2 resultados para Polynomial Roots
em Academic Archive On-line (Stockholm University
Resumo:
In the village'of Citing in the northern highlands of Tanzania, the factors: social stratification, land tenure, production strategies, investment patterns and the economic uncertainties of society are studied and their relationship to land degradation is examined. The main assumption of the study is that the causes of land degradation are so complex that a methodology that emphasises contextualisation has to be used. A methodological framework that considers inter-linkages between all these factors is developed and tested. The result of the test shows that contextualisation gives a more in-depth and complex explanation than conventional, positivist research. The study gives a detailed account of the relationship that various wealth groups have to land and land degradation in the village. It is found that all wealth groups are destructive to the land but in varying ways. The rich farmers are over-cultivating land marginal to agriculture, the middle peasants have too many cattle in the village while the poor peasants are so marginalised socially that they hardly influence land management. Those identified as having economic as well as social incentives to maintain soil fertility are the middle peasants, while the rich farmers are shown to be consciously soil-mining the former grazing areas.
Resumo:
We study the power series ring R= K[[x1,x2,x3,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R. Of particular interest are the homogeneous, finitely generated ideals in R', among them the generic ideals. The definition of S as an inverse limit yields a set of truncation homomorphisms from S to K[x1,...,xn] which restrict to R'. We have that the truncation of a generic I in R' is a generic ideal in K[x1,...,xn]. It is shown in Initial ideals of Truncated Homogeneous Ideals that the initial ideal of such an ideal converge to the initial ideal of the corresponding ideal in R'. This initial ideal need no longer be finitely generated, but it is always locally finitely generated: this is proved in Gröbner Bases in R'. We show in Reverse lexicographic initial ideals of generic ideals are finitely generated that the initial ideal of a generic ideal in R' is finitely generated. This contrast to the lexicographic term order. If I in R' is a homogeneous, locally finitely generated ideal, and if we write the Hilbert series of the truncated algebras K[x1,...,xn] module the truncation of I as qn(t)/(1-t)n, then we show in Generalized Hilbert Numerators that the qn's converge to a power series in t which we call the generalized Hilbert numerator of the algebra R'/I. In Gröbner bases for non-homogeneous ideals in R' we show that the calculations of Gröbner bases and initial ideals in R' can be done also for some non-homogeneous ideals, namely those which have an associated homogeneous ideal which is locally finitely generated. The fact that S is an inverse limit of polynomial rings, which are naturally endowed with the discrete topology, provides S with a topology which makes it into a complete Hausdorff topological ring. The ring R', with the subspace topology, is dense in R, and the latter ring is the Cauchy completion of the former. In Topological properties of R' we show that with respect to this topology, locally finitely generated ideals in R'are closed.