Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

Basaltic Dyke with Specific Volcanogenic Structures and its geomorphic evolution: Unique Geoheritage of the Faroe Islands (North Atlantic Ocean)

Volcanic landforms resulting from Cenozoic volcanism represent the most peculiar features of global geodiversity and provide eminent narratives for geoeducation. Among them, however, relict volcanic forms and site-specific landforms in remote areas have received less attention. In this paper, we provide the first description of unique volcanogenic features (hereinafter referred to as pseudo-hieroglyphs) developed on a summit rock wall at the Sandfelli ridge near the village of Gjógv in the N Eysturoy Island (Faroe Islands). The geomorphic evolution of the ridge and rock wall during the Quaternary is described and detailed petrographic analyses of the volcanogenic features are provided. Based on observed petrographical features, we interpret the pseudo-hieroglyphs to probably represent unique examples of chaotic horizontal columnar jointing. Following the geomorphological and petrographic examination of the study site, we analyse current Faroese legislation aiming at nature conservation and use this case to discuss broader implications of geoheritage conservation and geotourism in distant regions.Vulkanická krajina vzniklá kenozoickým vulkanismem představuje nejpodivnější rysy globální geodiversity a poskytuje vynikající příběhy pro geovzdělávání. Méně pozornosti se však dostává reliktním vulkanickým formám a lokálním tvarům reliéfu v odlehlých oblastech. V tomto článku přinášíme první popis unikátních vulkanogenních tvarů (dále jen "pseudo-hieroglyfy"), které se vyvíjely na skalní stěně vrcholu na hřbetě Sandfelli u vesnice Gjógv v severní části ostrova Eysturoy (Faerské ostrovy). Je popsán geomorfologický vývoj hřbetu a skalní stěny během kvartéru a jsou uvedeny podrobné petrografické analýzy vulkanogenních vlastností. Na základě pozorovaných petrografických rysů interpretujeme pseudo-hieroglyfy, které pravděpodobně představují jedinečné příklady chaotické horizontální sloupcovité odlučnosti. Po geomorfologickém a petrografickém studiu zájmové lokality analyzujeme současnou faerskou legislativu zaměřenou na ochranu přírody a užíváme tohoto příkladu k diskusi širších důsledků zachování a geoturistiky geografického dědictví ve vzdálených regionech

Crise de abastecimento de água em São Paulo e falta de planejamento estratégico

Embora a crise no abastecimento de água na Região Metropolitana de São Paulo (RMSP) tenha se manifestado de maneira mais intensa no verão de 2013-2014, ela revela um problema crônico que vem afetando toda a Região nos últimos dez anos. Esse problema foi gerado pela falta de um planejamento estratégico que considere questões climatológicas que podem indicar, com meses de antecedência, problemas de recomposição dos níveis dos mananciais, permitindo que ações sejam empreendidas com razoável antecedência, reduzindo os impactos para a população. Este estudo mostra como é possível utilizar informações climáticas na gestão estratégica do sistema de abastecimento da RMSP.Though the crisis in the water supplying system in the Metropolitan Region of São Paulo (RMSP) was more intensively felt in the 2013-2014 summer, it reveals a chronic problem that has been affecting the whole RMSP for the past ten years. This problem is originated from the lack of a strategic planning that takes into consideration climate issues that could, months before, foresee problems to restore the levels of water resources, allowing measures to be implemented within a reasonable anticipation, therefore reducing the impacts on the population. This study shows how it is possible to use climate information in the strategic management of the water supply in the RMSP

Swimming alone? Why linking flood risk perception and behavior requires more than it's the individual, stupid

A common assertion in discussions of flooding is that risk perception is critical and is linked to risk-mitigating behavior. Furthermore, many assert that the adverse effects of floods could be reduced by changes in risk communication, thereby influencing risk perception to foster mitigating behavior. We argue that these assertions are based on quite questionable underlying assumptions: That stakeholders are generally aware of flood risk, that they have the capacity to engage in disaster risk reduction, and that their actions can be effective. The belief in and policies influenced by these three questionable assertions support, in turn, policies that shift responsibility for flood risk reduction onto individuals and homeowners, without regard for social and spatial justice issues. In contrast, we argue that context matters to understanding the complexity of the relation between flood risk perception and behavior, local power relations, and other constraints and opportunities that affect stakeholders. While the academic community has long played a pivotal role in supporting practical flood risk management, future research should take a more critical perspective on the underlying assumptions and focus on improving coordination across theories, methods, and variables, fostering comparative studies across disciplines, contexts, and scales. This article is categorized under: Engineering Water > Planning Water Human Water > Water as Imagined and Represented Science of Water > Water Extreme