EMS Tracts in Mathematics Vol. 21
ISBN 978-3-03719-124-8
DOI 10.4171/124
August 2013, 225 pages, hardcover, 17 x 24 cm.
In this book dynamical systems are investigated from a geometric viewpoint. Admitting an invariant manifold is a strong geometric property of a dynamical system. This text presents rigorous results on invariant manifolds and gives examples of possible applications.
In the first part discrete dynamical systems in Banach spaces are considered. Results on the existence and smoothness of attractive and repulsive invariant manifolds are derived. In addition, perturbations and approximations of the manifolds and the foliation of the adjacent space are treated. In the second part analogous results for continuous dynamical systems in finite dimensions are established. In the third part the theory developed is applied to problems in numerical analysis and to singularly perturbed systems of ordinary differential equations.
The mathematical approach is based on the so-called graph transform, already used by Hadamard in 1901. The aim is to establish invariant manifold results in a simple setting providing quantitative estimates.
The book is targeted at researchers in the field of dynamical systems interested in precise theorems easy to apply. The application part might also serve as an underlying text for a student seminar in mathematics.
Proceedings of the Gokova Geometry-Topology Conference 2012
Published: May 2013
Paperback
153 pages
Lively and engaging articles from the lecturers and the participants of the 19th Gokova Geometry-Topology Conference, held on the shores of Gokova Bay, Turkey, in May of 2012.
This volume is part of the Gokova Geometry-Topology Conferences book series.
9781571462701
1571462708
paperback
7” x 10”
In Print
ISBN: 978-1-118-60550-9
Hardcover
572 pages
February 2014
This book presents examples that illustrate the theory of mathematical statistics and details how to apply the methods for solving problems. While other books on the topic contain problems and exercises, they do not focus on problem solving. This book fills an important niche in the statistical theory literature by providing a theory/example/problem approach. Each chapter is divided into four parts: Part I provides the needed theory so readers can become familiar with the concepts, notations, and proven results; Part II presents examples from a variety of fields including engineering, mathematics, and statistics; Part III contains the problems for solutions; and Part IV features selected problems with solutions. Within the book's nine chapters, the authors provides 200 examples and over 300 problems, and solutions are provided for approximately 10% of the problems. Chapter coverage includes: Basic Probability Theory; Statistical Distributions; Sufficient Statistics and Information in Samples; Testing Statistical Hypothesis; Statistical Estimation; Confidence and Tolerance Intervals; Large Sample Theory for Estimation and Testing; Bayesian Analysis in Testing and Estimation; and Advanced Topics in Estimation Theory.
Series: Abel Symposia, Vol. 8
2013, XX, 298 p. 23 illus., 1 illus. in color.
Hardcover version
ISBN 978-3-642-39484-3
Due: September 30, 2013
Contains survey and research papers on the very active research area of cluster algebras and related topics
Includes new results on the omnipresent triangulated categories ?
This book features survey and research papers from The Abel Symposium 2011, held in Balestrand, Norway 2011. It examines a very active research area that has had a growing influence and profound impact in many other areas of mathematics like commutative algebra, algebraic geometry, algebraic groups and combinatorics. This volume illustrates and extends such connections with algebraic geometry, cluster algebra theory, commutative algebra, dynamical systems and triangulated categories. In addition, it includes contributions on further developments in representation theory of quivers and algebras.
Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulated categories.
C. Amiot: Preprojective algebras, singularity categories and orthogonal decompositions.- L. Avramov : (Contravariant) Koszul duality for DG algebras.- R. Buchweitz: The fundamental group of a morphism in a triangulated category.- K. Erdmann: On Hochschild cohomology of weakly symmetric special biserial algebras.- D. Happel: Algebras of finite global dimension.- K. Igusa (with G. Todorov): Continuous Frobenius categories.- D.A. Jorgensen: Triangle functors from generic hypersurfaces.- Y. Kodama (with L. Williams): Combinatorics of KP solutions from the real Grassmannian.- H. Krause: Morphisms determined by objects in triangulated categories.- P. Malicki (with J. A. de la Pena and A. Skowronski): Cycle-finite module categories.- J.A. de la Pena, P. Malicki and A. Skowronski: Cycle-finite module categories.- C.M. Ringel: Distinguished bases of exceptional modules.- A. Skowronski (with P. Malicki and J. A. de la Pena): Cycle-finite module categories.- D. Speyer and H. Thomas: Acyclic cluster algebras revisited.- H. Thomas and D. Speyer: Acyclic cluster algebras revisited.- G. Todorov and K. Igusa: Continuous Frobenius categories.- L. Williams and Y. Kodama: Combinatorics of KP solutions from the real Grassmannian.- D. Zacharia and D. Happel: Algebras of finite global dimension.
Series: Fields Institute Monographs, Vol. 32
2013, XII, 175 p. 18 illus. in color.
Hardcover
ISBN 978-1-4614-8117-1
Contains more than 40 open research problems proposed to help further research
Ideal for graduate students as well as researchers in mathematics and computer science
Acts as a short introduction to important and modern parts of discrete geometry
Ideal book for a one semester course at an advanced undergraduate or graduate level course
Features proofs that cover a broad range of methods of discrete geometry, often presentable in short talks
This monograph gives a short introduction to parts of modern discrete geometry, in addition to leading the reader to the frontiers of geometric research on sphere arrangements. The readership is aimed at advanced undergraduate and early graduate students, as well as interested researchers. It contains 30 open research problems ideal for graduate students and researchers in mathematics and computer science. Additionally, this book may be considered ideal for a one-semester advanced undergraduate or graduate level course.
The core of this book is based on three lectures given by the author at the Fields Institute during the thematic program on Discrete Geometry and Applications and contains four basic topics. The first two deal with active areas that have been outstanding from the birth of discrete geometry, namely dense sphere packings and tilings. Sphere packings and tilings have a very strong connection to number theory, coding, groups, and mathematical programming. Extending the tradition of studying packings of spheres is the investigation of the monotonicity of volume under contractions of arbitrary arrangements of spheres. The third major topic can be found under the sections on ball-polyhedra that study the possibility of extending the theory of convex polytopes to the family of intersections of congruent balls. This section of the text is connected in many ways to the above-mentioned major topics as well as to some other important research areas such as that on coverings by planks (with close ties to geometric analysis). The fourth basic topic is discussed under covering balls by cylinders.