Thompson’s Group

2017 ◽  
Author(s):  
Sean Cleary
Keyword(s):  
Group Action ◽  
Word Length ◽  
Research Projects ◽  
Direct Sum ◽  
Group Presentations ◽  
Thompson’S Group ◽  
Rank 2 ◽  
Definition Of ◽  
Finitely Presented ◽  
Length Distortion

This chapter considers the Thompson's group F. Thompson's group F exhibits several behaviors that appear paradoxical. For example: F is finitely presented and contains a copy of F x F, indicating that F contains the direct sum of infinitely many copies of F. In addition, F has exponential growth but contains no free groups of rank 2. After providing an overview of the analytic definition and basic properties of the Thompson's group, the chapter introduces a combinatorial definition of F and two group presentations for F, an infinite one and a finite one. It also explores the subgroups, quotients, endomorphisms, and group action of F before concluding with an analysis of several geometric properties of F such as word length, distortion, dead ends, and growth. The discussion includes exercises and research projects.

Development and Evaluation of Enhanced Airfield Signage for Temporary Information

2017 ◽  
Vol 2626 (1) ◽  
pp. 66-73
Author(s):  
Gaël Le Bris
Keyword(s):  
Human Factors ◽  
Situational Awareness ◽  
Weak Link ◽  
Advisory Council ◽  
Parallel Study ◽  
Research Projects ◽  
Charles De Gaulle ◽  
Definition Of ◽  
De Gaulle ◽  
Construction Works

The aviation community has faced several accidents and incidents on infrastructures and procedures temporarily modified for the purpose of construction works. The analysis of these events shows that usual means of communication to the air crews are the weak link of the safety chain. To address the key challenge of situational awareness during construction works, the Airport Construction Advisory Council of FAA and Paris–Charles de Gaulle Airport (Paris-CDG) developed and evaluated with the airfield community, from 2011 to 2016, an innovative aviation signage. Parallel and complementary studies in human factors led to the definition of specifications for a temporary information signage, also called orange construction sign. Paris-CDG focused on the development of specific messages for each one of the major hazards that could require an increased situational awareness of the air crews during taxiing and takeoff. The results of the evaluation conducted by FAA were published in September 2015. The purpose of this paper is to present the parallel study performed by the author at Paris-CDG with the coalition of the airside operations stakeholders. Both research projects are convergent and confirm the relevance of the orange sign concept for increasing the situational awareness and preventing safety events during airfield construction.

scholarly journals The Structure of n Harmonic Points and Generalization of Desargues’ Theorems

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1018
Author(s):  
Xhevdet Thaqi ◽  
Ekrem Aljimi
Keyword(s):  
Fourth Harmonic ◽  
New Findings ◽  
Rank 2 ◽  
Definition Of ◽  
Special Case

: In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n = 4) of the sets of H-points of rank 2, which is indicated by P42.

scholarly journals Nilpotent Group C*-algebras as Compact Quantum Metric Spaces

2017 ◽  
Vol 60 (1) ◽  
pp. 77-94 ◽  
Author(s):  
Michael Christ ◽  
Marc A. Rieòel
Keyword(s):  
Finite Groups ◽  
Word Length ◽  
Polynomial Growth ◽  
Metric Spaces ◽  
Length Function ◽  
C Algebra ◽  
Pointwise Multiplication ◽  
C Algebras ◽  
Definition Of ◽  
Compact Quantum Metric Space

AbstractLet be a length function on a group G, and let M denote the operator of pointwise multiplication by on l2(G). Following Connes, M𝕃 can be used as a “Dirac” operator for the reduced group C*-algebra (G). It deûnes a Lipschitz seminorm on (G), which defines a metric on the state space of (G). We show that for any length function satisfying a strong form of polynomial growth on a discrete group, the topology from this metric coincides with the weak-* topology (a key property for the definition of a “compact quantum metric space”). In particular, this holds for all word-length functions on ûnitely generated nilpotent-by-finite groups.

