Existence and uniqueness of maximal regular flows for non-smooth vector fields

In this paper we provide a complete analogy between the Cauchy-Lipschitz and the DiPerna-Lions theories for ODE's, by developing a local version of the DiPerna-Lions theory. More precisely, we prove existence and uniqueness of a maximal regular flow for the DiPerna-Lions theory using only local regularity and summability assumptions on the vector field, in analogy with the classical theory, which uses only local regularity assumptions. We also study the behaviour of the ODE trajectories before the maximal existence time. Unlike the Cauchy-Lipschitz theory, this behaviour crucially depends on the nature of the bounds imposed on the spatial divergence of the vector field. In particular, a global assumption on the divergence is needed to obtain a proper blow-up of the trajectories.Comment: 38 page

Bedrock and soil geochemistry influence the content of chemical elements in wild edible mushrooms (Morchella group) from South Italy (Sicily)

Chemical elements in the samples of wild edible mushrooms of the Morchellagroup collected from different unpolluted Sicilian sites was analyzed by the ICP-MS (method) to detect the content of their minerals and determine whether soil geology and geochemistry can influence the chemical composition in fungi. Results showed that the mushroom samples mainly contained a high concentration of K and P and a wide variety of minor and trace elements (V, Mo, Pb, Ce, Cs, Zr), including heavy metals. Statistical analysis showed that the mushrooms differed in their content of minor and trace elements based on the geological/geographic site of origin. Comparison with other studies showed differences in the content detected in the Sicilian morels with those collected from other geographical sites. Conversely, dif-ferent fungal species collected from similar geological sites in Sicily showed different patterns of accumulation of the elements confirming that bioconcentration in fungi is species- and site-dependent

Understanding rural areas dynamics from a complex perspective. An application of Prospective Structural Analysis

The development of rural areas continues to be an international priority. The urgent need to fight poverty (mainly concentrated in rural areas) in developing countries, and the demand for increasing economic and social cohesion in developed countries, explain this priority on the political agendas of multilateral bodies, the EU and most other countries. When Development Economics was acknowledged as part of the social and economic theory in the 50’s, different theories and models have tried to explain the unevenness of development and the key elements or conditions that foster it. Traditional rural development programmes were characterised by the implementation of non coordinated, sectoral, horizontal and top-down policies and strategies. The lack of effectiveness and the failures prompted by these policies have propelled the development of new approaches. Territorial rural development is a policy approach embracing contributions from different theoretical frameworks that attempt to foster development strategies based on the consideration of territory as a social construction. Thus, the territory (including all the existing elements and its interactions) has become a key actor for development. However, most of these approaches contemplate rural world through simplistic and monodimensional analysis based on methodologies from single disciplines and on quantitative and/or qualitative morphological descriptions. The pretended multidisciplinarity, frequently ends up on an addition of mono-disciplinary analysis around the object of study. The objective of the present paper is to check the role different elements considered relevant for development by literature´s recent approaches play or can play in rural territories with a very different development situation, using techniques and tools that allow the analysis of rural areas from a complex perspective.territorial rural development, complexity, prospective structural analysis, Community/Rural/Urban Development,

Rational expectations and optimal monetary policy: estimates for Brazil and the U.S.

This paper uses Taylor's macroeconomic model with rational agents. The model is designed to allow the researcher to estimate aggregate demand and price equations under rational expectations and some inflexibility in wage adjustment arising from contracts. The generalized method ofmoments is applied to estimate the model for the Brazilian and U.S. economies in the period 1973-85. Government monetary policy functions based on losses arising from inflation and unemployment are then used to construct a second-order Phillips curve, which shows the different variances of inflation and unemployment that are optimal depending on loss function weights. The main conclusions are that there is a tradeoff between the variabilities of inflation and output in both economies, and that monetary policies were not optimal in either economy during the period.A base teórica deste trabalho e o modelo macroeconômico de Taylor com contratos salariais justapostos, o qual permite estimar equações de preço e demanda agregada sob a hipótese de expectativas racionais. Utilizando o método generalizado dos momentos, o modelo é aplicado para as economias do Brasil e do Estados Unidos da América, para o período de 1973 a 1985. Então, a regra de política monetária ótima de Taylor é aplicada para as duas economias com o intuito de minimizar uma função de perdas advindas de inflação e desemprego, através da qual deriva-se uma curva de Phillips de segunda ordem, mostrando as diferentes variâncias de inflação e desemprego que são ótimas, dependendo dos pesos que cada variância representa nesta função de perdas. Os principais resultados são: existe uma interrelação entre as variabilidades da inflação e do produto; e, em ambas economias, as políticas monetárias não foram ótimas no período analisado

EDUCAÇÃO DOS JOVENS, ANALFABETISMO E O CUSTO GOVERNO: TEORIA E APLICAÇÕES ECONOMÉTRICAS PARA O BRASIL

The objective of this paper is to develop a theoretical model that take into account the role of institutions in the Brazilian States and their impact on the education of the youth and on illiterate people. Here, the institutions mean educational policies, government efficiency, level of technology, and labor market structure. In the empirical test we use panel data for the Brazilian States for the period 1991-2000. In general the results are the following ones: i) The education investment showed to be effective only in curbing illiteracy and has opposite effect on keeping youth at high school; ii) The government efficiency seems to affect the youth to get education above eight years; iii) The institutions formed by labor market structure, level of technology and educational infrastructure showed to be the most important aspect for youth to educate and illiterate people to become literate.

Sobolev spaces in metric measure spaces: reflexivity and lower semicontinuity of slope

IIn this paper we make a survey of some recent developments of the theory of Sobolev spaces W-1,W-q (X, d, m), 1 < q < infinity, in metric measure spaces (X, d, m). In the final part of the paper we provide a new proof of the reflexivity of the Sobolev space based on Gamma-convergence; this result extends Cheeger's work because no Poincare inequality is needed and the measure-theoretic doubling property is weakened to the metric doubling property of the support of m. We also discuss the lower semicontinuity of the slope of Lipschitz functions and some open problems

Appunti in tema di bonifiche agricole

Novità in tema di bonifiche applicabili alle aree agricol