Estimates of the first Dirichlet eigenvalue from exit time moment spectra

We compute the first Dirichlet eigenvalue of a geodesic ball in a rotationally symmetric model space in terms of the moment spectrum for the Brownian motion exit times from the ball. This expression implies an estimate as exact as you want for the first Dirichlet eigenvalue of a geodesic ball in these rotationally symmetric spaces, including the real space forms of constant curvature. As an application of the model space theory we prove lower and upper bounds for the first Dirichlet eigenvalues of extrinsic metric balls in submanifolds of ambient Riemannian spaces which have model space controlled curvatures. Moreover, from this general setting we thereby obtain new generalizations of the classical and celebrated results due to McKean and Cheung--Leung concerning the fundamental tones of Cartan-Hadamard manifolds and the fundamental tones of submanifolds with bounded mean curvature in hyperbolic spaces, respectively.Comment: 23 pages. arXiv admin note: text overlap with arXiv:1009.125

On the viability of m**2 phi**2 and natural inflation

In the context of single field inflation, models with a quadratic potential and models with a natural potential with subplanckian decay constant are in tension with the Planck data. We show that, when embedded in a two-field model with an additional super massive field, they can become consistent with observations. Our results follow if the inflaton is the phase of a complex field (or an angular variable) protected by a mildly broken U(1) symmetry, and the radial component, whose mass is much greater than the Hubble scale, is stabilized at subplanckian values. The presence of the super massive field, besides modifying the effective single field potential, causes a reduction in the speed of sound of the inflaton fluctuations, which drives the prediction for the primordial spectrum towards the allowed experimental values. We discuss these effects also for the linear potential, and show that this model increases its agreement with data as wellComment: 14 pages, 7 figures. v2 added missing abstract in the pdf, references and very minor changes. v3. typos corrected, references adde

Parabolicity criteria and characterization results for submanifoldsof bounded mean curvature in model manifolds with weights

Let P be a submanifold properly immersed in a rotationally symmetric manifold having a pole and endowed with a weight e h. The aim of this paper is twofold. First, by assuming certain control on the h-mean curvature of P, we establish comparisons for the h-capacity of extrinsic balls in P, from which we deduce criteria ensuring the h-parabolicity or h-hyperbolicity of P. Second, we employ functions with geometric meaning to describe submanifolds of bounded h-mean curvature which are confined into some regions of the ambient manifold. As a consequence, we derive half-space and Bernstein-type theorems generalizing previous ones. Our results apply for some relevant h-minimal submanifolds appearing in the singularity theory of the mean curvature flow

Rumo aos desafios da economia circular : ferramentas de apoio a uma nova estratégia na prática de design

