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Differential Geometry and Mathematical Physics: Lectures given at the Meetings of the Belgian Contact Group on Differential Geometry held at Liège, May 2-3, 1980 and at Leuven, February 6-8, 1981 by M. Cahen, M. Wilde, L. Lemaire, L. Vanhecke
English | PDF | 1983 | 187 Pages | ISBN : 9027715084 | 13.2 MB
This volume contains the text of the lectures which were given at the Differential Geometry Meeting held at Liege in 1980 and at the Differential Geometry Meeting held at Leuven in 1981. The first of these meetings was more orientated toward mathematical physics; the second has a stronger flavour of analysis. The Editors are pleased to thank the lectures who contributed scientifically to these two meetings. They are also grateful to Professor M. F1ato who has encouraged publication of these contributions in the Mathematical Physics Studies Series. We also thank the F.N.R.S. who supported financially the Contact group in differential geometry. The Universite de Liege and the Katholieke Universiteit Leuven which have given us a warm hospitality have contributed to the success of these meetings. We express our gratitude. The Editors. M. Caken et al. (6ds.), Differential Geametry and Mathematical Physics, vii. vii Copyright e 1983 by D. Reidel Publishing Company. Lectures given at the Meeting of the Belgian Contact Group on Differential Geometry held at Liege, May 2-3,1980 SIMULTANEOUS DEFORMATIONS OF A LIE ALGEBRA AND ITS MODULES D. Arnal University of Dijon INTRODUCTION We expose here some results which are obtained by a team at the University of Dijon. This team included Jean-Claude Cortet, Georges Pinczon and myself.

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Differential Geometry and Relativity: A Volume in Honour of André Lichnerowicz on His 60th Birthday by M. Cahen, M. Flato
English | PDF | 1976 | 302 Pages | ISBN : 9027707456 | 34.2 MB
On the occasion of the sixtieth birthday of Andre Lichnerowicz a number of his friends, many of whom have been his students or coworkers, decided to celebrate this event by preparing a jubilee volume of contributed articles in the two main fields of research marked by Lichnerowicz's work, namely differential geometry and mathematical physics. Limitations of space and time did not enable us to include papers from all Lichnerowicz's friends nor from all his former students. It was equally impossible to reflect in a single book the great variety of subjects tackled by Lichnerowicz. In spite of these limitations, we hope that this book reflects some of the present trends of fields in which he worked, and some of the subjects to which he contributed in his long - and not yet finished - career. This career was very much marked by the influence of his masters, Elie Cartan who introduced him to research in mathematics, mainly in geometry and its relations with mathematical physics, and Georges Darmois who developed his interest for mechanics and physics, especially the theory of relativity and electromagnetism. This par ticular combination, and his personal talent, made of him a natural scientific heir and continuator of the French mathematical physics school in the tradition of Henri Poincare. Some of his works would even be best qualified by a new field name, that of physical ma thematics: branches of pure mathematics entirely motivated by physics.

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Differential Geometry: Basic Notions and Physical Examples by Marcelo Epstein
English | PDF (True) | 2014 | 147 Pages | ISBN : 3319069195 | 1.9 MB
Differential Geometry offers a concise introduction to some basic notions of modern differential geometry and their applications to solid mechanics and physics.

Concepts such as manifolds, groups, fibre bundles and groupoids are first introduced within a purely topological framework. They are shown to be relevant to the description of space-time, configuration spaces of mechanical systems, symmetries in general, microstructure and local and distant symmetries of the constitutive response of continuous media.
Once these ideas have been grasped at the topological level, the differential structure needed for the description of physical fields is introduced in terms of differentiable manifolds and principal frame bundles. These mathematical concepts are then illustrated with examples from continuum kinematics, Lagrangian and Hamiltonian mechanics, Cauchy fluxes and dislocation theory.
This book will be useful for researchers and graduate students in science and engineering.
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Differential Geometry in the Large: Seminar Lectures New York University 1946 and Stanford University 1956 by Heinz Hopf
English | PDF | 1983 | 192 Pages | ISBN : 3540120041 | 11.9 MB
These notes consist of two parts: 1) Selected Topics in Geometry, New York University 1946, Notes by Peter Lax. 2) Lectures on Differential Geometry in the Large, Stanford University 1956, Notes by J. W. Gray. They are reproduced here with no essential change. Heinz Hopf was a mathematician who recognized important mathema tical ideas and new mathematical phenomena through special cases. In the simplest background the central idea or the difficulty of a problem usually becomes crystal clear. Doing geometry in this fashion is a joy. Hopf's great insight allows this approach to lead to serious ma thematics, for most of the topics in these notes have become the star ting-points of important further developments. I will try to mention a few. It is clear from these notes that Hopf laid the emphasis on poly hedral differential geometry. Most of the results in smooth differen tial geometry have polyhedral counterparts, whose understanding is both important and challenging. Among recent works I wish to mention those of Robert Connelly on rigidity, which is very much in the spirit of these notes (cf. R. Connelly, Conjectures and open questions in ri gidity, Proceedings of International Congress of Mathematicians, Hel sinki 1978, vol. 1, 407-414 ) * A theory of area and volume of rectilinear'polyhedra based on de compositions originated with Bolyai and Gauss.

