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This book constitutes the refereed proceedings of the 12th Conference on Computability in Europe, CiE 2016, held in Paris, France, in June/July 2016. The 18 revised full papers and 19 invited papers and invited extended abstracts were carefully reviewed and selected from 40 submissions. The conference CiE 2016 has six special sessions – two sessions, cryptography and information theory and symbolic dynamics, are organized for the first time in the conference series. In addition to this new developments in areas frequently covered in the CiE conference series were addressed in the following sessions: computable and constructive analysis; computation in biological systems; history and philosophy of computing; weak arithmetic.

This book presents articles at the interface of two active areas of research: classical topology and the relatively new field of geometric group theory. It includes two long survey articles, one on proofs of the Farrell–Jones conjectures, and the other on ends of spaces and groups. In 2010–2011, Ohio State University (OSU) hosted a special year in topology and geometric group theory. Over the course of the year, there were seminars, workshops, short weekend conferences, and a major conference out of which this book resulted.Four other research articles complement these surveys, making this book ideal for graduate students and established mathematicians interested in entering this area of research.

This book constitutes the refereed proceedings of the 26th International Symposium on Algorithms and Computation, ISAAC 2015, held in Nagoya, Japan, in December 2015. The 65 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 180 submissions for inclusion in the book. The focus of the volume is on the following topics: computational geometry; data structures; combinatorial optimization and approximation algorithms; randomized algorithms; graph algorithms and FPT; computational complexity; graph drawing and planar graphs; online and streaming algorithms; and string and DNA algorithms.

This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces. It is the first time that these objects are discussed from the points of view of algebraic geometry as well as group theory. The book also includes various open problems and conjectures related to these surfaces.Beauville surfaces are a class of rigid regular surfaces of general type, which can be described in a purely algebraic combinatoric way. They play an important role in different fields of mathematics like algebraic geometry, group theory and number theory. The notion of Beauville surface was introduced by Fabrizio Catanese in 2000 and after the first systematic study of these surfaces by Ingrid Bauer, Fabrizio Catanese and Fritz Grunewald, there has been an increasing interest in the subject.These proceedings reflect the topics of the lectures presented during the workshop ‘Beauville surfaces and groups 2012', held at Newcastle University, UK in June 2012. This conference brought together, for the first time, experts of different fields of mathematics interested in Beauville surfaces.

This volume constitutes the thoroughly refereed proceedings of the 21st International Workshop on Cellular Automata and Discrete Complex Systems, AUTOMATA 2015, held in Turku, Finland, in June 2015. This volume contains 4 invited talks in full-paper length and 15 regular papers, which were carefully reviewed and selected from a total of 33 submissions. Topics of interest include, the following aspects and features of such systems: dynamical, topological, ergodic and algebraic aspects; algorithmic and complexity issues; emergent properties; formal language processing aspects; symbolic dynamics; models of parallelism and distributed systems; timing schemes; phenomenological descriptions; scientific modeling; and practical applications.

Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory.Topics include:• an intuitive introduction to ergodic theory• an introduction to the basic notions, constructions, and standard examples of topological dynamical systems• Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem• measure-preserving dynamical systems• von Neumann's Mean Ergodic Theorem and Birkhoff's Pointwise Ergodic Theorem• strongly and weakly mixing systems• an examination of notions of isomorphism for measure-preserving systems• Markov operators, and the related concept of a factor of a measure preserving system• compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition• an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg's Correspondence Principle, theorems of Roth and Furstenberg–Sárközy)Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory

This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra.The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products.Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.

This book constitutes the refereed proceedings of the 5th International Conference on Model and Data Engineering, MEDI 2015, held in Rhodes, Greece, in September 2015. The 18 full papers and 9 short papers presented together with 2 invited talks were carefully reviewed and selected from 55 submissions. The papers are organized in topical sections such as modeling and meta modeling; ontology-based modeling, reasoning and reuse; event-B and modeling languages; context modeling and model transformation; data mining; query processing; modeling activities and inference; prediction and recommendation; requirement and systems engineering.

