الصفحة 79
الصفحة 79
Lie Theory Vol.229 : Unitary Representations and Compactifications of Symmetric Spaces
It focuses on two fundamental questions in the theory of semisimple Lie groups: the geometry of Riemannian symmetric spaces and their compactifications; and branching laws for unitary representations, i.e., restricting unitary representations to (typically, but not exclusively, symmetric) subgroups and decomposing the ensuing representations into irreducibles.Ji's introductory chapter motivates the subject of symmetric spaces and their compactifications with carefully selected examples. A discussion of Satake and Furstenberg boundaries and a survey of the geometry of Riemannian symmetric spaces in general provide a good background for the second chapter, namely, the Borel–Ji authoritative treatment of various types of compactifications useful for studying symmetric and locally symmetric spaces. Borel–Ji further examine constructions of Oshima, De Concini, Procesi, and Melrose, which demonstrate the wide applicability of compactification techniques. Kobayashi examines the important subject of branching laws. Important concepts from modern representation theory, such as Harish–Chandra modules, associated varieties, microlocal analysis, derived functor modules, and geometric quantization are introduced. Concrete examples and relevant exercises engage the reader.
Lie theory ; Vol.230 : Harmonic analysis on symmetric spaces, general Plancherel theorems
Van den Ban’s introductory chapter explains the basic setup of a reductive symmetric space along with a careful study of the structure theory, particularly for the ring of invariant differential operators for the relevant class of parabolic subgroups. Advanced topics for the formulation and understanding of the proof are covered, including Eisenstein integrals, regularity theorems, Maass–Selberg relations, and residue calculus for root systems. Schlichtkrull provides a cogent account of the basic ingredients in the harmonic analysis on a symmetric space through the explanation and definition of the Paley–Wiener theorem. Approaching the Plancherel theorem through an alternative viewpoint, the Schwartz space, Delorme bases his discussion and proof on asymptotic expansions of eigenfunctions and the theory of intertwining integrals.
Lie Sphere Geometry : With Applications to Submanifolds
Provides a clear and comprehensive modern treatment of Lie sphere geometry and its applications to the study of Euclidean submanifolds. It begins with the construction of the space of spheres, including the fundamental notions of oriented contact, parabolic pencils of spheres, and Lie sphere transformations. The link with Euclidean submanifold theory is established via the Legendre map, which provides a powerful framework for the study of submanifolds, especially those characterized by restrictions on their curvature spheres.
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.
Lie Algebras and Algebraic Groups
The theory of Lie algebras and algebraic groups has been an area of active research in the last 50 years. It intervenes in many different areas of mathematics : for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory so as to present the foundation of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the last chapters. All the prerequisites on commutative algebra and algebraic geometry are included.
Liberal Democracy : Prosperity through Freedom
Aims to show which factors have been decisive in the rise of successful countries. Never before have so many people been so well off. However, prosperity is not a law of nature; it has to be worked for. A liberal economy stands at the forefront of this success – not as a political system, but as a set of economic rules promoting competition, which in turn leads to innovation, research and enormous productivity.
Liapunov Functions and Stability in Control Theory
Presents a modern and self-contained treatment of the Liapunov method for stability analysis, in the framework of mathematical nonlinear control theory. A Particular focus is on the problem of the existence of Liapunov functions (converse Liapunov theorems) and their regularity, whose interest is especially motivated by applications to automatic control.
Leveraging applications of formal methods, verification and validation : Verification Principles ; 9th International Symposium on Leveraging Applications of Formal Methods, ISoLA 2020, Rhodes, Greece, October 20–30, 2020, Proceedings, Part I
Constitutes the refereed proceedings of the 9th International Symposium on Leveraging Applications of Formal Methods, ISoLA 2020, which was planned to take place during October 20–30, 2020, on Rhodes, Greece. The papers presented were carefully reviewed and selected for inclusion in the proceedings. Each volume focusses on an individual topic with topical section headings within the volume : Part I, Verification Principles : Modularity and (De-)Composition in Verification ; X-by-Construction: Correctness meets Probability ; 30 Years of Statistical Model Checking ; Verification and Validation of Concurrent and Distributed Systems.
Level Crossing Methods in Stochastic Models
Since its inception in 1974, the level crossing approach for analyzing a large class of stochastic models has become increasingly popular among researchers. This volume traces the evolution of level crossing theory for obtaining probability distributions of state variables and demonstrates solution methods in a variety of stochastic models including: queues, inventories, dams, renewal models, counter models, pharmacokinetics, and the natural sciences. Results for both steady-state and transient distributions are given, and numerous examples help the reader apply the method to solve problems faster, more easily, and more intuitively.
Leray–Schauder Type Alternatives, Complementarity Problems and Variational Inequalities
Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics and also has many applications in optimization, economics and engineering. The study of variational inequalities is another domain of applied mathematics with many applications to the study of certain problems with unilateral conditions. This book is the first to discuss complementarity theory and variational inequalities using Leray–Schauder type alternatives.
Lenses and Waves : Christiaan Huygens and the Mathematical Science of Optics in the Seventeenth Century
this book offers the first account of the development of Huygens’ mathematical analysis of lenses and telescopes and its significance for the origin of the wave theory of light. As Huygens applied his mathematical proficiency to practical issues pertaining to telescopes – including trying to design a perfect telescope by means of mathematical theory – his dioptrics is significant for our understanding of seventeenth-century relations between theory and practice. With this full account of Huygens’ optics, this book sheds new light on the history of seventeenth-century optics and the rise of the new mathematical sciences, as well as Huygens’ oeuvre as a whole. Students of the history of optics, of early mathematical physics, and the Scientific Revolution, will find this book enlightening.
Leibnizs Metaphysics of Time and Space
Leibniz’s metaphysics of space and time stands at the centre of his philosophy and is one of the high-water marks in the history of the philosophy of science. In this work, Futch provides the first systematic and comprehensive examination of Leibniz’s thought on this subject. In addition to elucidating the nature of Leibniz’s relationalism, the book fills a lacuna in existing scholarship by examining his views on the topological structure of space and time, including the unity and unboundedness of space and time. It is shown that, like many of his more recent counterparts, Leibniz adopts a causal theory of time where temporal facts are grounded on causal facts, and that his approach to time represents a precursor to non-tensed theories of time.
Legitimacy In European Nature Conservation Policy : Case Studies In Multilevel Governance
Focuses on the issue of legitimacy in the context of European nature conservation policy. It provides insights in the way in which democratic legitimacy is being ‘produced’ at different levels of governance. Building forth upon recent developments in democracy theory that have identified multiple forms of legitimacy, the volume observes a EU-wide shift from output legitimacy to input and throughput legitimacy. Top down policy making is increasingly meeting
Legal maxims in islamic criminal law : Theory and applications
Delves into the theoretical and practical studies of al-Qawaid al-Fiqhiyyah in Islamic legal theory. It elucidates the importance of this concept in the application of Islamic law and demonstrates how the concept relates to the objectives of Islamic law generally.
Lectures on Symplectic Geometry
Provides a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding.
Lectures on Quantum Mechanics
Presents theoretical physics with a breathtaking array of examples and anecdotes. Basdevant's style is clear and stimulating, in the manner of a brisk classroom lecture that students can follow with ease and enjoyment.
Lectures on Quantum Gravity
A primary goal was to foster interaction and communication between participants from different cultures, both in the layman’s sense of the term and in terms of approaches to quantum gravity. We hope that the links formed by students and the school will persist throughout their professional lives, continuing to promote interaction and the essential exchange of ideas that drives research forward. This volume contains improved and updated versions of the lectures given at the School. It has been prepared both as a reminder for the participants, and so that these pedagogical introductions can be made available to others who were unable to attend. We expect them to serve students of all ages well.
Lectures on Probability Theory and Statistics : Ecole d'Eté de Probabilités de Saint-Flour XXXIII - 2003
Contains two of the three lectures that were given at the 33rd Probability Summer School in Saint-Flour (July 6-23, 2003). Amir Dembo’s course is devoted to recent studies of the fractal nature of random sets, focusing on some fine properties of the sample path of random walk and Brownian motion. In particular, the cover time for Markov chains, the dimension of discrete limsup random fractals, the multi-scale truncated second moment and the Ciesielski-Taylor identities are explored. Tadahisa Funaki’s course reviews recent developments of the mathematical theory on stochastic interface models, mostly on the so-called nabla varphi interface model. The results are formulated as classical limit theorems in probability theory, and the text serves with good applications of basic probability techniques.
Lectures on Algebraic Geometry I : Sheaves, Cohomology of Sheaves, and Applications to Riemann Surfaces
This book and the following second volume is an introduction into modern algebraic geometry. In the first volume the methods of homological algebra, theory of sheaves, and sheaf cohomology are developed. These methods are indispensable for modern algebraic geometry, but they are also fundamental for other branches of mathematics and of great interest in their own.In the last chapter of volume I these concepts are applied to the theory of compact Riemann surfaces. In this chapter the author makes clear how influential the ideas of Abel, Riemann and Jacobi were and that many of the modern methods have been anticipated by them.
Lectures on Advances in Combinatorics
The main focus of these lectures is basis extremal problems and inequalities – two sides of the same coin. Additionally they prepare well for approaches and methods useful and applicable in a broader mathematical context. Highlights of the book include a solution to the famous 4m-conjecture of Erdös/Ko/Rado 1938, one of the oldest problems in combinatorial extremal theory, an answer to a question of Erdös (1962) in combinatorial number theory "What is the maximal cardinality of a set of numbers smaller than n with no k+1 of its members pair wise relatively prime?", and the discovery that the AD-inequality implies more general and sharper number theoretical inequalities than for instance Behrend's inequality.