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Differential Geometry: Manifolds, Curves, and Surfaces: Manifolds, Curves, and Surfaces by Marcel Berger , Bernard Gostiaux
English | PDF (True) | 1988 | 487 Pages | ISBN : 0387966269 | 34.9 MB
This book consists of two parts, different in form but similar in spirit. The first, which comprises chapters 0 through 9, is a revised and somewhat enlarged version of the 1972 book Geometrie Differentielle. The second part, chapters 10 and 11, is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of physics. Geometrie Differentielle was based on a course I taught in Paris in 1969- 70 and again in 1970-71. In designing this course I was decisively influ enced by a conversation with Serge Lang, and I let myself be guided by three general ideas. First, to avoid making the statement and proof of Stokes' formula the climax of the course and running out of time before any of its applications could be discussed. Second, to illustrate each new notion with non-trivial examples, as soon as possible after its introduc tion. And finally, to familiarize geometry-oriented students with analysis and analysis-oriented students with geometry, at least in what concerns manifolds.

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Differential Geometry of Foliations: The Fundamental Integrability Problem by Bruce L. Reinhart
English | PDF | 1983 | 204 Pages | ISBN : 3642690173 | 46.7 MB
Whoever you are! How can I but offer you divine leaves . . . ? Walt Whitman The object of study in modern differential geometry is a manifold with a differ ential structure, and usually some additional structure as well. Thus, one is given a topological space M and a family of homeomorphisms, called coordinate sys tems, between open subsets of the space and open subsets of a real vector space V. It is supposed that where two domains overlap, the images are related by a diffeomorphism, called a coordinate transformation, between open subsets of V. M has associated with it a tangent bundle, which is a vector bundle with fiber V and group the general linear group GL(V). The additional structures that occur include Riemannian metrics, connections, complex structures, foliations, and many more. Frequently there is associated to the structure a reduction of the group of the tangent bundle to some subgroup G of GL(V). It is particularly pleasant if one can choose the coordinate systems so that the Jacobian matrices of the coordinate transformations belong to G. A reduction to G is called a G-structure, which is called integrable (or flat) if the condition on the Jacobians is satisfied. The strength of the integrability hypothesis is well-illustrated by the case of the orthogonal group On. An On-structure is given by the choice of a Riemannian metric, and therefore exists on every smooth manifold.

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Differential Geometry of Frame Bundles by uis A. Cordero , C. T. J. Dodson , Manuel León
English | PDF | 1989 | 234 Pages | ISBN : 0792300122 | 13.5 MB
It isn't that they can't see the solution. It is Approach your problems from the right end and begin with the answers. Then one day, that they can't see the problem perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu!ik's The Chillese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

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Differential Manifolds by Serge Lang
English | PDF | 1985 | 232 Pages | ISBN : 0387961135 | 16.6 MB
The present volume supersedes my Introduction to Differentiable Manifolds written a few years back. I have expanded the book considerably, including things like the Lie derivative, and especially the basic integration theory of differential forms, with Stokes' theorem and its various special formulations in different contexts. The foreword which I wrote in the earlier book is still quite valid and needs only slight extension here. Between advanced calculus and the three great differential theories (differential topology, differential geometry, ordinary differential equations), there lies a no-man's-land for which there exists no systematic exposition in the literature. It is the purpose of this book to fill the gap. The three differential theories are by no means independent of each other, but proceed according to their own flavor. In differential topology, one studies for instance homotopy classes of maps and the possibility of finding suitable differentiable maps in them (immersions, embeddings, isomorphisms, etc.). One may also use differentiable structures on topological manifolds to determine the topological structure of the manifold (e.g. it la Smale [26]).

