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The Local Structure of Algebraic K-Theory (Algebra and Applications #18)

Algebraic K-theory encodes important invariants for several mathematical disciplines, spanning from geometric topology and functional analysis to number theory and algebraic geometry. As is commonly encountered, this powerful mathematical object is very hard to calculate. Apart from Quillen's calculations of finite fields and Suslin's calculation of algebraically closed fields, few complete calculations were available before the discovery of homological invariants offered by motivic cohomology and topological cyclic homology. This book covers the connection between algebraic K-theory and Bökstedt, Hsiang and Madsen's topological cyclic homology and proves that the difference between the theories are ‘locally constant’. The usefulness of this theorem stems from being more accessible for calculations than K-theory, and hence a single calculation of K-theory can be used with homological calculations to obtain a host of ‘nearby’ calculations in K-theory. For instance, Quillen's calculation of the K-theory of finite fields gives rise to Hesselholt and Madsen's calculations for local fields, and Voevodsky's calculations for the integers give insight into the diffeomorphisms of manifolds. In addition to the proof of the full integral version of the local correspondence between K-theory and topological cyclic homology, the book provides an introduction to the necessary background in algebraic K-theory and highly structured homotopy theory; collecting all necessary tools into one common framework. It relies on simplicial techniques, and contains an appendix summarizing the methods widely used in the field. The book is intended for graduate students and scientists interested in algebraic K-theory, and presupposes a basic knowledge of algebraic topology.

Local Systems in Algebraic-Arithmetic Geometry (Lecture Notes in Mathematics #2337)

The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci.This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.

Local Theory of Nonlinear Analytic Ordinary Differential Equations (Lecture Notes in Mathematics #702)

Local Times and Excursion Theory for Brownian Motion: A Tale of Wiener and Itô Measures (Lecture Notes in Mathematics #2088)

This monograph discusses the existence and regularity properties of local times associated to a continuous semimartingale, as well as excursion theory for Brownian paths. Realizations of Brownian excursion processes may be translated in terms of the realizations of a Wiener process under certain conditions. With this aim in mind, the monograph presents applications to topics which are not usually treated with the same tools, e.g.: arc sine law, laws of functionals of Brownian motion, and the Feynman-Kac formula.

Local Variance Estimation for Uncensored and Censored Observations

Paola Gloria Ferrario develops and investigates several methods of nonparametric local variance estimation. The first two methods use regression estimations (plug-in), achieving least squares estimates as well as local averaging estimates (partitioning or kernel type). Furthermore, the author uses a partitioning method for the estimation of the local variance based on first and second nearest neighbors (instead of regression estimation). Approaching specific problems of application fields, all the results are extended and generalised to the case where only censored observations are available. Further, simulations have been executed comparing the performance of two different estimators (R-Code available!). As a possible application of the given theory the author proposes a survival analysis of patients who are treated for a specific illness.

Localization in Group Theory and Homotopy Theory and Related Topics: Battelle Seattle 1974 Seminar (Lecture Notes in Mathematics #418)

The Localization Problem in Index Theory of Elliptic Operators (Pseudo-Differential Operators #10)

The book deals with the localization approach to the index problem for elliptic operators. Localization ideas have been widely used for solving various specific index problems for a long time, but the fact that there is actually a fundamental localization principle underlying all these solutions has mostly passed unnoticed. The ignorance of this general principle has often necessitated using various artificial tricks and hindered the solution of new important problems in index theory. So far, the localization principle has been only scarcely covered in journal papers and not covered at all in monographs. The suggested book is intended to fill the gap. So far, it is the first and only monograph dealing with the topic. Both the general localization principle and its applications to specific problems, existing and new, are covered. The book will be of interest to working mathematicians as well as graduate and postgraduate university students specializing in differential equations and related topics.​

Localized Excitations in Nonlinear Complex Systems: Current State of the Art and Future Perspectives (Nonlinear Systems and Complexity #7)

The study of nonlinear localized excitations is a long-standing challenge for research in basic and applied science, as well as engineering, due to their importance in understanding and predicting phenomena arising in nonlinear and complex systems, but also due to their potential for the development and design of novel applications. This volume is a compilation of chapters representing the current state-of-the-art on the field of localized excitations and their role in the dynamics of complex physical systems.

