Global, Local and Vector-Valued Tb Theorems on Non-Homogeneous Metric Spaces

Various Tb theorems play a key role in the modern harmonic analysis. They provide characterizations for the boundedness of Calderón-Zygmund type singular integral operators. The general philosophy is that to conclude the boundedness of an operator T on some function space, one needs only to test it on some suitable function b. The main object of this dissertation is to prove very general Tb theorems. The dissertation consists of four research articles and an introductory part. The framework is general with respect to the domain (a metric space), the measure (an upper doubling measure) and the range (a UMD Banach space). Moreover, the used testing conditions are weak. In the first article a (global) Tb theorem on non-homogeneous metric spaces is proved. One of the main technical components is the construction of a randomization procedure for the metric dyadic cubes. The difficulty lies in the fact that metric spaces do not, in general, have a translation group. Also, the measures considered are more general than in the existing literature. This generality is genuinely important for some applications, including the result of Volberg and Wick concerning the characterization of measures for which the analytic Besov-Sobolev space embeds continuously into the space of square integrable functions. In the second article a vector-valued extension of the main result of the first article is considered. This theorem is a new contribution to the vector-valued literature, since previously such general domains and measures were not allowed. The third article deals with local Tb theorems both in the homogeneous and non-homogeneous situations. A modified version of the general non-homogeneous proof technique of Nazarov, Treil and Volberg is extended to cover the case of upper doubling measures. This technique is also used in the homogeneous setting to prove local Tb theorems with weak testing conditions introduced by Auscher, Hofmann, Muscalu, Tao and Thiele. This gives a completely new and direct proof of such results utilizing the full force of non-homogeneous analysis. The final article has to do with sharp weighted theory for maximal truncations of Calderón-Zygmund operators. This includes a reduction to certain Sawyer-type testing conditions, which are in the spirit of Tb theorems and thus of the dissertation. The article extends the sharp bounds previously known only for untruncated operators, and also proves sharp weak type results, which are new even for untruncated operators. New techniques are introduced to overcome the difficulties introduced by the non-linearity of maximal truncations.

Local structural disorder and its influence on the average global structure and polar properties in Na0.5Bi0.5TiO3

Na0.5Bi0.5TiO3 (NBT) and its derivatives have prompted a great surge in interest owing to their potential as lead-free piezoelectrics. In spite of five decades since its discovery, there is still a lack of clarity on crucial issues such as the origin of significant dielectric relaxation at room temperature, structural factors influencing its depoling, and the status of the recently proposed monoclinic (Cc) structure vis-a-vis the nanosized structural heterogeneities. In this work, these issues are resolved by comparative analysis of local and global structures on poled and unpoled NBT specimens using electron, x-ray, and neutron diffraction in conjunction with first-principles calculation, dielectric, ferroelectric, and piezoelectric measurements. The reported global monoclinic (Cc) distortion is shown not to correspond to the thermodynamic equilibrium state at room temperature. The global monocliniclike appearance rather owes its origin to the presence of local structural and strain heterogeneities. Poling removes the structural inhomogeneities and establishes a long-range rhombohedral distortion. In the process the system gets irreversibly transformed from a nonergodic relaxor to a normal ferroelectric state. The thermal depoling is shown to be associated with the onset of incompatible in-phase tilted octahedral regions in the field-stabilized long range rhombohedral distortion.

Local air pollution and global climate change taxes: a distributional analysis

25 p.

Performing the Local and the Global : The Theatre Festivals of Lake Constance

Wilkinson, Jane, Performing the Local and the Global: The Theatre Festivals of Lake Constance (Peter Lang, 2007), pp.286 RAE2008

Acculturation and Global Mindsponge

Much research on acculturation around global experiences has focused on the “type” of overseas experience—e.g. expatriate, repatriate, inpatriate, flexpatriate. The experiences of people in those categories and across various demographics (single/married/divorced; gender; sexual orientation) can differ dramatically. In addition, given the explosion of people working in global business, some global business citizens could well fit into several of those various types of experiences over the course of their careers. In this paper, we propose to push in a somewhat different direction and explore something that for us would be quite new. Rather than focusing on the various categories and their resulting experiences, we take a step back to consider what attributes and ways of thinking a global citizen may need to become better as a global business citizen, regardless of type of experience. The question is less one of “Who am I” than “How can I become better?”. Essentially, we would like to explore what might be required in moving the global citizen from thinking about “global mindset” to “global mindsponge.” When we hear the term mindset, we think of a certain way of thinking that stays rather fixed. So part of the challenge of the paper will be to define and examine what mindsponge might mean in the global context—what does it take to unlearn or squeeze out certain ways of thinking or behaving before absorbing and reshaping new ways of thinking and behaving? Moreover, how might that become part of a natural and regular way of operating, especially in a rapidly changing developing country like Vietnam, in particular? At this early stage, we think of mind sponge as a mechanism that encourages flexibility and receptiveness through a process of using multiple filters and more focus on creativity, or doing things differently to improve an organization or individual performance. Our goal is to develop a basic conceptual framework for “mindsponge,” drawing upon a broad literature review as well as several unstructured interviews, to assess whether the idea of mindsponge helps people perceive that they are more culturally versatile and culturally mobile, regardless of whether they work in or outside of their “home environment.” We hope this would enhance their ability to shape an emerging set of cultural values that erases the divide between “foreign” and “local” cultural differences that so often dominates in emerging economies.

