The approximate nature of measurement is stressed, with examples given of elementary school mathematics problems which confuse reality with its mathematical model. Examples relating measurement to mathematical structure are given. (DT)

A procedure is outlined showing how the axiom of local independence for latent structure models can be weakened. (CK)

Describes some continuous models for growth of the seaweed Macrocystis pyrifera. Uses observed growth rates over several months to derive first-order differential equations as models for growth rates of individual fronds. The nature of the solutions is analyzed and comparison between these theoretical results and documented characteristics of…

Paper reports research related to mathematics, philosophy, computer science and linguistics. It gives a system of axioms for a relatively simple form of fuzzy set theory, and uses these axioms to consider the accuracy of representing concepts in various ways by fuzzy sets. (Author)

POLYFACT is a learning program that attempts to factor multivariable polynomials. The program has been successful in factoring polynomials (in simplified form) with a maximum of 84 terms, each term consisting of as many as five variables and a maximum degree of 67. The complexity of this learning task placed unusual requirements on the…

The statistician has n independent estimates of a parameter he knows is positive, but, as is the case in components-of-variance problems, some of the estimates may be negative. If the n estimates are to be combined into a single number, we compare the obvious rule, that of averaging the n values and taking the positive part of the result, with…

The inadequacies in present measurement models are indicated and a description is given of how tree theory, a theory-generative model, overcomes these inadequacies. Among the weaknesses cited in many measurement models are their untested assumptions of linear order and unidimensionality and their inability to generate non-associational…

Fixed-width confidence intervals for a population regression line over a finite interval of x have recently been derived by Gafarian. The method is extended to provide fixed-width confidence intervals for the difference between two population regression lines, resulting in a simple procedure analogous to the Johnson-Neyman technique. (Author)

Discusses an introductory chemical engineering course in which mathematical models are used to analyze experimental data. Concepts illustrated include dimensional analysis, scaleup, heat transfer, and energy conservation. (MLH)

Elementary differential calculus is used to analyze and to discuss some complex economic situations. (JT)

The author uses mathematical models that involve only algebra and a few basic ideas in discrete probability to describe the frequency of conception in large human societies. A number of calculations which can be done by students as exercises are given. (MN)

Mathematical observations are made about some continuous curves, called transitions, encountered in well-known experiences. The transition parabola, the transition spiral, and the sidestep maneuver are presented. (MNS)

Two models for psychological distances, the hierarchical clustering model and the multidimensional Euclidean model, are compared to see how they relate to each other. (Author/RK)