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Symplectic Geometry
Over the course of his distinguished career, Claude Viterbo has made a number of groundbreaking contributions in the development of symplectic geometry/topology and Hamiltonian dynamics. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and pay tribute to his many significant and lasting achievements.
The Restricted Three-Body Problem and Holomorphic Curves
The book serves as an introduction to holomorphic curves in symplectic manifolds, focusing on the case of four-dimensional symplectizations and symplectic cobordisms, and their applications to celestial mechanics. The authors study the restricted three-body problem using recent techniques coming from the theory of pseudo-holomorphic curves. The book starts with an introduction to relevant topics in symplectic topology and Hamiltonian dynamics before introducing some well-known systems from celestial mechanics, such as the Kepler problem and the restricted three-body problem. After an overview of different regularizations of these systems, the book continues with a discussion of periodic orbi...
J-holomorphic Curves and Symplectic Topology
The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.
Global Differential Geometry
This volume contains a collection of well-written surveys provided by experts in Global Differential Geometry to give an overview over recent developments in Riemannian Geometry, Geometric Analysis and Symplectic Geometry. The papers are written for graduate students and researchers with a general interest in geometry, who want to get acquainted with the current trends in these central fields of modern mathematics.
Embedding Problems in Symplectic Geometry
Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems. The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.
Geometry, Spectral Theory, Groups, and Dynamics
This volume contains articles based on talks given at the Robert Brooks Memorial Conference on Geometry and Spectral Theory and the Workshop on Groups, Geometry and Dynamics held at Technion - the Israel Institute of Technology (Haifa). Robert Brooks' (1952 - 2002) broad range of mathematical interests is represented in the volume, which is devoted to various aspects of global analysis, spectral theory, the theory of Riemann surfaces, Riemannian and discrete geometry, and numbertheory. A survey of Brooks' work has been written by his close colleague, Peter Buser. Also included in the volume are articles on analytic topics, such as Szego's theorem, and on geometric topics, such as isoperimetric inequalities and symmetries of manifolds. The book is suitable for graduate studentsand researchers interested in various aspects of geometry and global analysis.
Polyfold and Fredholm Theory
This book pioneers a nonlinear Fredholm theory in a general class of spaces called polyfolds. The theory generalizes certain aspects of nonlinear analysis and differential geometry, and combines them with a pinch of category theory to incorporate local symmetries. On the differential geometrical side, the book introduces a large class of `smooth’ spaces and bundles which can have locally varying dimensions (finite or infinite-dimensional). These bundles come with an important class of sections, which display properties reminiscent of classical nonlinear Fredholm theory and allow for implicit function theorems. Within this nonlinear analysis framework, a versatile transversality and perturb...
Fixed Point Theory and Related Topics
Fixed point theory arose from the Banach contraction principle and has been studied for a long time. Its application mostly relies on the existence of solutions to mathematical problems that are formulated from economics and engineering. After the existence of the solutions is guaranteed, the numerical methodology will be established to obtain the approximated solution. Fixed points of function depend heavily on the considered spaces that are defined using the intuitive axioms. In particular, variant metrics spaces are proposed, like a partial metric space, b-metric space, fuzzy metric space and probabilistic metric space, etc. Different spaces will result in different types of fixed point t...
Alternativer Warentransport: Kann ein Segway Personal Transporter herk”mmliche Methoden ersetzen?
Diese Studie befasst sich mit dem Thema "innerbetrieblicher Warentransport," welches f r sich betrachtet ein enorm gro es Gebiet ist. Daher liegt das Hauptaugenmerk auf der Nutzung eines Segway Personal Transporters als Warentransportfahrzeug. In weiterer Folge wird untersucht, welches Potenzial das Fahrzeug f r diese Art der Anwendung beinhaltet. Dies geschieht mittels einer Technologielebenszyklusbetrachtung und einer Anwendungsstudie im Autoteilezentrum der Firma Franz Hofbauer Automobile GmbH & Co. KG. Bei dieser Studie wird ein Segway i2 mit einer Transportbox ausgestattet. Verschiedene Testauftr ge werden erstellt, diese von freiwilligen Testpersonen erledigt und die Fahrzeit gemessen. In weiterer Folge wird die fiktive Situation analysiert, die Firma SEGWAY Deutschland wolle dieses Fahrzeug als Prozesstechnologie anbieten. Die f nf Schritte der Substitutionsplanung finden hierbei Anwendung und verdeutlichen die Anforderungen an diese Aufgabe. Letztendlich werden alle Ergebnisse analysiert und damit die Frage beantwortet, welches Substitutions- und Entwicklungspotenzial der Segway PT f r diese Anwendung beherbergt.
Das Entwicklungs- und Substitutionspotenzial des Segway Personal Transporters mit Schwerpunkt auf dem innerbetrieblichen Transport von Waren
Inhaltsangabe:Einleitung: Der Transport von Waren in Betrieben kann auf viele Arten und Weisen geschehen. Letztlich ist dies von mehreren Faktoren abhängig: die Größe des Betriebs, der Art der Waren, der Unternehmenspolitik und vieles mehr. Daher ist auch die Auswahl der entsprechenden Hilfsmittel für den Transport sehr weit gefächert und eine Auswahl des passenden Transportmittels kann schwierig werden. Relevanz des Themas: Diese Masterarbeit soll vor allem Unternehmen von Nutzen sein, die selbst Interesse an alternativen Methoden für den innerbetrieblichen Warentransport haben. Allen voran für jene, die bereits Interesse am Segway Personal Transporter gezeigt haben. Zu diesem Zweck ...
