The twin prime problem and generalizations (après Yitang Zhang)

We give a short introduction to the recent breakthrough theorem of Yitang Zhang that there are infinitely many pairs of distinct primes (p, q) with |p ? q| < 70 million.     

Analog of parental empathy: Association with physical child abuse risk and punishment intentions

Objectives

Current research has been inconsistent in corroborating that parents’ compromised empathy is associated with elevated physical child abuse risk, perhaps in part because of an emphasis on dispositional empathy rather than empathy directed at their own children. Research has also relied on self-reports of empathy that are susceptible to participant misrepresentation. The present study utilized an analog task of parental empathy to investigate the association of parental empathy toward one's own child with physical child abuse potential and with their tendency to punish perceived child misbehavior.

Methods

A sample of 135 mothers and their 4–9 year old children were recruited, with mothers estimating their children's emotional reactions using a behavioral simulation of parental empathy. Mothers also provided self-reports on two measures of child abuse potential, a measure of negative attributions and expected punishment of children using vignettes, as well as a traditional measure of dispositional empathic concern and perspective-taking.

Results

Findings suggest that parental demonstration of poorer empathic ability on the analog task was significantly related to increased physical abuse potential, likelihood to punish, and negative child attributions. However, self-reported dispositional empathy exhibited the pattern of inconsistent associations previously observed in the literature.

Conclusions

Parental empathy appears to be a relevant target for prevention and intervention programs. Future research should also consider similar analog approaches to investigate such constructs to better uncover the factors that elevate abuse risk.     

Evaluating fifth- and sixth-grade students’ expository writing: task development, scoring, and psychometric issues

Drawing from multiple theoretical frameworks representing cognitive and educational psychology, we present a writing task and scoring system for measurement of students’ informative writing. Participants in this study were 72 fifth- and sixth-grade students who wrote compositions describing real-world problems and how mathematics, science, and social studies information could be used to solve those problems. Of the 72 students, 69 were able to craft a cohesive response that not only demonstrated planning in writing structure but also elaboration of relevant knowledge in one or more domains. Many-facet Rasch Modeling (MFRM) techniques were used to examine the reliability and validity of scores for the writing rating scale. Additionally, comparison of fifth- and sixth-grade responses supported the validity of scores, as did the results of a correlational analysis with scores from an overall interest measure. Recommendations for improving writing scoring systems based on the findings of this investigation are provided.     

Numerical investigation of penetration performance of non-ideal segmented-rod projectiles

The design of a segmented-rod projectile is often simplified into an ideal one in theoretical analysis for the convenience of modeling of its performance. But the actual performance of non-ideal segmented-rod projectiles over the impact velocity range in practical applications was rarely explored. AUTODYN numerical code is used to investigate the influence of the component design upon the penetration performance of non-ideal segmented-rod projectiles over a wide range of impact velocities, which can be used to guide the optimal design of weaponry segmented-rod projectiles.