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الصفحة 27
الصفحة 27
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).
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.
Arguing Fundamental Rights
The book is unique in combining a challenging interpretation of one the foremost European conceptions of fundamental rights with the discussion of the pragmatics of constitutional adjudication.
Arctic Alpine ecosystems and people in a changing environment
This book addresses the significant environmental changes experienced by high latitude and high altitude ecosystems at the beginning of the 21st c- tury. Increased temperatures and precipitation, reduction in sea ice and glacier ice, the increased levels of UV-radiation and the long-range tra- ported contaminants in arctic and alpine regions are stress factors that challenge terrestrial and aquatic ecosystems. The large natural variation in the physical parameters of these extreme environments is a key factor in structuring the biodiversity and biotic productivity, and the effect of the new stress factors can be critical for the population structures and the - teraction between species. These changes may also have socio-economic effects if the changes affect the bio-production, which form the basis for the marine and terrestrial food chains. The book is uniquely multidisciplinary and provides examples of va- ous aspects of contemporary environmental change in arctic and alpine - gions. The 21 chapters of the book are organised under the fields of •Climate change and ecosystem response, •Long range transport of poll- ants and ecological impacts, and •UV radiation and biological effects, each also including aspects of the •Socio-economic effects of environmental change. The introductory chapter presents and explains the internal c- nection and integration of all chapters.
Approximation of Additive Convolution-Like Operators : Real C*-Algebra Approach
Various aspects of numerical analysis for equations arising in boundary integral equation methods have been the subject of several books published in the last 15 years [95, 102, 183, 196, 198]. Prominent examples include various classes of o- dimensional singular integral equations or equations related to single and double layer potentials. Usually, a mathematically rigorous foundation and error analysis for the approximate solution of such equations is by no means an easy task. One reason is the fact that boundary integral operators generally are neither integral operatorsof the formidentity plus compact operatornor identity plus an operator with a small norm. Consequently, existing standard theories for the numerical analysis of Fredholm integral equations of the second kind are not applicable. In the last 15 years it became clear that the Banach algebra technique is a powerful tool to analyze the stability problem for relevant approximation methods [102, 103, 183, 189]. The starting point for this approach is the observation that the ? stability problem is an invertibility problem in a certain BanachorC -algebra. As a rule, this algebra is very complicated – and one has to ?nd relevant subalgebras to use such tools as local principles and representation theory.
Approaches to Metaphysics
Today, when systematic philosophy - and reason itself - are challenged both outside of and within philosophy, is it still possible to do metaphysics? This volume provides a broad perspective on contemporary approaches to the nature and the fundamental questions of metaphysics. Drawing on scholars from continental Europe, Asia, Canada, the United States, and Great Britain, and representing a variety of philosophical cultures and traditions, this volume surveys and extends work in metaphysics and its implications for broader philosophical concerns (e.g., in ethics and social philosophy, in mathematics and logic, and in epistemology). It also addresses such questions as the role of history and historicity in undertaking metaphysics, the nature of metaphysics, the priority of metaphysics over epistemology, and the challenges of empiricism and postmodernism.
Applied Stochastic Control of Jump Diffusions
The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and its applications.
Applied Stochastic Control of Jump Diffusions
The main purpose of the book is to give a rigorous, yet mostly nontechnical, introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusionsThe types of control problems covered include classical stochastic control, optimal stopping, impulse control and singular control. Both the dynamic programming method and the maximum principle method are discussed, as well as the relation between them. Corresponding verification theorems involving the Hamilton-Jacobi Bellman equation and/or (quasi-)variational inequalities are formulated. There are also chapters on the viscosity solution formulation and numerical methods.The text emphasises applications, mostly to finance. All the main results are illustrated by examples and exercises appear at the end of each chapter with complete solutions. This will help the reader understand the theory and see how to apply it.The book assumes some basic knowledge of stochastic analysis, measure theory and partial differential equations.
Applied Reliability and Quality : Fundamentals, Methods and Procedures
"Reliability and quality professionals need to know about each other's work activities because this may help them - directly or indirectly - to perform their tasks more effectively. Applied Reliability and Quality: Fundamentals, Methods and Procedures meets the need for a single volume that considers applied areas of both reliability and quality. Before now, there has not been one book that covers both applied reliability and quality; so to gain knowledge of each other's specialties, these people had to study various books, articles, or reports on each area."
Applied Probability and Statistics
This text is designed for a one-semester course on Probability and Statistics. The exposition unfolds systematically from an introductory chapter to such topics as random variables and vectors, stochastic processes, estimation, testing and regression. The topics are well chosen and the presentation is enriched by many examples from real life. Following every chapter, the reader will find many original, solved and unsolved problems and hundreds of multiple choice questions, enabling those unfamiliar with the topics to master them. Additionally appealing are the interesting historical notes on the mathematicians mentioned throughout and a useful bibliography. A distinguishing character of the book is the thorough and succinct handling of the various topics.