This monograph is the first book-length treatment of valuation theory on finite-dimensional division algebras, a subject of active and substantial research over the last forty years. Its development was spurred in the last decades of the twentieth century by important advances such as Amitsur's construction of non crossed products and Platonov's solution of the Tannaka-Artin problem.This study is particularly timely because it approaches the subject from the perspective of associated graded structures. This new approach has been developed by the authors in the last few years and has significantly clarified the theory. Various constructions of division algebras are obtained as applications of the theory, such as noncrossed products and indecomposable algebras. In addition, the use of valuation theory in reduced Whitehead group calculations (after Hazrat and Wadsworth) and in essential dimension computations (after Baek and Merkurjev) is showcased.The intended audience consists of graduate students and research mathematicians.

This volume addresses recent developments in weed science. These developments include conservation agriculture and conservation tillage, climate change, environmental concerns about the runoff of agrochemicals, resistance of weeds and crops to herbicides, and the need for a vastly improved understanding of weed ecology and herbicide use. The book provides details on harnessing knowledge of weed ecology to improve weed management in different crops and presents information on opportunities in weed management in different crops. Current management practices are also covered, along with guidance for selecting herbicides and using them effectively.Written by experts in the field and supplemented with instructive illustrations and tables, Recent Advances in Weed Management is an essential reference for agricultural specialists and researchers, government agents, extension specialists, and professionals throughout the agrochemical industry, as well as a foundation for advanced students taking courses in weed science.

Forget Hawaii or the Mediterranean. Soon – very soon – you'll be able to add a much more exotic stamp to your passport: space. How will you get there, what will the trip be like and how much training will you need? All you need to know is right here in this guide. Tourists in Space: A Practical Guide supplies all the advice and information you need to make your spaceflight the most rewarding experience of your life. This definitive, real-world guide is packed with helpful facts and suggestions on everything from training, equipment, safety and in-flight procedures to techniques for avoiding space motion sickness and bone demineralization. You'll also find: • Advice on choosing your training agency • Techniques for minimizing the risk of space motion sickness • Information you need to prepare for your medical examination, training and flight • Tips on activities near your training location and much more.

In a knowledge-based society, research into fundamental physics plays a vital role not only in the enhancement of human knowledge but also in the development of new technology that affects everyday life.The international symposium series Frontiers of Fundamental Physics (FFP) regularly brings together eminent scholars and researchers working in various areas in physics to exchange expertise, ideas, results, and new research perspectives. The twelfth such symposium, FFP12, took place at the University of Udine, Italy, and covered diverse fields of research: astrophysics, high energy physics and particle physics, theoretical physics, gravitation and cosmology, condensed matter physics, statistical physics, computational physics, and mathematical physics. Importantly, it also devoted a great deal of attention to physics education research, teacher training in modern physics, and popularization of physics. The high scientific level of FFP12 was guaranteed by the careful selection made by scientific coordinators from among 250 submissions from 28 countries across the world. During the three days of the conference, nine general talks were delivered in plenary sessions, 29 invited talks were given in specific topic areas, and 59 oral presentations were made. This book presents a selection of the best contributions at FFP12 with the aim of acquainting readers with the most important recent advances in fundamental physics and in physics education and teacher development.

In 1842 the Belgian mathematician Eugène Charles Catalan asked whether 8 and 9 are the only consecutive pure powers of non-zero integers. 160 years after, the question was answered affirmatively by the Swiss mathematician of Romanian origin Preda Mihăilescu. In other words, 32 – 23 = 1 is the only solution of the equation xp – yq = 1 in integers x, y, p, q with xy ≠ 0 and p, q ≥ 2.In this book we give a complete and (almost) self-contained exposition of Mihăilescu's work, which must be understandable by a curious university student, not necessarily specializing in Number Theory. We assume a very modest background:a standard university course of algebra, including basic Galois theory, and working knowledge of basic algebraic number theory.

This book provides an overview of the complex challenges and opportunities related to forest-based rural development in the tropics and subtropics. Applying a socio-ecological perspective, the book traces the changing paradigms of forestry in rural development throughout history, summarizes the major aspects of the rural development challenge in forest areas and documents innovative approaches in fields such as land utilization, technology and organizational development, rural advisory services, financing mechanisms, participative planning and forest governance. It brings together scholars and practitioners dealing with the topics from various theoretical and practical angles. Calling for an approach that carefully balances market forces with government intervention, the book shows that forests in rural areas have the potential to provide a solid foundation for a green global economy.