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Johannes Kabatek, "Differential Object Marking in Romance: The third wave "
English | ISBN: 3110646560 | 2021 | 379 pages | EPUB | 2 MB
After a "first wave" of traditional studies on prepositional accusatives and a "second wave" exploring the typological dimensions of Differential Object Marking in Bossong's footsteps, a new line of research is currently introducing new methods, deepening the level of analysis, and offering new perspectives on the issue. This volume presents 11 innovative, original contributions representative of this "third wave" of studies on DOM in Romance.

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Differential Topology by Morris W. Hirsch
English | PDF | 1976 | 230 Pages | ISBN : 0387901485 | 18.4 MB
This book presents some of the basic topological ideas used in studying differentiable manifolds and maps. Mathematical prerequisites have been kept to a minimum; the standard course in analysis and general topology is adequate preparation. An appendix briefly summarizes some of the back ground material. In order to emphasize the geometrical and intuitive aspects of differen tial topology, I have avoided the use of algebraic topology, except in a few isolated places that can easily be skipped. For the same reason I make no use of differential forms or tensors. In my view, advanced algebraic techniques like homology theory are better understood after one has seen several examples of how the raw material of geometry and analysis is distilled down to numerical invariants, such as those developed in this book: the degree of a map, the Euler number of a vector bundle, the genus of a surface, the cobordism class of a manifold, and so forth. With these as motivating examples, the use of homology and homotopy theory in topology should seem quite natural. There are hundreds of exercises, ranging in difficulty from the routine to the unsolved. While these provide examples and further developments of the theory, they are only rarely relied on in the proofs of theorems.

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Differenzhaftung im Umwandlungsrecht By Moog, Tobias
2009 | 278 Pages | ISBN: 3428130073 | PDF | 1 MB
Haften Gesellschafter persönlich für Wertdifferenzen, wenn bei Umwandlungen Unternehmen oder Unternehmensteile überbewertet wurden? Wenn ja, wie ist diese Haftung ausgestaltet? Und kann eine Haftung gegebenenfalls vermieden werden?Diese Fragen, die im März 2007 Gegenstand eines Urteils des Bundesgerichtshofs waren, werden von Tobias Moog für Verschmelzungen, Spaltungen und den Formwechsel untersucht. Das BGH-Urteil vom 12. März 2007 (II ZR302/05) und dessen kontroverse Diskussion hat hier zu erheblichem Klärungsbedarf geführt. Schließlich geht es um eine persönliche Haftung, die bei Umwandlungen in eine Kapitalgesellschaft grundsätzlich jeden Gesellschafter treffen kann. Werden im GmbH- oder im Aktienrecht Sacheinlagen überbewertet, besteht kein Zweifel, dass die Sacheinleger bei Überbewertungen für die Wertdifferenz einstehen müssen (Differenzhaftung). Auch Verschmelzungen und Spaltungen, nach einer Mindermeinung auch der Formwechsel, haben Sachgründungscharakter. Muss deshalb auch hier die Kapitalaufbringung durch eine Differenzhaftung gesichert werden?Tobias Moog kommt zunächst mit der herrschenden Ansicht zu dem Ergebnis, dass diese Frage für Verschmelzungen und Spaltungen auf eine GmbH zu bejahen ist. Aber auch für die Verschmelzung und Spaltung unter Beteiligung einer Aktiengesellschaft legt er überzeugend dar, dass entgegen der Auffassung des Bundesgerichtshofs auch Aktionäre haftbar gemacht werden können. Der Autor systematisiert die umwandlungsspezifischen Problemstellungen und bietet differenzierte Antworten, gerade was die Ausgestaltung der Haftung angeht. Stichtag und Umfang der Haftung, Minderheitenschutz und Gestaltungsmöglichkeiten werden eingehend untersucht.