Applied Partial Differential Equations : A Visual Approach
This book presents selected topics in science and engineering from an applied-mathematics point of view. The described natural, socioeconomic, and engineering phenomena are modeled by partial differential equations that relate state variables.
Applied Multivariate Statistical Analysis
This book presents the tools and concepts of multivariate data analysis in a way that is understandable for non-mathematicians and practitioners who face statistical data analysis.
Applied Linguistics and Language Teacher Education
Applied Linguistics and Language Teacher Education is aimed at applied linguists who are interested in understanding more about the learning of novice teachers in their classes. The 21 studies in this volume provide information on the complexity of novice teachers’ learning and use of knowledge in a variety of applied linguistics classes such as SLA, Syntax, Pragmatics, Sociolinguistics, Phonetics and Phonology, L2 Reading and Writing, Testing, and Content Based Instruction. These studies were conducted in a variety of contexts, from North and South America to Europe, Asia and Australia, and look at the preparation of teachers of English, Spanish and Chinese.
Applied computational materials modeling : Theory, simulation and experiment
this book provides the average person working in the materials field with a more balanced perspective of the role that computational modeling can play in every day research and development efforts. This is done by presenting a series of examples of the successful application of various computational modeling procedures (everything from first principles to quantum approximate to CALPHAD methods) to real life surface and bulk alloy problems.This book should have a large appeal in the materials community, both for experimentalists who would greatly benefit from adding computational methods to their everyday research regimes, as well as for those scientists/engineers familiar with a particular computational method who would like to add complementary techniques to their arsenal of research and development tools
Ancient Philosophy of the Self
This volume explores the various ways in which selfhood was approached and conceptualised in antiquity. They also describe how the ancient philosophers understood human agents as capable of causing changes and being affected in and by the world. The themes of persistence, identity, self-examination and self-improvement recur in many of these essays. The articles of the collection combine systematic and historical approaches to ancient sources that range from Socrates to Plotinus and Augustine.
Analysis, Synthesis, and Perception of Musical Sounds : The Sound of Music
Analysis, Synthesis, and Perception of Musical Sounds contains a detailed treatment of basic methods for analysis and synthesis of musical sounds, including the phase vocoder method, the McAulay-Quatieri frequency-tracking method, the constant-Q transform, and methods for pitch tracking with several examples shown. Various aspects of musical sound spectra such as spectral envelope, spectral centroid, spectral flux, and spectral irregularity are defined and discussed. One chapter is devoted to the control and synthesis of spectral envelopes. Two advanced methods of analysis/synthesis are given: "Sines Plus Transients Plus Noise" and "Spectrotemporal Reassignment" are covered. Methods for timbre morphing are given. The last two chapters discuss the perception of musical sounds based on discrimination and multidimensional scaling timbre models.
Analysis of variance for random models, Vol. 2 : Unbalanced data : Theory, methods, applications, and data analysis
Analysis of variance (ANOVA) models have become widely used tools and play a fundamental role in much of the application of statistics today. In particular, ANOVA models involving random effects have found widespread application to experimental design in a variety of fields requiring measurements of variance, including agriculture, biology, animal breeding, applied genetics, econometrics, quality control, medicine, engineering, and social sciences. This two-volume work is a comprehensive presentation of different methods and techniques for point estimation, interval estimation, and tests of hypotheses for linear models involving random effects. Both Bayesian and repeated sampling procedures are considered. Volume I examines models with balanced data (orthogonal models); Volume II studies models with unbalanced data (nonorthogonal models).
Analysis of phylogenetics and evolution with R
This book integrates a wide variety of data analysis methods into a single and flexible interface: the R language. This open source language is available for a wide range of computer systems and has been adopted as a computational environment by many authors of statistical software. Adopting R as a main tool for phylogenetic analyses will ease the workflow in biologists' data analyses, ensure greater scientific repeatability, and enhance the exchange of ideas and methodological developments.
Analysis of integrated and cointegrated time series with R
The analysis of integrated and co-integrated time series can be considered as the main methodology employed in applied econometrics. This book not only introduces the reader to this topic but enables him to conduct the various unit root tests and co-integration methods on his own by utilizing the free statistical programming environment R. The book encompasses seasonal unit roots, fractional integration, coping with structural breaks, and multivariate time series models. The book is enriched by numerous programming examples to artificial and real data so that it is ideally suited as an accompanying text book to computer lab classes.
Analysis II
As with the first, the second volume contains substantially more material than can be covered in a one-semester course. Such courses may omit many beautiful and well-grounded applications which connect broadly to many areas of mathematics. We of course hope that students will pursue this material independently; teachers may find it useful for undergraduate seminars. For an overview of the material presented, consult the table of contents and the chapter introductions. As before, we stress that doing the numerous exercises is indispensable for understanding the subject matter, and they also round out and amplify the main text. In writing this volume, we are indebted to the help of many.
