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Binary Quadratic Forms: An Algorithmic Approach
This book deals with algorithmic problems concerning binary quadratic forms 2 2 f(X,Y)= aX +bXY +cY with integer coe?cients a, b, c, the mathem- ical theories that permit the solution of these problems, and applications to cryptography.
Beyond partial differential equations : On linear and Quasi-Linear abstract hyperbolic evolution equations
The present volume is self-contained and introduces to the treatment of linear and nonlinear (quasi-linear) abstract evolution equations by methods from the theory of strongly continuous semigroups.
Bernoulli potential in superconductors : How the electrostatic field helps to understand superconductivity
The motion of electrons in superconductors seems to defy our imagination based on daily experience with Newtonian mechanics. This book shows that the classical concepts, such as the balance of forces acting on electrons, are useful for understanding superconductivity. The electrostatic field plays a natural part in this balance as it mediates forces between electrons at long distances. Due to its classical interpretation, the theory presented in this book is suitable for introductory courses.
Becoming a teacher educator : Theory and practice for teacher educators
It is the first book that addresses a range of important topics related to the work of teacher educators, the induction of teacher educators and their further professional development.Becoming a Teacher Educator has a practical focus and it provides theoretical insights, experiences of experts and practical recommendations. The book is rooted in the Association of Teacher Education in Europe (ATEE) and many of the chapters are written by authors who are active members of the ATEE. Distinguished researchers and practitioners from different parts of Europe, and beyond, joined their efforts to write a book that is truly international and combines research, practice and reflection.
Bayesian core : A practical approach to computational Bayesian statistics
This Bayesian modeling book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical justifications. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models.
Basic Real Analysis
Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically develop those concepts and tools in real analysis that are vital to every mathematician, whether pure or applied, aspiring or established. These works present a comprehensive treatment with a global view of the subject, emphasizing the connections between real analysis and other branches of mathematics.
Basic Probability Theory with Applications
This book presents elementary probability theory with interesting and well-chosen applications that illustrate the theory. An introductory chapter reviews the basic elements of differential calculus which are used in the material to follow. The theory is presented systematically, beginning with the main results in elementary probability theory. This is followed by material on random variables. Random vectors, including the all important central limit theorem, are treated next. The last three chapters concentrate on applications of this theory in the areas of reliability theory, basic queuing models, and time series. Examples are elegantly woven into the text and over 400 exercises reinforce the material and provide students with ample practice.
Basic principles and applications of probability theory
This introductory chapter discusses such notions as determinism, chaos and randomness, p- dictibility and unpredictibility, some initial approaches to formalizing r- domness and it surveys certain problems that can be solved by probability theory. This will perhaps give one an idea to what extent the theory can - swer questions arising in speci?c random occurrences and the character of the answers provided by the theory. 1. 1 The Nature of Randomness The phrase “by chance” has no single meaning in ordinary language. For instance, it may mean unpremeditated, nonobligatory, unexpected, and so on. Its opposite sense is simpler: “not by chance” signi?es obliged to or bound to (happen). In philosophy, necessity counteracts randomness. Necessity signi?es conforming to law – it can be expressed by an exact law. The basic laws of mechanics, physics and astronomy can be formulated in terms of precise quantitativerelationswhichmustholdwithironcladnecessity.
Basic Notions of Algebra
Aims to present a general survey of algebra, of its basic notions and main branches.Those parts of the book devoted to the systematic treatment of notions and results of algebra make very limited demands on the reader: we presuppose only that the reader knows calculus, analytic geometry and linear algebra in the form taught in many high schools and colleges. The extent of the prerequisites required in our treatment of examples is harder to state; an acquaintance with projective space, topological spaces, differentiable and complex analytic manifolds and the basic theory of functions of a complex variable is desirable, but the reader should bear in mind that difficulties arising in the treatment of some specific example are likely to be purely local in nature, and not to affect the understanding of the rest of the book.
Basic bundle theory and K-Cohomology invariants
Based on several recent courses given to mathematical physics students, this volume is an introduction to bundle theory with the aim to provide newcomers to the field with solid foundations in topological K-theory. A fundamental theme, emphasized in the book, centers around the gluing of local bundle data related to bundles into a global object. One renewed motivation for studying this subject, which has developed for almost 50 years in many directions, comes from quantum field theory, especially string theory, where topological invariants play an important role.
