We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper.

Contribution: Two general rules for calculating, in the time domain, step discontinuities of voltages and currents in electric circuits, combining physical principles and basic mathematical treatment. The two general rules, resulting from a formal method of analysis, provide a straightforward way to update the states of a circuit, immediately…

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to…

Traffic on motorways can slow down for no apparent reason. Sudden changes in speed by one or two drivers can create a chain reaction that causes a traffic jam for the vehicles that are following. This kind of phantom traffic jam is called a "jamiton" and the article discusses some of the ways in which traffic engineers produce…

Laufer and Nation (1995) proposed that the Lexical Frequency Profile (LFP) can estimate the size of a second-language writer's productive vocabulary. Meara (2005) questioned the sensitivity and the reliability of LFPs for estimating vocabulary sizes, based on the results obtained from probabilistic simulations of LFPs. However, the underlying…

Accuracy is often analyzed using analysis of variance techniques in which the data are assumed to be normally distributed. However, accuracy data are discrete rather than continuous, and proportion correct are constrained to the range 0-1. Monte Carlo simulations are presented illustrating how this can lead to distortions in the pattern of means.…

A localist, parallel constraint satisfaction, artificial neural network model is presented that accounts for a broad collection of attitude and attitude-change phenomena. The network represents the attitude object and cognitions and beliefs related to the attitude, as well as how to integrate a persuasive message into this network. Short-term…

This discussion of new methods for calibrating item response theory (IRT) models looks into new optimization procedures, such as the Genetic Algorithm (GA) to improve on the use of the Newton-Raphson procedure. The advantages of using a global optimization procedure like GA is that this kind of procedure is not easily affected by local optima and…

The problem of chance model modifications under varying levels of sample size, model size, and severity of misspecification in confirmatory factor analysis models was examined through Monte Carlo simulations. Findings suggest that practitioners should exercise caution when interpreting modified models unless sample size is quite large. (SLD)

It is argued that the reduction of cognitive dissonance can be viewed as a constraint satisfaction problem, and a computational model of the process of consonance seeking is proposed. Simulations from this model matched psychological findings from the insufficient justification and free-choice paradigms of cognitive dissonance theory. (SLD)

N. S. Raju, W. J. van der Linden, and P. F. Fleer (in press) have proposed an item response theory-based, parametric procedure for the detection of differential item functioning (DIF)/differential test functioning (DTF) known as differential functioning of item and test (DFIT). DFIT can be used with dichotomous, polytomous, or multidimensional…

The methods, procedures, and results of a sensitivity test on NETMAN, a stochastic digital computer model designed to simulate the information collection and scoring control systems used in tactical warfare training exercises, are described. NETMAN enables its users to obtain information such as personnel requirements, training requirements, and…

The use of analogy in human thinking is examined from the perspective of a multiconstraint theory that postulates similarity, structure, and purpose as three kinds of constraints. The theory has been implemented in computational simulations of the analogical human mind using the Analogical Mapping by Constraint Satisfaction (ACME) model. (SLD)

Two forms, pure-rank and mixed-rank, of a nonparametric, general, linear model-based statistic that can be used to test several hypotheses are presented. A Monte Carlo study was used to investigate the distributional properties of these forms, and their use is discussed. (SLD)

Evaluated the performance of several alternative cluster analytic approaches to initial model specification using population parameter analyses and a Monte Carlo simulation. Of the six cluster approaches evaluated, the one using the correlations of item correlations as a proximity metric and average linking as a clustering algorithm performed the…