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Digital Communication Systems
by Simon Haykin
English | 2021 | ISBN: 9354242464 | 652 Pages | True ePUB | 5.1 MB

Digital Communication Systems is a comprehensive textbook, focusing on the core principles of digital communications and relating theory to practice. Starting with the background of Fourier analysis, probability theory, and stochastic processes to analyze random signals, the book covers sampling theory, pulse-amplitude modulation, pulse-code modulation, delta modulation, matched filter, intersymbol interference, and adaptive equalization. It then discusses passband digital modulation techniques such as ASK, PSK, FSK, and QAM, followed by multiple access techniques such as FDMA, TDMA, and CDMA. Lastly, it discourses on information theory in detail and various coding schemes to control the occurrences of errors in communication systems.

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Digital Degrowth: Technology in the Age of Survival
by Michael Kwet
English | 2024 | ISBN: 0745349862 | 321 Pages | PDF | 6.46 MB

'A fascinating book that takes degrowth in new directions' - Jason Hickel, author of Less is More
'A must-read for anyone who wants to know the brutal truth of digital colonialism driven by the American empire' - Kohei Saito, author of Slow Down
The world is racing toward an irreversible ecological catastrophe. Environmental science makes clear that humans must reduce total material resource use, requiring a radical redistribution of wealth within and between countries. Yet little attention has been paid to how the digital economy fits into this equation.
Michael Kwet, a leading expert on digital colonialism, presents a new paradigm for the digital society. Merging the science of degrowth with a global analysis of the high-tech economy, he argues that digital capitalism and colonialism must be abolished quickly. In Digital Degrowth, Kwet maps out a path to a people's tech future. He calls for direct action against Silicon Valley, US imperialism and power elites everywhere in order to realize a radically egalitarian digital society that fosters equality in harmony with nature.

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Digital Degrowth: Technology in the Age of Survival
by Michael Kwet
English | 2024 | ISBN: 0745349862 | 321 Pages | True ePUB | 5.03 MB

'A fascinating book that takes degrowth in new directions' - Jason Hickel, author of Less is More
'A must-read for anyone who wants to know the brutal truth of digital colonialism driven by the American empire' - Kohei Saito, author of Slow Down
The world is racing toward an irreversible ecological catastrophe. Environmental science makes clear that humans must reduce total material resource use, requiring a radical redistribution of wealth within and between countries. Yet little attention has been paid to how the digital economy fits into this equation.
Michael Kwet, a leading expert on digital colonialism, presents a new paradigm for the digital society. Merging the science of degrowth with a global analysis of the high-tech economy, he argues that digital capitalism and colonialism must be abolished quickly. In Digital Degrowth, Kwet maps out a path to a people's tech future. He calls for direct action against Silicon Valley, US imperialism and power elites everywhere in order to realize a radically egalitarian digital society that fosters equality in harmony with nature.

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Digital Diplomacy in the OSCE Region: From Theory to Practice
by Erman Akıllı, Burak Güneş
English | 2024 | ISBN: 303150965X | 168 Pages | True PDF | 5.1 MB

This edited volume examines the practices and applications of digital diplomacy in the OSCE Region. As a security organization, the Organization for Security and Cooperation in Europe (OSCE) prioritizes its member states' cyber security and cyberspace activities. The book examines two key areas where digital diplomacy challenges traditional diplomatic practices of the OSCE member States: institutional adaptation and policy innovation in the OSCE Region. It (1) investigates how capable and motivated foreign ministries are at the institutional level to shift to digital diplomacy, and (2) explores how digital diplomacy affects the fundamental diplomatic tasks of representation, communication, and relationship management at the policy level.
Technological advances in IT and the Internet's widespread introduction in the wake of the 2000s provided new territories to conquer for states to pursue their interests. Moreover, technological developments and media attention enhanced information flow and communication through new platforms like online encyclopedias (i.e., Wikipedia), video-sharing sites (i.e., YouTube), and social media platforms (i.e., Facebook, Instagram, Twitter). Because of these transformations, public opinion became influential in diplomacy, and a greater need to include foreign publics as part of foreign policy goals emerged.
Introducing case studies from several OSCE countries, presented by an international group of authors, this book provides a timely response to current affairs and policy debates by providing pluralistic perspectives from different countries and disciplines, such as international relations, political science, international law, and political economy). It will appeal to students, researchers, and scholars of the aforementioned disciplines, as well as policy-makers and practitioners interested in a better understanding of digital democracy and digital diplomacy in the OSCE region.

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