The analysis explains the basis set superposition error (BSSE) and fragment relaxation involved in calculating the interaction energies using various first principle theories. Interacting the correlated fragment and increasing the size of the basis set can help in decreasing the BSSE to a great extent.

Vieta's famous product using factors that are nested radicals is the oldest infinite product as well as the first non-iterative method for finding [pi]. In this paper a simple geometric construction intimately related to this product is described. The construction provides the same approximations to [pi] as are given by partial products from…

After prolonged viewing of a slowly drifting or rotating pattern under strict fixation, the pattern appears to slow down and then momentarily stop. The authors show that grouping can slow down the process of "motion fading," suggesting that cortical configural form analysis interacts with the computation of motion signals during motion fading. The…

This article tackles several issues involved in specifying, fitting, and interpreting the results of multilevel factor models for ordinal variables. First, the problem of model specification and identification is addressed, outlining parameter interpretation. Special attention is devoted to the consequences on interpretation stemming from the…

Many students have difficulty seeing the conceptual link between bivariate data displayed in a scatterplot and the statistical summary of the relationship, "r." This article shows how to teach (and compute) "r" such that each datum's direct and indirect influences are made apparent and used in a new formula for calculating Pearson's "r."

This study identified 10 savants with developmental disabilities and an exceptional ability to calculate calendar dates. These "calendar calculators" were asked to demonstrate their abilities, and their strategies were analyzed. The study found that the ability to calculate dates into the past or future varied widely among these…

Addition strategies used by 36 kindergarten children were examined. Children were given written stimuli (such as "2+5" and "3+7") during two sessions taking place a week apart. Results indicated that once children came to rely on mental addition strategies, they often quickly invented more economical procedures to compute sums. Also confirmed was…

Pre-kindergarten programs are expanding in states around the nation. Decades of research on the impact of these programs show that high quality standards produce substantial benefits for children, working families, and communities. As state leaders seek to increase investments in pre-k, they face a number of choices and potential tradeoffs that…

Computational models have played a central role in the debate over language learnability. This article discusses how they have been used in different "stances", from generative views to more recently introduced explanatory frameworks based on embodiment, cognitive development and cultural evolution. By digging into the details of certain specific…

The Arab Open University (AOU) has adopted the standard deviation method (SDM) as a grading system in replacement of a fixed scale. Adopting SDM was intended to remedy a problem that has resulted from discrepancies between AOU's graduation requirements and those of its partner, UK Open University. This paper aims mainly at investigating whether…

The tendency to underestimate egocentric distances in immersive virtual environments (VEs) is not well understood. However, previous research (A. R. Richardson & D. Waller, 2007) has demonstrated that a brief period of interaction with the VE prior to making distance judgments can effectively eliminate subsequent underestimation. Here the authors…

Integrity[TM], an online application for testing both the statistical integrity of the test and the academic integrity of the examinees, was evaluated for this review. Program features and the program output are described. An overview of the statistics in Integrity[TM] is provided, and the application is illustrated with a small simulation study.…

The classical twin study provides a useful resource for testing hypotheses about how the family environment influences children's development, including how genes can influence sensitivity to environmental effects. However, existing statistical models do not account for the possibility that children can inherit exposure to family environments…

Deliberate self-harm (DSH; i.e., nonfatal self-poisoning or self-injury) occurs much more frequently than suicide, yet there has been little detailed investigation of the comparative rates of DSH and suicide. We conducted a study of how rates of DSH relate to suicide rates across the life cycle by gender and by method of estimation of DSH rates,…

In this experiment, linear polyynes are synthesized and then the predictions of a one-dimensional, particle in a box are used to calculate the quantum mechanical box length for the polyynes. A solution of graphite in ethanol is irradiated with a Nd:YAG laser (532 nm) and the resulting solution is filtered and analyzed. Data from gas…