Discusses an alternative form of the quadratic formula to solve quadratic equations. Presents an application to chemistry to illustrate the need for quadratic formulas better suited to approximations obtained using hand-held calculators. Addresses the problems of rounding errors, accuracy of solutions, and factoring as a method of solution. (MDH)

Presented are formulas that calculate the area of quadrilaterals when the diagonals are viewed as vectors. The area can be expressed in terms of the vector product of the diagonals (in space) and in terms of the scalar product of related vectors (in the plane). (MDH)

Describes the use of loglinear statistical models in the field of informetrics, especially for the analysis of information systems. A detailed example is given of developing a model based on loglinear analysis to determine book acquisition patterns in libraries, including mathematical considerations and algorithms. (19 references) (LRW)

Factors in alumni giving to colleges are discussed, some aspects of alumni giving to all higher education are forecast, and for illustration, probable giving to one college (Amherst College, Massachusetts) is predicted. Factors considered include alumni numbers, dollar amounts given, and the link between stock market activities and donations. (MSE)

Utilized is the technique of expanding circles to explore the truth of the statement that, if the sums of the lengths of the opposite sides of a quadrilateral are equal, then a circle can be inscribed within that quadrilateral. This statement is the converse of a well-known geometric theorem. (JJK)

Discusses the use of citation networks for constructing measures of the relative standing of journals in scientific journal-to-journal networks. Topics addressed include eigenvectors; measuring the standing of national scientific communities; and an empirical comparison of two measures of standing, one considering the environment and one without…

Discusses distributed information retrieval systems that take into account the weights of descriptors from thesauri. Topics addressed include a mathematical model for information retrieval subsystems; organization of inverted files; models for the distributed homogeneous information systems; a distributed information retrieval system based on…

Explains how a competition-based connectionist model for diagnostic problem-solving is adapted to information retrieval. Topics include probabilistic causal networks; Bayesian networks; the neural network model; empirical studies of test collections that evaluated retrieval performance; precision results; and the use of a thesaurus to provide…

Bias due to attrition of respondents poses a threat to the internal and external validity of research findings. Discusses methods of detecting attrition bias in longitudinal family research, and presents Heckman's procedure to correct attrition bias. Data from the University of California Longitudinal Study of Generations are used to illustrate…

While it is most often the case that an understanding of physics can simplify mathematical calculations, occasionally mathematical precision leads directly to a better physical understanding of a situation. Presents an example of a mechanics problem in which careful mathematical derivation can lead directly to a deeper physical understanding of…

Games are promoted as examples for classroom discussion of stationary Markov chains. In a game context Markov chain terminology and results are made concrete, interesting, and entertaining. Game length for several-player games such as "Hi Ho! Cherry-O" and "Chutes and Ladders" is investigated and new, simple formulas are given. Slight…

A new methodology is proposed for the simultaneous reduction of units, variables, and occasions of a three-mode data set. Units are partitioned into a reduced number of classes, while, simultaneously, components for variables and occasions accounting for the largest common information for the classification are identified. The model is a…

This note describes a method for evaluating the sums of the m -th powers of n consecutive terms of a general arithmetic sequence: { S[subscript m] = 0, 1, 2,...}. The method is based on the use of a differential operator that is repeatedly applied to a generating function. A known linear recurrence is then obtained and the m-th sum, S[subscript…

This paper considers the problem of analysis of correlation coefficients from a multivariate normal population. A unified theorem is derived for the regression model with normally distributed explanatory variables and the general results are employed to provide useful expressions for the distributions of simple, multiple, and partial-multiple…

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel…