0.1 Introduction These lecture notes describe a new development in the calculus of variations which is called Aubry-Mather-Theory. The starting point for the theoretical physicist Aubry was a model for the descrip tion of the motion of electrons in a two-dimensional crystal. Aubry investigated a related discrete variational problem and the corresponding minimal solutions. On the other hand, Mather started with a specific class of area-preserving annulus mappings, the so-called monotone twist maps. These maps appear in mechanics as Poincare maps. Such maps were studied by Birkhoff during the 1920s in several papers. In 1982, Mather succeeded to make essential progress in this field and to prove the existence of a class of closed invariant subsets which are now called Mather sets. His existence theorem is based again on a variational principle. Although these two investigations have different motivations, they are closely re lated and have the same mathematical foundation. We will not follow those ap proaches but will make a connection to classical results of Jacobi, Legendre, Weier strass and others from the 19th century. Therefore in Chapter I, we will put together the results of the classical theory which are the most important for us. The notion of extremal fields will be most relevant. In Chapter II we will investigate variational problems on the 2-dimensional torus. We will look at the corresponding global minimals as well as at the relation be tween minimals and extremal fields. In this way, we will be led to Mather sets.
This second edition has a unique approach that provides a broad and wide introduction into the fascinating area of probability theory. It starts on a fast track with the treatment of probability theory and stochastic processes by providing short proofs. The last chapter is unique as it features a wide range of applications in other fields like Vlasov dynamics of fluids, statistics of circular data, singular continuous random variables, Diophantine equations, percolation theory, random Schrödinger operators, spectral graph theory, integral geometry, computer vision, and processes with high risk.Many of these areas are under active investigation and this volume is highly suited for ambitious undergraduate students, graduate students and researchers.
This book offers a rigorous empirical and theoretical analysis of an important dimension of European integration - the implementation of EU legislation and its effect in the wake of the accession of ten new member states to the EU in 2004. The authors concentrate on the key field of social policy, which is of vital interest for the viability of the welfare state and the future of labour law standards in Europe. Following on from a previous prize-winning study, Complying with Europe: EU Harmonization and Soft Law in the Member States, this new volume looks at how EU social legislation works in practice, particularly in Central and Eastern European countries. The authors offer in-depth empirical case studies of three of the most significant pieces of EU social legislation: the Working Time Directive, the Equal Treatment Directive and the Employment Equality Directive. Their analysis makes it possible for the authors to make useful generalizations for the policy field as a whole.
The book series European Studies in the Caucasus offers innovative perspectives on regional studies of the Caucasus. By embracing the South Caucasus as well as Turkey and Russia, it moves away from a traditional viewpoint of European Studies that considers the countries of the region as objects of Europeanization. This second volume demonstrates this by looking into forms of inter-regionalism in the Black Sea–South Caucasus area in fields of economic cooperation, Europeanization of energy and environmental policies, discussing how the region is addressed in the elaboration of a new German Eastern Policy. In the section on norm diffusion, the contributors assess the normative power strategy of the EU and its paradoxes in the region, its impact on civil society development in Armenia, and democracy promotion in Georgia. In the section on legal approximation, issues of a global climate change regime and competition law in Georgia as well as penitentiary governance reform in the South Caucasus according to EU standards and policies are analyzed. All contributions also review regional or local contestations for the topics discussed here.
Foundations of European Politics: A Comparative Approach offers an accessible introduction to European politics using a coherent comparative and analytical framework. It presents students with the basic theoretical and empirical toolkit of social scientific researchers, and explains how ananalytic approach can be used to understand both domestic and EU-level policy-making in Europe.The book draws on cutting edge research from all areas of European politics - from national and EU institutions, to political behaviour and policy-making - and uses case studies and examples throughout to help students compare different electoral systems, parties and governments across Europe.The book is structured thematically in five parts, beginning with theoretical foundations; moving on to examine citizens and voters, elections and parties, governments and policy; and finally covering the rule of law, democracy and backsliding.Digital formats and resourcesFoundations of European Politics: A Comparative Approach is available for students and institutions to purchase in a variety of formats, and is supported by online resources.DT The e-book offers a mobile experience and convenient access along with functionality tools, navigation features and links that offer extra learning support: www.oxfordtextbooks.co.uk/ebooks http://www.oxfordtextbooks.co.uk/ebooksDT Online resources for students include: multiple choice questions, web links, essay questions, and data descriptions and data exercises.DT Online resources for lecturers include: adaptable PowerPoint slides, test bank questions, figures and tables from the book.
This book highlights state-of-the-art qubit implementations in semiconductors and provides an extensive overview of this newly emerging field. Semiconductor nanostructures have huge potential as future quantum information devices as they provide various ways of qubit implementation (electron spin, electronic excitation) as well as a way to transfer quantum information from stationary qubits to flying qubits (photons). Therefore, this book unites contributions from leading experts in the field, reporting cutting-edge results on spin qubit preparation, read-out and transfer. The latest theoretical as well as experimental studies of decoherence in these quantum information systems are also provided. Novel demonstrations of complex flying qubit states and first applications of semiconductor-based quantum information devices are given, too.
