الصفحة 3
الصفحة 3
Number Theory : An Introduction to Mathematics ; Part B
This book attempts to provide such an understanding of the nature and extent of mathematics. It is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. This part B is more advanced than the first and should give the reader some idea of the scope of mathematics today. The connecting theme is the theory of numbers. By exploring its many connections with other branches, we may obtain a broad picture.
Number Theory : An Introduction to Mathematics ; Part A
This book attempts to provide such an understanding of the nature and extent of mathematics. It is a modern introduction to the theory of numbers, emphasizing its connections with other branches of mathematics. This part A, which should be accessible to a first-year undergraduate, deals with elementary number theory.
Number Story : From Counting to Cryptography
Numbers have fascinated people for centuries. They are familiar to everyone, forming a central pillar of our understanding of the world, yet the number system was not presented to us "gift-wrapped" but, rather, was developed over millennia. Today, despite all this development, it remains true that a child may ask a question about numbers that no one can answer. Many unsolved problems surrounding number matters appear as quirky oddities of little account while others are holding up fundamental progress in mainstream mathematics.
Number Fields and Function Fields – Two Parallel Worlds
These invited articles by leading researchers in the field explore various aspects of the parallel worlds of function fields and number fields. Topics range from Arakelov geometry, the search for a theory of varieties over the field with one element, via Eisenstein series to Drinfeld modules, and t-motives.
Notions of Convexity
The first two chapters of this book are devoted to convexity in the classical sense, for functions of one and several real variables respectively. This gives a background for the study in the following chapters of related notions which occur in the theory of linear partial differential equations and complex analysis such as (pluri-)subharmonic functions, pseudoconvex sets, and sets which are convex for supports or singular supports with respect to a differential operator. In addition, the convexity conditions which are relevant for local or global existence of holomorphic differential equations are discussed, leading up to Trépreau’s theorem on sufficiency of condition (capital Greek letter Psi) for microlocal solvability in the analytic category.
Notes on Set Theory
This is introduction to axiomatic set theory, viewed both as a foundation of mathematics and as a branch of mathematics with its own subject matter, basic results, open problems.
Notes on Coxeter Transformations and the McKay Correspondence
One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram. The Coxeter transformation is the main tool in the proof of the McKay correspondence, and is closely interrelated with the Cartan matrix and Poincaré series. The Coxeter functors constructed by Bernstein, Gelfand and Ponomarev plays a distinguished role in the representation theory of quivers.
Nonstandard Analysis
The book is an introduction with emphasis on those more advanced applications in analysis which are hardly accessible by other methods. Examples of such topics are a deeper analysis of certain functionals like Hahn-Banach limits or of finitely additive measures: From the viewpoint of classical analysis these are strange objects whose mere existence is even hard to prove. From the viewpoint of nonstandard analysis, these are rather 'explicit' objects.
Non-spectral Asymptotic Analysis of One-Parameter Operator Semigroups
In this book, non-spectral methods are presented and discussed that have been developed over the last two decades for the investigation of asymptotic behavior of one-parameter operator semigroups in Banach spaces. This concerns in particular Markov semigroups in L1-spaces, motivated by applications to probability theory and dynamical systems. Recently many results on the asymptotic behaviour of Markov semigroups were extended to positive semigroups in Banach lattices with order-continuous norm, and to positive semigroups in non-commutative L1-spaces. Related results, historical notes, exercises, and open problems accompany each chapter.
Nonsmooth Vector Functions and Continuous Optimization
A recent significant innovation in mathematical sciences has been the progressive use of nonsmooth calculus, an extension of the differential calculus, as a key tool of modern analysis in many areas of mathematics, operations research, and engineering. Focusing on the study of nonsmooth vector functions, this book presents a comprehensive account of the calculus of generalized Jacobian matrices and their applications to continuous nonsmooth optimization problems and variational inequalities in finite dimensions.
Nonsmooth Variational Problems and their Inequalities : Comparison Principles and Applications
The main purpose of this book is to provide a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method. This method is an effective and flexible technique to obtain existence and comparison results of solutions. Also, it can be employed for the investigation of various qualitative properties, such as location, multiplicity and extremality of solutions. In the treatment of the problems under consideration a wide range of methods and techniques from nonlinear and nonsmooth analysis is applied, a brief outline of which has been provided in a preliminary chapter in order to make the book self-contained.
