الصفحة 57
الصفحة 57
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.
Arithmetic and geometry around hypergeometric functions : Lecture notes of a CIMPA Summer School held at Galatasaray University, Istanbul, 2005
This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results of a problem session.
Arakelov Geometry and Diophantine Applications
Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry.The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research.
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.
Approval Voting
The book proposes a compelling way to elect some 500,000 officials in public elections. After a generation of discussion and debate on the subject, the authors remain convinced that Approval Voting is as relevant today.
Applied Stochastic Processes
Applied Stochastic Processes uses a distinctly applied framework to present the most important topics in the field of stochastic processes.
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 Statistics Using SPSS, STATISTICA, MATLAB and R
The book provides a comprehensive coverage of the main statistical analysis topics important for practical applications such as data description, statistical inference, classification and regression, factor analysis, survival data and directional statistics.
Applied Spatial Data Analysis with R
Applied Spatial Data Analysis with R is divided into two basic parts, the first presenting R packages, functions, classes and methods for handling spatial data, The second part showcases more specialised kinds of spatial data analysis, including spatial point pattern analysis, interpolation and geostatistics, areal data analysis and disease mapping.
Applied Semi-Markov Processes
The book presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes. These concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.This book is intended for graduate students and researchers in mathematics, operations research and engineering; it might also appeal to actuaries and financial managers, and anyone interested in its applications for banks, mechanical industries for reliability aspects, and insurance companies.
Applied Research in Uncertainty Modeling and Analysis
For a long time uncertainty has been considered synonymous with random, stochastic, statistic, or probabilistic. Since the early sixties views on uncertainty have become more heterogeneous. In the past forty years numerous tools that model uncertainty, above and beyond statistics, have been proposed by several engineers and scientists. The tool/method to model uncertainty in a specific context should really be chosen by considering the features of the phenomenon under consideration, not independent of what is known about the system and what causes uncertainty. In this fascinating overview of the field, the authors provide broad coverage of uncertainty analysis/modeling and its application. Applied Research in Uncertainty Modeling and Analysis presents the perspectives of various researchers and practitioners on uncertainty analysis and modeling outside their own fields and domain expertise. Rather than focusing explicitly on theory, the authors use real-world examples to demonstrate the strength of the chosen methodology. Applied Research in Uncertainty Modeling and Analysis concentrates on general aspects of uncertainty, modeling, and methods, and focuses on various applications, included Biomedical Engineering, Chemical Engineering, Structural Engineering, and Transportation Engineering.
Applied Quantitative Finance
Applied Quantitative Finance (2nd edition) provides a comprehensive and state-of-the-art treatment of cutting-edge topics and methods. It provides solutions to and presents theoretical developments in many practical problems such as risk management, pricing of credit derivatives, quantification of volatility and copula modelling. The synthesis of theory and practice supported by computational tools is reflected in the selection of topics as well as in a finely tuned balance of scientific contributions on practical implementation and theoretical concepts. This linkage between theory and practice offers theoreticians insights into considerations of applicability and, vice versa, provides practitioners comfortable access to new techniques in quantitative finance.
Applied Proof Theory : Proof Interpretations and Their Use in Mathematics
Ulrich Kohlenbach presents an applied form of proof theory that has led in recent years to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others). This applied approach is based on logical transformations (so-called proof interpretations) and concerns the extraction of effective data (such as bounds) from prima facie ineffective proofs as well as new qualitative results such as independence of solutions from certain parameters, generalizations of proofs by elimination of premises. The book first develops the necessary logical machinery emphasizing novel forms of Gödel's famous functional ('Dialectica') interpretation. It then establishes general logical metatheorems that connect these techniques with concrete mathematics. Finally, two extended case studies (one in approximation theory and one in fixed point theory) show in detail how this machinery can be applied to concrete proofs in different areas of mathematics.
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 Pattern Recognition
The main goal of this book is to cover some of the latest application domains of pattern recognition while presenting novel techniques that have been developed or customized in those domains.
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 Parallel Computing ; State of the Art in Scientific Computing
Introduction The PARA workshops in the past were devoted to parallel computing methods in science and technology. There have been seven PARA meetings to date: PARA’94, PARA’95 and PARA’96 in Lyngby, Denmark, PARA’98 in Umea, ? Sweden, PARA 2000 in Bergen, N- way, PARA 2002 in Espoo, Finland, and PARA 2004 again in Lyngby, Denmark. The ?rst six meetings featured lectures in modern numerical algorithms, computer science, en- neering, and industrial applications, all in the context of scienti?c parallel computing. This meeting in the series, the PARA 2004 Workshop with the title “State of the Art in Scienti?c Computing.
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.
