An extension of the rasch model for ratings providing both location and dispersion parameters

An elaboration of a psychometric model for rated data, which belongs to the class of Rasch models, is shown to provide a model with two parameters, one characterising location and one characterising dispersion. The later parameter, derived from the idea of a unit of scale, is also shown to reflect the shape of rating distributions, ranging from unimodal, through uniform, and then to U-shaped distributions. A brief case is made that when a rating distribution is treated as a random error distribution, then the distribution should be unimodal.     

Testing the identity of trends under the restriction of monotonicity in repeated measures designs

Procedures are described for the analysis of profiles of means in repeated measures designs under order restriction for patterns of mean change. The exact likelihood ratio is derived for the case of two groups of subjects, and a computationally simple alternative to the exact likelihood ratio test is provided for designs involving more than two groups. Tables of critical values are provided for the case of simple-order alternatives.The author wishes to thank Joseph C. Saunders for his editorial assistance.     

A new solution to the problem of finding all numerical solutions to ordered metric structures

A new algorithm is used to test and describe the set of all possible solutions for any linear model of an empirical ordering derived from techniques such as additive conjoint measurement, unfolding theory, general Fechnerian scaling and ordinal multiple regression. The algorithm is computationally faster and numerically superior to previous algorithms.This research was supported in part by NIGMS grant GM-01231 to the University of Michigan. Authors' names are in alphabetic order.     

Priestley Duality for Quasi-Stone Algebras

In this paper we describe the Priestley space of a quasi-Stone algebra and use it to show that the class of finite quasi-Stone algebras has the amalgamation property. We also describe the Priestley space of the free quasi-Stone algebra over a finite set. This revised version was published online in June 2006 with corrections to the Cover Date.     

Systems evolution,structures of long‐waves,and systems management

By classifying the evolution of systems into inter‐level evolution and intra‐level evolution and dividing the intra‐level evolution into four stages which are interrelated but quite different from each other, we discuss structures of several typical systems long‐waves, and strategies of systems management.     

Defect formation in Nd2Fe14B grains caused by Zn diffusion

Defect formation in Nd₂Fe₁₄B grains, caused by a low-pressure-pack-sublimation Zn coating process, has been investigated. The results indicate that, in the Zn-affected region, low-angle boundaries decorated with precipitates form within the Nd2Fe14B grains. Zn, which is almost insoluble in Nd₂Fe₁₄     

Skew lattices and binary operations on functions

A recent study of the override and update operations defined on sets of partial functions placed both operations within the algebraic context of a certain variety of algebras. We show the latter to be term equivalent to the variety of right-handed skew Boolean algebras. Both operations are then studied within the broader context of skew lattices with an eye towards achieving greater insight into their joint algebraic behavior. A decision procedure is given to determine whether an equation in both operations holds for all sets of partial functions.     

On the Ranges of Algebraic Functions on Lattices

We study ranges of algebraic functions in lattices and in algebras, such as Łukasiewicz-Moisil algebras which are obtained by extending standard lattice signatures with unary operations.We characterize algebraic functions in such lattices having intervals as their ranges and we show that in Artinian or Noetherian lattices the requirement that every algebraic function has an interval as its range implies the distributivity of the lattice. Presented by Daniele Mundici