Locally Finite Planar Edge Transitive Graphs
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Locally Finite Planar Edge Transitive Graphs
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Author : Jack E. Graver
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Locally Finite Planar Edge Transitive Graphs written by Jack E. Graver and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
The nine finite, planar, 3-connected, edge-transitive graphs have been known and studied for many centuries. The infinite, locally finite, planar, 3-connected, edge-transitive graphs can be classified according to the number of their end. The 1-ended graphs in this class were identified by Grünbaum and Shephard; Watkins characterized the 2-ended members. Any remaining graphs in this class must have uncountably may ends. In this work, infinite-ended members of this class are shown to exist. A more detailed classification scheme in terms of the types of Petrie walks in the graphs in this class and the local structure of their automorphism groups is presented.
Abelian Galois Cohomology Of Reductive Groups
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Author : Mikhail Borovoi
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Abelian Galois Cohomology Of Reductive Groups written by Mikhail Borovoi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this volume, a new function H 2/ab (K, G) of abelian Galois cohomology is introduced from the category of connected reductive groups G over a field K of characteristic 0 to the category of abelian groups. The abelian Galois cohomology and the abelianization map ab1: H1 (K, G) -- H 2/ab (K, G) are used to give a functorial, almost explicit description of the usual Galois cohomology set H1 (K, G) when K is a number field
Hodge Theory In The Sobolev Topology For The De Rham Complex
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Author : Luigi Fontana
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Hodge Theory In The Sobolev Topology For The De Rham Complex written by Luigi Fontana and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this book, the authors treat the full Hodge theory for the de Rham complex when calculated in the Sobolev topology rather than in the $L2$ topology. The use of the Sobolev topology strikingly alters the problem from the classical setup and gives rise to a new class of elliptic boundary value problems. The study takes place on both the upper half space and on a smoothly bounded domain. It features: a good introduction to elliptic theory, pseudo-differential operators, and boundary value problems; theorems completely explained and proved; and new geometric tools for differential analysis on domains and manifolds.
Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds
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Author : Józef Dodziuk
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Spectral Asymptotics On Degenerating Hyperbolic 3 Manifolds written by Józef Dodziuk and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this volume, the authors study asymptotics of the geometry and spectral theory of degenerating sequences of finite volume hyperbolic manifolds of three dimensions. Thurston's hyperbolic surgery theorem assets the existence of non-trivial sequences of finite volume hyperbolic three manifolds which converge to a three manifold with additional cusps. In the geometric aspect of their study, the authors use the convergence of hyperbolic metrics on the thick parts of the manifolds under consideration to investigate convergentce of tubes in the manifolds of the sequence to cusps of the limiting manifold. In the specral theory aspect of the work, they prove convergence of heat kernels. They then define a regualrized heat race associated to any finite volume, complete, hyperbolic three manifold, and study its asymptotic behaviour through degeneration. As an application of the analysis of the regularized heat trace, they study asymptotic behaviours of the spectral zeta function, determinant of the Laplacian, Selberg zeta function, and spectral counting functions through degeneration. The authors' methods are an adaptation to three dimensions of the earlier work of Jorgenson and Lundelius who investigated the asymptotic behaviour of spectral functions on degenerating families of finite area hyperbolic Riemann surfaces.
Model Theory And Linear Extreme Points In The Numerical Radius Unit Ball
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Author : Michael A. Dritschel
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Model Theory And Linear Extreme Points In The Numerical Radius Unit Ball written by Michael A. Dritschel and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
This memoir initiates a model theory-based study of the numerical radius norm. Guided by the abstract model theory of Jim Agler, the authors propose a decomposition for operators that is particularly useful in understanding their properties with respect to the numerical radius norm. Of the topics amenable to investigation with these tools, the following are presented: a complete description of the linear extreme points of the non-matrix (numerical radius) unit ball; several equivalent characterizations of matricial extremals in the unit ball, that is, those members which do not allow a nontrivial extension remaining in the unit ball; and applications to numerical ranges of matrices, including a complete parameterization of all matrices whose numerical ranges are closed disks.
Geometric Structure Of Chemistry Relevant Graphs
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Author : Michel-Marie Deza
language : en
Publisher: Springer
Release Date : 2015-05-26
Geometric Structure Of Chemistry Relevant Graphs written by Michel-Marie Deza and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-26 with Mathematics categories.
