Images formed from light rays refracting a spherical surface are often introduced in textbooks using the paraxial approximation. Incoming rays propagating from the object meeting the surface of a transparent medium at a given point for which the angle is larger than 15 degrees with respect to the normal are not described accurately from the…

The dipole radiation from an oscillating charge is treated using the Hamiltonian approach to electrodynamics where the concept of cavity modes plays a central role. We show that the calculation of the radiation field can be obtained in a closed form within this approach by emphasizing the role of coherence between the cavity modes, which is…

Fluency with basic number facts is vital for students' progress in mathematics. Not only does it contribute to students' facility with mental computation and algorithms, but an understanding of numbers and their properties builds a foundation for future mathematical work including algebra. There are many activities that can help students…

A bivariate lognormal model for the distribution of the response times on a test by a pair of test takers is presented. As the model has parameters for the item effects on the response times, its correlation parameter automatically corrects for the spuriousness in the observed correlation between the response times of different test takers because…

The estimation of fetal birth weight is an important factor in the management of high risk pregnancies. The information and knowledge gained through this study, comparing a combination of various fetal parameters using computer assisted analysis, will help the obstetrician to screen the high risk pregnancies, monitor the growth and development,…

This article uses photographs as a springboard for mathematical inquiry to encourage readers to see patterns and relationships that they can think about and extend in a mathematically playful way. Herein, two photographs are presented along with a discussion of the meaning of slopes and their relationship to gradient and pitch. (Contains 6…

The capital accumulation ratio (CAR) is commonly used in academic research as a measure of household portfolio quality. This study tested whether a higher initial CAR impacts change in wealth over a decade among households in the accumulation life cycle stage. Meeting the 25% CAR guideline resulted in a 28.1% increase in net worth between 1994 and…

The mythology surrounding Hercules has been a part of human culture for over 2,500 years. In ancient Greek mythology, Eurystheus assigns various labors to Hercules, who has to perform them in order to cleanse his soul. This article treats one of the more famous labors, the fifth labor: The Augean Stables. The labor is provided verbatim from…

A comprehensive understanding of biological functions requires new systemic perspectives, such as those provided by systems biology. Systems biology approaches are hypothesis-driven and involve iterative rounds of model building, prediction, experimentation, model refinement, and development. Developments in computer science are allowing for ever…

This paper reviews some of the most popular policy evaluation methods in empirical microeconomics: social experiments, natural experiments, matching, instrumental variables, discontinuity design, and control functions. It discusses identification of traditionally used average parameters and more complex distributional parameters. The adequacy,…

Despite the fact that categories are often composed of correlated features, the evidence that people detect and use these correlations during intentional category learning has been overwhelmingly negative to date. Nonetheless, on other categorization tasks, such as feature prediction, people show evidence of correlational sensitivity. A…

Educated adults solve simple addition problems primarily by direct memory retrieval, as opposed to by counting or other procedural strategies, but they report using retrieval substantially less often with problems in written-word format (four = eight) compared with digit format (4 = 8). It was hypothesized that retrieval efficiency is relatively…

This paper describes a process control experiment. The apparatus includes a three-vessel glass flow system with a variable flow configuration, means for feeding dye solution controlled by a stepper-motor driven valve, and a flow spectrophotometer. Students use impulse response data and nonlinear regression to estimate three parameters of a model…

In this article, our main objective is to present the use of Microsoft Software Excel 2007/2003 for teaching college and university level curriculum in science and engineering. In particular, we discuss two interesting and fascinating examples of interactive applications of Microsoft Excel targeted for undergraduate students in: 1) computational…

Confidence intervals (CIs) for parameters are usually constructed based on the estimated standard errors. These are known as Wald CIs. This article argues that likelihood-based CIs (CIs based on likelihood ratio statistics) are often preferred to Wald CIs. It shows how the likelihood-based CIs and the Wald CIs for many statistics and psychometric…