Functions without Preference or Value Functions: 21. Attribute dominance utility
• 22. The two-attribute utility tree
• 23. Independence conditions for two attributes
• 24. The multi-attribute utility tree
• 25. Independence conditions for three or more attributes
• 26. Higher-order independence conditions
• 27. One-switch utility independence
• Part VI. Utility Copula Formulations: 28. Multi-attribute utility copulas
• 29. Archimedean utility copulas
• 30. Assessing Archimedean utility copulas
• 31. Utility copula functions matching all boundary assessments
• 32. Bidirectional one-switch ordinal copulas
• 33. Reflections of what we have learned.
• (source: Nielsen Book Data)

Many of the complex problems faced by decision makers involve uncertainty as well as multiple conflicting objectives. This book provides a complete understanding of the types of objective functions that should be used in multiattribute decision making. By using tools such as preference, value, and utility functions, readers will learn state-of-the-art methods to analyze prospects to guide decision making and will develop a process that guarantees a defensible analysis to rationalize choices. Summarizing and distilling classical techniques and providing extensive coverage of recent advances in the field, the author offers practical guidance on how to make good decisions in the face of uncertainty. This text will appeal to graduate students and practitioners alike in systems engineering, operations research, business, management, government, climate change, energy, and healthcare.
(source: Nielsen Book Data)

This book provides an introduction to symplectic field theory, a new and important subject which is currently being developed. The starting point of this theory are compactness results for holomorphic curves established in the last decade. The author presents a systematic introduction providing a lot of background material, much of which is scattered throughout the literature. Since the content grew out of lectures given by the author, the main aim is to provide an entry point into symplectic field theory for non-specialists and for graduate students. Extensions of certain compactness results, which are believed to be true by the specialists but have not yet been published in the literature in detail, top off the scope of this monograph.
(source: Nielsen Book Data)

• v.
• 1. Construction et étude géométrique des espaces rigides.

• *Frontmatter, pg. i*Contents, pg. vii*Foreword, pg. ix*
• Chapter I. Representations of the fundamental group and the torsor of deformations. An overview, pg. 1*
• Chapter II. Representations of the fundamental group and the torsor of deformations. Local study, pg. 27*
• Chapter III. Representations of the fundamental group and the torsor of deformations. Global aspects, pg. 179*
• Chapter IV. Cohomology of Higgs isocrystals, pg. 307*
• Chapter V. Almost etale coverings, pg. 449*
• Chapter VI. Covanishing topos and generalizations, pg. 485*Facsimile : A p-adic Simpson correspondence, pg. 577*Bibliography, pg. 595*Indexes, pg. 599.
• (source: Nielsen Book Data)

The p-adic Simpson correspondence, recently initiated by Gerd Faltings, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra--namely Higgs bundles. This book undertakes a systematic development of the theory following two new approaches, one by Ahmed Abbes and Michel Gros, the other by Takeshi Tsuji. The authors mainly focus on generalized representations of the fundamental group that are p-adically close to the trivial representation. The first approach relies on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J. M. Fontaine. The second approach introduces a crystalline-type topos and replaces the notion of Higgs bundles with that of Higgs isocrystals. The authors show the compatibility of the two constructions and the compatibility of the correspondence with the natural cohomologies. The last part of the volume contains results of wider interest in p-adic Hodge theory. The reader will find a concise introduction to Faltings' theory of almost etale extensions and a chapter devoted to the Faltings topos. Though this topos is the general framework for Faltings' approach in p-adic Hodge theory, it remains relatively unexplored. The authors present a new approach based on a generalization of P. Deligne's covanishing topos.
(source: Nielsen Book Data)

• Introduction
• Beginnings and Basics
• Developing Visual Perception
• The Development of Thinking
• Emotional Development
• Language Development
• The Learning Brain
• Neurodevelopmental Disorders
• The Future.
• (source: Nielsen Book Data)

This book explores how our increasing knowledge of neuroscience and advances in methods of investigation is changing our understanding of child development. It looks at key aspects of development such as emotion, memory, learning, perception and language, as well as neurodevelopmental disorders. This text is written in clear and simple language with a full glossary of technical terms, learning checklists and reflection points. It will appeal to students on a range of courses including childhood studies, early years, psychology, counselling, teaching, nursing and social work.
(source: Nielsen Book Data)