The central theme of the present book is zigzags and central-circuits of three- or four-regular plane graphs, which allow a double covering or covering of the edgeset to be obtained. The book presents zigzag and central circuit structures of geometric fullerenes and several other classes of graph of interest in the fields of chemistry and mathematics. It also discusses the symmetries, parameterization and the Goldberg–Coxeter construction for those graphs. It is the first book on this subject, presenting full structure theory of such graphs. While many previous publications only addressed particular questions about selected graphs, this book is based on numerous computations and presents extensive data (tables and figures), as well as algorithmic and computational information. It will be of interest to researchers and students of discrete geometry, mathematical chemistry and combinatorics, as well as to lay mathematicians.
Families Of Curves In Mathbb P 3 And Zeuthen S Problem
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Author : Robin Hartshorne
language : en
Publisher: American Mathematical Soc.
Release Date : 1997
Families Of Curves In Mathbb P 3 And Zeuthen S Problem written by Robin Hartshorne and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Content Description #"November 1997, volume 130, number 617 (first of 4 numbers)."#On t.p. "P" is blackboard bold.#Includes bibliographical references.
Graph Symmetry
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Author : Gena Hahn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Graph Symmetry written by Gena Hahn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Mathematics categories.
The last decade has seen two parallel developments, one in computer science, the other in mathematics, both dealing with the same kind of combinatorial structures: networks with strong symmetry properties or, in graph-theoretical language, vertex-transitive graphs, in particular their prototypical examples, Cayley graphs. In the design of large interconnection networks it was realised that many of the most fre quently used models for such networks are Cayley graphs of various well-known groups. This has spawned a considerable amount of activity in the study of the combinatorial properties of such graphs. A number of symposia and congresses (such as the bi-annual IWIN, starting in 1991) bear witness to the interest of the computer science community in this subject. On the mathematical side, and independently of any interest in applications, progress in group theory has made it possible to make a realistic attempt at a complete description of vertex-transitive graphs. The classification of the finite simple groups has played an important role in this respect.
Controllability Stabilization And The Regulator Problem For Random Differential Systems
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Author : Russell Johnson
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Controllability Stabilization And The Regulator Problem For Random Differential Systems written by Russell Johnson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Computers categories.
This volume develops a systematic study of time-dependent control processes. The basic problem of null controllability of linear systems is first considered. Using methods of ergodic theory and topological dynamics, general local null controllability criteria are given. Then the subtle question of global null controllability is studied. Next, the random linear feedback and stabilization problem is posed and solved. Using concepts of exponential dichotomy and rotation number for linear Hamiltonian systems, a solution of the Riccati equation is obtained which has extremely good robustness properties and which also preserves all the smoothness and recurrence properties of the coefficients. Finally, a general version of the local nonlinear feedback stabilization problem is solved.
Flat Extensions Of Positive Moment Matrices Recursively Generated Relations
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Author : Raúl E. Curto
language : en
Publisher: American Mathematical Soc.
Release Date : 1998
Flat Extensions Of Positive Moment Matrices Recursively Generated Relations written by Raúl E. Curto and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
In this book, the authors develop new computational tests for existence and uniqueness of representing measures $\mu$ in the Truncated Complex Moment Problem: $\gamma {ij}=\int \bar zizj\, d\mu$ $(0\le i+j\le 2n)$. Conditions for the existence of finitely atomic representing measures are expressed in terms of positivity and extension properties of the moment matrix $M(n)(\gamma )$ associated with $\gamma \equiv \gamma {(2n)}$: $\gamma {00}, \dots ,\gamma {0,2n},\dots ,\gamma {2n,0}$, $\gamma {00}>0$. This study includes new conditions for flat (i.e., rank-preserving) extensions $M(n+1)$ of $M(n)\ge 0$; each such extension corresponds to a distinct rank $M(n)$-atomic representing measure, and each such measure is minimal among representing measures in terms of the cardinality of its support. For a natural class of moment matrices satisfying the tests of recursive generation, recursive consistency, and normal consistency, the existence problem for minimal representing measures is reduced to the solubility of small systems of multivariable algebraic equations. In a variety of applications, including cases of the quartic moment problem ($n=2$), the text includes explicit contructions of minimal representing measures via the theory of flat extensions. Additional computational texts are used to prove non-existence of representing measures or the non-existence of minimal representing measures. These tests are used to illustrate, in very concrete terms, new phenomena, associated with higher-dimensional moment problems that do not appear in the classical one-dimensional moment problem.