Basic Algebra
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs.
Bandwidth Extension of Speech Signals
Bandwidth Extension of Speech Signals provides discussion on different approaches for efficient and robust bandwidth extension of speech signals while acknowledging the influence of noise corrupted real-world signals. The book describes the theory and methods for quality enhancement of clean speech signals and distorted speech signals.
Axions : Theory, Cosmology, and Experimental Searches
Axions are peculiar hypothetical particles that could both solve the CP problem of quantum chromodynamics and at the same time account for the dark matter of the universe. Based on a series of lectures by world experts in this field held at CERN (Geneva), this volume provides a pedagogical introduction to the theory, cosmology and astrophysics of these fascinating particles and gives an up-to-date account of the status and prospect of ongoing and planned experimental searches. Learners and practitioners of astroparticle physics will find in this book both a concise introduction and a current reference work to a showcase topic that connects the "inner space" of the elementary particle world with the "outer space" of the universe at large.
Axiom of Choice
AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom, shunned by some, used indiscriminately by others. This treatise shows paradigmatically that:Disasters happen without AC: Many fundamental mathematical results fail (being equivalent in ZF to AC or to some weak form of AC).Disasters happen with AC: Many undesirable mathematical monsters are being created (e.g., non measurable sets and undeterminate games).Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.
Average-Cost Control of Stochastic Manufacturing Systems
This book is concerned with hierarchical control of manufacturing systems under uncertainty. It focuses on system performance measured in long-run average cost criteria, exploring the relationship between control problems with a discounted cost and that with a long-run average cost in connection with hierarchical control. A new theory is articulated that shows that hierarchical decision making in the context of a goal-seeking manufacturing system can lead to a near optimization of its objective. The approach in the book considers manufacturing systems in which events occur at different time scales.
Automorphic Forms and Lie Superalgebras
Most known examples of Lie superalgebras with a related automorphic form such as the Fake Monster Lie algebra whose reflection group is given by the Leech lattice arise from (super)string theory and can be derived from lattice vertex algebras. The No-Ghost Theorem from dual resonance theory and a conjecture of Berger-Li-Sarnak on the eigenvalues of the hyperbolic Laplacian provide strong evidence that they are of rank at most 26.The aim of this book is to give the reader the tools to understand the ongoing classification and construction project of this class of Lie superalgebras and is ideal for a graduate course.
Automatic Differentiation : Applications, Theory, and Implementations
This collection covers the state of the art in automatic differentiation theory and practice. Practitioners and students will learn about advances in automatic differentiation techniques and strategies for the implementation of robust and powerful tools. Computational scientists and engineers will benefit from the discussion of applications, which provide insight into effective strategies for using automatic differentiation for design optimization, sensitivity analysis, and uncertainty quantification.
Autistic community and the neurodiversity movement : Stories from the frontline
This book marks the first historical overview of the autism rights branch of the neurodiversity movement, describing the activities and rationales of key leaders in their own words since it organized into a unique community in 1992. Sandwiched by editorial chapters that include critical analysis, the book contains 19 chapters by 21 authors about the forming of the autistic community and neurodiversity movement, progress in their influence on the broader autism community and field, and their possible threshold of the advocacy establishment
Attractivity and bifurcation for nonautonomous dynamical systems
Although, bifurcation theory of equations with autonomous and periodic time dependence is a major object of research in the study of dynamical systems since decades, the notion of a nonautonomous bifurcation is not yet established. In this book, two different approaches are developed which are based on special definitions of local attractivity and repulsivity.
Atomic structure theory : Lectures on atomic physics
This is a textbook for students with a background in quantum mechanics. The text is designed to give hands-on experience with atomic structure calculations. Material covered includes angular momentum methods, the central field Schrödinger and Dirac equations, Hartree-Fock and Dirac-Hartree-Fock equations, multiplet structure, hyperfine structure, the isotope shift, dipole and multipole transitions, basic many-body perturbation theory, configuration interaction, and correlation corrections to matrix elements.
