On the Milnor fibre and L numbers of semi-weighted homogeneous arrangements

Inthispaperwestudygermsofpolynomialsformedbytheproductofsemi-weighted homogeneous polynomials of the same type, which we call semi-weighted homogeneous arrangements. It is shown how the L numbers of such polynomials are computed using only their weights and degree of homogeneity. A key point of the main theorem is to find the number called polar ratio of this polynomial class. An important consequence is the description of the Euler characteristic of the Milnor fibre of such arrangements only depending on their weights and degree of homogeneity. The constancy of the L numbers in families formed by such arrangements is shown, with the deformed terms having weighted degree greater than the weighted degree of the initial germ. Moreover, using the results of Massey applied to families of function germs, we obtain the constancy of the homology of the Milnor fibre in this family of semi-weighted homogeneous arrangements.

Institutional arrangements in the emerging biodiesel industry: Case studies from Minas Gerais-Brazil

Connecting (small) family farmers to the emerging biodiesel industry requires careful design of the institutional arrangements between the producers of oil crops and the processing companies. According to institutional economics theory, the design of effective and efficient arrangements depends on production and transaction characteristics, the institutional environment, and the organizational environment supporting the transaction between producers and the industry. This paper presents a comparative study on two cases in the feedstock-for-biodiesel industry in the state of Minas Gerais, Brazil. The two case studies represent the production and transaction system of soybeans (Glycine max L Merrill) and castor beans (Ricinus communis L). Important elements of effective and efficient institutional arrangements are farmer collective action, availability of technical and financial support, and farmer experience with particular crops. (C) 2011 Elsevier Ltd. All rights reserved.