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Linear Models for Optimal Test Design
Begins with a reflection on the history of test design--the core activity of all educational and psychological testing. It then presents a standard language for modeling test design problems as instances of multi-objective constrained optimization. The main portion of the book discusses test design models for a large variety of problems from the daily practice of testing, and illustrates their use with the help of numerous empirical examples. The presentation includes models for the assembly of tests to an absolute or relative target for their information functions, classical test assembly, test equating problems, item matching, test splitting, simultaneous assembly of multiple tests, tests with item sets, multidimensional tests, and adaptive test assembly. Two separate chapters are devoted to the questions of how to design item banks for optimal support of programs with fixed and adaptive tests. Linear Models for Optimal Test Design, which does not require any specific mathematical background, has been written to be a helpful resource on the desk of any test specialist.
Linear Models and Generalizations : Least Squares and Alternatives
Gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions
Linear Functional Analysis
This introduction to the ideas and methods of linear functional analysis shows how familiar and useful concepts from finite-dimensional linear algebra can be extended or generalized to infinite-dimensional spaces. Aimed at advanced undergraduates in mathematics and physics, the book assumes a standard background of linear algebra, real analysis (including the theory of metric spaces), and Lebesgue integration, although an introductory chapter summarizes the requisite material. The initial chapters develop the theory of infinite-dimensional normed spaces, in particular Hilbert spaces, after which the emphasis shifts to studying operators between such spaces. Functional analysis has applications to a vast range of areas of mathematics; the final chapters discuss the particularly important areas of integral and differential equations.
Linear and Nonlinear Programming
"Linear and Nonlinear Programming" is considered a classic textbook in Optimization. While it is a classic, it also reflects modern theoretical insights. These insights provide structure to what might otherwise be simply a collection of techniques and results, and this is valuable both as a means for learning existing material and for developing new results. One major insight of this type is the connection between the purely analytical character of an optimization problem, expressed perhaps by properties of the necessary conditions, and the behavior of algorithms used to solve a problem. This was a major theme of the first and second editions. Now the third edition has been completely updated with recent Optimization Methods. Yinyu Ye has written chapters and chapter material on a number of these areas including Interior Point Methods.
Linear Algebraic Monoids
The theory of linear algebraic monoids culminates in a coherent blend of algebraic groups, convex geometry, and semigroup theory. The book discusses all the key topics in detail, including classification, orbit structure, representations, universal constructions, and abstract analogues. An explicit cell decomposition is constructed for the wonderful compactification, as is a universal deformation for any semisimple group. A final chapter summarizes important connections with other areas of algebra and geometry. The book will serve as a solid basis for further research. Open problems are discussed as they arise and many useful exercises are included.
Light Scattering Reviews 3 : Light Scattering and Reflection
Ddevoted to modern knowledge and milestones in both experimental and theoretical techniques related to light scattering and radiative transport problems. It will consist of 3 parts comprising 11 contributions written by world leading experts in their respective fields. The general focus of the book will be on remote sensing of geophysical media. The first part will be devoted exclusively to studies of single light scattering by particles of different shapes and chemical compositions. The first chapter will review in situ measurements of cloud optical characteristics like cloud extinction and phase function, with the emphasis on ice clouds. Chapter 2 will cover opitcally soft particles common in marine environments and bio-suspensions while Chapter 3 will describe numerical techniques applicable not only to isotropic but also to chiral and anisotropic mdia. The final chapter in this part will deal with spatial symmetries in light scattering problems.
Lifting Modules : Supplements and Projectivity in Module Theory
Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and text books, the purpose of our monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules. The text begins with an introduction to small submodules, the radical, variations on projectivity, and hollow dimension. The subsequent chapters consider preradicals and torsion theories (in particular related to small modules), decompositions of modules (including the exchange property and local semi-T-nilpotency), supplements in modules (with specific emphasis on semilocal endomorphism rings), finishing with a long chapter on lifting modules, leading up their use in the theory of perfect rings, Harada rings, and quasi-Frobenius rings.
Lie Theory Vol.229 : Unitary Representations and Compactifications of Symmetric Spaces
It focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles.Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader.
Lie theory ; Vol.230 : Harmonic analysis on symmetric spaces, general Plancherel theorems
Van den Ban’s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass–Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley–Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals.
Lie Algebras and Algebraic Groups
The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics : for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
Leibniz : What Kind of Rationalist?
