How many triangles does it take to make a square? The answer is simple: two. This problem has a direct analogue in dimensions three and higher, but the answers are much harder to find. We provide new lower bounds in dimensions 4 through 13, an asymptotic lower bound which is inferior to the best known bound in high dimensions, and some new ideas which produce good upper bounds in both low and high dimensions.

Recent years have seen increased awareness about the potential adverse impacts of climate change on hydrologic systems and human communities. The concept of community resilience – the capacity of communities to respond to drivers of change in a manner that maintains or improves upon community well-being – is widely recognized as a suitable framework for informing climate change adaptation policies. Emerging insights from the community resilience literature highlight the importance of the distinction between general resilience, which refers to the resilience of social-ecological systems to all kinds of drivers of change, and specified resilience, which is concerned with the resilience of social-ecological systems to particular drivers of change. While capital assets and institutions are generally considered to be the contextual factors shaping general resilience, the roles of these contextual factors in shaping specified resilience have not been adequately explored. To fill this knowledge gap, we developed a synthesized conceptual model that describes how community contextual factors influence the process and outcomes of community responses to specific drivers of change. This qualitative study was designed to test the proposed conceptual model by analyzing the responses of two rural communities (Belknap and Tamms) to floods in particular, and climate change impacts in general in the Cache River watershed of Southern Illinois. Both communities selected for the study have historical experience with flooding and consist of different population sizes. Hence, they are likely to have different levels of endowment of the assets and institutions that shape community resilience. Data for the study were collected through document review, as well as semi-structured interviews with 23 purposively sampled key informants representing various sectors of the local society (e.g. commerce, education, religion, local government). The data were analyzed using deductive coding in NVivo software based on analytical constructs derived from the proposed conceptual model. The results showed that communities in the Cache River watershed draw from a network of formal and informal institutions at multiple levels (local, state, national) in their responses to floods, although responses to other climate change impacts are less noticeable. Community capacity to respond to these impacts are also enabled by the availability of high levels of some capital assets (such as social capital), but also constrained by low levels of other community capital assets (such as economic capital and physical capital). Community assets and institutions also seemed to shape community perceptions and responses to future climate change scenarios where community relocation may be a viable response option. In all, our results provide rich insights on how community capital assets and institutions interact to either constrain or enhance the awareness, motivation, capacity, and opportunities that influence community responses to current and future drivers of change. Future research should seek to further refine and test this and related frameworks, as well as develop relevant indicators for further understanding the general and specified resilience of communities. With regard to policy, the results highlight the need for policies on climate change impacts and other disasters to move towards more targeted approaches to prepare communities to deal with specific threats in addition to those policies that focus on the general well-being and capacity of communities to deal with all kinds of drivers of change. Building the specified resilience of communities will require the utilization of existing scientific and non-scientific knowledge on the types of institutions and assets that are critical to community responses to the drivers of change under consideration in particular contexts.

Mémoire (M.Sc.A.)-- Université du Québec à Chicoutimi, 1992. / Bibliogr.: f. [1-5]. Document électronique également accessible en format PDF. CaQCU

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A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, December 2014. / In this thesis the evolution equations of the Yukawa couplings and quark flavour mixings are derived for the one-loop renormalisation group equations in five and six-dimensional models, compactified in different possible ways to yield standard four space-time dimensions. Different possibilities for the matter fields are discussed, such as the case of bulk propagating or brane localized fields. We discuss in both cases the evolution of the Yukawa couplings, the Jarlskog parameter and the Cabibbo-Kobayashi-Maskawa matrix elements, finding that for both scenarios, as we run up to the unification scale, significant renormalisation group corrections are present. We also discuss the results of different observables of the five-dimensional universal extra dimension model in comparison with those of six-dimensional models and the model dependence of the results. We also studied the scaling of the mass ratios and the implications for the mixing angles in these six-dimensional model as well as the 5D Minimal Supersymmetric Standard Model on an S1/Z2 orbifold. The renormalisation group equation evolutions for the Higgs sector and for the neutrino sector in six-dimensional models are also investigated. The recent experimental results of the Higgs boson from the LHC allow, in some scenarios, stronger constraints on the cutoff scale to be placed, from the requirement of the stability of the Higgs potential.

Thèse doctorat : Médecine. Génie biologique et médical : Rennes 1 : 2006. / Bibliogr. p.187-202.

Habilitation à diriger des recherches : Sciences médicales : Faculté de médecine, Rennes 1 : 2005. / Bibliogr. p. 154.

Thesis(M.S.)--Auburn University, 2006. / Abstract. Includes bibliographic references.