The Theory of Fusion Systems

The Theory of Fusion Systems
Author: David A. Craven
Publisher:
Total Pages: 371
Release: 2011
Genre: Algebraic topology
ISBN: 9781139091237

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The first book to deal comprehensively with the theory of fusion systems.

The Theory of Fusion Systems

The Theory of Fusion Systems
Author: David A. Craven
Publisher: Cambridge University Press
Total Pages: 385
Release: 2011-06-23
Genre: Mathematics
ISBN: 1107005965

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The first book to deal comprehensively with the theory of fusion systems.

Fusion Systems in Algebra and Topology

Fusion Systems in Algebra and Topology
Author: Michael Aschbacher
Publisher: Cambridge University Press
Total Pages: 329
Release: 2011-08-25
Genre: Mathematics
ISBN: 1107601002

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A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. This book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.

Finite Group Theory

Finite Group Theory
Author: M. Aschbacher
Publisher: Cambridge University Press
Total Pages: 320
Release: 2000-06-26
Genre: Mathematics
ISBN: 9780521786751

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The book provides the basic foundations for the local theory of finite groups, the theory of classical linear groups, and the theory of buildings and BN-pairs.

Fusion Neutronics

Fusion Neutronics
Author: Yican Wu
Publisher: Springer
Total Pages: 402
Release: 2017-08-16
Genre: Science
ISBN: 981105469X

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This book provides a systematic and comprehensive introduction to fusion neutronics, covering all key topics from the fundamental theories and methodologies, as well as a wide range of fusion system designs and experiments. It is the first-ever book focusing on the subject of fusion neutronics research. Compared with other nuclear devices such as fission reactors and accelerators, fusion systems are normally characterized by their complex geometry and nuclear physics, which entail new challenges for neutronics such as complicated modeling, deep penetration, low simulation efficiency, multi-physics coupling, etc. The book focuses on the neutronic characteristics of fusion systems and introduces a series of theories and methodologies that were developed to address the challenges of fusion neutronics. Further, it introduces readers to the unique principles and procedures of neutronics design, experimental methodologies and methodologies for fusion systems. The book not only highlights the latest advances and trends in the field, but also draws on the experiences and skills collected in the author’s more than 40 years of research. To make it more accessible and enhance its practical value, various representative examples are included to illustrate the application and efficiency of the methods, designs and experimental techniques discussed.

Principles Of Fusion Energy: An Introduction To Fusion Energy For Students Of Science And Engineering

Principles Of Fusion Energy: An Introduction To Fusion Energy For Students Of Science And Engineering
Author: Archie A Harms
Publisher: World Scientific Publishing Company
Total Pages: 309
Release: 2000-06-15
Genre: Science
ISBN: 981310273X

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This textbook accommodates the two divergent developmental paths which have become solidly established in the field of fusion energy: the process of sequential tokamak development toward a prototype and the need for a more fundamental and integrative research approach before costly design choices are made.Emphasis is placed on the development of physically coherent and mathematically clear characterizations of the scientific and technological foundations of fusion energy which are specifically suitable for a first course on the subject. Of interest, therefore, are selected aspects of nuclear physics, electromagnetics, plasma physics, reaction dynamics, materials science, and engineering systems, all brought together to form an integrated perspective on nuclear fusion and its practical utilization.The book identifies several distinct themes. The first is concerned with preliminary and introductory topics which relate to the basic and relevant physical processes associated with nuclear fusion. Then, the authors undertake an analysis of magnetically confined, inertially confined, and low-temperature fusion energy concepts. Subsequently, they introduce the important blanket domains surrounding the fusion core and discuss synergetic fusion-fission systems. Finally, they consider selected conceptual and technological subjects germane to the continuing development of fusion energy systems.

Fusion Action Systems

Fusion Action Systems
Author: Matthew Justin Karcher Gelvin
Publisher:
Total Pages: 132
Release: 2010
Genre:
ISBN:

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The study of fusion first arose in the local theory of finite groups. Puig abstracted the fusion data of a finite group to the notion of fusion system, an object that reflects local data in more abstract algebraic settings, such as the block theory of finite groups. Martino and Priddy conjectured that the algebraic data of a fusion system of a finite group should have a topological interpretation, which result was proved by Oliver using the notion of p-local finite group introduced by the team of Broto, Levi, and Oliver. The study of fusion systems and p-local finite groups thus provides a bridge between algebraic fields related to local group theory and algebraic topology. In this thesis we generalize the notion of abstract fusion system to model the local structure of a group action on a finite set. The resulting fusion action systems can be seen as a generalization of the notion of abstract fusion system, though we describe other possible interpretations as well. We also develop the notion of a p-local finite group action, which allows for connections between fusion action system theory and algebraic topology.

On Fusion Systems of Component Type

On Fusion Systems of Component Type
Author: Michael Aschbacher
Publisher: American Mathematical Soc.
Total Pages: 182
Release: 2019-02-21
Genre:
ISBN: 1470435209

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This memoir begins a program to classify a large subclass of the class of simple saturated 2-fusion systems of component type. Such a classification would be of great interest in its own right, but in addition it should lead to a significant simplification of the proof of the theorem classifying the finite simple groups. Why should such a simplification be possible? Part of the answer lies in the fact that there are advantages to be gained by working with fusion systems rather than groups. In particular one can hope to avoid a proof of the B-Conjecture, a important but difficult result in finite group theory, established only with great effort.

Fusion Systems in Algebra and Topology

Fusion Systems in Algebra and Topology
Author: Michael Aschbacher
Publisher:
Total Pages: 330
Release: 2014-05-14
Genre: MATHEMATICS
ISBN: 9781139101844

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A fusion system over a p-group S is a category whose objects form the set of all subgroups of S, whose morphisms are certain injective group homomorphisms, and which satisfies axioms first formulated by Puig that are modelled on conjugacy relations in finite groups. The definition was originally motivated by representation theory, but fusion systems also have applications to local group theory and to homotopy theory. The connection with homotopy theory arises through classifying spaces which can be associated to fusion systems and which have many of the nice properties of p-completed classifying spaces of finite groups. Beginning with a detailed exposition of the foundational material, the authors then proceed to discuss the role of fusion systems in local finite group theory, homotopy theory and modular representation theory. The book serves as a basic reference and as an introduction to the field, particularly for students and other young mathematicians.

Mathematics of Data Fusion

Mathematics of Data Fusion
Author: I.R. Goodman
Publisher: Springer Science & Business Media
Total Pages: 503
Release: 2013-03-14
Genre: Mathematics
ISBN: 9401589291

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Data fusion or information fusion are names which have been primarily assigned to military-oriented problems. In military applications, typical data fusion problems are: multisensor, multitarget detection, object identification, tracking, threat assessment, mission assessment and mission planning, among many others. However, it is clear that the basic underlying concepts underlying such fusion procedures can often be used in nonmilitary applications as well. The purpose of this book is twofold: First, to point out present gaps in the way data fusion problems are conceptually treated. Second, to address this issue by exhibiting mathematical tools which treat combination of evidence in the presence of uncertainty in a more systematic and comprehensive way. These techniques are based essentially on two novel ideas relating to probability theory: the newly developed fields of random set theory and conditional and relational event algebra. This volume is intended to be both an update on research progress on data fusion and an introduction to potentially powerful new techniques: fuzzy logic, random set theory, and conditional and relational event algebra. Audience: This volume can be used as a reference book for researchers and practitioners in data fusion or expert systems theory, or for graduate students as text for a research seminar or graduate level course.