A Two-Step Approach to Diagnostic Assessment in College Math, Fall 2007

This study examines a modified strategy for diagnostic testing and its use as a predictor of performance in college math. A study conducted in 2005 analyzed the results of a single diagnostic test given at the beginning of first semester to all students in the School of Manufacturing Sciences post-secondary programs at Fanshawe College. The range of topics covered by this single test was comprehensive. The attempt to find correlation between the results of this test and grade outcomes in first semester college technology math was inconclusive. The current study examines the results of a system of two similar tests, administered to students of the 2007 Fall intake of the same school. The first of the two tests was given during the first mathematics class of the semester; the second test after approximately two weeks of the semester. The content of the first test was reviewed during lectures in the intervening two week period so that student progress could be gauged with respect to results from the first assessment. The results of the combined diagnostic test results provide a more effective predictive tool than the results from the 2005 study. Specifically, the findings of this study show that 67.9% of students who failed the diagnostic tests (combined mark) failed first semester mathematics in the Fall of 2007. The current study and the 2005 study show that both grade 11 and 12 mathematics courses have a significant effect on performance in first semester college mathematics. The pathway MBF3C–MAP4C (11C-12C) is the most common pathway chosen by first semester entrants and further, this pathway is insufficient preparation for first semester college technology mathematics of post-secondary programs offered by the School of Manufacturing Sciences. This study finds that an overwhelming number of students who took the applied stream mathematics course in grade 10 pursued the pathway MBF3C-MAP4C. Students who chose an alternate pathway culminating in the grade 12C course, MAP4C, fared much better in first semester technology mathematics, suggesting that the choice of grade 11 mathematics course has the greater impact on success in college mathematics. Both this study and the previous study show that all students who had taken Mathematics for College Technology in grade 12 (MCT4C) passed first semester college technology mathematics in the School of Manufacturing Sciences post-secondary programs in the Fall of 2005 and 2007

Analytical computation of moderate-degree fully-symmetric cubature rules on the triangle

A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of good quality, are computed and presented.Comment: 13 pages, submitted to Journal of Computational and Applied Mathematic

Further studies on square-root boundaries for Bessel processes

We look at decompositions of perpetuities and apply that to the study of the distributions of hitting times of Bessel processes of two types of square root boundaries. These distributions are linked giving a new proof of some Mellin transforms results obtained by David M. DeLong and M. Yor. Several random factorizations and characterizations of the studied distributions are established

Carbon-rich presolar grains from massive stars : subsolar ¹²C/¹³C and ¹⁴N/¹⁵N ratios and the mystery of ¹⁵N

Carbon-rich grains with isotopic anomalies compared to the Sun are found in primitive meteorites. They were made by stars, and carry the original stellar nucleosynthesis signature. Silicon carbide grains of Type X and C and low-density (LD) graphites condensed in the ejecta of core-collapse supernovae. We present a new set of models for the explosive He shell and compare them with the grains showing ¹²C/¹³C and ¹⁴N/¹⁵N ratios lower than solar. In the stellar progenitor H was ingested into the He shell and not fully destroyed before the explosion. Different explosion energies and H concentrations are considered. If the supernova shock hits the He-shell region with some H still present, the models can reproduce the C and N isotopic signatures in C-rich grains. Hot-CNO cycle isotopic signatures are obtained, including a large production of ¹³C and ¹⁵N. The short-lived radionuclides ²²Na and ²⁶Al are increased by orders of magnitude. The production of radiogenic ²²Ne from the decay of ²²Na in the He shell might solve the puzzle of the Ne-E(L) component in LD graphite grains. This scenario is attractive for the SiC grains of type AB with ¹⁴N/¹⁵N ratios lower than solar, and provides an alternative solution for SiC grains originally classified as nova grains. Finally, this process may contribute to the production of ¹⁴N and ¹⁵N in the Galaxy, helping to produce the ¹⁴N/¹⁵N ratio in the solar system

Search for extraterrestrial antineutrino sources with the KamLAND detector

We present the results of a search for extraterrestrial electron antineutrinos ($\bar{\nu}_{e}$'s) in the energy range $8.3 MeV < E_{\bar{\nu}_{e}} < 31.8 MeV$ using the KamLAND detector. In an exposure of 4.53 kton-year, we identify 25 candidate events. All of the candidate events can be attributed to background, most importantly neutral current atmospheric neutrino interactions, setting an upper limit on the probability of $^{8}$B solar $\nu_{e}$'s converting into $\bar{\nu}_{e}$'s at $5.3 \times 10^{-5}$ (90% C.L.), if we assume an undistorted $\bar{\nu}_{e}$ shape. This limit corresponds to a solar $\bar{\nu}_{e}$ flux of $93 cm^{-2} s^{-1}$ or an event rate of $1.6 events (kton-year)^{-1}$ above the energy threshold $(E_{\bar{\nu}_{e}} > 8.3 MeV)$. The present data also allows us to set more stringent limits on the diffuse supernova neutrino flux and on the annihilation rates for light dark matter particles.Comment: 22 pages, 6 figure