1 option
Analysis on graphs and its applications : Isaac Newton Institute for Mathematical Sciences, Cambridge, UK, January 8-June 29, 2007 / Pavel Exner [and four others], editors.
- Format:
- Book
- Series:
- Proceedings of symposia in pure mathematics ; volume 77.
- Proceedings of symposia in pure mathematics ; volume 77
- Language:
- English
- Subjects (All):
- Graph theory--Congresses.
- Graph theory.
- Quantum graphs--Congresses.
- Quantum graphs.
- Combinatorial analysis--Congresses.
- Combinatorial analysis.
- Graphic methods--Congresses.
- Graphic methods.
- Physical Description:
- 1 online resource (721 p.)
- Place of Publication:
- Providence, Rhode Island : American Mathematical Society, [2008]
- Language Note:
- English
- Summary:
- This book addresses a new interdisciplinary area emerging on the border between various areas of mathematics, physics, chemistry, nanotechnology, and computer science. The focus here is on problems and techniques related to graphs, quantum graphs, and fractals that parallel those from differential equations, differential geometry, or geometric analysis. Also included are such diverse topics as number theory, geometric group theory, waveguide theory, quantum chaos, quantum wiresystems, carbon nano-structures, metal-insulator transition, computer vision, and communication networks.This volume contains a unique collection of expert reviews on the main directions in analysis on graphs (e.g., on discrete geometric analysis, zeta-functions on graphs, recently emerging connections between the geometric group theory and fractals, quantum graphs, quantum chaos on graphs, modeling waveguide systems and modeling quantum graph systems with waveguides, control theory on graphs), as well as research articles.
- Contents:
- ""Contents""; ""Preface""; ""Vladimir A. Geyler, April 29, 1943 - April 2, 2007""; ""Chapter 1. Analysis on combinatorial graphs""; ""Review articles""; ""Nodal domains on graphs - How to count them and why?""; ""Zeta functions of weighted graphs and covering graphs""; ""Discrete geometric analysis""; ""Research articles""; ""Uniform existence of the integrated density of states for combinatorial and metric graphs over Z[sup(d)]""; ""Bartholdi zeta functions for periodic simple graphs""; ""Asymptotic properties of Markov processes on Cayley trees""; ""Chapter 2. Analysis on fractals""
- ""Review articles""""Groups and analysis on fractals""; ""Research articles""; ""Schreier spectrum of the Hanoi Towers group on three pegs""; ""On the dichotomy in the heat kernel two sided estimates""; ""Tube formulas for self-similar fractals""; ""Existence of eigenforms on nicely separated fractals""; ""Chapter 3. Analysis on quantum graphs""; ""Review articles""; ""Trace formulae for quantum graphs""; ""Quantum graphs with spin Hamiltonians""; ""Quantum graphs and quantum chaos""; ""Quantum graphs: an introduction and a brief survey""; ""Research articles""
- ""Localization in a quasiperiodic model on quantum graphs""""Equilateral quantum graphs and boundary triples""; ""A conditionally convergent trace formula for quantum graphs""; ""Chapter 4. Applications""; ""Review articles""; ""Control problems on quantum graphs""; ""Leaky quantum graphs: a review""; ""Thin tubes in mathematical physics, global analysis and spectral geometry""; ""Simulation of quantum graphs by microwave networks""; ""Twisting versus bending in quantum waveguides""; ""Research articles""; ""Quantum field theory on star graphs""
- ""On the skeleton method and an application to a quantum scissor""""Vacuum energy and closed orbits in quantum graphs""; ""Spectra of graphs and semi-conducting polymers""
- Notes:
- Description based upon print version of record.
- Includes bibliographical references.
- Description based on print version record.
- ISBN:
- 0-8218-9384-X
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.