112,664 research outputs found

    Curve diffusion and straightening flows on parallel lines

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    In this paper, we study families of immersed curves γ:(−1,1)×[0,T)→R2\gamma:(-1,1)\times[0,T)\rightarrow\mathbb{R}^2 with free boundary supported on parallel lines {η1,η2}:R→R2\{\eta_1, \eta_2\}:\mathbb{R}\rightarrow\mathbb{R}^2 evolving by the curve diffusion flow and the curve straightening flow. The evolving curves are orthogonal to the boundary and satisfy a no-flux condition. We give estimates and monotonicity on the normalised oscillation of curvature, yielding global results for the flows.Comment: 35 pages, 3 figure

    A checklist of the ants of Wyoming (Hymenoptera: Formicidae)

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    The history of myrmrecology in Wyoming began when Fore1 described a new species, obscuripes in the genus Formica from Green River in 1886, four years before Wyoming Territory became a state. There was a long hiatus until 1932 when Cole cited ten records for Pogonomyrmex occidentalis. Since then a dozen authors have published one to many records each. During the summers of 1957, 1958, 1961, 1963, 1964,1965 and 1966, while we were still at the University of North Dakota (Grand Forks), we made a dozen field trips into Wyoming to observe and collect ants in 12 of the 23 counties and in Yellowstone National Park. These expeditions yielded a total of 168 records for 45 species (a record is a species in a locality)

    Mean curvature flow with free boundary outside a hypersphere

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    The purpose of this paper is twofold: firstly, to establish sufficient conditions under which the mean curvature flow supported on a hypersphere with exterior Dirichlet boundary exists globally in time and converges to a minimal surface, and secondly, to illustrate the application of Killing vector fields in the preservation of graphicality for the mean curvature flow with free boundary. To this end we focus on the mean curvature flow of a topological annulus with inner boundary meeting a standard n-sphere in \R^{n+1} perpendicularly and outer boundary fixed to an (n-1)-sphere with radius R>1 at a fixed height h. We call this the \emph{sphere problem}. Our work is set in the context of graphical mean curvature flow with either symmetry or mean concavity/convexity restrictions. For rotationally symmetric initial data we obtain, depending on the exact configuration of the initial graph, either long time existence and convergence to a minimal hypersurface with boundary or the development of a finite-time curvature singularity. With reflectively symmetric initial data we are able to use Killing vector fields to preserve graphicality of the flow and uniformly bound the mean curvature pointwise along the flow. Finally we prove that the mean curvature flow of an initially mean concave/convex graphical surface exists globally in time and converges to a piece of a minimal surface.Comment: 23 page

    Concentration-compactness and finite-time singularities for Chen's flow

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    Chen's flow is a fourth-order curvature flow motivated by the spectral decomposition of immersions, a program classically pushed by B.-Y. Chen since the 1970s. In curvature flow terms the flow sits at the critical level of scaling together with the most popular extrinsic fourth-order curvature flow, the Willmore and surface diffusion flows. Unlike them however the famous Chen conjecture indicates that there should be no stationary nonminimal data, and so in particular the flow should drive all closed submanifolds to singularities. We investigate this idea, proving that (1) closed data becomes extinct in finite time in all dimensions and for any codimension; (2) singularities are characterised by concentration of curvature in LnL^n for intrinsic dimension n∈{2,4}n \in \{2,4\} and any codimension (a Lifespan Theorem); and (3) for n=2n = 2 and in one codimension only, there exists an explicit small constant ε2\varepsilon_2 such that if the L2L^2 norm of the tracefree curvature is initially smaller than ε2\varepsilon_2, the flow remains smooth until it shrinks to a point, and that the blowup of that point is an embedded smooth round sphere.Comment: 48 page

    On a curvature flow model for embryonic epidermal wound healing

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    The paper studies a curvature flow linked to the physical phenomenon of wound closure. Under the flow we show that a closed, initially convex or close-to-convex curve shrinks to a round point in finite time. We also study the singularity, showing that the singularity profile after continuous rescaling is that of a circle. We additionally give a maximal time estimate, with an application to the classification of blowups.Comment: 43 page

    Celebrity diplomacy: United Nations’ Goodwill Ambassadors and Messengers of Peace

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    This article will examine the meaning of celebrity diplomacy. In particular, it will discuss how this phenomenon has emerged from a transition between state-centric to public forms of diplomatic initiatives. This has led to a debate about the credible use of celebrity forms of activism in international political affairs. To analyse this phenomenon, this article will focus on the role and impact of the United Nations' (UN) Goodwill Ambassadors and Messengers of Peace programmes. It refers to Andrew F. Cooper's concept of ‘celebrity diplomacy’ as an alternative form of agency and employs John Street's framework of ‘celebrity performance’ to define how the UN has utilised stars to draw attention to its activities. These examples demonstrate how celebrity diplomats provide focus for causes to become integral in the sphere of international diplomacy

    Effect of Change in Apportionment Formula on Georgia Corporate Tax Liability - Brief

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    The purpose of this brief is to identify the number and characteristics of corporations that are expected to benefit from the switch to a single-factor apportionment formula and the number and characteristics of those that are not. FRC Brief 20

    European Union state aid, public subsidies and analogue switch-off/digital switchover

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    This article considers the European Union’s (EU) role in the media and communications field concerning analogue switch-off/digital switchover. It focuses on the EU Competition Directorate’s approach concerning the application of the State Aid mechanism with regard to those Member States who have used public subsidies for digital switchover. Therefore, this analysis considers how the Directorate has sought to balance its market-driven set of rules with the need to be adaptable to the Member States’ specific requirements. In turn, this account will discuss how the demand to achieve the 2012 completion deadline, alongside the requirement to release analogue spectrum to realize a digital dividend, impacted upon the EU’s principles of competition. Finally, this analysis will reflect on how the employment of State Aid in relation to digital switchover relates to a wider debate concerning the EU’s neo-liberal agendas against Member States’ interests to promote their national cultures

    The Largest Environmental Movement: Recycling and Consumption Work in Sweden

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    By sorting their waste for recycling, Swedes are told that they are part of 'Sweden's largest environmental movement' (Avfall Sverige, 2008). Recycling in Sweden is understood as an environmental action by all parties within society (including consumers, municipalities, and producers) and the country is proud of its identity as a world-leader on environmental issues. The system for recycling in Sweden asks a lot of the consumer who must not only sort their waste into different fractions but transport it to the appropriate bring station. Yet the country achieves high rates of materials (33 per cent) and biological recycling (15 per cent) and they proudly proclaim to recycle 99 per cent of their waste, with their belief that incineration with energy recovery is a form of recycling (Avfall Sverige, 2012). This paper explores how recycling has developed as an everyday ethical practice, considering the role of different institutions in the promotion of recycling and responsible waste management. This paper has been developed as part of an ERC-funded project, 'Consumption Work and Societal Divisions of Labour', whose key aim is to demonstrate the role that consumers play in the labour process, using comparative methods. In the case of recycling, by sorting their waste, consumers play an integral role in the division of labour within waste management in Sweden and their role differs substantially to the role of consumers in England (the other country in which recycling consumption work has been explored, see Wheeler, 2013). This paper illustrates how the consumer is encouraged to perform this work, drawing attention to what the work actually comprises. It also uncovers the organisations that shape this distinctive system of provision and moral economy of recycling
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