Smith Normal Form of a Multivariate Matrix Associated with Partitions

Consideration of a question of E. R. Berlekamp led Carlitz, Roselle, and Scoville to give a combinatorial interpretation of the entries of certain matrices of determinant~1 in terms of lattice paths. Here we generalize this result by refining the matrix entries to be multivariate polynomials, and by determining not only the determinant but also the Smith normal form of these matrices. A priori the Smith form need not exist but its existence follows from the explicit computation. It will be more convenient for us to state our results in terms of partitions rather than lattice paths.Comment: 12 pages; revised version (minor changes on first version); to appear in J. Algebraic Combinatoric

Price endings and consumer segmentation

Purpose – To investigate the area of price endings to determine which groups of consumers are more likely to use odd-endings as opposed to round-endings. Design/methodology/approach – A questionnaire was developed that tested respondents' use of odd-endings as opposed to round-endings dependent on classification by gender and age. Respondents were required to estimate the price they would be expected to pay in stores for six products. This methodology enabled the researchers to generate a large sample size and to encourage accuracy of response. Findings – The main finding was that there was a difference between gender groups; women were more likely to respond with odd-endings than men and hence segmenting the market is the way forward when investigating price endings. Research limitations/implications – The research only considers segmentation by gender and age. Further research needs to be undertaken to fully understand the consumer responses. Practical implications – Although the difference between 99 cents and a $1.00 is small, for high volume items this can have a significant impact on gross profit and margins, particularly for low value items. If retailers understand which groups of consumers were more likely to be attracted to the round-endings they could use this knowledge to determine the most effective prices. Originality/value – This research follows on from a price trial conducted into price endings and is the second phase of an investigation into whether odd-endings are effective. It proposes a theory that has been empirically tested and points the way forward for future research in this area

An Undergraduate Collaborative Team Model to Engage Nursing Students in Research

Purpose: Student-faculty collaboration on research is an effective model to engage undergraduate students in the research process outside of the traditional curriculum. Using this model, a student-faculty team developed a longitudinal study about college students’ alcohol use behaviors and implemented an intervention to influence the culture of drinking on campus. Methods: A longitudinal design was used to assess drinking behaviors and evaluate the effect of a mass media campaign with social norm messages and alcohol education. Undergraduate students on a faith-based, Midwestern campus completed baseline (N = 1,095) and post-intervention (N = 1,011) electronic surveys. Results: In addition to helping students learn about and develop enthusiasm for research, this project had an impact on the drinking culture on campus. Findings showed 88% of students observed media campaign messages with 82% viewing the printed posters, 47% viewing the outdoor displays, and 25% viewing messages on social media. There was a significant change in binge drinking from the pre- (72%) to post-intervention (40%) surveys. Conclusions: Collaborative undergraduate research teams are an effective model to help students learn how to carry out research and develop interest and enthusiasm for the process. The outcomes of the project demonstrated interventions were effective at influencing the drinking culture on campus. The development of a research program outside the required curriculum can be a successful strategy to engage students in all phases of the research process, increase enthusiasm for research, and enhance health care outcomes in various settings

Potential impacts on important bird habitats in Eiderstedt (Schleswig-Holstein) caused by agricultural land use changes

Agricultural land on the Eiderstedt peninsula in Schleswig-Holstein (Germany) is traditionally dominated by extensively used grassland. These grassland areas are home to many (endangered) bird species, making Eiderstedt one of the prime bird habitats at the West coast of Schleswig-Holstein. Plans exist to convert large shares of grassland to arable farm land to grow crops needed in an intensified dairy production and for biofuels. In this study, three possible scenarios of agricultural land use change on Eiderstedt in the next couple of decades are developed. Using a GIS the possible impacts of such conversions on breeding bird populations of four key species are determined. The results indicate that an increase of arable farm land to approximately two thirds of the whole agricultural area drastically reduces suitable bird habitat, thus considerably diminishing the number of breeding pairs supported by the environment. The ornithological impact is greatest if conversion takes place throughout Eiderstedt extending from already existing areas of arable farm land. But even though the reduction in suitable breeding habitat is less pronounced in the other scenarios, every one of them induces a severe pressure on populations of meadowbirds that rely on habitat on Eiderstedt for successful reproduction.land use

High School Choice in New York City: A Report on the School Choices and Placements of Low-Achieving Students

School choice policies, a fixture of efforts to improve public education in many cities. aim to enable families to choose a school that they believe will best meet their child's needs. In New York City, choice and the development of a diverse portfolio of options have played central roles in the Department of Education's high school reform efforts. This report examines the choices and placements of New York City's lowest-achieving students: those scoring among the bottom 20 percent on standardized state tests in middle school. Focusing on data from 2007 to 2011, the report looks at who these low-achieving students are, including how their demographics compare to other students in NYC, the educational challenges they face, and where they live. The bulk of the report reviews low-achieving students' most preferred schools and the ones to which they were ultimately assigned, assessing how these schools compare to those of their higher-achieving peers. The findings show that low-achieving students attended schools that were lower performing, on average, than those of all other students. This was driven by differences in students' initial choices: low-achieving students' first-choice schools were less selective, lower-performing, and more disadvantaged. Overall, lower-achievingand higher-achieving students were matched to their top choices at the same rate. Importantly, both low- and higher-achieving students appear to prefer schools that are close to home, suggesting that differences in students' choices likely reflect, at least in part, the fact that lower-achieving students are highly concentrated in poor neighborhoods, where options may be more limited

The effect of background knowledge on young children's comprehension of explicit and implicit information

Bibliography: leaves 15-16Supported in part by the National Institute of Educatio

Screening fifth forces in k-essence and DBI models

New fifth forces have not yet been detected in the laboratory or in the solar system, hence it is typically difficult to introduce new light scalar fields that would mediate such forces. In recent years it has been shown that a number of non-linear scalar field theories allow for a dynamical mechanism, such as the Vainshtein and chameleon ones, that suppresses the strength of the scalar fifth force in experimental environments. This is known as screening, however it is unclear how common screening is within non-linear scalar field theories. k-essence models are commonly studied examples of non-linear models, with DBI as the best motivated example, and so we ask whether these non-linearities are able to screen a scalar fifth force. We find that a Vainshtein-like screening mechanism exists for such models although with limited applicability. For instance, we cannot find a screening mechanism for DBI models. On the other hand, we construct a large class of k-essence models which lead to the acceleration of the Universe in the recent past for which the fifth force mediated by the scalar can be screened.Comment: 26 page