The two volume-set, LNCS 8616 and LNCS 8617, constitutes the refereed proceedings of the 34th Annual International Cryptology Conference, CRYPTO 2014, held in Santa Barbara, CA, USA, in August 2014.The 60 revised full papers presented in LNCS 8616 and LNCS 8617 were carefully reviewed and selected from 227 submissions. The papers are organized in topical sections on symmetric encryption and PRFs; formal methods; hash functions; groups and maps; lattices; asymmetric encryption and signatures; side channels and leakage resilience; obfuscation; FHE; quantum cryptography; foundations of hardness; number-theoretic hardness; information-theoretic security; key exchange and secure communication; zero knowledge; composable security; secure computation - foundations; secure computation - implementations.

Presenting recent developments and applications, the book focuses on four main topics in current model theory: 1) the model theory of valued fields; 2) undecidability in arithmetic; 3) NIP theories; and 4) the model theory of real and complex exponentiation. Young researchers in model theory will particularly benefit from the book, as will more senior researchers in other branches of mathematics.

This book is focused on the recent advances in computer vision methodologies and technical solutions using conventional and intelligent paradigms. The Contributions include:· Morphological Image Analysis for Computer Vision Applications.· Methods for Detecting of Structural Changes in Computer Vision Systems.· Hierarchical Adaptive KL-based Transform: Algorithms and Applications.· Automatic Estimation for Parameters of Image Projective Transforms Based on Object-invariant Cores.· A Way of Energy Analysis for Image and Video Sequence Processing.· Optimal Measurement of Visual Motion Across Spatial and Temporal Scales.· Scene Analysis Using Morphological Mathematics and Fuzzy Logic.· Digital Video Stabilization in Static and Dynamic Scenes.· Implementation of Hadamard Matrices for Image Processing.· A Generalized Criterion of Efficiency forTelecommunication Systems.The book is directed to PhD students, professors, researchers and software developers working in the areas of digital video processing and computer vision technologies.

About the first edition: “The text is geared to the needs of the beginning graduate student, covering with complete, well-written proofs the usual major branches of groups, rings, fields, and modules...[n]one of the material one expects in a book like this is missing, and the level of detail is appropriate for its intended audience.” (Alberto Delgado, MathSciNet) “This text promotes the conceptual understanding of algebra as a whole, and that with great methodological mastery. Although the presentation is predominantly abstract...it nevertheless features a careful selection of important examples, together with a remarkably detailed and strategically skillful elaboration of the more sophisticated, abstract theories.” (Werner Kleinert, Zentralblatt) For the new edition, the author has completely rewritten the text, reorganized many of the sections, and even cut or shortened material which is no longer essential. He has added a chapter on Ext and Tor, as well as a bit of topology.

The Lie Theory Workshop, founded by Joe Wolf (UC, Berkeley), has been running for over two decades. These workshops have been sponsored by the NSF, noting the talks have been seminal in describing new perspectives in the field covering broad areas of current research. At the beginning, the top universities in California and Utah hosted the meetings which continue to run on a quarterly basis. Experts in representation theory/Lie theory from various parts of the US, Europe, Asia (China, Japan, Singapore, Russia), Canada, and South and Central America were routinely invited to give talks at these meetings. Nowadays, the workshops are also hosted at universities in Louisiana, Virginia, and Oklahoma. The contributors to this volume have all participated in these Lie theory workshops and include in this volume expository articles which cover representation theory from the algebraic, geometric, analytic, and topological perspectives with also important connections to math physics. These survey articles, review and update the prominent seminal series of workshops in representation/Lie theory mentioned-above, and reflects the widespread influence of those workshops in such areas as harmonic analysis, representation theory, differential geometry, algebraic geometry, number theory, and mathematical physics. Many of the contributors have had prominent roles in both the classical and modern developments of Lie theory and its applications.

The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compressed form using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressed word problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups.

IT changes everyday's life, especially in education and medicine. The goal of ITME 2013 is to further explore the theoretical and practical issues of IT in education and medicine. It also aims to foster new ideas and collaboration between researchers and practitioners.

Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.

This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take a classical-like view of quantum states in physics.Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups, Gazeau-Klauder coherent states, coherent states for the relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potential applications, from the quantum physically oriented, like the quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing.Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the researchliterature, the first edition of the book is already a proven compendium for physicists and mathematicians active in the field, and with full coverage of the latest theory and results the revised second edition is even more valuable.