Localized Quality of Service Routing for the Internet (The Springer International Series in Engineering and Computer Science #739)

The exponential growth of Internet brings to focus the need to control such large scale networks so that they appear as coherent, almost intelligent, organ­ isms. It is a challenge to regulate such a complex network of heterogeneous elements with dynamically changing traffic conditions. To make such a sys­ tem reliable and manageable, the decision making should be decentralized. It is desirable to find simple local rules and strategies that can produce coherent and purposeful global behavior. Furthermore, these control mechanisms must be adaptive to effectively respond to continually varying network conditions. Such adaptive, distributed, localized mechanisms would provide a scalable so­ lution for controlling large networks. The need for such schemes arises in a variety of settings. In this monograph, we focus on localized approach to quality of service routing. Routing in the current Internet focuses primarily on connectivity and typi­ cally supports only the "best-effort" datagram service. The routing protocols deployed such as OSPF use the shortest path only routing paradigm, where routing is optimized for a single metric such as hop count or administrative weight. While these protocols are well suited for traditional data applications such as ftp and telnet, they are not adequate for many emerging applications such as IP telephony, video on demand and teleconferencing, which require stringent delay and bandwidth guarantees. The "shortest paths" chosen for the "best effort" service may not have sufficient resources to provide the requisite service for these applications.

Localized States in Physics: Solitons and Patterns

Systems driven far from thermodynamic equilibrium can create dissipative structures through the spontaneous breaking of symmetries. A particularly fascinating feature of these pattern-forming systems is their tendency to produce spatially confined states. These localized wave packets can exist as propagating entities through space and/or time. Various examples of such systems will be dealt with in this book, including localized states in fluids, chemical reactions on surfaces, neural networks, optical systems, granular systems, population models, and Bose-Einstein condensates.This book should appeal to all physicists, mathematicians and electrical engineers interested in localization in far-from-equilibrium systems. The authors - all recognized experts in their fields - strive to achieve a balance between theoretical and experimental considerations thereby giving an overview of fascinating physical principles, their manifestations in diverse systems, and the novel technical applications on the horizon.

Locally Conformal Kähler Geometry (Progress in Mathematics #155)

. E C, 0 '1 . be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.

Locally Convex Quasi *-Algebras and their Representations (Lecture Notes in Mathematics #2257)

This book offers a review of the theory of locally convex quasi *-algebras, authored by two of its contributors over the last 25 years. Quasi *-algebras are partial algebraic structures that are motivated by certain applications in Mathematical Physics. They arise in a natural way by completing a *-algebra under a locally convex *-algebra topology, with respect to which the multiplication is separately continuous. Among other things, the book presents an unbounded representation theory of quasi *-algebras, together with an analysis of normed quasi *-algebras, their spectral theory and a study of the structure of locally convex quasi *-algebras. Special attention is given to the case where the locally convex quasi *-algebra is obtained by completing a C*-algebra under a locally convex *-algebra topology, coarser than the C*-topology.Introducing the subject to graduate students and researchers wishing to build on their knowledge of the usual theory of Banach and/or locally convex algebras, this approach is supported by basic results and a wide variety of examples.

Locally Convex Spaces (Graduate Texts in Mathematics #269)

For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis.While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.

Locally Convex Spaces and Linear Partial Differential Equations (Grundlehren der mathematischen Wissenschaften #146)

It is hardly an exaggeration to say that, if the study of general topolog­ ical vector spaces is justified at all, it is because of the needs of distribu­ tion and Linear PDE * theories (to which one may add the theory of convolution in spaces of hoi om orphic functions). The theorems based on TVS ** theory are generally of the "foundation" type: they will often be statements of equivalence between, say, the existence - or the approx­ imability -of solutions to an equation Pu = v, and certain more "formal" properties of the differential operator P, for example that P be elliptic or hyperboJic, together with properties of the manifold X on which P is defined. The latter are generally geometric or topological, e. g. that X be P-convex (Definition 20. 1). Also, naturally, suitable conditions will have to be imposed upon the data, the v's, and upon the stock of possible solutions u. The effect of such theorems is to subdivide the study of an equation like Pu = v into two quite different stages. In the first stage, we shall look for the relevant equivalences, and if none is already available in the literature, we shall try to establish them. The second stage will consist of checking if the "formal" or "geometric" conditions are satisfied.

