Ross Lawther's Books

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

By: Ross Lawther,Donna M. Testerman

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Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

By: Ross Lawther,Donna M. Testerman

Let G be a simple algebraic group defined over an algebraically closed field k whose characteristic is either 0 or a good prime for G, and let uEG be unipotent. The authors study the centralizer CG(u), especially its centre Z(CG(u)). They calculate the Lie algebra of Z(CG(u)), in particular determining its dimension; they prove a succession of theorems of increasing generality, the last of which provides a formula for dim Z(CG(u)) in terms of the labelled diagram associated to the conjugacy class containing u.

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Page Count

201

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821847694

ISBN 13

9780821847695

$A_1$ Subgroups of Exceptional Algebraic Groups

By: Ross Lawther,Donna M. Testerman

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$A_1$ Subgroups of Exceptional Algebraic Groups

By: Ross Lawther,Donna M. Testerman

This book is intended for graduate students and research mathematicians interested in group theory and genralizations

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Page Count

146

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821819666

ISBN 13

9780821819661

Human Factors for Naval Marine Vehicle Design and Operation

By: Jonathan M. Ross

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Human Factors for Naval Marine Vehicle Design and Operation

By: Jonathan M. Ross

There is a driving need for naval professionals to focus on human factors issues. The number of maritime accidents is increasing and the chief cause is human error, both by the designer and the operator. Decreasing crew size, lack of experienced operators, operations in higher sea states and fatigue worsen the situation. Automation can be a partial solution, but flawed automated systems actually contribute to accidents at sea. Up to now, there has been no overarching resource available to naval marine vehicle designers and human factors professionals which bridges the gap between the human and the machine in this context. Designers understand the marine vehicle; human factors professionals understand how a particular environment affects people. Yet neither has a practical understanding of the other's field, and thus communicating requirements and solutions is difficult. This book integrates knowledge from numerous sources as well as the advice of a panel of eight recognized experts in the fields of related research, development and operation. The result is a reference that bridges the communications gap, and stands to help enhance the design and operation of all naval marine vehicles.

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Page Count

244

Publisher

CRC Press

Published Date

ISBN 10

135192981X

ISBN 13

9781351929813

Mechanics of Underwater Noise

By: Donald Ross

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Mechanics of Underwater Noise

By: Donald Ross

Mechanics of Underwater Noise elucidates the basic mechanisms by which noise is generated, transmitted by structures and radiated into the sea. Organized into 10 chapters, this book begins with a description of noise, decibels and levels, significance of spectra, and passive sonar equation. Subsequent chapters discuss sound waves in liquids; acoustic radiation fundamentals; wind-generated ocean ambient noise; vibration isolation and structural damping; and radiation by plate flexural vibrations. Other chapters address cavitation, propeller cavitation noise, radiation by fluctuating-force (dipole) sources, and mechanical noise sources. This book will be helpful as a self-education text and as a reference for workers in the field.

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Page Count

390

Publisher

Elsevier

Published Date

ISBN 10

1483160467

ISBN 13

9781483160467

Digital Privacy, Terrorism and Law Enforcement

The UK's Response to Terrorist Communication

By: Simon Hale-Ross

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Digital Privacy, Terrorism and Law Enforcement

The UK's Response to Terrorist Communication

By: Simon Hale-Ross

This book examines the UK’s response to terrorist communication. Its principle question asks, has individual privacy and collective security been successfully managed and balanced? The author begins by assessing several technologically-based problems facing British law enforcement agencies, including use of the Internet; the existence of ‘darknet’; untraceable Internet telephone calls and messages; smart encrypted device direct messaging applications; and commercially available encryption software. These problems are then related to the traceability and typecasting of potential terrorists, showing that law enforcement agencies are searching for needles in the ever-expanding haystacks. To this end, the book examines the bulk powers of digital surveillance introduced by the Investigatory Powers Act 2016. The book then moves on to assess whether these new powers and the new legislative safeguards introduced are compatible with international human rights standards. The author creates a ‘digital rights criterion’ from which to challenge the bulk surveillance powers against human rights norms. Lord Carlile of Berriew CBE QC in recommending this book notes this particular legal advancement, commenting that rightly so the author concludes the UK has fairly balanced individual privacy with collective security. The book further analyses the potential impact on intelligence exchange between the EU and the UK, following Brexit. Using the US as a case study, the book shows that UK laws must remain within the ambit of EU law and the Court of Justice of the European Union's (CJEU's) jurisprudence, to maintain the effectiveness of the exchange. It addresses the topics with regard to terrorism and counterterrorism methods and will be of interest to researchers, academics, professionals, and students researching counterterrorism and digital electronic communications, international human rights, data protection, and international intelligence exchange.

