Discussion of information retrieval focuses on an Interaction Information Retrieval model in which documents are interconnected; queries and documents are treated in the same way; and retrieval is the result of the interconnection between query and documents. A theoretical mathematical formulation of this type of retrieval is given. (Contains 31…

Discusses information production processes (IPP)--i.e., continuous mathematical models of production processes such as bibliographies, economic production processes, and social usages of words in a text--from the point of view of concentration theory. Gini's index is studied in the dual framework of IPPs. (27 references) (LRW)

Discussion of probabilistic information retrieval (IR) systems challenges the probability ranking principle in IR from the perspective of (1) signal detection-decision theory and (2) utility theory. Calibration, certainty, and independent assessment are discussed in terms of the relevance of documents, and standard retrieval policies are analyzed.…

Discussion of the interpolation methodology expounded by Goosen and Kusel to model business functions for simulation design criticizes the approach's simplicity because interactive effects between variables in the functional relationships are not considered. (six references) (EA)

Discussion of information-retrieval effectiveness focuses on the use of multiple query or document representations, or multiple retrieval techniques, and combining the retrieval results (also known as data fusion). Experimental results with the SMART System (developed at Harvard and Cornell Universities for over 38 years) indicate combining…

Proposes a theory of attentional dynamics and aims at explaining how listeners respond to systematic change in everyday events while retaining a general sense of their rhythmic structure. A mathematical formulation of the theory describes internal oscillations, called attending rhythms, that focus on pulses of attending energy and interact in…

Describes SENTINEL, a prototype information-retrieval system that is a fusion of multiple information-retrieval technologies, integrating n-grams, a vector space model, and a neural network training rule. Discusses three-dimensional visualization capability, precision and recall, mathematical representation of a document, query building, and…

Presents a unified mathematical definition for the classical models of information retrieval and identifies a mathematical structure behind relevance feedback. Highlights include vector information retrieval; probabilistic information retrieval; and similarity information retrieval. (Contains 118 references.) (Author/LRW)

Presents a new model for combining multiple sources of evidence in database merging based on logistic regression, and occurring only when ranks are available as a key to be used to merge different ranked lists obtained by various retrieval schemes. Results indicate better retrieval effectiveness than other approaches. (LRW)

Presents two alternative computational procedures for solving the modified Bessel equation of zero order: the Frobenius method, and the power series method coupled with a curve fit. Students in heat transfer courses can benefit from these alternative procedures; a course on ordinary differential equations is the only mathematical background that…

Studies concentration aspects of bibliographies, particularly the impact of incompleteness on its concentration values (i.e. its degree of inequality of production of its sources). Models incompleteness by different sampling techniques and discusses implications for the measurement of production inequality in incomplete bibliographies. (Author/LRW)

Direct sum decomposition of Abelian groups appears in almost all textbooks on algebra for undergraduate students. This concept plays an important role in group theory. One simple example of this decomposition is obtained by using the kernel and range of a projection map on an Abelian group. The aim in this pedagogical note is to establish a direct…

In this note, an integrated form of some significant means with two variables is provided, and some chains for mean value inequalities are obtained. At the same time, a concise family of algebraic functions appears, which satisfy Mitrinovic's requirements.

Worker's wage increase is directly proportionate to the investment on the worker's training. A mathematical method of determining the return from investment in training a worker is presented.

It is reasonably well known that the ratios of consecutive terms of a Fibonacci series converge to the golden ratio. This note presents a simple, complete proof of an interesting generalization of this result to a whole family of 'precious metal ratios'.