Locally Interacting Systems and Their Application in Biology: Proceedings of the School-Seminar on Markov Processes in Biology, Held in Pushchino, Moscow Region, March, 1976 (Lecture Notes in Mathematics #653)

Locally Mixed Symmetric Spaces (Springer Monographs in Mathematics)

What do the classification of algebraic surfaces, Weyl's dimension formula and maximal orders in central simple algebras have in common? All are related to a type of manifold called locally mixed symmetric spaces in this book. The presentation emphasizes geometric concepts and relations and gives each reader the "roter Faden", starting from the basics and proceeding towards quite advanced topics which lie at the intersection of differential and algebraic geometry, algebra and topology.Avoiding technicalities and assuming only a working knowledge of real Lie groups, the text provides a wealth of examples of symmetric spaces. The last two chapters deal with one particular case (Kuga fiber spaces) and a generalization (elliptic surfaces), both of which require some knowledge of algebraic geometry.Of interest to topologists, differential or algebraic geometers working in areas related to arithmetic groups, the book also offers an introduction to the ideas for non-experts.

Locally Semialgebraic Spaces (Lecture Notes in Mathematics #1173)

Locating Eigenvalues in Graphs: Algorithms and Applications (SpringerBriefs in Mathematics)

This book focuses on linear time eigenvalue location algorithms for graphs. This subject relates to spectral graph theory, a field that combines tools and concepts of linear algebra and combinatorics, with applications ranging from image processing and data analysis to molecular descriptors and random walks. It has attracted a lot of attention and has since emerged as an area on its own.Studies in spectral graph theory seek to determine properties of a graph through matrices associated with it. It turns out that eigenvalues and eigenvectors have surprisingly many connections with the structure of a graph. This book approaches this subject under the perspective of eigenvalue location algorithms. These are algorithms that, given a symmetric graph matrix M and a real interval I, return the number of eigenvalues of M that lie in I. Since the algorithms described here are typically very fast, they allow one to quickly approximate the value of any eigenvalue, which is a basic step in most applications of spectral graph theory. Moreover, these algorithms are convenient theoretical tools for proving bounds on eigenvalues and their multiplicities, which was quite useful to solve longstanding open problems in the area. This book brings these algorithms together, revealing how similar they are in spirit, and presents some of their main applications.This work can be of special interest to graduate students and researchers in spectral graph theory, and to any mathematician who wishes to know more about eigenvalues associated with graphs. It can also serve as a compact textbook for short courses on the topic.

Locating Lines and Hyperplanes: Theory and Algorithms (Applied Optimization #25)

Line and hyperplane location problems play an important role not only in operations research and location theory, but also in computational geometry and robust statistics. This book provides a survey on line and hyperplane location combining analytical and geometrical methods. The major portion of the text presents new results on this topic, including the extension of some special cases to all distances derived from norms and a discussion of restricted problems in the plane. Almost all results are proven in the text and most of them are illustrated by examples. Furthermore, relations to classical facility location and to problems in computational geometry are pointed out. Audience: The book is suitable for researchers, lecturers, and graduate students working in the fields of location theory or computational geometry.

