Unavoidable sample size issues beset psychological research that involves scarce populations or costly laboratory procedures. When incorporating longitudinal designs these samples are further reduced by traditional modeling techniques, which perform listwise deletion for any instance of missing data. Moreover, these techniques are limited in their…

A new design-based theory has recently been developed to estimate impacts for randomized controlled trials (RCTs) and basic quasi-experimental designs (QEDs) for a wide range of designs used in social policy research (Imbens & Rubin, 2015; Schochet, 2016). These methods use the potential outcomes framework and known features of study designs…

If the point of suspension of a multiple pendulum is suitably oscillated then the pendulum can remain in motion in an upside-down position. Since such pendulums can model flexible materials, this inverted motion is sometimes referred to as an 'Indian rope trick'. Despite the complexity of the governing differential equations, this rope trick can…

This paper investigates a general identity which expresses an apparently complicated and intriguing sum of fractions as an elegant and straightforward sum of simple terms.

A method for the numerical evaluation of the error term in Gaussian quadrature rules is derived by means of Chebyshev polynomials of the first kind.

The Bernoulli numbers are among the most interesting and important number sequences in mathematics. They first appeared in the posthumous work "Ars Conjectandi" (1713) by Jacob Bernoulli (1654-1705) in connection with sums of powers of consecutive integers (Bernoulli, 1713; or Smith, 1959). Bernoulli numbers are particularly important in number…

Within the general framework of a multifactor term structure model, the fundamental partial differential equation (PDE) satisfied by a default-free zero-coupon bond price is derived via a martingale-oriented approach. Using this PDE, a result characterizing a model belonging to an exponential affine class is established using only a system of…

In this work, we present an algorithm for computing logarithms of positive real numbers, that bears structural resemblance to the elementary school algorithm of long division. Using this algorithm, we can compute successive digits of a logarithm using a 4-operation pocket calculator. The algorithm makes no use of Taylor series or calculus, but…

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.

This note takes up the issue of parallel curves while illustrating the utility of "Mathematica" in computations. This work complements results presented earlier. The presented treatment, considering the more general case of parametric curves, provides an analysis of the appearance of cusp singularities, and emphasizes the utility of symbolic…

Teachers of first-year college mathematics and engineering courses must often spend considerable time reviewing material originally taught in high school. Instead of this being a mere exercise in repetition, this article suggests that such a review can enrich and revitalize by unifying some of the subjects that need to be re-taught. In the example…