A model with fixed relations between manifest and latent variables is presented for investigating choice reaction time data. The numbers for fixation originate from the polynomial function. Two options are considered: the component-based (1 latent variable for each component of the polynomial function) and composite-based options (1 latent…

Some examples from different areas of mathematics are explored to give a working knowledge of the computer algebra system Maple. Perfect numbers and Mersenne primes, which have fascinated people for a very long time and continue to do so, are studied using Maple and some questions are posed that still await answers.

In this work, the authors present a commonly used example in electrostatics that could be solved exactly in a conventional manner, yet expressed in a compact form, and simultaneously work out special cases using the method of images. Then, by plotting the potentials and electric fields obtained from these two methods, the authors demonstrate that…

One theoretical feature that makes item response theory (IRT) models those of choice for many psychometric data analysts is parameter invariance, the equality of item and examinee parameters from different examinee populations or measurement conditions. In this article, using the well-known fact that item and examinee parameters are identical only…

In this note we consider a type of integral that is usually presented as an example in any textbook discussion of integration by parts. Invariably this integral is determined by integrating by parts twice and solving. We will present an alternate approach to this integral which makes use of the linearity of the integral, i.e., the fact that…

In this note we consider an experiment involving an urn and k balls with numbers 1, 2, 3, ..., k. The experiment consists of drawing n balls either with replacement or without replacement. We note some surprising results.

Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…

As part of a discussion on Monte Carlo methods, which outlines how to use probability expectations to approximate the value of a definite integral. The purpose of this paper is to elaborate on this technique and then to show several examples using visual basic as a programming tool. It is an interesting method because it combines two branches of…

The sequence 1, 1, 2, 3, 5, 8, 13, 21, ..., known as Fibonacci sequence, has a long history and special importance in mathematics. This sequence came about as a solution to the famous rabbits' problem posed by Fibonacci in his landmark book, "Liber abaci" (1202). If the "n"th term of Fibonacci sequence is denoted by [f][subscript n], then it may…

The study of preservice elementary teachers' knowledge of fractions is important because fractions are notoriously difficult to learn and teach. Unfortunately, studies of preservice teachers' fraction knowledge are limited and have focused primarily on division. The present study included all four operations to provide a more comprehensive…

Transformations or equating of raw test scores on two or more forms of the same test are made interchangeable by empirical procedures deriving the standard error of an equipercentile equating for four different situations. Some numerical results are checked by Monte Carlo methods. Numerical standard errors are computed for two sets of real data.…

The standard error of measurement (SEM) is a measure of the inconsistency in the scores of a particular group of test-takers. It is largest for test-takers with scores ranging in the 50 percent correct bracket; with nearly perfect scores, it is smaller. On tests used to make pass/fail decisions, the test-takers' scores tend to cluster in the range…

The major accomplishments in the development of a management system for academic library collection development were (1) the development of translation tables which express HEGIS (Higher Education General Information Survey) taxonomy terms as sets of LC (Library of Congress) class numbers; (2) the use of these tables to compare library…

The concept of prime factorization is discussed and two rules are developed: one for finding the number of divisors of a number and the other for finding the sum of the divisors. (MP)

Suggests some ways to overcome the problems connected with the use of the Syntactic Density Score. (DD)