الصفحة 1
الصفحة 1
Morse Theoretic Methods in Nonlinear Analysis and in Symplectic Topology
It covered an ample spectrum of subjects which are re ected in the present volume: Morse theory and related techniques in in nite dim- sional spaces, Floer theory and its recent extensions and generalizations, Morse and Floer theory in relation to string topology, generating functions, structure of the group of Hamiltonian difieomorphisms and related dynamical problems, applications to robotics and many others. We thank all our main speakers for their stimulating lectures and all p- ticipants for creating a friendly atmosphere
Metodi Matematici della Fisica = Mathematical Methods of Physics
This text draws its origin from my old notes, prepared for the course of Mathematical Methods of Physics and gradually arranged, refined and updated over the course of many years of teaching. The aim has always been to provide as simple and direct a presentation as possible of the mathematical methods relevant to Physics: Fourier series, Hilbert spaces, linear operators, functions of complex variables, Fourier and Laplace transforms, distributions. In addition to these basic topics, a brief introduction to the first notions of group theory, Lie algebras and symmetries in view of their applications to Physics is presented in the Appendix.
Methods of nonlinear analysis : Applications to differential equations
In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Every method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. Applications and generalizations are shown. In particular, a large number of methods is applied to boundary value problems for partial differential equations.
Metamorphoses of Hamiltonian Systems with Symmetries
Modern notions and important tools of classical mechanics are used in the study of concrete examples that model physically significant molecular and atomic systems. The parametric nature of these examples leads naturally to the study of the major qualitative changes of such systems (metamorphoses) as the parameters are varied. The symmetries of these systems, discrete or continuous, exact or approximate, are used to simplify the problem through a number of mathematical tools and techniques like normalization and reduction. The book moves gradually from finding relative equilibria using symmetry, to the Hamiltonian Hopf bifurcation and its relation to monodromy and, finally, to generalizations of monodromy.
Mathematics of Financial Markets
This book presents the mathematics that underpins pricing models for derivative securities, such as options, futures and swaps, in modern financial markets. The idealized continuous-time models built upon the famous Black-Scholes theory require sophisticated mathematical tools drawn from modern stochastic calculus. However, many of the underlying ideas can be explained more simply within a discrete-time framework. This is developed extensively in this substantially revised second edition to motivate the technically more demanding continuous-time theory, which includes a detailed analysis of the Black-Scholes model and its generalizations, American put options, term structure models and consumption-investment problems. The mathematics of martingales and stochastic calculus is developed where it is needed.
Introduction to Modern Number Theory: Fundamental Problems, Ideas and Theories
"Introduction to Modern Number Theory" surveys from a unified point of view both the modern state and the trends of continuing development of various branches of number theory. Motivated by elementary problems, the central ideas of modern theories are exposed. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories. Moreover, the authors have added a part dedicated to arithmetical cohomology and noncommutative geometry, a report on point counts on varieties with many rational points, the recent polynomial time algorithm for primality testing, and some others subjects.
Interpolation, Schur Functions and Moment Problems
In signal processing, they are often named reflection coefficients. Under the word "Schur analysis" one encounters a variety of problems related to Schur functions, such as interpolation problems, moment problems, the study of the relationships between the Schur coefficients and the properties of the function, or the study of underlying operators. Such questions are also considered for some generalizations of Schur functions. Furthermore, there is an extension of the notion of a Schur function for functions that are analytic and have a positive real part in the open upper half-plane; these functions are called Carathéodory functions. This volume is almost entirely dedicated to the analysis of Schur and Carathéodory functions and to the solutions of problems for these classes.
Intégration : Chapitres 7 et 8 = Integration : Chapters 7 and 8
Nicolas BOURBAKI's Elements of Mathematics aim to provide a rigorous, systematic presentation without prerequisites of mathematics from their foundations. applications. The concepts introduced, such as Haar measures and the convolution product, are the basis of harmonic analysis. It includes the chapters: Haar measure; Convolution and representations.
Gruppi : Una introduzione a idee e metodi della Teoria dei Gruppi = Groups : An introduction to the ideas and methods of Group Theory
Born from the university courses of Group Theory held by the author for several years, this book deals with the fundamental arguments of the theory: abelian, nilpotent and solvable groups, free groups, permutations, representations and cohomology. After the first notions, Hölder's program for the classification of finite groups is exposed. A long chapter is dedicated to the action of a group on a set and to the permutations, both under the algebraic and combinatorial aspects, with references to the theory of equations. Some questions of a logical nature are also considered, such as the decidability of the word problem for certain classes of groups. An essential aspect of the book is the presence of a great variety of exercises, about 400, mostly solved.
Group theory : Application to the physics of condensed matter
Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra. This concise and class-tested book has been pedagogically tailored over 30 years MIT and 2 years at the University Federal of Minas Gerais (UFMG) in Brazil. The approach centers on the conviction that teaching group theory in close connection with applications helps students to learn, understand and use it for their own needs. For this reason, the theoretical background is confined to the first 4 introductory chapters (6-8 classroom hours). From there, each chapter develops new theory while introducing applications so that the students can best retain new concepts, build on concepts learned the previous week, and see interrelations between topics as presented.