• 1 The Real Numbers.- 1.1 Discussion: The Irrationality of % MathType!MTEF!2!1!+- % feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbiqaaaSbdaGcaa % qaaiaaikdaaSqabaaaaa!3794! $$\sqrt 2 $$.- 1.2 Some Preliminaries.- 1.3 The Axiom of Completeness.- 1.4 Consequences of Completeness.- 1.5 Cantor's Theorem.- 1.6 Epilogue.- 2 Sequences and Series.- 2.1 Discussion: Rearrangements of Infinite Series.- 2.2 The Limit of a Sequence.- 2.3 The Algebraic and Order Limit Theorems.- 2.4 The Monotone Convergence Theorem and a First Look at Infinite Series.- 2.5 Subsequences and the Bolzano-Weierstrass Theorem.- 2.6 The Cauchy Criterion.- 2.7 Properties of Infinite Series.- 2.8 Double Summations and Products of Infinite Series.- 2.9 Epilogue.- 3 Basic Topology of R.- 3.1 Discussion: The Cantor Set.- 3.2 Open and Closed Sets.- 3.3 Compact Sets.- 3.4 Perfect Sets and Connected Sets.- 3.5 Baire's Theorem.- 3.6 Epilogue.- 4 Functional Limits and Continuity.- 4.1 Discussion: Examples of Dirichlet and Thomae.- 4.2 Functional Limits.- 4.3 Combinations of Continuous Functions.- 4.4 Continuous Functions on Compact Sets.- 4.5 The Intermediate Value Theorem.- 4.6 Sets of Discontinuity.- 4.7 Epilogue.- 5 The Derivative.- 5.1 Discussion: Are Derivatives Continuous?.- 5.2 Derivatives and the Intermediate Value Property.- 5.3 The Mean Value Theorem.- 5.4 A Continuous Nowhere-Differentiable Function.- 5.5 Epilogue.- 6 Sequences and Series of Functions.- 6.1 Discussion: Branching Processes.- 6.2 Uniform Convergence of a Sequence of Functions.- 6.3 Uniform Convergence and Differentiation.- 6.4 Series of Functions.- 6.5 Power Series.- 6.6 Taylor Series.- 6.7 Epilogue.- 7 The Riemann Integral.- 7.1 Discussion: How Should Integration be Defined?.- 7.2 The Definition of the Riemann Integral.- 7.3 Integrating Functions with Discontinuities.- 7.4 Properties of the Integral.- 7.5 The Fundamental Theorem of Calculus.- 7.6 Lebesgue's Criterion for Riemann Integrability.- 7.7 Epilogue.- 8 Additional Topics.- 8.1 The Generalized Riemann Integral.- 8.2 Metric Spaces and the Baire Category Theorem.- 8.3 Fourier Series.- 8.4 A Construction of R From Q.
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This elementary presentation exposes readers to both the process of rigor and the rewards inherent in taking an axiomatic approach to the study of functions of a real variable. The aim is to challenge and improve mathematical intuition rather than to verify it. The philosophy of this book is to focus attention on questions which give analysis its inherent fascination. Each chapter begins with the discussion of some motivating examples and concludes with a series of questions.
(source: Nielsen Book Data)

• Preface.- 1 The Real Numbers.- 2 Sequences and Series.- 3 Basic Topology of R.- 4 Functional Limits and Continuity.- 5 The Derivative.- 6 Sequences and Series of Functions.- 7 The Riemann Integral.- 8 Additional Topics.- Bibliography.- Index.
• (source: Nielsen Book Data)

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler's computation of zeta(2), the Weierstrass Approximation - Theorem, and the gamma function are now among the book's cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: "This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks...Understanding Analysis is perfectly titled; if your students read it, that's what's going to happen...This terrific book will become the text of choice for the single-variable introductory analysis course ..." - Steve Kennedy, MAA Reviews.
(source: Nielsen Book Data)

• Free Fields
• The Thirring Model
• Determinants and Heat Kernels
• Self-Interacting Fermionic Models
• Nonlinear [sigma] Models: Classical Aspects
• Nonlinear [sigma] Models - Quantum Aspects
• Exact S-Matrices of 2D Models
• The Wess-Zumino-Witten Theory
• QED2: Operator Approach
• Quantum Chromodynamics
• QED2: Functional Approach
• The Finite Temperature Schwinger Model
• Non-Abelian Chiral Gauge Theories
• Chiral Quantum Electrodynamics
• Conformally Invariant Field Theory
• Conformal Field Theory with Internal Symmetry
• 2D Gravity and String-Related Topics.
• (source: Nielsen Book Data)

The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings.This book is intended for students working for their PhD degree and post-doctoral researchers wishing to acquaint themselves with the non-perturbative aspects of quantum field theory.
(source: Nielsen Book Data)

• Preface.- Notation and Terminology.- Levy Processes and Their Characteristics.- Degradation Processes.- Storage Models: Control of Dams Using P^M_{\lambda, \tau} Policies.- Appendix.- Index.
• (source: Nielsen Book Data)

This book covers Levy processes and their applications in the contexts of reliability and storage. Special attention is paid to life distributions and the maintenance of devices subject to degradation; estimating the parameters of the degradation process is also discussed, as is the maintenance of dams subject to Levy input.
(source: Nielsen Book Data)

Simulate realistic human motion in a virtual world with an optimization-based approach to motion prediction. With this approach, motion is governed by human performance measures, such as speed and energy, which act as objective functions to be optimized. Constraints on joint torques and angles are imposed quite easily. Predicting motion in this way allows one to use avatars to study how and why humans move the way they do, given specific scenarios. It also enables avatars to react to infinitely many scenarios with substantial autonomy. With this approach it is possible to predict dynamic motion without having to integrate equations of motion - rather than solving equations of motion, this approach solves for a continuous time-dependent curve characterizing joint variables (also called joint profiles) for every degree of freedom. It introduces rigorous mathematical methods for digital human modelling and simulation. It focuses on understanding and representing spatial relationships (3D) of biomechanics. It develops an innovative optimization-based approach to predicting human movement. It is extensively illustrated with 3D images of simulated human motion (full color in the ebook version).
(source: Nielsen Book Data)

• Preface
• Notation
• 1. Modules and algebras
• 2. Hopf algebras
• 3. Hopf algebras and representations of groups
• 4. Applications to algebraic groups
• 5. Applications to field theory
• Appendix
• References
• Index.
• (source: Nielsen Book Data)

