Generalized Lyubeznik numbers

Given a local ring containing a field, we define and investigate a family of invariants that includes the Lyubeznik numbers, but that captures finer information. These "generalized Lyubeznik numbers" are defined as lengths of certain iterated local cohomology modules in a category of D-modules, and in order to define them, we develop the theory of a functor Lyubeznik utilized in proving that his original invariants are well defined. In particular, this functor gives an equivalence of categories with a category of D-modules. These new invariants are indicators of F-regularity and F-rationality in characteristic p>0, and have close connections with characteristic cycle multiplicities in characteristic zero. We compute the generalized Lyubeznik numbers associated to monomial ideals using interpretations as lengths in a category of straight modules, as well as provide examples of these invariants associated to certain determinantal ideals.Comment: 25 pages; comments welcom

Double layers on auroral field lines

Time-stationary solutions to the Vlasov-Poisson equation for ion holes and double layers were examined along with particle simulations which pertain to recent observations of small amplitude (e phi)/t sub e approx. 1 electric field structures on auroral field lines. Both the time-stationary analysis and the simulations suggest that double layers evolve from holes in ion phase space when their amplitude reaches (e phi)/t sub e approx. 1. Multiple small amplitude double layers which are seen in long simulation systems and are seen to propagate past spacecraft may account for the acceleration of plasma sheet electrons to produce the discrete aurora

Secure Identification of Free-Floating Planets

Among the methods proposed to detect extrasolar planets, microlensing is the only technique that can detect free-floating planets. Free-floating planets are detected through the channel of short-duration isolated lensing events. However, if a seemingly isolated planetary event is detected, it is difficult to firmly conclude that the event is caused by a free-floating planet because a wide-separation planet can also produce an isolated event. There were several methods proposed to break the degeneracy between the isolated planetary events produced by the free-floating and wide-separation planets, but they are incomplete. In this paper, we show that free-floating planets can be securely identified by conducting astrometric follow-up observations of isolated events to be detected in future photometric lensing surveys by using high-precision interferometers to be operated contemporarily with the photometric surveys. The method is based on the fact that astrometric lensing effect covers much longer range of the lens-source separation than the photometric effect. We demonstrate that several astrometric follow-up observations of isolated planetary events associated with source stars brighter than $V\sim 19$ by using the {\it Space Interferometry Mission} with an exposure time of $\lesssim 10 {\rm min}$ for each observation will make it possible to measure the centroid shift induced by primaries with projected separations up to $\sim 100 {\rm AU}$. Therefore, the proposed method is far more complete than previously proposed methods that are flawed by the limited applicability only to planets with projected separations $\lesssim 20 {\rm AU}$ or planets accompanied by bright primaries.Comment: 5 pages including 2 figure

Diffusion of information among small-scale farmers in Senegal: the concept of Farmer Field Schools

Recent research on the Farmer Field School (FFS) approach in agriculture in developing countries has raised some doubts on the economic impacts of this concept and especially the knowledge diffusion effects from trained to non-trained farmers. Based on a study in Senegal this paper hypothesizes that the question of the project placement strategy is vital when analyzing knowledge diffusion effects of FFS in Africa. Results show that the share of trained farmers in a community is a decisive factor for adoption behavior and knowledge diffusion. It is concluded that when introducing an FFS, a critical mass of trained farmers is important to attain effective dissemination of information and to generate positive stimuli for adoption and learning among non-participants.Africa,Senegal,agricultural extension,Farmer Field School,diffusion

Small-scale inland fisheries in Africa: How to collect data for poverty assessment?

Accurate poverty assessments in developing countries require efforts to collect detailed household level data. Especially in Africa, such procedures are time consuming, expensive and can be subject to numerous constraints. In this paper we discuss the procedure of the collection of data on consumption, income and assets from poor households involved in small-scale inland fisheries as well as agricultural activities. A sampling scheme has been developed that captures the heterogeneity in ecological conditions and the seasonality of livelihood options. Sampling includes a three point panel survey of 300 households. The respondents belong to four different ethnic groups randomly chosen from three strata representing different ecological zones. In the first part of the paper the methodological framework, the survey design and interview procedure adapted to the conditions in Northern Cameroon is discussed. The second part of the paper presents selected results of the baseline study on consumption, income and assets for different types of households. In addition the record of past ecological, economic and social shocks is presented. --