The chapters of the book are the result of intense discussion in the course of an international conference focused on the title question of this book, and were selected in view of their contribution to this topic. They are clustered in thematically organized parts. No effort has been made to hide the controversies underlying the different interpretations of Leibniz’s “rationalism” – in each particular domain and as a whole. On the contrary, the editor firmly believes that only through a variety of conflicting interpretive perspectives can the multi-faceted nature of an oeuvre of such a magnitude and variety as Leibniz’s be brought to light and understood as it deserves.
Lectures on Algebraic Geometry I : Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own.In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
Le choix bayésien: Principes et pratique
Covers the so-called Bayesian approach to statistical inference and in particular its decision-making aspects. The bases of this axiomatics (choice of the a priori, optimal decisions, tests and regions of confidence) are discussed in detail, as well as more recent openings of Bayesian analysis such as the choice of models, the use of numerical methods. Stochastic approximation (MCMC), the theory of noninformative laws (Berger-Bernardo axioms) and the relation to the classical theory of admissibility. Each chapter is completed by an extensive series of exercises of increasing difficulty and by bibliographical notes on the themes addressed. This book can be used in a Master's program in Applied Mathematics, Biometrics, Econometrics or any other program that uses quantitative information processing techniques. It only requires a basic course in probability theory and mathematical statistics as a preliminary.
Lattices and Ordered Sets
This book is intended to be a thorough introduction to the subject of ordered sets and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. The book has an excellent choice of topics, including a chapter on well ordering and ordinal numbers, which is not usually found in other texts. The approach is user-friendly and the presentation is lucid. There are more than 240 carefully chosen exercises.
Laser Resonators and Beam Propagation : Fundamentals, Advanced Concepts, Applications
Optical Resonators provides a detailed discussion of the properties of optical resonators for lasers from basic theory to recent research. In addition to describing the fundamental theories of resonators such as geometrical optics, diffraction, and polarisation the characteristics of all important resonator schemes and their calculation are presented. Experimental examples, practical problems and a collection of measurement techniques support the comprehensive treatment of the subject. Optical Resonators is the only book currently available that provides a comprehensive overview of the the subject. Combined with the structure of the text and the autonomous nature of the chapters this work will be as suitable for those new to the field as it will be invaluable to specialists conducting research. This second edition has been enlarged by new sections on Q-switching and resonators with internal phase/amplitude control. In addition, the whole book has been brought up-to-date.
Large-Scale Nonlinear Optimization
Large-Scale Nonlinear Optimization reviews and discusses recent advances in the development of methods and algorithms for nonlinear optimization and its applications, focusing on the large-dimensional case, the current forefront of much research.The chapters of the book including theoretical analysis, algorithmic development, implementation issues and applications.
Language, Expressivity and Cognition
The book presents how language shapes communicative and cognitive processes but at the same time is also shaped by those processes. The chapters put forward a number of disciplinary and methodological perspectives encompassing insights from cognitive and social psychology, (critical) discourse analysis, cognitive linguistics, corpus linguistics and sociolinguistics. Both intralingual as well as contrastive, each chapter also engages with qualitative and quantitative methods.
Language Production
This comprehensive text presents an up-to-date overview of the key topics in the field, providing important theoretical and empirical challenges to the traditional and accepted modal view of language production. Each chapter explores in detail a different aspect of language production, covering traditional methods including written and signed production alongside emerging research on joint action production. Emphasizing the neurobiological underpinnings of language, chapter authors showcase research that moves from a monologue-only approach to one that that considers production in more ecologically valid circumstances.
Language Choice in a Nation Under Transition : English Language Spread in Cambodia
This book examines language choice in contemporary Cambodia, and uses the case study to explore and evaluate competing explanations for the spread of English globally. the multiple contexts in which Cambodians make individual and institutional language policy choices are considered. Chapters 2 and 3 examine the economic and political contexts for language choice, as Cambodia has transitioned from a planned economy and communism to a market economy and democracy. Chapters 4, 5, and 6 examine the assistance context for language choice; the bilateral, multilateral, and nongovernmental development agencies that have recently begun to work in Cambodia demand certain language skills of Cambodian employees and government counterparts, and support the learning of these languages in both nonformal and formal education.
Landscapes of Mars : A Visual Tour
Landscapes of Mars is essentially a picture book that provides a visual tour of Mars. All the major regions and topographical features will be shown and supplemented with chapter introductions and extended captions. In a way, think of it as a visual tourist guide. Other topics covered are Martian uplands on the order of the elevation of Mt. Everest, Giant volcanoes and a rift system, the Grand Canyon of Mars, craters and the absence of craters over large regions (erosion), and wind shadows around craters, sand dunes, and dust devils.
