Stability of oscillations in systems obeying Mathieu's equation

Numerous relatively simple physical systems give rise under appropriate circumstances to oscillations which obey the equation y″ + ?(1 + k cos t)y = 0 (Mathieu's equation). These oscillations may be either stable, periodic, or unstable, depending upon parameters of the physical system as expressed by the parameters ? and k in the basic equation. It has been customary to distinguish between the stable and unstable states by diagrams of the type of Fig. 1, from which it is possible to tell whether a given set of values of the parameters ?, k will yield a stable or unstable solution. In this paper are given curves which not only present this information, but in addition give for an important part of the stable state the values of the characteristic exponent μ. The solution of the equation y″ + ?(1 + k cos t)y = 0 depends to a large extent on this exponent, and the availability of values of μ should greatly facilitate the practical application of the equation.     

Weak Ties in Networked Communities

Communities with high levels of social capital are likely to have a higher quality of life than communities with low social capital. This is due to the greater ability of such communities to organize and mobilize effectively for collective action because they have high levels of social trust, dense social networks, and well-established norms of mutuality (the major features of social capital). Communities with “bridging” social capital (weak ties across groups) as well as “bonding” social capital (strong ties within groups) are the most effective in organizing for collective action. People who belong to multiple groups act as bridging ties. When people with bridging ties use communication media, such as the Internet, they enhance their capability to educate community members and to organize, as needed, for collective action. This article summarizes evidence from stratified household survey data in Blacksburg, VA, showing that people with weak (bridging) ties across groups have higher levels of community involvement, civic interest, and collective efficacy than people without bridging ties among groups. Moreover, heavy Internet users with bridging ties have higher social engagement, use the Internet for social purposes, and have been attending more local meetings and events since going online than heavy Internet users with no bridging ties. These findings may suggest that the Internet—in the hands of bridging individuals-is a tool for enhancing social relations and information exchange, and for increasing face-to-face interaction, all of which help to build both bonding and bridging social capital in communities.     

Science Instruction for Students with Learning Disabilities: A Meta‐Analysis

Although science has received much attention as a political and educational initiative, students with learning disabilities (LD) perform significantly lower than their nondisabled peers. This meta‐analysis evaluates the effectiveness of instructional strategies in science for students with LD. Twelve studies were examined, summarized, and grouped according to the type of strategy implemented. Effect sizes (ES) were calculated for each study. Across all studies, a mean ES of .78 was obtained, indicating a moderate positive effect on students with LD science achievement. Findings also align with past reviews of inquiry‐based instruction for students with special needs, indicating that students with LD need structure within an inquiry science approach in order to be successful. Additionally, results suggest that mnemonic instruction is highly effective at increasing learning disabled students' acquisition and retention of science facts.     

Elitism and Meritocracy in UK Universities: the UK Needs Investment in its Labour Force

This article summarises previous academic research into university education, distinguishing between arguments for and against improving access. Several views are summarised, including structural‐functionalism, which claims that powerful social groups maintain their status and income, and human capital theory, which focuses on employee productivity. Almost all viewpoints discussed in this article support meritocracy. UK universities differ in their openness to people from disadvantaged backgrounds. Many universities, referred to here as ‘inclusive’, deserve credit for encouraging disadvantaged people to become students; in contrast, ‘exclusive’ universities tend to have fewer disadvantaged students than expected. There are barriers facing disadvantaged students, including unequal access to universities, which can at least partly be explained by private schools for rich pupils and financial burdens at university causing some students to take paid work (reducing time available for study). The UK spends less per student on universities than the world average and less than half as much as some European countries. The UK Government could increase university funding, concentrating on universities that are most inclusive and that tend to have the largest problems in affording sufficient staff and teaching facilities. This investment would give long‐term benefits to the UK economy.     

Peer choice – does reviewer self‐selection work?

The British Journal of Educational Technology (BJET) uses a novel system for obtaining referees by e‐mailing the abstracts of submissions to a panel of over 250 referees and allowing these individuals to choose which papers they would like to review. An analysis of 13 experienced referees showed that, of 473 reviews assessed, these referees were slightly more lenient than the editor and that electronic records provide useful data that can be mined in interesting ways.