Field Arithmetic ; 3rd ed.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.
Field Arithmetic ; 2nd ed.
Field Arithmetic explores Diophantine fields through their absolute Galois groups. This largely self-contained treatment starts with techniques from algebraic geometry, number theory, and profinite groups. Graduate students can effectively learn generalizations of finite field ideas. We use Haar measure on the absolute Galois group to replace counting arguments. New Chebotarev density variants interpret diophantine properties. Here we have the only complete treatment of Galois stratifications, used by Denef and Loeser, et al, to study Chow motives of Diophantine statements.Now we know they include valuable Galois extensions of the rationals that present its absolute Galois group through known groups. PAC fields have projective absolute Galois group. Those that are Hilbertian are characterized by this group being pro-free. These last decade results are tools for studying fields by their relation to those with projective absolute group. There are still mysterious problems to guide a new generation: Is the solvable closure of the rationals PAC; and do projective Hilbertian fields have pro-free absolute Galois group (includes Shafarevich's conjecture)?
Failure rate modelling for reliability and risk
Failure Rate Modelling for Reliability and Risk focuses on reliability theory and, specifically, on the failure rate (the hazard rate, the force of mortality) modelling and its generalizations, on systems operating in a random environment and on repairable systems. The failure rate is one of the crucial probabilistic characteristics for a number of disciplines; including reliability, survival analysis, risk analysis and demography.
Exercises in Modules and Rings
This Problem Book offers a compendium of 639 exercises of varying degrees of difficulty in the subject of modules and rings at the graduate level. The material covered includes projective, injective, and flat modules, homological and uniform dimensions, noncommutative localizations and Goldie’s theorems, maximal rings of quotients, Frobenius and quasi-Frobenius rings, as well as Morita’s classical theory of category dualities and equivalences. Each of the nineteen sections begins with an introduction giving the general background and the theoretical basis for the problems that follow. All exercises are solved in full detail; many are accompanied by pertinent historical and bibliographical information, or a commentary on possible improvements, generalizations, and latent connections to other problems.
Darboux Transformations in Integrable Systems : Theory and their Applications to Geometry
This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail.
Linear Models and Generalizations : Least Squares and Alternatives
Gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions
Lifting Modules : Supplements and Projectivity in Module Theory
Extending modules are generalizations of injective modules and, dually, lifting modules generalize projective supplemented modules. There is a certain asymmetry in this duality. While the theory of extending modules is well documented in monographs and text books, the purpose of our monograph is to provide a thorough study of supplements and projectivity conditions needed to investigate classes of modules related to lifting modules. The text begins with an introduction to small submodules, the radical, variations on projectivity, and hollow dimension. The subsequent chapters consider preradicals and torsion theories (in particular related to small modules), decompositions of modules (including the exchange property and local semi-T-nilpotency), supplements in modules (with specific emphasis on semilocal endomorphism rings), finishing with a long chapter on lifting modules, leading up their use in the theory of perfect rings, Harada rings, and quasi-Frobenius rings.
Lie Groups : An Approach through Invariants and Representations
Lie groups has been an increasing area of focus and rich research since the middle of the 20th century. Procesi's masterful approach to Lie groups through invariants and representations gives the reader a comprehensive treatment of the classical groups along with an extensive introduction to a wide range of topics associated with Lie groups: symmetric functions, theory of algebraic forms, Lie algebras, tensor algebra and symmetry, semisimple Lie algebras, algebraic groups, group representations, invariants, Hilbert theory, and binary forms with fields ranging from pure algebra to functional analysis.
Knowledge Discovery in Inductive Databases ; Vol.3377 : 3rd International Workshop, KDID 2004, Pisa, Italy, September 20, 2004, Revised Selected and Invited Papers
Cnstitutes the thoroughly refereed joint postproceedings of the Third International Workshop on Knowledge Discovery in Inductive Databases, KDID 2004, held in Pisa, Italy in September 2004 in association with ECML/PKDD. Inductive Databases support data mining and the knowledge discovery process in a natural way. In addition to usual data, an inductive database also contains inductive generalizations, like patterns and models extracted from the data. This book presents nine revised full papers selected from 23 submissions during two rounds of reviewing and improvement together with one invited paper. Various current topics in knowledge discovery and data mining in the framework of inductive databases are addressed.
Classification des Groupes Algébriques Semi-simples = The Classification of Semi-Simple Algebraic Groups
The third volume of the Collected Works of Claude Chevalley assembles his work on semi-simple algebraic groups contained, for the most part, in the notes of the famous "Sminaire Chevalley" held at the Ecole Normale Suprieure in Paris between 1956 and 1958 and written up by participants of the seminar namely, P. Cartier, A. Grothendieck, R. Lazard and J.L. Verdier. These texts have been entirely reset in TeX for this edition, and edited and annotated by Pierre Cartier. Almost 50 years after the original writing, these texts still constitute a choice reference from which to enter