The concept of Hopf algebras was first introduced in the theory of algebraic topology but in recent years has been developed by many mathematicians and applied to other areas of mathematics such as Lie groups, algebraic groups and Galois theory. This book is an introduction to the basic theory of Hopf algebras for the reader already familiar with the basic ideas of linear algebra and commutative algebra. After introducing and discussing the basic properties of coalgebras, bialgebras and Hopf algebras, the author treats the fundamental structure theorem of bi-modules and Sullivan's proof of the existence and uniqueness of integrals of Hopf algebras. This book will interest graduate students and research workers who specialise in algebra.
(source: Nielsen Book Data)

• The concept of toroidal groups: Irrationality and toroidal coordinates
• Toroidal subgroups and pseudoconvexity. Line bundles and cohomology: Line bundles on toroidal groups
• Comohology of toroidal groups. Quasi-Abelian Varieties: Ample Riemann forms
• Characterisation of quasi-Abelian varieties. Reduction and extension: Automorphic forms
• Extendable line bundles.
• (source: Nielsen Book Data)

Toroidal groups are the connecting link between torus groups and any complex Lie groups. Many properties of complex Lie groups such as the pseudoconvexity and cohomology are determined by their maximal toroidal subgroups. Quasi-Abelian varieties are meromorphically separable toroidal groups. They are the natural generalisation of the Abelian varieties. Nevertheless, their behavior can be completely different as the wild groups show.
(source: Nielsen Book Data)

• Introduction to Differential Equations. First-Order Ordinary Differential Equations. Applications of First-Order Ordinary Differential Equations. Higher-Order Differential Equations. Applications of Higher-Order Differential Equations. Ordinary Differential Equations with Nonconstant Coefficients. Laplace Transform Methods. Systems of Ordinary Differential Equations. Applications of Systems of Ordinary Differential Equations. Eigenvalue Problems and Fourier Series. Partial Differential Equations.
• (source: Nielsen Book Data)

NON-TECHNICAL DESCRIPTION Mathematica is an extremely powerful computer algebra system (with both symbolic and numerical capabilities), a graphing tool for any mathematical function in two or three dimensions, a self-contained programming language, and also a typesetting program. Using both symbolic and numerical capabilities, Mathematica is a two or three-dimensional graphing tool for any mathematical function, a self-contained programming language, and also a typesetting program. Intended for Mathematica beginners, this book/CD-ROM package contains built-in commands that can be used to solve problems directly and can also be used to visualise solutions. This Second Edition of the groundbreaking Differential Equations with Mathematica integrates new applications from a variety of fields, especially biology, physics, and engineering. The new handbook is also completely compatible with Mathematica version 3.0 and is a perfect introduction for Mathematica beginners. The book/CD-ROM package contains built-in commands that lets the user solve problems directly using graphical solutions. Features: * Focuses on the most often used features of Mathematica for the beginning Mathematica user * CD-ROM contains all Mathematica inputs from the text * New applications from a variety of fields, including engineering, biology, and physics * All applications were completed using version 3.0 of Mathematica.
(source: Nielsen Book Data)

"Mathematica by Example, 4e" is designed to introduce the Mathematica programming language to a wide audience. This is the ideal text for all scientific students, researchers, and programmers wishing to learn or deepen their understanding of Mathematica. The program is used to help professionals, researchers, scientists, students and instructors solve complex problems in a variety of fields, including biology, physics, and engineering. This title offers clear organization, complete topic coverage, and accessible exposition for novices. It is fully compatible with Mathematica 6.0. It offers new applications, exercises and examples from a variety of fields including biology, physics and engineering. It also includes a CD-ROM with all Mathematica input appearing in the book, useful to students so they do not have to type in code and commands.
(source: Nielsen Book Data)

• 1. Classical Mechanics.
• 2. Fundamentals of Quantum Mechanics.
• 3. Stationary States.
• 4. Symmetry Transformations on States.
• 5. Symmetry Transformations on Operators.
• 6. Interlude.
• 7. Approximation Methods for Bound States.
• 8. Potential Scattering.
• 9. Transitions.
• 10. Further Topics in Quantum Dynamics.
• 11. The Quantized Electromagnetic Field.
• 12. Relativistic Wave Equations.
• 13. Identical Particles. Appendix A. Mathematical Tools. Appendix B. Rotation Matrices. Appendix C. SU
• 3. Appendix D. References. Index.
• (source: Nielsen Book Data)

For graduate courses in Quantum Mechanics. With clear discussion and numerous problems, this text adequately and comprehensively covers all the subjects of quantum mechanics.
(source: Nielsen Book Data)