Local, European and global: An exploration of migration patterns of social workers into Ireland

Whilst the project to increase workforce mobility is part of a common labour force policy across the European Union, for some social workers, it has also been coupled with an aspiration to develop a pan-European identity within the profession (Lorenz, 1994, 2000; Frost, 2008). In this article, taking the island of Ireland as an example, we examine empirical data on the movement of social workers in recent years, both within Ireland and inward from outside the island, and consider the challenges and opportunities this has presented for the profession, also drawing on the British experience. From this analysis, some tentative conclusions are drawn about what is happening, what is possible and what is desirable in balancing aspirations for increased mobility within the European Union and a pan-European social work identity against the needs and interests of local, European and global communities.

Education for global citizenship in a divided society? Young people's views and experiences

Global citizenship education has been suggested as a means of overcoming the limitations of national citizenship in an increasingly globalised world. In divided societies, global citizenship education is especially relevant and problematic as it offers the opportunity to explore identities and conflict in a wider context. This paper therefore explores young people's understandings of global citizenship in Northern Ireland, a divided society emerging from conflict. Results from focus groups with primary and post-primary pupils reflect some theoretical conceptualisations of global citizenship, including an awareness of global issues, understandings of environmental interdependence and global responsibility, though other elements appear to be less well understood. We argue that global citizenship education will fail to overcome engrained cultural divisions locally and may perpetuate cultural stereotypes globally, unless local and global controversial issues are acknowledged and issues of identity and interdependence critically examined at both levels.

“Local politics and global corporate crime in Irish crime fiction : Alan Glynn's Winterland trilogy",

Global migration : patriarchy, propoganda and the well- being of women and children

This critical analysis explores the conflicted position of women as ''trailing spouses" and the effects on families who relocate globally under the auspices of a multinational corporation, by utilizing a discursive analysis of two contemporary films and available literature. Current portrayals of women and children in contemporary media provide emotional yet conflicting images of the perfect woman, wife, mother, child and family. The basic tenets of a North American patriarchal economic system are being televised around the world. Technological advancements have made it possible to advertise political agendas on a global television screen. Much of what we see is propaganda couched in films and advertisements that are designed to romantic~e the practice of deriving profits from the unpaid labor of woman and invisibility of children and child rearing. I intend to show that the materiality of trailing a spouse globally conflicts with these romanticized images and supports feminist literature that asserts the notion that mothers and children are oppressed and managed for the benefit of capital.

Framing the local and the global in the anti-nuclear movement: Law and the politics of place

This article examines the politics of place in relation to legal mobilization by the anti-nuclear movement. It examines two case examples - citizens' weapons inspections and civil disobedience strategies - which have involved the movement drawing upon the law in particular spatial contexts. The article begins by examining a number of factors which have been employed in recent social movement literature to explain strategy choice, including ideology, resources, political and legal opportunity, and framing. It then proceeds to argue that the issues of scale, space, and place play an important role in relation to framing by the movement in the two case examples. Both can be seen to involve scalar reframing, with the movement attempting to resist localizing tendencies and to replace them with a global frame. Both also involve an attempt to reframe the issue of nuclear weapons away from the contested frame of the past (unilateral disarmament) towards the more universal and widely accepted frame of international law.

A global quantitative synthesis of local and landscape effects on wild bee pollinators in agroecosystems

Bees provide essential pollination services that are potentially affected both by local farm management and the surrounding landscape. To better understand these different factors, we modelled the relative effects of landscape composition (nesting and floral resources within foraging distances), landscape configuration (patch shape, interpatch connectivity and habitat aggregation) and farm management (organic vs. conventional and local-scale field diversity), and their interactions, on wild bee abundance and richness for 39 crop systems globally. Bee abundance and richness were higher in diversified and organic fields and in landscapes comprising more high-quality habitats; bee richness on conventional fields with low diversity benefited most from high-quality surrounding land cover. Landscape configuration effects were weak. Bee responses varied slightly by biome. Our synthesis reveals that pollinator persistence will depend on both the maintenance of high-quality habitats around farms and on local management practices that may offset impacts of intensive monoculture agriculture.

Genetic algorithm inversion of the average 1D crustal structure using local and regional earthquakes

Knowing the best 1D model of the crustal and upper mantle structure is useful not only for routine hypocenter determination, but also for linearized joint inversions of hypocenters and 3D crustal structure, where a good choice of the initial model can be very important. Here, we tested the combination of a simple GA inversion with the widely used HYPO71 program to find the best three-layer model (upper crust, lower crust, and upper mantle) by minimizing the overall P- and S-arrival residuals, using local and regional earthquakes in two areas of the Brazilian shield. Results from the Tocantins Province (Central Brazil) and the southern border of the Sao Francisco craton (SE Brazil) indicated an average crustal thickness of 38 and 43 km, respectively, consistent with previous estimates from receiver functions and seismic refraction lines. The GA + HYPO71 inversion produced correct Vp/Vs ratios (1.73 and 1.71, respectively), as expected from Wadati diagrams. Tests with synthetic data showed that the method is robust for the crustal thickness, Pn velocity, and Vp/Vs ratio when using events with distance up to about 400 km, despite the small number of events available (7 and 22, respectively). The velocities of the upper and lower crusts, however, are less well constrained. Interestingly, in the Tocantins Province, the GA + HYPO71 inversion showed a secondary solution (local minimum) for the average crustal thickness, besides the global minimum solution, which was caused by the existence of two distinct domains in the Central Brazil with very different crustal thicknesses. (C) 2010 Elsevier Ltd. All rights reserved.