A Monte Carlo experiment was used to evaluate four procedures for estimating the population squared cross-validity of a sample least squares regression equation. One estimator was particularly recommended. (Author/BH)

Attention is drawn to an ancient Greek method for finding the least common multiple (LCM) of two numbers. A link is established between this method and a well-known method of obtaining the highest common factor (HCF) numbers. This leads to consideration of some relationships between HCF and LCM. (Author/MK)

An analogy, which has been drawn between black hole physics and thermodynamics, is mathematically broadened in this article. Equations similar to the standard partial differential relations of thermodynamics are found for black holes. The results can be used to supplement an undergraduate thermodynamics course. (Author/SK)

By using the method of moments, it is shown that several important and apparently unrelated theorems describing average properties of stochastic systems are in fact particular cases of a general law; this method is applied to generalize the virial theorem and the fluctuation-dissipation theorem to the time-dependent case. (Author/SK)

This study recalculates outdated values for thermochemical radii using more reliable and elaborate calculations of lattice energy and recently obtained ancillary thermodynamic data. (BT)

Presents a derivation which yields a general relationship between the relaxation time, and equilibrium concentrations and rate constants. (BT)

Discussion of evaluation methodology in information retrieval focuses on the average precision over a set of fixed recall values in an effort to evaluate the retrieval effectiveness of a search algorithm. Highlights include a review of traditional evaluation methodology with examples; and a statistical inference methodology called bootstrap.…

Analyzes student progress within the framework of models of choice based on experiences at the Open University (United Kingdom). Investigates why students choose to continue studying in light of their success or failure in previous study and suggests that mathematical models need to be further developed to assist in this field. (Author/LRW)

Discussion of hypermedia systems focuses on a comparison of two types of adaptive algorithm (genetic algorithm and neural network) in clustering hypermedia documents. These clusters allow the user to index into the nodes to find needed information more quickly, since clustering is "personalized" based on the user's paths rather than…

Discusses indexes for text databases and presents an efficient implementation of an index for text searching called PAT array, or suffix array, where the database is stored on secondary storage devices such as magnetic or optical disks. Additional hierarchical index structures and searching algorithms are proposed that improve searching time, and…

Discussion of text analysis and information retrieval and measurement of document similarity focuses on a new text manipulation system called FA (field association)-Sim that is useful for retrieving information in large heterogeneous texts and for recognizing content similarity in text excerpts. Discusses recall and precision, automatic indexing…

Document retrieval tasks composed of human relevance judgments need test sets that allow comparison of human retrieval and automated retrieval and that place absolute limits on performance by any method. Results suggest that it should be possible to improve retrieval system performance within recommended limits by incorporating specific subject…

Illustrates ways of using algebra tiles to give students a visual model of competing squares that appear in algebra as well as in higher mathematics. Such visual representations give substance to the symbolic manipulation and give students who do not learn symbolically a way of understanding the underlying concepts of completing the square. (KHR)

Based on Gestalt theory, the author assumes the existence of a field-force equilibrium to explain how, according to the conciseness principle, mathematically precise gestalts could exist in coauthorship networks. Develops a mathematical function to describe these gestalts in scientific literature and discusses structural characteristics of…

In response to Fischer (HE 527 626), the author considers his proposal to simplify need analysis in Pell grants and other federal need-based student aid as ignoring important considerations. It is suggested that a single formula will be difficult to derive until a coherent philosophy of needs analysis and specific current purpose for the grant…