We give, for every finite group G, a combinatorial description of the ring of G-Witt vectors on a polynomial algebra over the integers. Using this description we show that the functor, which takes a commutative ring with trivial action of G to its ring of Witt vectors, coincides with the left adjoint of the algebraic functor from the category of G-Tambara functors to the category of commutative rings with an action of G.

Abstract. We introduce toric complexes as polyhedral complexes consisting of rational cones together with a set of integral generators for each cone, and we define their associated face rings. Abstract simplicial complexes and rational fans can be considered as toric complexes, and the face ring for toric complexes extends Stanley and Reisner's face ring for abstract simplicial complexes [20] and Stanley's face ring for rational fans [21]. Given a toric complex with defining ideal I for the face ring we give a geometrical interpretation of the initial ideals of I with respect to weight orders in terms of subdivisions of the toric complex generalizing a theorem of Sturmfels in [23]. We apply our results to study edgewise subdivisions of abstract simplicial complexes.

No abstract

Neurofuzzy approaches for predicting financial time series are investigated and shown to perform well in the context of various trading strategies involving stocks and options. The horizon of prediction is typically a few days and trading strategies are examined using historical data. Two methodologies are presented wherein neural predictors are used to anticipate the general behavior of financial indexes (moving up, down, or staying constant) in the context of stocks and options trading. The methodologies are tested with actual financial data and show considerable promise as a decision making and planning tool.

We study local cohomology of rings of global sections of sheafs on the Alexandrov space of a partially ordered set. We give a criterion for a splitting of the local cohomology groups into summands determined by the cohomology of the poset and the local cohomology of the stalks. The face ring of a rational pointed fan can be considered as the ring of global sections of a flasque sheaf on the face poset of the fan. Thus we obtain a decomposition of the local cohomology of such face rings. Since the Stanley-Reisner ring of a simplicial complex is the face ring of a rational pointed fan, our main result can be interpreted as a generalization of Hochster's decomposition of local cohomology of Stanley-Reisner rings.