Explains the use of a topological structure to examine the closeness between documents in retrieval systems and analyzes the topological structure of a vector-space model, a fuzzy-set model, an extended Boolean model, a probabilistic model, and a TIRS (Topological Information Retrieval System) model. Proofs for the results are appended. (17…

Analyzes the amount of compression possible when arithmetic coding is used for text compression in conjunction with various input models. Algorithms are analyzed; modeling effects are considered; scaling is discussed; higher order models are examined, including prediction by partial matching; and coding effects are described. (34 references) (LRW)

Recommendations are made for the appropriate use and identification of traditional Kuder-Richardson formulas for the estimation of reliability. "Alpha" should be used for reliabilities estimated for tests or scales composed of items yielding scores distributed on more than two points. (SLD)

Shows how mathematical concepts can be displayed on World Wide Web pages. Discusses HTML; embedding mathematical formulae into text as pictures; the use of word-processing tools; MathML, a version of HTML for math; IBM Techexplorer, a browser plug-in; and Java applets. (Author/LRW)

Discussion of models for information retrieval focuses on an application of linear algebra to text clustering, namely, a metric for measuring cluster quality based on the theory that cluster quality is proportional to the number of terms that are disjoint across the clusters. Explains term-document matrices and clustering algorithms. (Author/LRW)

Discussion of impact factors for "Journal Citation Reports" subject categories focuses on the difference between an average of quotients and a global average, obtained as a quotient of averages. Applications in the context of informetrics and scientometrics are given, including journal prices and subject discipline influence scores.…

Presents an indexing and information retrieval method that, based on the vector space model, incorporates term dependencies and thus obtains semantically richer representations of documents. Highlights include term context vectors; techniques for estimating the dependencies among terms; term weights; experimental results on four text collections;…

Discussion of XML focuses on a description of Tequyla-TX, a typed text retrieval query language for XML documents that can search on both content and structures. Highlights include motivations; numerous examples; word-based and char-based searches; tag-dependent full-text searches; text normalization; query algebra; data models and term language;…

Proposes a fuzzy-image database model and a concept of fuzzy space; describes fuzzy-query processing in fuzzy space and fuzzy indexing on complete fuzzy vectors; and uses an example image database, the computer-aided facial-image inference and retrieval system (CAFIIR), for explanation throughout. (Author/LRW)

The topic of orthogonal trajectories is taught as a geometric application of first order differential equations. Instructors usually elaborate on the concept of a family of curves to emphasize that they are different even if their members are of the same type. In this article the author considers five families of ellipses, discusses their…

The Chebyshev polynomials named after a Russian mathematician, Pafnuty Lvovich Chebyshev, have various mathematical applications. A process for obtaining Chebyshev polynomials, and a mathematical inquiry into the patterns they generate, is presented.

Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.

Mathematics should not be studied simply because it is useful; mathematics should be also studied because it nurtures both the mind and soul with its beauty. By completing the four activities described in this paper, students will appreciate mathematical ideas both rationally and emotionally. Since students' appreciation of mathematical ideas…

The problem considered in this paper demonstrates that quite profound and inherently fascinating mathematics is accessible to students who have a sound number sense and deep conceptual understanding of very basic mathematics. This is one of many reasons why we should teach mathematics in ways that promote these attributes in students.

An intuitive derivation of Stirling's formula is presented, together with a modification that greatly improves its accuracy. The derivation is based on the closed form evaluation of the gamma function at an integer plus one-half. The modification is easily implemented on a hand-held calculator and often triples the number of significant digits…