This volume consists of the English translations of the letters exchanged between Emil Artin to Helmut Hasse written from 1921 until 1958. The letters are accompanied by extensive comments explaining the mathematical background and giving the information needed for understanding these letters. Most letters deal with class field theory and shed a light on the birth of one of its most profound results: Artin's reciprocity law.

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe­ matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by'Soviet Encyclopaedia Publishing House'in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi­ sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en­ gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

This book is based on several courses given by the authors since 1966. It introduces the reader to the representation theory of compact Lie groups. We have chosen a geometrical and analytical approach since we feel that this is the easiest way to motivate and establish the theory and to indicate relations to other branches of mathematics. Lie algebras, though mentioned occasionally, are not used in an essential way. The material as well as its presentation are classical; one might say that the foundations were known to Hermann Weyl at least 50 years ago. Prerequisites to the book are standard linear algebra and analysis, including Stokes'theorem for manifolds. The book can be read by German students in their third year, or by first-year graduate students in the United States. Generally speaking the book should be useful for mathematicians with geometric interests and, we hope, for physicists. At the end of each section the reader will find a set of exercises. These vary in character:Some ask the reader to verify statements used in the text, some contain additional information, and some present examples and counter­ examples. We advise the reader at least to read through the exercises.

Over the past two decades, software engineering has come a long way from object-based to object-oriented to component-based design and development. Invasive software composition is a new technique that unifies and extends recent software engineering concepts like generic programming, aspect-oriented development, architecture systems, or subject-oriented development. To improve reuse, this new method regards software components as grayboxes and integrates them during composition. Building on a minimal set of program transformations, composition operator libraries can be developed that parameterize, extend, connect, mediate, and aspect-weave components. The book is centered around the JAVA language and the freely available demonstrator library COMPOST. It provides a wealth of materials for researchers, students, and professional software architects alike.

This book constitutes the refereed proceedings of the 10th International Conference on Theory and Applications of Models of Computation, TAMC 2013, held in Hong Kong, China, in May 2013. The 31 revised full papers presented were carefully reviewed and selected from 70 submissions. Bringing together a wide range of researchers with interests in computational theory and applications, the papers address the three main themes of the conference which were computability, complexity, and algorithms and present current research in these fields with aspects to theoretical computer science, algorithmic mathematics, and applications to the physical sciences.

Parasitic weeds of the families Cuscutaceae, Orobanchaceae and Scrophulariaceae are considered to be among the major problems facing agriculture in the Tropics and Subtropics. In the last decades, enormous efforts have been made and success achieved by scientists all over the world in gaining a better understanding of their biology and ecology as well as of control methods. However, no substantial reduction of infestation has been achieved in the past and control strategies specific to the different parasites, crops and farming systems must be further developed or adapted and realised among a wider farming population with suitable extension methods. This `Technical Manual'provides up-to-date methodologies for various aspects of research and extension related to parasitic weed species of the genera Striga, Alectra, Orobanche and Cuscuta. It has the intention to support scientists and extension workers of international and national research and extension institutes and universities, who are either new to the subject or plan to apply further techniques they are not yet familiar with.

Proceedings of a high-level conference on discrete mathematics, focusing on group actions in the areas of pure mathematics, applied mathematics, computer science, physics, and chemistry. A useful tool for researchers and graduate students in discrete mathematics and theoretical computer science.

In 1961 Smale established the generalized Poincare Conjecture in dimensions greater than or equal to 5 [129] and proceeded to prove the h-cobordism theorem [130]. This result inaugurated a major effort to classify all possible smooth and topological structures on manifolds of dimension at least 5. By the mid 1970's the main outlines of this theory were complete, and explicit answers (especially concerning simply connected manifolds) as well as general qualitative results had been obtained. As an example of such a qualitative result, a closed, simply connected manifold of dimension 2: 5 is determined up to finitely many diffeomorphism possibilities by its homotopy type and its Pontrjagin classes. There are similar results for self-diffeomorphisms, which, at least in the simply connected case, say that the group of self-diffeomorphisms of a closed manifold M of dimension at least 5 is commensurate with an arithmetic subgroup of the linear algebraic group of all automorphisms of its so-called rational minimal model which preserve the Pontrjagin classes [131]. Once the high dimensional theory was in good shape, attention shifted to the remaining, and seemingly exceptional, dimensions 3 and 4. The theory behind the results for manifolds of dimension at least 5 does not carryover to manifolds of these low dimensions, essentially because there is no longer enough room to maneuver. Thus new ideas are necessary to study manifolds of these'low'dimensions.