• Part I. Introduction: 1. What this monograph is about
• 2. Some experiments
• 3. Continuum mechanics
• 4. Quasilinear systems
• 5. Outline of monograph
• Part II. Two-Well Potentials, Governing Equations and Energetics: 1. Introduction
• 2. Two-phase nonlinearly elastic materials
• 3. Field equations and jump conditions
• 4. Energetics of motion, driving force and dissipation inequality
• Part III. Equilibrium Phase Mixtures and Quasistatic Processes: 1. Introduction
• 2. Equilibrium states
• 3. Variational theory of equilibrium mixtures of phases
• 4. Quasistatic processes
• 5. Nucleation and kinetics
• 6. Constant elongation rate processes
• 7. Hysteresis
• Part IV. Impact-Induced Transitions in Two-Phase Elastic Materials: 1. Introduction
• 2. The impact problem for trilinear two-phase materials
• 3. Scale-invariant solutions of the impact problem
• 4. Nucleation and kinetics
• 5. Comparison with experiment
• 6. Other types of kinetic relations
• 7. Related work
• Part V. Multiple-Well Free Energy Potentials: 1. Introduction
• 2. Helmholtz free energy potential
• 3. Potential energy function and the effect of stress
• 4. Example 1: the van der Waals fluid
• 5. Example 2: two-phase martensitic material with cubic and tetragonal phases
• Part VI. The Continuum Theory of Driving Force: 1. Introduction
• 2. Balance laws, field equations and jump conditions
• 3. The second law of thermodynamics and the driving force
• Part VII. Thermoelastic Materials: 1. Introduction
• 2. The thermoelastic constitutive law
• 3. Stability of a thermoelastic material
• 4. A one-dimensional special case: uniaxial strain
• Part VIII. Kinetics and Nucleation: 1. Introduction
• 2. Nonequilibrium processes, thermodynamic fluxes and forces, kinetic relation
• 3. Phenomenological examples of kinetic relations
• 4. Micromechanically-based examples of kinetic relations
• 5. Nucleation
• Part IX. Models for Two-Phase Thermoelastic Materials in One Dimension: 1. Preliminaries
• 2. Materials of Mie-Gruneisen type
• 3. Two-phase Mie-Gruneisen materials
• Part X. Quasistatic Hysteresis in Two-Phase Thermoelastic Tensile Bars: 1. Preliminaries
• 2. Thermomechanical equilibrium states for a two-phase material
• 3. Quasistatic processes
• 4. Trilinear thermoelastic material
• 5. Stress cycles at constant temperature
• 6. Temperature cycles at constant stress
• 7. The shape-memory cycle
• 8. The experiments of Shaw and Kyriakides
• 9. Slow thermomechanical processes
• Part XI. Dynamics of Phase Transitions in Uniaxially Strained Thermoelastic Solids: 1. Introduction
• 2. Uniaxial strain in adiabatic thermoelasticity
• 3. The impact problem
• Part XII. Statics: Geometric Compatibility: 1. Preliminaries
• 2. Examples
• Part XIII. Dynamics: Impact-Induced Transition in a CuA1Nl Single Crystal: 1. Introduction
• 2. Preliminaries
• 3. Impact without phase transformation
• 4. Impact with phase transformation
• 5. Application to austenite-B1 martensite transformation in CuA1Nl
• Part XIV. Quasistatics: Kinetics of Martensitic Twinning: 1. Introduction
• 2. The material and loading device
• 3. Observations
• 4. The model
• 5. The energy of the system
• 6. The effect of the transition layers: further observations
• 7. The effect of the transition layers: further modeling
• 8. Kinetics.
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This 2006 work began with the author's exploration of the applicability of the finite deformation theory of elasticity when various standard assumptions such as convexity of various energies or ellipticity of the field equations of equilibrium are relinquished. The finite deformation theory of elasticity turns out to be a natural vehicle for the study of phase transitions in solids where thermal effects can be neglected. This text will be of interest to those interested in the development and application of continuum-mechanical models that describe the macroscopic response of materials capable of undergoing stress- or temperature-induced transitions between two solid phases. The focus is on the evolution of phase transitions which may be either dynamic or quasi-static, controlled by a kinetic relation which in the framework of classical thermomechanics represents information that is supplementary to the usual balance principles and constitutive laws of conventional theory.
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• Rational and polynomial parametrizations Fractional linear transformations Cubic curves Cubic surfaces and general hypersurfaces Outline of the theory of plane curves Affine plane and projective plane Sphere with handles Functions and differentials on a curve Polynomials and power series Review of abstract algebra Some commutative algebra Hensel's lemma and Newton's theorem More about Newton's theorem Branches and valuations Divisors of functions and differentials Weierstrass preparation theorem Intersection multiplicity Resolution of singularities of plane curves Infinitely near singularities Parametrizing a quartic with three double points Characteristic pairs Criterion for one place and Jacobian problem Inversion formula and Jacobian problem Surfaces Hypersurfaces Resolution of singularities of algebraic surfaces Birational and polyrational transformations Valuations and birational correspondence Rational cylinders through a variety Resultants.
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This book, based on lectures presented in courses on algebraic geometry taught by the author at Purdue University, is intended for engineers and scientists (especially computer scientists), as well as graduate students and advanced undergraduates in mathematics. In addition to providing a concrete or algorithmic approach to algebraic geometry, the author also attempts to motivate and explain its link to more modern algebraic geometry based on abstract algebra.The book covers various topics in the theory of algebraic curves and surfaces, such as rational and polynomial parametrization, functions and differentials on a curve, branches and valuations, and resolution of singularities. The emphasis is on presenting heuristic ideas and suggestive arguments rather than formal proofs. Readers will gain new insight into the subject of algebraic geometry in a way that should increase appreciation of modern treatments of the subject, as well as enhance its utility in applications in science and industry.
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• Part I. 1. Complex numbers and elementary functions
• 2. Analytic functions and integration
• 3. Sequences, series and singularities of complex functions
• 4. Residue calculus and applications of contour integration
• Part II. 5. Conformal mapping and applications
• 6. Asymptotic evaluation of integrals
• 7. Riemann-Hilbert problems
• Index.
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In addition to being mathematically elegant, complex variables provide a powerful tool for solving problems that are either very difficult or virtually impossible to solve in any other way. Part I of this text provides an introduction to the subject, including analytic functions, integration, series, and residue calculus and also includes transform methods, ODEs in the complex plane, numerical methods and more. Part II contains conformal mappings, asymptotic expansions, and the study of Riemann-Hilbert problems. The authors also provide an extensive array of applications, illustrative examples and homework exercises. This book is ideal for use in introductory undergraduate and graduate level courses in complex variables.
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• Classical fuzzy cluster analysis.- Visualization of the clustering results.- Clustering for fuzzy model identification.- Fuzzy clustering for system identification.- Fuzzy model based classifiers.- Segmentation of multivariate time-series.
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This book presents new approaches to data mining and system identification. Algorithms that can be used for the clustering of data have been overviewed. New techniques and tools are presented for the clustering, classification, regression and visualization of complex datasets. Special attention is given to the analysis of historical process data, tailored algorithms are presented for the data driven modeling of dynamical systems, determining the model order of nonlinear input-output black box models, and the segmentation of multivariate time-series. The main methods and techniques are illustrated through several simulated and real-world applications from data mining and process engineering practice. The books are aimed primarily at practitioners, researches, and professionals in statistics, data mining, business intelligence, and systems engineering, but it is also accessible to graduate and undergraduate students in applied mathematics, computer science, electrical and process engineering. Familiarity with the basics of system identification and fuzzy systems is helpful but not required.
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• Wavelets, Fingerprints, and Image Processing. Wavelets and Orthogonal Decompositions. Multiresolutions, Cascades, and Filters. Sample Projects. Appendices. References. Index.
• (source: Nielsen Book Data)

