Property valuation is a particularly complex and large problem domain that requires diverse, highly sophisticated skills, expertise and knowledge. Experienced valuers have framed sets of assumptions to be applied in estimating the ‘most likely selling price’ or the ‘worth’ of a property. In order to implement a valuation, these valuers use mathematical models called ‘valuation methods’. Previou...

The ideals of the ring Zp are {0} and pZp, n ≥ 0. From this it follows that Zp is a discrete valuation ring, a principal ideal domain with exactly one maximal ideal, namely pZp; Zp is the valuation ring of Qp with the valuation vp. For n ≥ 1, Zp/pZp is isomorphic as a ring with Z/pZ. |x|p = p−vp(x), dp(x, y) = |x− y|p. With the topology induced by the metric dp, Qp is a locally compact abelian ...

This study examines the market valuation of accounting earnings during the period before it is publicly revealed that the earnings are fraudulent. Using both cross-sectional and time-series valuation models, we first find that the market accords less weight to earnings when the accounting numbers are fraudulent. We also show that the market better anticipates the presence of fraud when there is...

We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel-algebra of the dcpo with the Scott topology. It follows that every bounded and continuous valuation on a continuous domain can be extended uniquely to a Borel measure. The...

Let R be an n-dimensional regular local domain essentially of finite type over a ground field k of characteristic zero, and let ν be a rank one valuation centered on R. Recall that this is equivalent to asking that ν be an R-valued valuation on the fraction field K of R, taking non-negative values on R and positive values on the maximal ideal m ⊆ R. A theorem of Zariski and Abhyankar states tha...

This expository paper contains history, definitions, constructions, and the basic properties of Rees valuations of ideals. A section is devoted to one-fibered ideals, that is, ideals with only one Rees valuation. Cutkosky [5] proved that there exists a two-dimensional complete Noetherian local integrally closed domain in which no zero-dimensional ideal is one-fibered. However, no concrete ring ...

Preference reversals between choice and valuation are typically studied with probabilities or time delays. I extend them to social distances document their existence in this new domain.