E. O. Milton’s research while affiliated with University of California, Davis and other places

A multiple-answer multiple-choice test item has a certain number of alternatives,any number of which might be keyed. The examinee is also allowed to mark any number of alternatives. This increased flexibility over the one keyed alternative case is useful in practice but raises questions about appropriate scoring rules. In this article a certain class of item scoring rules called thebinary class is considered. The concepts ofstandard scoring rules and equivalence among these scoring rules are introduced in the misinformation model for which the traditional knowledge model is a special case. The examinee's strategy with respect to a scoring rule is examined. The critical role of a quantity called the scoring ratio is emphasized. In the case of examinee uncertainty about the number of correct alternatives on an item, a Bayes and a minimax strategy for the examinee are developed. Also an appropriate response for the examiner to the minimax strategy is outlined.

In this paper it is shown that elements of a space of analytic functions defined in the tube domain Tc=Rn+iC, where C is an open convex cone of a certain type, obtain distributional boundary values in the weak topology of the distribution spaces (Formula Presented) and representation results of the analytic functions in terms of the boundary values are given. Converse results are obtained in which an analytic function in the defined space is constructed from a given distribution in (Formula Presented), and some applications of the distributional boundary value theorems are obtained. The main results are proved with the aid of several new lemmas concerning the (Formula Presented) function spaces of type (Formula Presented) and their dual spaces. The results obtained here are motivated by known results used in the construction of local fields in quantum field theory.