scholarly journals Certain Types of Complex Lie Group Action

2018 ◽  
Vol 10 (3) ◽  
Author(s):  
Ahmed Khalaf Radhi ◽  
Taghreed Hur Majeed
Keyword(s):  
Tensor Product ◽  
Group Action ◽  
Lie Group ◽  
The Other ◽  
Smooth Representation ◽  
Equivalent Relation ◽  
Complex Group ◽  
Lie Group Action ◽  
Group 10 ◽  
Definition Of

     The main aim in this paper is to look for a novel action with new properties on       from the  , the Literature are concerned with studying the action of  of two representations , one is usual and the other is the dual, while our  interest in this work  is focused on some actions on complex Lie group[10] . Let G be a matrix complex  group , and  is representation of   In this study we will present and analytic  the  concepts of action of complex  group on    We recall the definition of  tensor  product of two representations of  group and construct  the definition of action of   group on , then by using the equivalent  relation   between  and  , we get a new action : The two actions are forming smooth  representation of    This  we have new action which called     denoted by    which acting on      This  is smooth representation of   The theoretical Justifications are developed and prove supported by some concluding  remarks and illustrations.

scholarly journals Strengthening the SSTC NRS Scientific and Technical Potential through Participation in the IAEA Coordinated Research Projects

2021 ◽  
pp. 5-13
Author(s):  
Yu. Balashevska ◽  
D. Gumenyuk ◽  
Iu. Ovdiienko ◽  
O. Pecherytsia ◽  
I. Shevchenko ◽  
...  
Keyword(s):  
Best Practices ◽  
Safety Assessment ◽  
Radiation Safety ◽  
Research Projects ◽  
Spent Fuel ◽  
Research Activities ◽  
Technical Potential ◽  
Technical Issues ◽  
Fuel Characterization ◽  
Definition Of

The State Scientific and Technical Center for Nuclear and Radiation Safety (SSTC NRS), a Ukrainian enterprise with a 29-year experience in the area of scientific and technical support to the national nuclear regulator (SNRIU), has been actively involved in international research activities. Participation in the IAEA coordinated research activities is among the SSTC NRS priorities. In the period of 2018–2020, the IAEA accepted four SSTC NRS proposals for participation in respective Coordinated Research Projects (CRPs). These CRPs address scientific and technical issues in different areas such as: 1) performance of probabilistic safety assessment for multi-unit/multi-reactor sites; 2) use of dose projection tools to ensure preparedness and response to nuclear and radiological emergencies; 3) phenomena related to in-vessel melt retention; 4) spent fuel characterization. This article presents a brief overview of the abovementioned projects with definition of scientific contributions by the SSTC NRS (participation in benchmarks, development of methodological documents on implementing research stages and of IAEA technical documents (TECDOC) for demonstration of best practices and results of research carried out by international teams).

Designing for Intergenerational Play

2018 ◽  
Author(s):  
Sinem Siyahhan ◽  
Elisabeth Gee
Keyword(s):  
Video Games ◽  
Family Engagement ◽  
After School ◽  
Research Projects ◽  
Community Learning ◽  
Design Based Research ◽  
Current Definition ◽  
Intergenerational Play ◽  
Family Friendly ◽  
Definition Of

In this chapter, we bring everything together and provide guidance on how educators and game designers can facilitate productive family engagement around video games. We discuss activity structures we designed and tested in after school and home environments that help connect school, home, and community learning. We also draw upon two design-based research projects to examine how to develop video games for families that expand the current definition of “family-friendly games.”

Directions and Trends in Knowledge Management Research

2003 ◽  
pp. 1-15
Author(s):  
George M. Giaglis
Keyword(s):  
Knowledge Management ◽  
Information Management ◽  
Learning Environments ◽  
Pattern Matching ◽  
Future Research ◽  
Research Projects ◽  
Knowledge Repositories ◽  
Accurate Definition ◽  
Research Themes ◽  
Definition Of