An accessible and practical introduction to wavelets With applications in image processing, audio restoration, seismology, and elsewhere, wavelets have been the subject of growing excitement and interest over the past several years. Unfortunately, most books on wavelets are accessible primarily to research mathematicians. Discovering Wavelets presents basic and advanced concepts of wavelets in a way that is accessible to anyone with only a fundamental knowledge of linear algebra. The basic concepts of wavelet theory are introduced in the context of an explanation of how the FBI uses wavelets to compress fingerprint images. Wavelet theory is further developed in the setting of function spaces. The book then moves on to present more advanced topics such as filters, multiresolution analysis, Daubechies' wavelets, and further applications. The book concludes with a series of projects and problems that introduce advanced topics and offer starting points for research. Sample projects that demonstrate real wavelet applications include image compression, a wavelet-based search engine, processing with Daubechies' wavelets, and more. Among the special features of Discovering Wavelets are: Real-life, hands-on examples that involve actual wavelet applications A companion Web site containing Pixel Images software and Maple files to be used with the projects in the book Challenging problems that reinforce and expand on the ideas being developed An appendix containing the linear algebra needed to understand wavelets as presented in the book.
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• Preface.
• Chapter 1: Introduction to 1H NMR. 1.1 Historical background. 1.2 Basic Theory. 1.3 The 1H chemical shift. 1.3.1.Nuclear shielding, reference compounds, . 1.4. 1H Substituent chemical shifts (SCS). 1.4.1. Two-bond effects (H.C.X), Shoolery's rules, . 1.4.2. Three-bond effects (H.C.C.X). 1.4.3.1H SCS in olefins and aromatics. 1.5 Long range effects on 1H chemical shifts. 1.5.1. Steric (Van-der-Waals) shifts. 1.5.2. electric field and anisotropic shifts. 1.5.3. a electron effects, aromatic ring currents. 1.5.4. Hydrogen bonding shifts. 1.6.Tables of 1H Chemical Shifts of Common Cyclic Systems.
• Chapter 2: Interpretation of 1H NMR coupling patterns. 2.1 Fine Structure due to HH coupling. 2.2 The Analysis of NMR Spectra. 2.2.1. Nomenclature of the spin system, chemical and magnetic equivalence. 2.2.2. Two interacting nuclei, the AB spectrum. 2.2.3. Three interacting nuclei, the ABX spectrum. 2.2.4. Four interacting nuclei, the ABRX spectrum, the AA?XX? spectrum. 2.2.5. Iterative Computer Analysis, examples. 2.3. The Mechanism of Spin-Spin Coupling. 2.3.1. Geminal HH Couplings. 2.3.2. Vicinal HH Couplings, CH:CH couplings, CH.CH couplings. 2.3.3. Ab-initio calculations of couplings. 2.3.4. Long-range HH Couplings. 2.4. HF Couplings. 2.4.1. Geminal HF Couplings. 2.4.2. Vicinal HF Couplings, CH:CF couplings, CH.CF couplings. 2.4.3. Long-range HF Couplings.
• Chapter 3: Methods of Predicting 1H Chemical Shifts. 3.1. Quantum mechanical calculations of 1H Chemical shifts. 3.2. The Data Base Approach, the Hose code. 3.3. Semi-empirical calculations, . 3.4. Theory of the CHARGE program, . 3.4.1 Through Bond Effects. 3.4.2 1H Chemical Shifts in Substituted Methanes and Ethanes. 3.4.3 Through Space Effects, steric, electric field, magnetic anisotropy. 3.4.4Hydrogen Bonding Shifts, ab-initio calculations. 3.4.5 Aromatic Compounds, ring currents, a-electron densities.
• Chapter 4: Modelling 1H Chemical Shifts, Alkanes, Alkenes and Alkynes. 4.1. Alkanes. 4.1.1 H..H and C..H steric effects. 4.1.2 The methyl effect. 4.1.3 C.C Bond Anisotropy. 4.1.4 Observed vs Calculated Shifts. a) Acyclic alkanes. b) Cyclic Alkanes. c) Methyl Cycloalkanes. d) Androstane. e) Chemical Shift contributions in Cyclohexane. 4.2 Alkenes. 4.2.1.C=C Bond Anisotropy and Shielding. 4.2.2 Observed vs Calculated Shifts. a) Acyclic alkenes. b) Monocyclic alkenes. c) Aromatic alkenes. d) Norbornenes and bicyclooctenes. e) Pinenes. f) Conclusions. 4.3.Alkynes. 4.3.1.CethC Bond Anisotropy and Shielding. 4.3.2 Observed vs Calculated Shifts. 4.3.3. Acetylene SCS. 4.3.4. Contributions to Acetylene SCS. 4.3.5. Napthyl and Phenanthryl acetylenes. 4.4. Summary.
• Chapter 5: MODELLING 1H CHEMICAL SHIFTS, Aromatics. 5.1 Aromatic Hydrocarbons. 5.1.1. Ring currents, a-electron density, steric effects. 5.1.2. Observed vs Calculated Shifts. a) Condensed aromatics. b) Cyclophanes. c)Substituted Benzenes. 5.2. Heteroaromatics. 5.2.1. Theory and Application to Heteroaromatics. 5.2.2. Observed vs Calculated Shifts. a) Furans, thiophenes and pyrroles. b) Indoles, quinolines ans isoquinolines. c) Diazabenzenes and azoles. 5.2.3. Ring current and a-electron shifts. 5.3. Summary.
