The Hahn Quantum Variational Calculus

We introduce the Hahn quantum variational calculus. Necessary and sufficient optimality conditions for the basic, isoperimetric, and Hahn quantum Lagrange problems, are studied. We also show the validity of Leitmann's direct method for the Hahn quantum variational calculus, and give explicit solutions to some concrete problems. To illustrate the results, we provide several examples and discuss a quantum version of the well known Ramsey model of economics.Comment: Submitted: 3/March/2010; 4th revision: 9/June/2010; accepted: 18/June/2010; for publication in Journal of Optimization Theory and Application

Desempenho de forrageiras hibernais sob distintos níveis de luminosidade Performance of hibernal forages under distinct brightness levels

Objetivou-se determinar os possíveis efeitos da restrição de luminosidade, obtida com distintas densidades de árvores de Pinnus taeda, sobre a produção e qualidade de: aveia-preta (Avena strigosa Schreb) cv. Comum, aveia-branca (Avena sativa L.) cv. Fapa 2, azevém (Lolium multiflorum L.) cv. Comum, trigo (Triticum aestivum L.) duplo propósito cv. BRS Tarumã e ervilhaca peluda (Vicia villosa L.). Avaliaram-se três níveis de luminosidade: a sol aberto (sem presença de árvores de Pinnus taeda), 30% de restrição de radiação (usando espaçamento entre árvores de 15 × 3 m, com 222 árvores/ha) e 60% de restrição de radiação (usando espaçamento de 9 × 3 m, com 370 árvores/ha). Foram realizadas avaliações da produção de forragem, da composição química e dos componentes estruturais das plantas, do potencial hídrico das plantas, da umidade do solo, das variáveis microclimáticas e da produção de acículas. O delineamento experimental foi de blocos completos ao acaso, em parcelas subdivididas e três repetições. O azevém foi a espécie mais produtiva em todos os níveis de luminosidade, embora a ervilhaca tenha apresentado a menor redução de produção quando sombreada. Houve maior potencial hídrico nas plantas e maior umidade no solo nos ambientes sombreados, mesmo assim, a produção de forragem reduziu significativamente no sombreamento mais intenso (81%). A composição química e os componentes estruturais de todas as forrageiras estudadas também são afetados pelo aumento da restrição luminosa.<br>Possible effects of brightness restriction, obtained by different Pinnus taeda tree densities, on the production and quality of black oat (Avena strigosa Schreb) cv. Common, white oat (Avena sativa L.) cv. FAPA 2, annual ryegrass (Lolium multiflorum L.) cv. Common, hairy vetch (Vicia villosa), wheat (Triticum aestivum L.) cv. dual purpose BRS Tarumã were studied. It was evaluated three brightness levels: 1 - full sunlight with no trees; 2 - 30% of radiation restriction, using 15 × 3 m spacing between trees (222 trees/ha), and; 3 - 60% of radiation restriction, using 9 × 3 m between trees (370 trees/ha). It was performed evaluations of forage production, chemical composition and structural component of plants, water potential of the plants, soil moisture, microclimate variables and production of needles. The experimental design was completely randomized blocks, in split-plots and three replicates. Ryegrass was the most productive species at all brightness levels, although hairy vetch showed the lowest reduction on production under shading. There was higher water potential in the plants and higher soil moisture under shading, however, forage production was significantly reduced in the most intense shading (81%). Chemical composition and structural components of all studied forage species are also affected by brightness restriction increase

How do epidemics induce behavioral changes?

Presented at GLOBELICS 2009, 7th International Conference, 6-8 October, Dakar, Senegal.Parallel session 2: Population, health and growthThis paper develops a theory of optimal fertility behavior under mortality shocks. In an OLG model, young adults determine their optimal fertility, labor supply and life-cycle consumption with both exogenous child and adult mortality risks. We show that a rise in adult mortality exerts an ambiguous effect on both net and total fertility in a general equilibrium framework, while child mortality shocks unambiguously lead to a rise in total fertility, leaving net fertility unchanged. We complement our theory with an empirical analysis using a sample of 39 Sub-Saharan African (SSA) countries over the 1980-2004 period, examining the overall effects of the child and adult mortality channels on both total and net fertility. We find child mortality to exert a robust, positive impact on total fertility but no impact on net fertility, whereas a rise in adult mortality is found to negatively influence both total and net fertility. Given the particular demographic profile of the HIV/AIDS epidemic (killing essentially young, active adults), we then conclude in favor of an unambiguous negative effect of the HIV/AIDS epidemic on net fertility in SS