Inverse Galois Theory is concerned with the question of which finite groups occur as Galois Groups over a given field. In particular, this includes the question of the structure and the representations of the absolute Galois group of K and also the question about its finite epimorphic images, the so-called inverse problem of Galois theory. In all these areas important progress was made in the last few years. The aim of the book is to give a consistent and reasonably complete survey of these results, with the main emphasis on the rigidity method and its applications. Among others the monograph presents the most successful known existence theorems and construction methods for Galois extensions and solutions of embedding problems combined with a collection of the existing Galois realizations.

Proceedings of Sessions from the First Congress of the International Society for Analysis, Applications, and Computind held in Newark, Delaware, June 2-6, 1997

Nowadays algebra is understood basically as the general theory of algebraic oper­ ations and relations. It is characterised by a considerable intrinsic naturalness of its initial notions and problems, the unity of its methods, and a breadth that far exceeds that of its basic concepts. It is more often that its power begins to be displayed when one moves outside its own limits. This characteristic ability is seen when one investigates not only complete operations, but partial operations. To a considerable extent these are related to algebraic operators and algebraic operations. The tendency to ever greater generality is amongst the reasons that playa role in explaining this development. But other important reasons play an even greater role. Within this same theory of total operations (that is, operations defined everywhere), there persistently arises in its different sections a necessity of examining the emergent feature of various partial operations. It is particularly important that this has been found in those parts of algebra it brings together and other areas of mathematics it interacts with as well as where algebra finds applica­ tion at the very limits of mathematics. In this connection we mention the theory of the composition of mappings, category theory, the theory of formal languages and the related theory of mathematical linguistics, coding theory, information theory, and algebraic automata theory. In all these areas (as well as in others) from time to time there arises the need to consider one or another partial operation.

This is a monograph on geometrical and topological features which arise in various quantization procedures. Quantization schemes consider the feasibility of arriving at a quantum system from a classical one and these involve three major procedures viz. i) geometric quantization, ii) Klauder quantization, and iii) stochastic quanti­ zation. In geometric quantization we have to incorporate a hermitian line bundle to effectively generate the quantum Hamiltonian operator from a classical Hamil­ tonian. Klauder quantization also takes into account the role of the connection one-form along with coordinate independence. In stochastic quantization as pro­ posed by Nelson, Schrodinger equation is derived from Brownian motion processes; however, we have difficulty in its relativistic generalization. It has been pointed out by several authors that this may be circumvented by formulating a new geometry where Brownian motion proceses are considered in external as well as in internal space and, when the complexified space-time is considered, the usual path integral formulation is achieved. When this internal space variable is considered as a direc­ tion vector introducing an anisotropy in the internal space, we have the quantization of a Fermi field. This helps us to formulate a stochastic phase space formalism when the internal extension can be treated as a gauge theoretic extension. This suggests that massive fermions may be considered as Skyrme solitons. The nonrelativistic quantum mechanics is achieved in the sharp point limit.

Convergence has gained an enormous amount of attention in media studies within the last several years. It is used to describe the merging of formerly distinct functions, markets and fields of application, which has changed the way companies operate and consumers perceive and process media content. These transformations have not only led business practices to change and required companies to adapt to new conditions, they also continue to have a lasting impact on research in this area. This book's main purpose is to shed some light on crucial phenomena of media and convergence management, while also addressing more specific issues brought about by innovations related to media, technologies, industries, business models, consumer behavior and content management.This book gathers insights from renowned academic researchers and pursues a highly interdisciplinary approach. It will serve as a valuable reference guide for students, practitioners and researchers interested in media convergence processes.