Nonsmooth Mechanics and Analysis : Theoretical and Numerical Advances
Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification. Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.
Nonsmooth Analysis
The book treats various concepts of generalized derivatives and subdifferentials in normed spaces, their geometric counterparts (tangent and normal cones) and their application to optimization problems. It starts with the subdifferential of convex analysis, passes to corresponding concepts for locally Lipschitz continuous functions and finally presents subdifferentials for general lower semicontinuous functions. All basic tools are presented where they are needed; this concerns separation theorems, variational and extremal principles as well as relevant parts of multifunction theory. The presentation is rigorous, with detailed proofs. Each chapter ends with bibliographic notes and exercises.
Nonparametric Monte Carlo Tests and Their Applications
A fundamental issue in statistical analysis is testing the fit of a particular probability model to a set of observed data. Monte Carlo approximation to the null distribution of the test provides a convenient and powerful means of testing model fit. Nonparametric Monte Carlo Tests and Their Applications proposes a new Monte Carlo-based methodology to construct this type of approximation Every chapter of the book includes algorithms, simulations, and theoretical deductions. The prerequisites for a full appreciation of the book are a modest knowledge of mathematical statistics and limit theorems in probability,empirical process theory.
Nonparametric Functional Data Analysis : Theory and Practice
Modern apparatuses allow us to collect samples of functional data, mainly curves but also images. On the other hand, nonparametric statistics produces useful tools for standard data exploration. This book links these two fields of modern statistics by explaining how functional data can be studied through parameter-free statistical ideas. This book starts from theoretical foundations including functional nonparametric modeling, description of the mathematical framework, construction of the statistical methods, and statements of their asymptotic behaviors. It proceeds to computational issues including R and S-PLUS routines. Several functional datasets in chemometrics, econometrics, and pattern recognition are used to emphasize the wide scope of nonparametric functional data analysis in applied sciences. The companion Web site includes R and S-PLUS routines, command lines for reproducing examples presented in the book, and the functional datasets. Rather than set application against theory, this book is really an interface of these two features of statistics. A special effort has been made in writing this book to accommodate several levels of reading.
Nonparametric Bayesian Learning for Collaborative Robot Multimodal Introspection
This book focuses on robot introspection, which has a direct impact on physical human–robot interaction and long-term autonomy, and which can benefit from autonomous anomaly monitoring and diagnosis, as well as anomaly recovery strategies.
Non-negative Matrices and Markov Chains
This book is a photographic reproduction of the book of the same title published in 1981, for which there has been continuing demand on account of its accessible technical level. Its appearance also helped generate considerable subsequent work on inhomogeneous products of matrices. This printing adds an additional bibliography on coefficients of ergodicity and a list of corrigenda.
Nonlinear Structural Engineering : With Unique Theories and Methods to Solve Effectively Complex Nonlinear Problems
This book is aiming to concentrate on the nonlinear static and dynamic analysis of structures and structural components that are widely used in everyday engineering applications. It approaches a nonlinear problem by mathematically converting it into an exact equivalent pseudolinear one, in contrast to commonly used approaches which are based on linear concepts. The new concepts, theories and methods introduced in this book, simplify a great deal the solution of the complex nonlinear problems, and also allow for the correct usage of the powerful existing linear methods of analysis.
Nonlinear Smoothing and Multiresolution Analysis
This monograph presents a new theory for analysis, comparison and design of nonlinear smoothers, linking to established practices. Although a part of mathematical morphology, the special properties yield many simple, powerful and illuminating results leading to a novel nonlinear multiresolution analysis with pulses that may be as natural to vision as wavelet analysis is to acoustics. Similar to median transforms, they have the advantages of a supporting theory, computational simplicity, remarkable consistency, full trend preservation, and a Parceval-type identity.
Nonlinear Problems of Elasticity
This second edition is an enlarged, completely updated, and extensively revised version of the authoritative first edition. It is devoted to the detailed study of illuminating specific problems of nonlinear elasticity. The mathematical tools from nonlinear analysis are given self-contained presentations where they are needed. This book begins with chapters on (geometrically exact theories of) strings, rods, and shells, and on the applications of bifurcation theory and the calculus of variations to problems for these bodies. The book continues with chapters on tensors, three-dimensional continuum mechanics, three-dimensional elasticity, large-strain plasticity, general theories of rods and shells, and dynamical problems. Each chapter contains a wealth of interesting, challenging, and tractable exercises.