• Chapter 6: MODELLING 1H CHEMICAL SHIFTS, Mono valent Substituents. 6.1. Flourocompounds. 6.1.1. Electric field theory. 6.1.2. Fluoroalkanes. 6.1.3. Fluoroalkenes. 6.2. Steric, Anisotropic and Electric Field Effects in Chloro, bromo and Iodo SCS. 6.2.1. Aromatic halides. 6.2.2. Alkyl halides. 6.2.3. Contributions to Halo SCS in cyclohexanes. 6.2.4. Steric Coefficients for Halogens. 6.3. Hydroxy Compounds. 6.3.1 Alcohols and diols. 6.3.2Phenols. 6.4. Amines. 6.4.1 Observed vs Calculated Shifts. 6.5. Cyanides. 6.5.1 Observed vs Calculated Shifts. 6.5.2. Cyano SCS. 6.6. Nitro Compounds. 6.6.1. Observed vs Calculated Shifts. 6.6.2.Conformational Analysis. 6.7. Summary.
• Chapter 7: MODELLING 1H CHEMICAL SHIFTS, Divalent Substituents. 7.1. Aldehydes and Ketones. 7.1.1.Aliphatic aldehydes and ketones. a) Observed vs Calculated shifts. 7.1.2. Aromatic aldehydes and ketones. a). Keto-enol tautomerism in anthrone. 7.2. Esters. 7.2.1.Observed vs Calculated shifts. 7.3 Amides. 7.3.1.Aliphatic and cyclic amides. 7.3.2 Aromatic amides. 7.4. Ethers. 7.4.1.Oxygen SCS in ethers. 7.4.2.Observed vs Calculated Shifts. 7.5. Sulfoxides, sulfones, sulphites. 7.5.1.Observed vs Calculated Shifts. 7.6. Summary.
• Chapter 8: 1H CHEMICAL SHIFTS AND STRUCTURAL CHEMISTRY. 8.1. Electronic Structure Calculations. 8.1.1. Basis sets. 8.2. Molecular Mechanics Calculations. 8.2.1. Conformer generation. 8.3. Molecular Geometries and 1H Chemical Shifts. 8.3.1. Methyl anthracene-9-carboxylate. 8.3.2. N-formyl aniline. 8.3.3. Benzosuberone. 8.4. Rate Processes and NMR Spectra. 8.4.1. Theory. 8.4.2. Amide rotation. 8.4.3. Proton exchange equilibria. 8.4.4. Rotation about single bonds, ring inversion processes. 8.5. Solvent Effects. 8.5.1. Non-polar compounds. 8.5.2. Polar Aprotic Compounds. 8.5.3. Protic Compounds. 8.5.4. Diols and Polyhydroxy Compounds. 8.5.5. Chemical Shift.Contributions. 8.6. Summary.
• Chapter 9: Strategies for 1H NMR prediction. 9.1. Calculating 1H NMR spectra. 9.1.1. Molecular Modelling, PCMODEL. 9.1.2. Calculating 1H chemical shifts and coupling constants, HNMRSPEC. 9.1.3. Displaying the calculated 1H spectrum, 1HPLOT. 9.1.4. Advanced use of HNMRSPEC-S. 9.1.5. Calculation/Iteration of 2nd order 1H spectra from specified delta's and J's. LAOCOON. 9.2. Automated spectral prediction, NMRPredict.
• Appendix 1. The observed vs calculated 1H NMR chemical shifts of ca 1000 spectra.
• Appendix 2. The observed vs calculated 1H NMR chemical shifts of 113 Substituted Benzenes.
• Appendix 3. The observed vs calculated 1H NMR chemical shifts of 65 Substituted Pyridines.
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This book provides a theoretical introduction to graduate scientists and industrial researchers towards the understanding of the assignment of 1H NMR spectra. It discusses, and includes on enclosed CD, one of the best, the fastest and most applicable pieces of NMR prediction software available. It allows students of organic chemistry to solve problems on 1H NMR with access to over 500 assigned spectra.
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• Preface * Background Notation *
• Chapter 1 Topology *
• Chapter 2 Banach Spaces and Differential Calculus *
• Chapter 3 Manifolds and Vector Bundles *
• Chapter 4 Vector Fields and Dynamical Systems *
• Chapter 5 Tensors *
• Chapter 6 Differential Forms *
• Chapter 7 Integration on Manifolds *
• Chapter 8 Applications * References * Index * Supplementary Chapters * S-1 Lie Groups * S-2 Introduction to Differential Topology * S-3 Topics in Riemannian Geometry.
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• 1 Topology.- 1.1 Topological Spaces.- 1.2 Metric Spaces.- 1.3 Continuity.- 1.4 Subspaces, Products, and Quotients.- 1.5 Compactness.- 1.6 Connectedness.- 1.7 Baire Spaces.- 2 Banach Spaces and Differential Calculus.- 2.1 Banach Spaces.- 2.2 Linear and Multilinear Mappings.- 2.3 The Derivative.- 2.4 Properties of the Derivative.- 2.5 The Inverse and Implicit Function Theorems.- 3 Manifolds and Vector Bundles.- 3.1 Manifolds.- 3.2 Submanifolds, Products, and Mappings.- 3.3 The Tangent Bundle.- 3.4 Vector Bundles.- 3.5 Submersions, Immersions and Transversality.- 4 Vector Fields and Dynamical Systems.- 4.1 Vector Fields and Flows.- 4.2 Vector Fields as Differential Operators.- 4.3 An Introduction to Dynamical Systems.- 4.4 Frobenius' Theorem and Foliations.- 5 Tensors.- 5.1 Tensors in Linear Spaces.- 5.2 Tensor Bundles and Tensor Fields.- 5.3 The Lie Derivative: Algebraic Approach.- 5.4 The Lie Derivative: Dynamic Approach.- 5.5 Partitions of Unity.- 6 Differential Forms.-
• 6. I Exterior Algebra.- 6.2 Determinants, Volumes, and the Hodge Star Operator.- 6.3 Differential Forms.- 6.4 The Exterior Derivative, Interior Product, and Lie Derivative.- 6.5 Orientation, Volume Elements, and the Codifferential.- 7 Integration on Manifolds.- 7.1 The Definition of the Integral.- 7.2 Stokes' Theorem.- 7.3 The Classical Theorems of Green, Gauss, and Stokes.- 7.4 Induced Flows on Function Spaces and Ergodicity.- 7.5 Introduction to Hodge-deRham Theory and Topological Applications of Differential Forms.- 8 Applications.- 8.1 Hamiltonian Mechanics.- 8.2 Fluid Mechanics.- 8.3 Electromagnetism.- 8.3 The Lie-Poisson Bracket in Continuum Mechanics and Plasma Physics.- 8.4 Constraints and Control.- References.