Knowledge and Information Management (KIM) has existed as a separate field of scientific research for almost a decade. It is therefore surprising that very few studies to date have been concerned with the identification of the scope and boundaries of the field, as well as the sub-topics and research themes that constitute it. This chapter reports on the results of an empirical analysis of more than 200 research projects in Knowledge and Information Management. Using an inductive methodology of pattern matching analysis, a more accurate definition of knowledge management is attempted, and an innovative taxonomy of research sub-themes within the ‘umbrella’ area of Knowledge and Information Management is proposed. Furthermore, a trend towards a gradual maturation of the presently prevailing research paradigm is identified, indicating a need for a ‘paradigm shift’ that will provide a new direction and vision for future research in the area. We suggest that targeted future research efforts in the area of knowledge technologies will contribute to the development of the ‘next generation’ knowledge management systems that will transform the existing ‘passive’ knowledge repositories into ‘active’ learning environments.

Directions and Trends in Knowledge Management Research

2011 ◽  
pp. 1438-1449
Author(s):  
George M. Giaglis
Keyword(s):  
Knowledge Management ◽  
Information Management ◽  
Learning Environments ◽  
Pattern Matching ◽  
Future Research ◽  
Research Projects ◽  
Knowledge Repositories ◽  
Accurate Definition ◽  
Research Themes ◽  
Definition Of

Knowledge and Information Management (KIM) has existed as a separate field of scientific research for almost a decade. It is therefore surprising that very few studies to date have been concerned with the identification of the scope and boundaries of the field, as well as the sub-topics and research themes that constitute it. This chapter reports on the results of an empirical analysis of more than 200 research projects in Knowledge and Information Management. Using an inductive methodology of pattern matching analysis, a more accurate definition of knowledge management is attempted, and an innovative taxonomy of research sub-themes within the ‘umbrella’ area of Knowledge and Information Management is proposed. Furthermore, a trend towards a gradual maturation of the presently prevailing research paradigm is identified, indicating a need for a ‘paradigm shift’ that will provide a new direction and vision for future research in the area. We suggest that targeted future research efforts in the area of knowledge technologies will contribute to the development of the ‘next generation’ knowledge management systems that will transform the existing ‘passive’ knowledge repositories into ‘active’ learning environments.

Definition of a Protocol for the Knowledge, the Analysis and the Communication of the Architectural Heritage

2017 ◽  
pp. 94-131
Author(s):  
Marinella Arena
Keyword(s):  
New Media ◽  
Scientific Community ◽  
The European Union ◽  
Research Projects ◽  
Architectural Heritage ◽  
Horizon 2020 ◽  
Research And Innovation ◽  
A Value ◽  
New Frontier ◽  
Definition Of

The communication of architecture is a complex and multidisciplinary process, indispensable for enhancing a monument properly and to allow understanding and knowledge to a large number of users. The European Architectural Heritage, and the Italian one in particular, is enormous; the processes of knowledge, cataloguing and analysis are far from being complete. This fact has prompted the European Union to invest, especially in recent years, in research projects designed to increase the communication strategies and put a value on the present assets in its territory. For example, the programs of the European Commission for Research and Innovation, found in “Horizon 2020”, define the communication based on the new media as the new frontier for the enhancement of architectural heritage (Reflective Cities). The main goal is to develop a better awareness of the Architectural Heritage through increased interaction between the citizen, the monument and the scientific community.

First Order Operators on Manifolds With a Group Action

1996 ◽  
Vol 48 (4) ◽  
pp. 758-776 ◽  
Author(s):  
H. D. Fegan ◽  
B. Steer
Keyword(s):  
Differential Operator ◽  
Group Action ◽  
Lie Group ◽  
Differential Operators ◽  
Order Differential Operator ◽  
Compact Lie Group ◽  
First Order ◽  
Rank 2 ◽  
Homogeneous Operators

AbstractWe investigate questions of spectral symmetry for certain first order differential operators acting on sections of bundles over manifolds which have a group action. We show that if the manifold is in fact a group we have simple spectral symmetry for all homogeneous operators. Furthermore if the manifold is not necessarily a group but has a compact Lie group of rank 2 or greater acting on it by isometries with discrete isotropy groups, and let D be a split invariant elliptic first order differential operator, then D has equivariant spectral symmetry.

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