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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.
Automatic Autocorrelation and Spectral Analysis
It takes advantage of greater computing power and robust algorithms to produce enough candidate models to be sure of providing a suitable candidate for given data. Improved order selection quality guarantees that one of the best (and often the best) will be selected automatically. The data themselves suggest their best representation. Should the analyst wish to intervene, alternatives can be provided. Written for graduate signal processing students and for researchers and engineers using time series analysis for practical applications ranging from breakdown prevention in heavy machinery to measuring lung noise for medical diagnosis.
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.
Attitudes, beliefs, motivation and identity in mathematics education : An overview of the field and future directions
Records the state of the art in research on mathematics-related affect. It discusses the concepts and theories of mathematics-related affect along the lines of three dimensions. The first dimension identifies three broad categories of affect: motivation, emotions, and beliefs. The book contains one chapter on motivation, including discussions on how emotions and beliefs relate to motivation. There are two chapters that focus on beliefs and a chapter on attitude which cross-cuts through all these categories. The second dimension covers a rapidly fluctuating state to a more stable trait. All chapters in the book focus on trait-type affect and the chapter on motivation discusses both these dimensions. The third dimension regards the three main levels of theorizing: physiological (embodied), psychological (individual) and social. All chapters reflect that mathematics-related affect has mainly been studied using psychological
Asymptotics for Dissipative Nonlinear Equations
Many of problems of the natural sciences lead to nonlinear partial differential equations. However, only a few of them have succeeded in being solved explicitly. Therefore different methods of qualitative analysis such as the asymptotic methods play a very important role. This is the first book in the world literature giving a systematic development of a general asymptotic theory for nonlinear partial differential equations with dissipation. Many typical well-known equations are considered as examples, such as: nonlinear heat equation, KdVB equation, nonlinear damped wave equation, Landau-Ginzburg equation, Sobolev type equations, systems of equations of Boussinesq, Navier-Stokes and others.
Asymptotic Theory of Statistics and Probability
An encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. The book has 34 chapters over a wide range of topics, nearly 600 exercises for practice and instruction, and another 300 worked out examples. It also includes a large compendium of 300 useful inequalities on probability, linear algebra, and analysis that are collected together from numerous sources, as an invaluable reference for researchers in statistics, probability, and mathematics.
Astrophysics is easy! : An introduction for the amateur astronomer
With some justification, many amateur astronomers believe astrophysics is a very difficult subject, requiring at least degree-level mathematics to understand it properly. This isn’t necessarily the case. Mike Inglis' quantitative approach to the subject explains all aspects of astrophysics in simple terms and cuts through the incomprehensible mathematics with which this fascinating subject is all too often associated. Astrophysics is Easy! begins by looking at the H-R diagram and other basic tools of astrophysics, then ranges across the universe, from a first look at the interstellar medium and nebulae, through the birth, evolution and death of stars, to the physics of galaxies and clusters of galaxies.
Astroparticle physics
The book describes the branch of astrophysics in which processes in the universe are investigated with experimental methods known from particle physics experiments. After a historical introduction to the basics of elementary particles, their interactions and the relevant detection techniques are described. The main body of the book concerns cosmic rays. The modern aspects of astroparticle physics are described in a chapter on cosmology. The book provides an orientation in the field of astroparticle physics that many beginners might look for. The physics issues are presented with little mathematics, and the results are illustrated by many diagrams. The reader has a chance to enter this field of astrophysics with a book that closes the gap between expert and popular level.
Assessment in mathematics education : Large-scale assessment and classroom assessment
Provides an overview of current research on a variety of topics related to both large-scale and classroom assessment. First, the purposes, traditions and principles of assessment are considered, with particular attention to those common to all levels of assessment and those more connected with either classroom or large-scale assessment. Assessment design based on sound assessment principles is discussed, differentiating between large-scale and classroom assessment, but also examining how the design principles overlap. The focus then shifts to classroom assessment and provides specific examples of assessment strategies, before examining the impact of large-scale assessment on curriculum, policy, instruction, and classroom assessment.