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The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid mechanics, electromagnetism, plasma dynamics and control theory are given using both invariant and index notation. The prerequisites required are solid undergraduate courses in linear algebra and advanced calculus.
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The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a working knowledge of manifolds, dynamical systems, tensors, and differential forms. Some applications to Hamiltonian mechanics, fluid me- chanics, electromagnetism, plasma dynamics and control thcory arc given in Chapter 8, using both invariant and index notation. The current edition of the book does not deal with Riemannian geometry in much detail, and it does not treat Lie groups, principal bundles, or Morse theory. Some of this is planned for a subsequent edition. Meanwhile, the authors will make available to interested readers supplementary chapters on Lie Groups and Differential Topology and invite comments on the book's contents and development. Throughout the text supplementary topics are given, marked with the symbols ~ and {l:; J. This device enables the reader to skip various topics without disturbing the main flow of the text. Some of these provide additional background material intended for completeness, to minimize the necessity of consulting too many outside references. We treat finite and infinite-dimensional manifolds simultaneously. This is partly for efficiency of exposition. Without advanced applications, using manifolds of mappings, the study of infinite-dimensional manifolds can be hard to motivate.
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Marc Abrahams, the founder of the Ig Nobel Prizes, offers an addictive, wryly funny expose of the oddest, most imaginative, and just plain improbable research from around the globe. He looks into why books on ethics are more likely to get stolen, the best way to slice a ham sandwich (mathematically), and what time of month generates highertips for Vegas lap dancers. Abrahams' tour through these unlikeliest investigations of animals, plants, and minerals (including humans) willfirst make you laugh, then make you think about the world in a new way.
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The mind behind the infamous Ig Nobel Prizes presents an addictive collection of improbable research all about us - and you Marc Abrahams collects the odd, the imaginative and the brilliantly improbable. Here he turns to research on the ins and outs of the very improbable evolutionary innovation that is the human body (brain included): * What's the best way to get a monkey to floss regularly? * How much dandruff do Pakistani soldiers have? * If you add an extra henchman to your bank-robbing gang, how much more money will you 'earn'? * How many dimples will be found on the cheeks of 28,282 Greek children? * Who is the Einstein of pork carcasses?
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• Introduction Preamble Likelihood Sufficiency Minimal sufficiency Completeness Exponential family of distributions
• Point Estimation Introduction Maximum likelihood estimation Method of moments Method of least squares Goodness-of-estimation. Mean squared error. Unbiased estimation
• Confidence Intervals, Bounds, and Regions Introduction Quoting the estimation error Confidence intervals Confidence bounds Confidence regions
• Hypothesis Testing Introduction Simple hypotheses Composite hypotheses Hypothesis testing and confidence intervals Sequential testing
• Asymptotic Analysis Introduction Convergence and consistency in MSE Convergence and consistency in probability Convergence in distribution The central limit theorem Asymptotically normal consistency Asymptotic confidence intervals Asymptotic normality of the MLE Multiparameter case Asymptotic distribution of the GLRT. Wilks' theorem.
• Bayesian Inference Introduction Choice of priors Point estimation Interval estimation. Credible sets. Hypothesis testing
• Elements of Statistical Decision Theory Introduction and notations Risk function and admissibility Minimax risk and minimax rules Bayes risk and Bayes rules Posterior expected loss and Bayes actions Admissibility and minimaxity of Bayes rules
• Linear Models Introduction Definition and examples Estimation of regression coefficients Residuals. Estimation of the variance. Examples Goodness-of-fit. Multiple correlation coefficient. Confidence intervals and regions for the coefficients Hypothesis testing in linear models Predictions Analysis of variance
• Appendix A: Probabilistic Review Appendix B: Solutions of Selected Exercises
• Index
• Exercises appear at the end of each chapter.