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Page Count

160

Publisher

Routledge

Published Date

ISBN 10

135111896X

ISBN 13

9781351118965

Generic Stabilizers in Actions of Simple Algebraic Groups

By: R. M. Guralnick,R. Lawther

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Generic Stabilizers in Actions of Simple Algebraic Groups

By: R. M. Guralnick,R. Lawther

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Page Count

316

Publisher

American Mathematical Society

Published Date

ISBN 10

1470470527

ISBN 13

9781470470524

Maximal Abelian Sets of Roots

By: R. Lawther

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Maximal Abelian Sets of Roots

By: R. Lawther

In this work the author lets be an irreducible root system, with Coxeter group . He considers subsets of which are abelian, meaning that no two roots in the set have sum in . He classifies all maximal abelian sets (i.e., abelian sets properly contained in no other) up to the action of : for each -orbit of maximal abelian sets we provide an explicit representative , identify the (setwise) stabilizer of in , and decompose into -orbits. Abelian sets of roots are closely related to abelian unipotent subgroups of simple algebraic groups, and thus to abelian -subgroups of finite groups of Lie type over fields of characteristic . Parts of the work presented here have been used to confirm the -rank of , and (somewhat unexpectedly) to obtain for the first time the -ranks of the Monster and Baby Monster sporadic groups, together with the double cover of the latter. Root systems of classical type are dealt with quickly here; the vast majority of the present work concerns those of exceptional type. In these root systems the author introduces the notion of a radical set; such a set corresponds to a subgroup of a simple algebraic group lying in the unipotent radical of a certain maximal parabolic subgroup. The classification of radical maximal abelian sets for the larger root systems of exceptional type presents an interesting challenge; it is accomplished by converting the problem to that of classifying certain graphs modulo a particular equivalence relation.

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Page Count

234

Publisher

American Mathematical Soc.

Published Date

ISBN 10

147042679X

ISBN 13

9781470426798

A1 Subgroups of Exceptional Algebraic Groups

By: Ross Lawther,Donna M. Testerman

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A1 Subgroups of Exceptional Algebraic Groups

By: Ross Lawther,Donna M. Testerman

Abstract. Let $G$ be a simple algebraic group of exceptional type over an algebraically closed field of characteristic $p$. Under some mild restrictions on $p$, we classify all conjugacy classes of closed connected subgroups $X$ of type $A_1$; for each such class of subgroups, we also determine the connected centralizer and the composition factors in the action on the Lie algebra ${\mathcal L}(G)$ of $G$. Moreover, we show that ${\mathcal L}(C_G(X))=C_{{\mathcal L}(G)}(X)$ for each subgroup $X$. These results build upon recent work of Liebeck and Seitz, who have provided similar detailed information for closed connected subgroups of rank at least $2$. In addition, for any such subgroup $X$ we identify the unipotent class ${\mathcal C}$ meeting it. Liebeck and Seitz proved that the labelled diagram of $X$, obtained by considering the weights in the action of a maximal torus of $X$ on ${\mathcal L}(G)$, determines the ($\mathrm{Aut}\,G$)-conjugacy class of $X$. We show that in almost all cases the labelled diagram of the class ${\mathcal C}$ may easily be obtained from that of $X$; furthermore, if ${\mathcal C}$ is a conjugacy class of elements of order $p$, we establish the existence of a subgroup $X$ meeting ${\mathcal C}$ and having the same labelled diagram as ${\mathcal C}$.

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Page Count

148

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821863975

ISBN 13

9780821863978

Book's by Ross Lawther

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

Centres of Centralizers of Unipotent Elements in Simple Algebraic Groups

$A_1$ Subgroups of Exceptional Algebraic Groups

$A_1$ Subgroups of Exceptional Algebraic Groups

Human Factors for Naval Marine Vehicle Design and Operation

Human Factors for Naval Marine Vehicle Design and Operation

Mechanics of Underwater Noise

Mechanics of Underwater Noise

Digital Privacy, Terrorism and Law Enforcement

Digital Privacy, Terrorism and Law Enforcement

Generic Stabilizers in Actions of Simple Algebraic Groups

Generic Stabilizers in Actions of Simple Algebraic Groups

Maximal Abelian Sets of Roots

Maximal Abelian Sets of Roots

A1 Subgroups of Exceptional Algebraic Groups

A1 Subgroups of Exceptional Algebraic Groups

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