This volume is an English translation of'Cohomologie Galoisienne'. The original edition (Springer LN5, 1964) was based on the notes, written with the help of Michel Raynaud, of a course I gave at the College de France in 1962-1963. In the present edition there are numerous additions and one suppression: Verdier's text on the duality of profinite groups. The most important addition is the photographic reproduction of R. Steinberg's'Regular elements of semisimple algebraic groups', Publ. Math. LH.E.S., 1965. I am very grateful to him, and to LH.E.S., for having authorized this reproduction. Other additions include: - A proof of the Golod-Shafarevich inequality (Chap. I, App. 2). - The'resume de cours'of my 1991-1992 lectures at the College de France on Galois cohomology of k(T) (Chap. II, App.). - The'resume de cours'of my 1990-1991 lectures at the College de France on Galois cohomology of semisimple groups, and its relation with abelian cohomology, especially in dimension 3 (Chap. III, App. 2). The bibliography has been extended, open questions have been updated (as far as possible) and several exercises have been added. In order to facilitate references, the numbering of propositions, lemmas and theorems has been kept as in the original 1964 text. Jean-Pierre Serre Harvard, Fall 1996 Table of Contents Foreword........................................................ V Chapter I. Cohomology of profinite groups §1. Profinite groups............................... 3..............

Following the concept of the EMS series this volume sets out to familiarize the reader to the fundamental ideas and results of modern ergodic theory and to its applications to dynamical systems and statistical mechanics. The exposition starts from the basic of the subject, introducing ergodicity, mixing and entropy. Then the ergodic theory of smooth dynamical systems is presented - hyperbolic theory, billiards, one-dimensional systems and the elements of KAM theory. Numerous examples are presented carefully along with the ideas underlying the most important results. The last part of the book deals with the dynamical systems of statistical mechanics, and in particular with various kinetic equations. This book is compulsory reading for all mathematicians working in this field, or wanting to learn about it.

Preface Among the various branches of mathematics, number theory is characterized to a lesser degree by its primary subject ('integers') than by a psychologi­ cal attitude. Actually, number theory also deals with rational, algebraic, and transcendental numbers, with some very specific analytic functions (such as Dirichlet series and modular forms), and with some geometric objects (such as lattices and schemes over Z). The question whether a given article belongs to number theory is answered by its author's system of values. If arithmetic is not there, the paper will hardly be considered as number-theoretical, even if it deals exclusively with integers and congruences. On the other hand, any mathematical tool, say, homotopy theory or dynamical systems may become an important source of number-theoretical inspiration. For this reason, com­ binatorics and the theory of recursive functions are not usually associated with number theory, whereas modular functions are. In this report we interpret number theory broadly. There are compelling reasons to adopt this viewpoint. First of all, the integers constitute (together with geometric images) one of the primary subjects of mathematics in general. Because of this, the history of elementary number theory is as long as the history of all mathematics, and the history of modern mathematic began when'numbers'and'figures'were united by the concept of coordinates (which in the opinion of LR. Shafarevich also forms the basic idea of algebra).

Early in this century, the newly discovered x-ray diffraction by crystals caused a complete change in crystallography and in the whole science of the atomic structure of matter, thus giving a new impetus to the development of solid-state physics. Crystallographic methods, primarily x-ray diffraction analysis, pene­ trated into materials sciences, molecular physics, and chemistry, and also into may other branches of science. Later, electron and neutron diffraction structure analyses became important since they not only complement x-ray data, but also supply new information on the atomic and the real structure of crystals. Electron microscopy and other modern methods of investigating matte- optical, electronic paramagnetic, nuclear magnetic, and other resonance tech­ niques - yield a large amount of information on the atomic, electronic, and real crystal structures. Crystal physics has also undergone vigorous development. Many remark­ able phenomena have been discovered in crystals and then found various practical applications. Other important factors promoting the development of crystallography were the elaboration of the theory of crystal growth (which brought crystallography closer to thermodynamics and physical chemistry) and the development of the various methods of growing synthetic crystals dictated by practical needs. Man­ made crystals became increasingly important for physical investigations, and they rapidly invaded technology. The production of synthetic crystals made a tremendous impact on the traditional branches: the mechanical treatment of materials, precision instrument making, and the jewelry industry.

