Forest diagrams for elements of Thompson's group F

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard action of F on the unit interval. Using forest diagrams, we give a conceptually simple length formula for elements of F with respect to the {x_0,x_1} generating set, and we discuss the construction of minimum-length words for positive elements. Finally, we use forest diagrams and the length formula to examine the structure of the Cayley graph of F.Comment: 44 pages, 70 figure

The effect of the electric field on the nucleation of the nanometer periodic structure of adatoms in GaAs semiconductor under the action of laser irradiation

In the paper, the effect of the electric field on the conditions of formation and on the period of the surface superlattice of adatoms in $n$-GaAs semiconductor is investigated. It is established that in GaAs semiconductor, an increase in the electric field strength, depending on the direction, leads to an increase or decrease of the critical temperature (the critical concentration of adatoms), at which the formation of self-organized nanostructure is possible. It is shown that in strongly alloyed $n$-GaAs semiconductor, an increase of the electric field strength leads to a monotonous change (decrease or increase depending on the direction of the electric field) of the period of self-organized surface nanostructures of adatoms.Comment: 9 pages, 4 figures. arXiv admin note: text overlap with arXiv:1512.0780

Growth rates of amenable groups

Let Fm be a free group with m generators and let R be a normal subgroup such that Fm /R projects onto ℤ. We give a lower bound for the growth rate of the group Fm / R′(where R′ is the derived subgroup of R) in terms of the length ρ= ρ(R) of the shortest non-trivial relation in R. It follows that the growth rate of Fm / R′ approaches 2m-1 as ρ approaches infinity. This implies that the growth rate of an m-generated amenable group can be arbitrarily close to the maximum value 2m- 1. This answers an open question of P. de la Harpe. We prove that such groups can be found in the class of abelian-by-nilpotent groups as well as in the class of virtually metabelian group

Family support and cardiac rehabilitation: A comparative study of the experiences of South Asian and White-European patients and their carer's living in the United Kingdom

Background: Effective lifestyle modification facilitated by cardiac rehabilitation is known to reduce the occurrence of adverse coronary events and mortality. South Asians have poorer outcomes after a myocardial infarction than the general UK population, but little is known about their experiences of family support, cardiac rehabilitation and lifestyle change. Aims: To explore the nature of family support available to a sample of South Asian and White-European cardiac patients and to highlight similarities and differences between these groups with regard to cardiac rehabilitation and lifestyle modification. Methods: Using a qualitative approach, semi-structured interviews (in 1 of 6 languages) were conducted by researchers with; 45 South Asian patients and 37 carers and 20 White-European patients and 17 carers. Interviews were conducted in a home setting, up to eighteen months after discharge from hospital following myocardial infarction, coronary artery bypass surgery or unstable angina. Results: The main themes that emerged related to the provision of advice and information, family support and burden, dietary change and exercise regimes. Conclusions: Several cultural and ethnic differences were identified between patients and their families alongside similarities, irrespective of ethnicity. These may represent generic characteristics of recovery after a cardiac event. Health professionals should develop a cultural repertoire to engage with diversity and difference. Not every difficulty a person encounters as they try to access appropriate service delivery can be attributed to ethnic background. By improving services generally, support for South Asian populations can be improved. The challenge is to know when ethnicity makes a difference and mediates a person's relationship with service support and when it does not. (C) 2007 European Society of Cardiology. Published by Elsevier B.V. All rights reserved

Strategies and innovations in modern trade marketing

Purpose: The article is devoted to the critical analysis of existing theoretical and methodological approaches to determining the content and nature of sales marketing as a factor and element of companies’ competitive strategy. Design/Methodology/Approach: Based on a critical retrospective analysis, authors presented the features of the trade marketing toolkit providing substantial increase in market sales. Authors considered key existing functional marketing strategies, as well as its innovative trends and ideas. Findings: The modern market of trade enterprises is characterized by fundamental changes in economic conditions caused by the transformation of the economic system, the market priority of consumers, the formation of the information society, and the integration of economic processes. The economic phenomena escalate the struggle in the trading business for its share of the competitive market. In order to maintain and strengthen their positions, trade enterprises should build their trade and technological processes more and more efficiently. Practical implications: Economic growth of a commercial enterprise could be carried out in line with intensive and extensive factors. With the growing level of concentration of the trade industry, factors of intensive economic growth of trade enterprises become relevant. Originality/Value: The author's approach could be used in the development of promising corporate marketing strategies in terms of the development and implementation of innovative marketing solutions available for implementation throughout the entire cycle of the strategic marketing process.peer-reviewe

Elementary amenable subgroups of R. Thompson's group F

The subgroup structure of Thompson's group F is not yet fully understood. The group F is a subgroup of the group PL(I) of orientation preserving, piecewise linear self homeomorphisms of the unit interval and this larger group thus also has a poorly understood subgroup structure. It is reasonable to guess that F is the "only" subgroup of PL(I) that is not elementary amenable. In this paper, we explore the complexity of the elementary amenable subgroups of F in an attempt to understand the boundary between the elementary amenable subgroups and the non-elementary amenable. We construct an example of an elementary amenable subgroup up to class (height) omega squared, where omega is the first infinite ordinal.Comment: 20 page

Self Management and Telehealth: Lessons Learnt from the Evaluation of a Dorset Telehealth Program

Dorset Clinical Commissioning Group