Analysis of existing mathematics textbooks for use in secondary schools.

Thesis (Ed.M.)--Boston University Thesis (M.A.)--Boston Universit

Global Properties of M31's Stellar Halo from the SPLASH Survey: III. Measuring the Stellar Velocity Dispersion Profile

We present the velocity dispersion of red giant branch (RGB) stars in M31's halo, derived by modeling the line of sight velocity distribution of over 5000 stars in 50 fields spread throughout M31's stellar halo. The dataset was obtained as part of the SPLASH (Spectroscopic and Photometric Landscape of Andromeda's Stellar Halo) Survey, and covers projected radii of 9 to 175 kpc from M31's center. All major structural components along the line of sight in both the Milky Way (MW) and M31 are incorporated in a Gaussian Mixture Model, including all previously identified M31 tidal debris features in the observed fields. The probability an individual star is a constituent of M31 or the MW, based on a set of empirical photometric and spectroscopic diagnostics, is included as a prior probability in the mixture model. The velocity dispersion of stars in M31's halo is found to decrease only mildly with projected radius, from 108 km/s in the innermost radial bin (8.2 to 14.1 kpc) to $\sim 80$ to 90 km/s at projected radii of $\sim 40$ to 130 kpc, and can be parameterized with a power-law of slope $-0.12\pm 0.05$. The quoted uncertainty on the power-law slope reflects only the precision of the method, although other sources of uncertainty we consider contribute negligibly to the overall error budget.Comment: Submitted to the Astrophysical Journa

Slicings of parallelogram polyominoes: Catalan, schröder, baxter, and other sequences

We provide a new succession rule (i.e. generating tree) associated with Schröder numbers, that interpolates between the known succession rules for Catalan and Baxter numbers. We define Schröder and Baxter generalizations of parallelogram polyominoes, called slicings, which grow according to these succession rules. In passing, we also exhibit Schröder subclasses of Baxter classes, namely a Schröder subset of triples of non-intersecting lattice paths, a new Schröder subset of Baxter permutations, and a new Schröder subset of mosaic floorplans. Finally, we define two families of subclasses of Baxter slicings: the m-skinny slicings and the m-rowrestricted slicings, for m ∈ N. Using functional equations and the kernel method, their generating functions are computed in some special cases, and we conjecture that they are algebraic for any m

Cognitive testing of the Colon Cancer Screening Behaviours Survey with South Asian immigrants in Canada

The purpose of this study was to cognitively test the Urdu and English language versions of a survey to assess colon cancer screening behaviours among South Asian immigrants in Canada.Brock University Library Open Access Publishing Fun

Disk Heating, Galactoseismology, and the Formation of Stellar Halos

Deep photometric surveys of the Milky Way have revealed diffuse structures encircling our Galaxy far beyond the "classical" limits of the stellar disk. This paper reviews results from our own and other observational programs, which together suggest that, despite their extreme positions, the stars in these structures were formed in our Galactic disk. Mounting evidence from recent observations and simulations implies kinematic connections between several of these distinct structures. This suggests the existence of collective disk oscillations that can plausibly be traced all the way to asymmetries seen in the stellar velocity distribution around the Sun. There are multiple interesting implications of these findings: they promise new perspectives on the process of disk heating, they provide direct evidence for a stellar halo formation mechanism in addition to the accretion and disruption of satellite galaxies, and, they motivate searches of current and near-future surveys to trace these oscillations across the Galaxy. Such maps could be used as dynamical diagnostics in the emerging field of "Galactoseismology", which promises to model the history of interactions between the Milky Way and its entourage of satellites, as well examine the density of our dark matter halo. As sensitivity to very low surface brightness features around external galaxies increases, many more examples of such disk oscillations will likely be identified. Statistical samples of such features not only encode detailed information about interaction rates and mergers, but also about long sought-after dark matter halo densities and shapes. Models for the Milky Way's own Galactoseismic history will therefore serve as a critical foundation for studying the weak dynamical interactions of galaxies across the universe.Comment: 20 pages, 5 figures, accepted in for publication in a special edition of the journal "Galaxies", reporting the proceedings of the conference "On the Origin (and Evolution) of Baryonic Galaxy Halos", Puerto Ayora, Ecuador, March 13-17 2017, Eds. Duncan A. Forbes and Ericson D. Lope

Studies of the decomposition of peroxy compounds

Abstract Not Provided

A numerical adaptation of SAW identities from the honeycomb to other 2D lattices

Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by Nienhuis that the connective constant of self-avoiding walks on the honeycomb lattice is $\sqrt{2+\sqrt{2}}.$ A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed on the honeycomb lattice persist on other lattices. This permits the accurate estimation, though not an exact evaluation, of certain critical amplitudes, as well as critical points, for these lattices. For the honeycomb lattice an exact amplitude for loops is proved.Comment: 21 pages, 7 figures. Changes in v2: Improved numerical analysis, giving greater precision. Explanation of why we observe what we do. Extra reference