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Designed for a one-semester advanced undergraduate or graduate course, Statistical Theory: A Concise Introduction clearly explains the underlying ideas and principles of major statistical concepts, including parameter estimation, confidence intervals, hypothesis testing, asymptotic analysis, Bayesian inference, and elements of decision theory. It introduces these topics on a clear intuitive level using illustrative examples in addition to the formal definitions, theorems, and proofs. Based on the authors' lecture notes, this student-oriented, self-contained book maintains a proper balance between the clarity and rigor of exposition. In a few cases, the authors present a "sketched" version of a proof, explaining its main ideas rather than giving detailed technical mathematical and probabilistic arguments. Chapters and sections marked by asterisks contain more advanced topics and may be omitted. A special chapter on linear models shows how the main theoretical concepts can be applied to the well-known and frequently used statistical tool of linear regression. Requiring no heavy calculus, simple questions throughout the text help students check their understanding of the material. Each chapter also includes a set of exercises that range in level of difficulty.
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• Setting forth the problems Some history Synopsis of the main results Preliminaries The McPolin-Wickstead and Huijsmans-de Pagter-Koldunov Theorems revisited d-bases Band preserving operators and band-projections Central operators and Problems A and B Range-domain exchange in the Huijsmans-de Pagter-Koldunov Theorem d-splitting number of disjointness preserving operators Essentially one-dimensional and discrete vector lattices Essentially constant functions and operators on $C[0,1]$ Counterexamples Dedekind complete vector lattices and Problems A and B Generalizations to $(r_u)$-complete vector lattices Open problems References Index.
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This book is intended for graduate students and research mathematicians interested in operator theory, functional analysis, and vector lattices.
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• Odds and ends Basic operator theory Operators on $AL$- and $AM$-spaces Special classes of operators Integral operators Spectral properties Some special spectra Positive matrices Irreducible operators Invariant subspaces The Daugavet equation Bibliography Index.
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This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices. Abramovich and Aliprantis give a unique presentation that includes many new developments in operator theory and also draws together results that are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time. The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out.The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere. The companion volume, "Problems in Operator Theory", also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the "Graduate Studies in Mathematics" series, and it contains complete solutions to all exercises in "An Invitation to Operator Theory". The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments.By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book "Problems in Operator Theory" will help achieve this goal. Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. "An Invitation to Operator Theory" is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. "Problems in Operator Theory" is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool.
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• 1 The basics of Leavitt path algebras: motivations, definitions and examples.- 2 Two-sided ideals.- 3 Idempotents, and finitely generated projective modules.- 4 General ring-theoretic results.- 5 Graph C*-algebras, and their relationship to Leavitt path algebras.- 6 K-theory.- 7 Generalizations, applications, and current lines of research.- References.- Index.
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This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume.Since Leavitt path algebras were first defined in 2005, interest in these algebras has grown substantially, with ring theorists as well as researchers working in graph C*-algebras, group theory and symbolic dynamics attracted to the topic. Providing a historical perspective on the subject, the authors review existing arguments, establish new results, and outline the major themes and ring-theoretic concepts, such as the ideal structure, Z-grading and the close link between Leavitt path algebras and graph C*-algebras. The book also presents key lines of current research, including the Algebraic Kirchberg Phillips Question, various additional classification questions, and connections to noncommutative algebraic geometry.Leavitt Path Algebras will appeal to graduate students and researchers working in the field and related areas, such as C*-algebras and symbolic dynamics. With its descriptive writing style, this book is highly accessible.
(source: Nielsen Book Data)