In this chapter we are largely influenced in our choice of material by the demands of the rest of the book. However, we take the view that this is an opportunity for the student to grasp basic categorical notions which permeate so much of mathematics today, including, of course, algebraic topology, so that we do not allow ourselves to be rigidly restricted by our immediate objectives. A reader totally unfamiliar with category theory may find it easiest to restrict his first reading of Chapter II to Sections 1 to 6; large parts of the book are understandable with the material presented in these sections. Another reader, who had already met many examples of categorical formulations and concepts might, in fact, prefer to look at Chapter II before reading Chapter I. Of course the reader thoroughly familiar with category theory could, in principal, omit Chapter II, except perhaps to familiarize himself with the notations employed. In Chapter III we begin the proper study of homological algebra by looking in particular at the group ExtA(A, B), where A and Bare A-modules. It is shown how this group can be calculated by means of a projective presentation of A, or an injective presentation of B; and how it may also be identified with the group of equivalence classes of extensions of the quotient module A by the submodule B.

Moderne Kommunikationstechnologien wie das Internet oder die Mobiltelefonie eröffnen neue Dimensionen der Kundenansprache und -bindung sowie der Optimierung von Geschäftsprozessen. Wer es versteht, diese Technologien effizient zu nutzen und sie in die Unternehmensstrategie zu integrieren, wird auch in enger werdenden Märkten erfolgreich sein. Dieses Praxishandbuch wendet sich an Führungskräfte in Produktion, Handel und Dienstleistung. Es soll ihnen helfen, die teilweise verwirrenden technischen Begriffe - soweit notwendig - zu durchschauen, vor allem aber die Potenziale neuer Technologien zu erkennen und diese gezielt einzusetzen. Das Handbuch beschreibt hierfür die Konzepte, gibt - soweit möglich - Rezepte und veranschaulicht beides durch zahlreiche Beispiele aus der Praxis verschiedener Unternehmen.

Some Historical Background This book deals with the cohomology of groups, particularly finite ones. Historically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homo­ logical algebra and algebraic K-theory. It arose primarily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work ofH. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the meanings of the low dimensional homology groups of a space X. For example, if the universal cover of X was three connected, it was known that H2(X; A.) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N

This book addresses the various challenges and open questions relating to CAN communication networks. Opening with a short introduction into the fundamentals of CAN, the book then examines the problems and solutions for the physical layout of networks, including EMC issues and topology layout. Additionally, a discussion of quality issues with a particular focus on test techniques is presented. Each chapter features a collection of illuminating insights and detailed technical information supplied by a selection of internationally-regarded experts from industry and academia. Features: presents thorough coverage of architectures, implementations and application of CAN transceiver, data link layer and so-called higher layer software; explains CAN EMC characteristics and countermeasures, as well as how to design CAN networks; demonstrates how to practically apply and test CAN systems; includes examples of real networks from diverse applications in automotive engineering, avionics, and home heating technology.

Southeast Asia constitutes one of the world's most extended rainforest regions. It is characterized by a high degree of biodiversity and contains a large variety of endemic species. Moreover, these forests provide a number of important and sin­ gular ecosystem services, like erosion protection and provision of high quality wa­ ter, which cannot be replaced by alternative ecosystems. However, various forms of encroachment, mostly those made by human interventions, seriously threaten the continuance of rainforests in this area. There is ample evidence that the rainforest resources, apart from large scale commercial logging, are exposed to danger particularly from its margin areas. These areas, which are characterized by intensive man-nature interaction, have been identified as extremely fragile systems. The dynamic equilibrium that bal­ ances human needs and interventions on the one hand, and natural regeneration capacity on the other, is at stake. The decrease of rainforest resources is, to a sub­ stantial degree, connected with the destabilization of these systems. Accordingly, the search for measures and processes, which prevent destabilization and promote stability is regarded as imperative. This refers to both the human and the natural part of the forest margin ecosystem.

In algebraic topology some classical invariants - such as Betti numbers and Reidemeister torsion - are defined for compact spaces and finite group actions. They can be generalized using von Neumann algebras and their traces, and applied also to non-compact spaces and infinite groups. These new L2-invariants contain very interesting and novel information and can be applied to problems arising in topology, K-Theory, differential geometry, non-commutative geometry and spectral theory. It is particularly these interactions with different fields that make L2-invariants very powerful and exciting. The book presents a comprehensive introduction to this area of research, as well as its most recent results and developments. It is written in a way which enables the reader to pick out a favourite topic and to find the result she or he is interested in quickly and without being forced to go through other material.