Aspects of mathematical modelling : Applications in science, medicine, economics and management
The construction of mathematical models is an essential scientific activity. Mathematics has long been associated with developments in the exact sciences and engineering, but more recently mathematical modelling has been used to investigate complex systems that arise in many other fields. The contributors to this book demonstrate the application of mathematics to modern research topics in ecology and environmental science, health and medicine, phylogenetics and neural networks, theoretical chemistry, economics and management. The reader will find some review papers outlining current research directions in hot topics such as pattern formation and applications to medicine, and more targeted research papers on current developments in the various disciplines included.
Aspects of Mathematical Finance
Considering the stupendous gain in importance, in the banking and insurance industries since the early 1990’s, of mathematical methodology, especially probabilistic methodology, it was a very natural idea for the French "Académie des Sciences" to propose a series of public lectures, accessible to an educated audience, to promote a wider understanding for some of the fundamental ideas, techniques and new tools of the financial industries. These lectures were given at the "Académie des Sciences" in Paris by internationally renowned experts in mathematical finance, and later written up for this volume which develops, in simple yet rigorous terms, some challenging topics such as risk measures, the notion of arbitrage, dynamic models involving fundamental stochastic processes like Brownian motion and Lévy processes.
Aspects of Brownian motion
Stochastic calculus and excursion theory are very efficient tools to obtain either exact or asymptotic results about Brownian motion and related processes. The emphasis of this book is on special classes of such Brownian functionals as: - Gaussian subspaces of the Gaussian space of Brownian motion; - Brownian quadratic funtionals; - Brownian local times, - Exponential functionals of Brownian motion with drift; - Winding number of one or several Brownian motions around one or several points or a straight line, or curves; - Time spent by Brownian motion below a multiple of its one-sided supremum.
Aspects of Automatic Text Analysis
This book It collects contributions of authors from a multidisciplinary area who focus on the topic of automatic text analysis from several (i.e. linguistic, mathematical, and information theoretical) perspectives. It describes methodological as well as methodical foundations and collects approaches in the field of text and corpus linguistics. In this sense, it contributes to the computational linguistic and information theoretical grounding of automatic text analysis.
Artinian Modules over Group Rings
This book highlights important developments on artinian modules over group rings of generalized nilpotent groups. Along with traditional topics such as direct decompositions of artinian modules, criteria of complementability for some important modules, and criteria of semisimplicity of artinian modules, it also focuses on recent advanced results on these matters.
Artificial intelligence in recognition and classification of astrophysical and medical images
This book presents innovative techniques in Recognition and Classification of Astrophysical and Medical Images. The contents include: Introduction to pattern recognition and classification in astrophysical and medical images. Image standardization and enhancement. Region-based methods for pattern recognition in medical and astrophysical images. Advanced information processing using statistical methods. Feature recognition and classification using spectral method
Arnolds Problems
Arnold's Problems contains mathematical problems.The invariable peculiarity of these problems was that Arnold did not consider mathematics a game with deductive reasoning and symbols, but a part of natural science (especially of physics), i.e. an experimental science. Many of these problems are still at the frontier of research today and are still open, and even those that are mainly solved keep stimulating new research, appearing every year in journals all over the world.The second part of the book is a collection of commentaries, mostly by Arnold's former students, on the current progress in the problems' solutions (featuring a bibliography inspired by them).
Aritmetica, crittografia e codici = Arithmetic, cryptography and codes
The basic techniques of algebra and number theory useful in recent applications to cryptography and codes are developed, with the aim of being elementary and self-sufficient. The emphasis is on computational problems. This part of the volume can be useful as a textbook for a first course in algebra for mathematicians, computer scientists or engineers. Important applications of algebra and geometry to cryptography and codes are then illustrated. Both, cryptography and codes have significant applications in daily life which are illustrated here. Cryptography is developed in detail in much of its classic and current aspects, and both private and public key cryptography are developed. Cryptography with the use of elliptic curves on finite fields is also illustrated. A chapter introducing the subject is dedicated to linear codes.
Aritmetica : Un approccio computazionale = Arithmetic : A computational approach
Intended to be a contribution to the algorithmic re-reading of some classic topics of elementary number theory and an invitation to more demanding reading, according to the indications provided by the bibliography annexed to it.
Arithmetical investigations : Representation theory, orthogonal polynomials, and quantum interpolations
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
