Kategoria BISAC: Mathematics >> Geometry - General

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local...

Aufbauend auf Grundkenntnissen der Analysis und der linearen Algebra behandelt dieses Lehrbuch die Geometrie der Kegel in geordneten normierten Raumen. Einerseits werden grundlegende Konzepte wie geordnete Vektorraume erlautert, andererseits werden - Grundkenntnisse in der Funktionalanalysis vorausgesetzt - Eigenschaften von Kegeln und deren dualen Kegeln in normierten Raumen systematisch untersucht sowie Kegel im Raum der linearen stetigen Operatoren behandelt.

Diese Ubersetzung vereint die beiden kleinen (in Russisch erschienenen) Broschuren "Einfuhrung in die Theorie der Kegel...

This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions.

Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of...

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems - those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas. It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad.

Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions. The author uses a...

This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of...

In Minkowski-Space the space-time of special relativity is discussed on the basis of fundamental results of space-time theory. This idea has the consequence that the Minkowski-space can be characterized by 5 axioms, which determine its geometrical and kinematical structure completely. In this sense Minkowski-Space is a prolegomenon for the formulation of other branches of special relativity, like mechanics, electrodynamics, thermodynamics etc. But these applications are not subjects of this book.

Contents

Basic properties of...

This book provides concise descriptions of the various solutions of transition curves, which can be used in geometric design of roads and highways. It presents mathematical methods and curvature functions for defining transition curves.

Sowohl im Studium als auch in der taglichen Arbeit benotigt der Physiker eine Vielzahl mathematischer Methoden, die uber die Methoden aus den Grundvorlesungen der Analysis und linearen Algebra hinausgehen. Das vorliegende Buch baut auf diesen Vorlesungen auf und stellt die grundlegenden und jeweils einfuhrenden Themen aus der Funktionentheorie, der Funktionalanalysis, der Theorie orthogonaler Polynome und Funktionen, der Fouriertheorie, der Tensorrechnung und der Distributionen dar. Bei der sehr kompakten Darstellung des Stoffes wurde darauf geachtet eine einheitliche und gebrauchliche...

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They...