Location, Scheduling, Design and Integer Programming (International Series in Operations Research & Management Science #3)

Location, scheduling and design problems are assignment type problems with quadratic cost functions and occur in many contexts stretching from spatial economics via plant and office layout planning to VLSI design and similar prob­ lems in high-technology production settings. The presence of nonlinear inter­ action terms in the objective function makes these, otherwise simple, problems NP hard. In the first two chapters of this monograph we provide a survey of models of this type and give a common framework for them as Boolean quadratic problems with special ordered sets (BQPSs). Special ordered sets associated with these BQPSs are of equal cardinality and either are disjoint as in clique partitioning problems, graph partitioning problems, class-room scheduling problems, operations-scheduling problems, multi-processor assign­ ment problems and VLSI circuit layout design problems or have intersections with well defined joins as in asymmetric and symmetric Koopmans-Beckmann problems and quadratic assignment problems. Applications of these problems abound in diverse disciplines, such as anthropology, archeology, architecture, chemistry, computer science, economics, electronics, ergonomics, marketing, operations management, political science, statistical physics, zoology, etc. We then give a survey of the traditional solution approaches to BQPSs. It is an unfortunate fact that even after years of investigation into these problems, the state of algorithmic development is nowhere close to solving large-scale real­ life problems exactly. In the main part of this book we follow the polyhedral approach to combinatorial problem solving because of the dramatic algorith­ mic successes of researchers who have pursued this approach.

Location Systems: An Introduction to the Technology Behind Location Awareness (Synthesis Lectures on Mobile & Pervasive Computing)

Advances in electronic location technology and the coming of age of mobile computing have opened the door for location-aware applications to permeate all aspects of everyday life. Location is at the core of a large number of high-value applications ranging from the life-and-death context of emergency response to serendipitous social meet-ups. For example, the market for GPS products and services alone is expected to grow to US$200 billion by 2015. Unfortunately, there is no single location technology that is good for every situation and exhibits high accuracy, low cost, and universal coverage. In fact, high accuracy and good coverage seldom coexist, and when they do, it comes at an extreme cost. Instead, the modern localization landscape is a kaleidoscope of location systems based on a multitude of different technologies including satellite, mobile telephony, 802.11, ultrasound, and infrared among others. This lecture introduces researchers and developers to the most popular technologies and systems for location estimation and the challenges and opportunities that accompany their use. For each technology, we discuss the history of its development, the various systems that are based on it, and their trade-offs and their effects on cost and performance. We also describe technology-independent algorithms that are commonly used to smooth streams of location estimates and improve the accuracy of object tracking. Finally, we provide an overview of the wide variety of application domains where location plays a key role, and discuss opportunities and new technologies on the horizon. Table of Contents: Introduction / The Global Positioning System / Infrared and Ultrasonic Systems / Location Esimation with 802.11 / Cellular-Based Systems / Other Approaches / Improving Localization Accuracy / Location-Based Applications and Services / Challenges and Opportunities / References

Location Theory: A Unified Approach

Although modern location theory is now more than 90 years old, the focus of researchers in this area has been mainly problem oriented. However, a common theory, which keeps the essential characteristics of classical location models, is still missing. This monograph addresses this issue. A flexible location problem called the Ordered Median Problem (OMP) is introduced. For all three main subareas of location theory (continuous, network and discrete location) structural properties of the OMP are presented and solution approaches provided. Numerous illustrations and examples help the reader to become familiar with this new location model. By using OMP classical results of location theory can be reproved in a more general and sometimes even simpler way. Algorithms enable the reader to solve very flexible location models with a single implementation. In addition, the code of some algorithms is available for download.

Loci - Circle and Perpendicular Bisector Examples (tactile)

This image shows two examples of loci. Diagram 1 at the top of the page shows a circle with the radiu labelled 4cm. Diagram 2 below shows and example of perpendicular bisector loci.

Locus of a point - Circle (tactile)

This diagram show a circle. The radius is labelled 2 cm and the centre is labelled D.

Loeb Measures in Practice: EMS Lectures 1997 (Lecture Notes in Mathematics #1751)

This expanded version of the 1997 European Mathematical Society Lectures given by the author in Helsinki, begins with a self-contained introduction to nonstandard analysis (NSA) and the construction of Loeb Measures, which are rich measures discovered in 1975 by Peter Loeb, using techniques from NSA. Subsequent chapters sketch a range of recent applications of Loeb measures due to the author and his collaborators, in such diverse fields as (stochastic) fluid mechanics, stochastic calculus of variations ("Malliavin" calculus) and the mathematical finance theory. The exposition is designed for a general audience, and no previous knowledge of either NSA or the various fields of applications is assumed.