Truncations of inductively minimal geometries

AbstractInductively minimal geometries form an infinite family of incidence geometries on which finite symmetric groups act flag-transitively. They were introduced in Buekenhout et al. (in: N.L. Johnson (Ed.), Mostly Finite Geometries, Marcel Dekker, New York, 1997, pp. 185–190) and satisfy, among other, the (IP)2 and RWPRI conditions (see Bull. Belg. Math. Soc. Simon Stevin 5 (1998) 213–219). In the present paper we characterize the truncations of inductively minimal geometries which satisfy both of these conditions. We also determine all rank 2 residues in these truncations. This enables one to find the diagram of these truncations

The isomorphism problem for linear representations and their graphs

In this paper, we study the isomorphism problem for linear representations. A linear representation Tn*(K) of a point set K is a point-line geometry, embedded in a projective space PG(n+1,q), where K is contained in a hyperplane. We put constraints on K which ensure that every automorphism of Tn*(K) is induced by a collineation of the ambient projective space. This allows us to show that, under certain conditions, two linear representations Tn*(K) and Tn*(K') are isomorphic if and only if the point sets K and K' are PGammaL-equivalent. We also deal with the slightly more general problem of isomorphic incidence graphs of linear representations. In the last part of this paper, we give an explicit description of the group of automorphisms of Tn*(K) that are induced by collineations of PG(n+1,q).Comment: 14 page

Economic Analysis of Summer Fallow Management to Reduce Take-All and N-Leaching in a Wheat Crop Rotation

This paper addresses the question of summer cover crop adoption by farmers in presence of a risk of yield loss due to take-all disease and climate variability. To analyse the public incentives needed to encourage farmers to adopt summer cover crops as a means of reducing N leaching, we combine outputs from an economic, an epidemiological and an agronomic model. The economic model is a simple model of choice under uncertainty. The farmer is assumed to choose among a range of summer fallow managements and input uses on the basis of the expected utility criterion (HARA assumption) in presence of both climate and take all risks. The epidemiological model proposed by Ennaïfar et al. (2007) is used to determine the impact of take all on yields and N-uptake. The crop-soil model (STICS) is used to\ud compute yield developments and N-leaching under various management options and climatic conditions. These models are calibrated to match the conditions prevailing in Grignon, located in the main wheatgrowing\ud area in France. Eight management systems are examined: 4 summer fallow managements: 'wheat volunteers' (WV), 'bare soil' (BS), 'early mustard' (EM), 'late mustard' (LM), and 2 input intensities. We show that the optimal systems are BS (WV) when the take-all risk is (not) taken into account by agents. We then compute the minimum payment to each system such that it emerges in the optimum. We thus derive the required amounts of transfer needed to trigger catch crop adoption. The results of the Monte Carlo sensitivity analysis show that the ranking of management systems is robust over a wide range of input parameters