In this article we explore the consequences of modifying the common definition of a parabola by considering the locus of all points equidistant from a focus and (not necessarily linear) directrix. The resulting derived curves, which we call "generalized parabolas," are often quite beautiful and possess many interesting properties. We show that…

Subitizing is the immediate apprehension of the exact number of items in small sets. Despite more than a 100 years of research around this phenomenon, its nature and origin are still unknown. One view posits that it reflects a number estimation process common for small and large sets, which precision decreases as the number of items increases,…

In the first part of the paper, using a direct calculation two-dimensional motion of a particle sliding on an inclined plane is investigated for general values of friction coefficient ([mu]). A parametric equation for the trajectory of the particle is also obtained. In the second part of the paper, the motion of a sphere on the inclined plane is…

Deaf students often lag behind hearing peers in numerical and mathematical abilities. Studies of hearing children with mathematical difficulties highlight the importance of estimation skills as the foundation for formal mathematical abilities, but research with adults is limited. Deaf and hearing college students were assessed on the…

Standardized coefficients in logistic regression analysis have the same utility as standardized coefficients in linear regression analysis. Although there has been no consensus on the best way to construct standardized logistic regression coefficients, there is now sufficient evidence to suggest a single best approach to the construction of a…

We will first recall useful formulas in integration that simplify the calculation of certain definite integrals with the quadratic function. A main formula relies only on the coefficients of the function. We will then explore a geometric proof of one of these formulas. Finally, we will extend the formulas to more general cases. (Contains 3…

How effective is training frogs to jump? This is perhaps the most frequent question in biology that is subjected to statistical analysis: does a treatment make a difference? One can examine whether there is indeed a training effect, by first assuming the opposite. That is, the authors assume that training has no effect on the mean distance jumped.…

This article comes from a question asked by a student of mine: if the Sun radiates energy in the form of electromagnetic waves, could they shift the Earth from its current orbit on a suitable timescale? The answer to such a question is apparently obvious and trivial. Nevertheless, it requires an instructive reasoning and interesting estimates of…

Structural equation models have wide applications. One of the most important issues in analyzing structural equation models is model comparison. This article proposes a Bayesian model comparison statistic, namely the "L[subscript nu]"-measure for both semiparametric and parametric structural equation models. For illustration purposes, we consider…

Purpose: To estimate false-positive rates for rules proposed to identify early noise-induced hearing loss (NIHL) using the presence of notches in audiograms. Method: Audiograms collected from school-age children in a national survey of health and nutrition (the Third National Health and Nutrition Examination Survey [NHANES III]; National Center…

Looking for closed forms for an integral depending on one parameter, we obtain integral identities and new integral presentations of Catalan numbers. Wallis formula appears as an important tool.

A simple and direct method for measuring the absorption of carbon dioxide by two different substances is described. Lithium hydroxide has been used for decades to remove the gas from enclosed living spaces, such as spacecraft and submarines. The ratio of the mass of carbon dioxide absorbed to the mass of lithium hydroxide used obtained from this…

Engagement influences participation, progression and retention in game-based e-learning (GBeL). Therefore, GBeL systems should engage the players in order to support them to maximize their learning outcomes, and provide the players with adequate feedback to maintain their motivation. Innovative engagement monitoring solutions based on players'…

Receiver operating characteristic curve (ROC) analysis was used to investigate the ability of early numeracy curriculum-based measures (EN-CBM) administered in preschool to predict performance below the 25th and 40th percentiles on a quantity discrimination measure in kindergarten. Areas under the curve derived from a sample of 279 students ranged…

Oklahoma is one of 16 states electing to use an A-F letter grade as an indicator of school quality. On the surface, letter grades are an attractive policy instrument for school improvement; they are seemingly clear, simple, and easy to interpret. Evidence, however, on the use of letter grades as an instrument to rank and improve schools is scant…