Optimal SL(2)-homomorphisms

Let G be a semisimple group over an algebraically closed field of very good characteristic for G. In the context of geometric invariant theory, G. Kempf has associated optimal cocharacters of G to an unstable vector in a linear G-representation. If the nilpotent element X in Lie(G) lies in the image of the differential of a homomorphism SL(2) --> G, we say that homomorphism is optimal for X, or simply optimal, provided that its restriction to a suitable torus of SL(2) is optimal for X in Kempf's sense. We show here that any two SL(2)-homomorphisms which are optimal for X are conjugate under the connected centralizer of X. This implies, for example, that there is a unique conjugacy class of principal homomorphisms for G. We show that the image of an optimal SL(2)-homomorphism is a completely reducible subgroup of G; this is a notion defined recently by J-P. Serre. Finally, if G is defined over the (arbitrary) subfield K of k, and if X in Lie(G)(K) is a K-rational nilpotent element whose p-th power is 0, we show that there is an optimal homomorphism for X which is defined over K.Comment: AMS-LaTeX, 26 pages. To appear in Comment. Math. Helv. The most substantial modification found in the revision is a proof of the G(K)-conjugacy of any 2 optimal SL(2)-homomorphisms for X in Lie(G)(K) which are defined over K; see Prop/Def 21 and Theorem 4

Assessing the potential impact on poverty of rising cereals prices : the case of Mali

Concerns have been raised about the impact of rising food prices worldwide on the poor. To assess the (short term) impact of rising food prices in any particular country it is necessary to look at both the impact on food producers (who benefit from an increase in prices) and food consumers (who loose out when the price increases), with a focus on poor producers and consumers. In Mali the impact of a change in the price of rice is not ambiguous because about half of the rice consumed in the country is imported, so that the negative impact for consumers is much larger than the positive impact for producers. By contrast, for millet and sorghum, as well as corn, the impact is more ambiguoussince much of the consumption is locally produced. Using a recent and comprehensive household survey, this paper provides an assessment of the potential impact of higher food prices on the poor in Mali using both simple statistical analysis and non-parametric methods. The paper finds that rising food prices for rice, millet and sorghum, corn, as well as wheat and bread could together lead to a substantial increase in poverty, with the increase in the price of rice having by far the largest negative impact.Rural Poverty Reduction,Population Policies,Achieving Shared Growth,Food&Beverage Industry

Why are goods so cheap in some countries?

Looking around the world, we observe substantial differences across countries in prices for most goods. These price differences also tend to be positively correlated with income differences, so that citizens of high-income countries tend to pay more for the same goods than citizens in low-income countries. In “Why Are Goods So Cheap in Some Countries?,” George Alessandria and Joseph Kaboski summarize some of the evidence related to the big price differences across countries for a broad set of goods. They then discuss the relationship between prices and income levels and some possible explanations for that relationship.Prices

Pricing-to-market and the failure of absolute PPP

The authors show that deviations from the law of one price in tradable goods are an important source of violations of absolute PPP across countries. Using highly disaggregated export data, they document systematic international price discrimination: at the U.S. dock, U.S. exporters ship the same good to low-income countries at lower prices. This pricing-to-market is about twice as important as any local non-traded inputs, such as distribution costs, in explaining the differences in tradable prices across countries. The authors propose a model of consumer search that generates pricing-to-market. In this model, consumers in low-income countries have a comparative advantage in producing non-traded, non-market search activities and therefore are more price sensitive than consumers in high-income countries. They present cross-country time use evidence and evidence from U.S. export prices that are consistent with the model.

Spectral imaging in preclinical research and clinical pathology.

Spectral imaging methods are attracting increased interest from researchers and practitioners in basic science, pre-clinical and clinical arenas. A combination of better labeling reagents and better optics creates opportunities to detect and measure multiple parameters at the molecular and cellular level. These tools can provide valuable insights into the basic mechanisms of life, and yield diagnostic and prognostic information for clinical applications. There are many multispectral technologies available, each with its own advantages and limitations. This chapter will present an overview of the rationale for spectral imaging, and discuss the hardware, software and sample labeling strategies that can optimize its usefulness in clinical settings

Storage and ripening of plantains

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