Recently, Lima lamented on the 'time-consuming and tiresome' pedagogical nature of repeated integration by parts, throwing down the challenge of providing a pencil-and-paper solution to a related problem in a few seconds. Lima put forth a simple formula as an alternative. In this work, I offer a response to Lima's challenge and his formula.…

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is…

Algebraic notation has been bedazzling learners for generations, yet despite research, learned papers, comparative studies, and a great deal of hard work on the part of classroom practitioners the situation remains a stubborn constant. In this article some small-scale research has highlighted some issues that might find a resonance in many…

We describe composite Gauss-Legendre quadrature for determining definite integrals, including a means of controlling the approximation error. We compare the form and performance of the algorithm with standard Newton-Cotes quadrature. (Contains 1 table.)

Polynomial loglinear models for one-, two-, and higher-way contingency tables have important applications to measurement and assessment. They are essentially regarded as a smoothing technique, which is commonly referred to as loglinear smoothing. A SAS IML (SAS Institute, 2002a) macro was created to implement loglinear smoothing according to…

The boiling point of a monofunctional organic compound is expressed as the sum of two parts: a contribution to the boiling point due to the R group and a contribution due to the functional group. The boiling point in absolute temperature of the corresponding RH hydrocarbon is chosen for the contribution to the boiling point of the R group and is a…

An account is made of the relationship between the convergence behaviour of a sequence and the accumulation points of the underlying set of the sequence. The aim is to provide students with opportunities to contrast two types of mathematical entities through their commonalities and differences in structure. The more set-oriented perspective that…

Benford's law of the "first digits" states that in spite of intuitively expected equal frequency of 1/9 of the decimal digits r = 1, ... , 9 appearance on the first place of any number, various empirical studies show another pattern of these frequencies distribution, which is log[subscript 10](1 + 1/r). The article considers this law and other…

Describes a string-searching algorithm for multiple patterns in a text string; explains the construction of a pattern-matching machine; presents a theoretical analysis and empirical evidence that supports the sublinearity of the algorithm; and compares this algorithm with the Boyer-Moore algorithm for a single pattern. (Contains 10 references.)…

Explains Type/Token-Taken informetrics as a new part of informetrics that studies the use of items rather than the items themselves. Highlights include the frequency distribution of Type/Token-Taken informetrics; the Lotka frequency law; linguistics; a comparison of Type/Token with Type/Token-Taken informetrics; and proofs of theorems. (Author/LRW)

Studies aggressive automated word removal in text categorization in large databases based on corpus statistics to reduce the noise in free texts and to enhance the computational efficiency of categorization. Topics include stop word identification, categorization methods for comparison, tests on four document collections, and evaluation…

Describes an index of cohesion for the investigation of communication between authors or academic units and compares it with the Brillouin-Shaw index. Communication and cooperation between researchers is discussed and graph theory is explained, especially cooperation graphs. (Author/LRW)

Discussion of image database systems focuses on semantic queries and shows how an image is abstracted into a hierarchy of entity names and features; how relations are established between entities visible in the image; and how a "fuzzy" matching technique is used to compare semantic queries to image abstractions. (Author/LRW)

Discusses genetic algorithms in information retrieval, especially for relevance feedback, and evaluates the efficacy of a genetic algorithm with various order-based fitness functions for relevance feedback in a test database. Compares results with the Ide dec-hi method, one of the best traditional methods. (Contains 56 references.) (Author/LRW)

Presents an improved inverted region quadtree variation called Dynamic Inverted Quadtree that is able to support and index a pictorial database. Pattern-searching algorithms are described, and the space needs of Fully Inverted and Dynamic Inverted Quadtrees are analytically compared based on a model of image randomness expressed as a branching…