This study has two central research questions: Do democracy profiles affect policy performance? And what causes democracy profiles? Oliver Schlenkrich conceptualizes and measures different democracy profiles (e.g., libertarian-majoritarian or egalitarian-majoritarian democracies) based on trade-offs between the central democracy dimensions of political freedom, political equality, and political and legal control. In addition, the study conceptually and empirically develops a typology of political performance. Regarding the first research question, the empirical analyses of about 80 democracies from 1974 to 2017 indicate that there is not an overall better performing democracy profile. Thereby, the democracy profiles do not have an immediate effect, instead their effects require a longer period of time to manifest. With respect to the second research question, the empirical findings show that several structural and cultural factors are relevant (e.g., British heritage or a competitive culture). This work is mainly based on Bayesian statistics to cope with the complexity of the data and models. About the authorOliver Schlenkrich works currently on the DFG research project ‘Causes of Transformation and Democracy Profiles: Empirical Findings of the Democracy Matrix’ located at the Institute of Political Science and Sociology, University of Wuerzburg, Germany. His research interests concern democracy, political culture, political participation, quality of statehood, and quantitative methods.
Lonely Planet: The world's number one travel guide publisher* Lonely Planet's Great Britain is your passport to the most relevant, up-to-date advice on what to see and skip, and what hidden discoveries await you. Gaze at the graceful architecture of Canterbury Cathedral, stride around the ramparts of Edinburgh Castle or through the mountains of Wales, and soak up Roman, medieval and Victorian history - all with your trusted travel companion. Get to the heart of Great Britain and begin your journey now! Inside Lonely Planet's Great Britain: Full-colour maps and images throughout Highlights and itineraries help you tailor your trip to your personal needs and interests Insider tips to save time and money and get around like a local, avoiding crowds and trouble spots Essential info at your fingertips - hours of operation, phone numbers, websites, transit tips, prices Honest reviews for all budgets - eating, sightseeing, going out, shopping, hidden gems that most guidebooks miss Cultural insights provide a richer, more rewarding travel experience - history, art, food, drink, sport, politics Covers London, Canterbury, Southeast England, Oxford, Cotswolds, Southwest England, Cambridge, East Anglia, Birmingham, the Midlands, the Marches, Yorkshire, Manchester, Liverpool, Northwest England, The Lake District, Cumbria, Newcastle, Northeast England, Cardiff (Caerdydd), Pembrokeshire, South Wales, Hay-on-Wye, Mid-Wales, Snowdonia, North Wales, Edinburgh, Glasgow, Southern Scotland, Stirling, Central Scotland, Inverness, Northern Highlands & Islands, and more. The Perfect Choice: Lonely Planet's Great Britain is our most comprehensive guide to Britain, and is perfect for discovering both popular and off-the-beaten-path experiences. Need a city guide? Check out Lonely Planet's London for an in-depth look at all the city has to offer. About Lonely Planet: Lonely Planet is a leading travel media company and the world's number one travel guidebook brand, providing both inspiring and trustworthy information for every kind of traveller since 1973. Over the past four decades, we've printed over 145 million guidebooks and grown a dedicated, passionate global community of travellers. You'll also find our content online, and in mobile apps, video, 14 languages, nine international magazines, armchair and lifestyle books, ebooks, and more. 'Lonely Planet guides are, quite simply, like no other.' - New York Times 'Lonely Planet. It's on everyone's bookshelves, it's in every traveller's hands. It's on mobile phones. It's on the Internet. It's everywhere, and it's telling entire generations of people how to travel the world.' - Fairfax Media (Australia) *Source: Nielsen BookScan: Australia, UK, USA, 5/2016-4/2017 eBook Features: (Best viewed on tablet devices and smartphones) Downloadable PDF and offline maps prevent roaming and data charges Effortlessly navigate and jump between maps and reviews Add notes to personalise your guidebook experience Seamlessly flip between pages Bookmarks and speedy search capabilities get you to key pages in a flash Embedded links to recommendations' websites Zoom-in maps and images Inbuilt dictionary for quick referencing Important Notice: The digital edition of this book may not contain all of the images found in the physical edition.
Do nation-states act to facilitate or limit immigration and integration, how and why? How do nation-states themselves transform in understanding and interpreting rights respond to immigration? Does the European Union make a difference in terms of how immigrants are perceived or how they act as stakeholders in liberal democracies?
Blockchains have become increasingly important for organizing contemporary economic and social activities. This Element offers a deeper understanding of blockchains to both management scholars and practitioners, with an emphasis on blockchains' strategic implications for fundamental issues in organizing. It provides a critical examination of the core themes, theoretical lenses, and methodologies used in blockchain research in business and management scholarship. Furthermore, it offers an in-depth discussion of why and how blockchains offer a new way of organizing, providing profound implications for three major issues of strategic organization: contracting, trust, and organizational design. It also discusses several limitations of the technology in its current stage of development. Finally, this Element points to the implication of blockchains on both scholarly research and business practice.
Family firms are of particular importance for many economies. We know little about family firm buyouts and how they are different from non-family firm buyouts. Oliver Ahlers investigates this under-researched topic. After a comprehensive literature review on family firm buyouts, the focus of his book is on the key steps of the investment process such as family firm valuation and negotiations between PE investors and family sellers. Additionally, it is investigated how “soft factors” such as trust, reputation or commitment could play an important role when PE and family firms interact. Throughout the book, differences between family and non-family firm buyouts are highlighted.
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