ABSTRACT : The circular economy is a new strategic concept to meet society's needs in a more efficient and sustainable manner based in decoupling the economic growth and welfare from the increase in the consumption of natural resources. It implies the transition from the traditional linear model to a more innovative and circular approach in the development of the economy by designing new products, new services, and new systems, supported, in most cases, by the re-thinking and creation of new business models. Designers and product developers have an important and crucial role to achieve a successful and wide implementation of the concept which has to be accepted and applied in practice by businesses along the whole value chain and meet the current and future needs of consumers and the society. Currently, several methods, principles, practices, tools, training initiatives, and many resources are being developed globally as a result of the wide exploitation of the concept, but there is still a large gap between what is available to companies and designers, and what is applied in practice on product and service development. This paper reflects part of the PhD research project under development by the authors which is based on the promotion of the design practice within Circular Economy. It explores the results of the review of circularity tools available that can be used by design professionals to systematize and guide their development process. The analysis will support the development of a toolkit and guidelines oriented for the practical implementation of the circular economy in the development of innovative and efficient products and services. (Camocho, Ferreira, & Vicente, 2018).A economia circular é um novo conceito estratégico que visa responder às necessidades da sociedade de uma forma mais eficiente e sustentável que se baseia na dissociação entre crescimento económico e bem-estar do aumento do consumo de recursos naturais. Esta transição, do modelo linear tradicional para uma abordagem mais inovadora e circular no desenvolvimento da economia implica o desenvolvimento de novos produtos, novos serviços e novos sistemas, apoiados, na maioria dos casos, no repensar e na criação de novos modelos de negócio. Os designers e os responsáveis pelo desenvolvimento de produtos têm um papel importante e crucial para alcançar uma implementação ampla e bem-sucedida do conceito. Este deve ser aceite e aplicado na prática pelas empresas ao longo de toda a cadeia de valor atendendo às necessidades atuais e futuras dos consumidores e da sociedade. Atualmente, vários métodos, princípios, práticas, ferramentas, iniciativas de formação e outros recursos têm sido desenvolvidos globalmente como resultado da ampla exploração do conceito, no entanto, ainda existe uma grande lacuna entre o que está disponível para empresas e designers e o que é aplicado na prática no desenvolvimento de produtos e serviços. Este artigo reflete parte do projeto de investigação de doutoramento em desenvolvimento pelos autores, o qual se baseia na promoção da prática de design no âmbito da Economia Circular. Explora os resultados da revisão de ferramentas de circularidade disponíveis que podem ser aplicadas pelos profissionais de design na sistematização e orientação do processo de desenvolvimento. Esta análise irá apoiar o desenvolvimento de um conjunto de ferramentas e orientações para a implementação prática da economia circular no desenvolvimento de produtos e serviços mais inovadores e mais eficientes. (Camocho, Ferreira & Vicente, 2018).info:eu-repo/semantics/publishedVersio

Geometric analysis of Lorentzian distance function on spacelike hypersurfaces

Some analysis on the Lorentzian distance in a spacetime with controlled sectional (or Ricci) curvatures is done. In particular, we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the Omori-Yau maximum principle. As a consequence, and under appropriate hypotheses on the (sectional or Ricci) curvatures of the ambient spacetime, we obtain sharp estimates for the mean curvature of those hypersurfaces. Moreover, we also give a suficient condition for its hyperbolicity.Comment: Final version (January 2009). To appear in the Transactions of the American Mathematical Societ

Guide to the classics: Don Quixote, the world’s first novel – and one of the best

Completed by Cervantes when he was in prison, Don Quixote is the tale of a man so passionate about reading he leaves home to live the life of his fictional heroes

The two-field regime of natural inflation

The simplest two-field completion of natural inflation has a regime in which both fields are active and in which its predictions are within the Planck 1-$\sigma$ confidence contour. We show this for the original model of natural inflation, in which inflation is achieved through the explicit breaking of a U(1) symmetry. We consider the case in which the mass coming from explicit breaking of this symmetry is comparable to that from spontaneous breaking, which we show is consistent with a hierarchy between the corresponding energy scales. While both masses are comparable when the observable modes left the horizon, the mass hierarchy is restored in the last e-foldings of inflation, rendering the predictions consistent with the isocurvature bounds. For completeness, we also study the predictions for the case in which there is a large hierarchy of masses and an initial period of inflation driven by the (heavy) radial field.Comment: 18 pages, 9 figure

Looking backward to look forward: water use and economic growth from a long-term perspective

Recent research has examined the relationship between natural resources and economic growth. Considered vitally important, not only for humanity’s well-being but also for ecosystem integrity, the relationship between water use and economic growth has traditionally garnered little attention by analysts. This paper studies water use trends from 1900 to 2000 throughout the world, and their main determinants. To do this, we first analyse historical water use trajectories. Second, to proceed with the determinants of water use, we reformulate the IPAT equation (Ehrlich and Holdren, 1971; Commoner et al. 1971), decomposing water use trends into changes in economic demands and in water use intensity. Finally, a simple scenario analysis is conducted, to project future water use trends under different economic, demographic and technological assumptions. The empirical evidence shows that economic and population growth have been crucial for explaining the increase in water use over the past 100 years, with significant regional differences. Nevertheless, the decline in water use intensity has been responsible for a significant reduction in the growth of total water use.Water use, environmental impacts, economic growth, IPAT model, scenario analysis