Analysis of existing mathematics textbooks for use in secondary schools.

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

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

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

Diagnosis and outcome of oesophageal Crohn's disease

BACKGROUND AND AIMS: Crohn's disease (CD) can involve any part of the gastrointestinal tract. We aimed to characterize clinical, endoscopic, histologic features and treatment outcomes of CD patients with oesophageal involvement. METHODS: We collected cases through a retrospective multicentre European Crohn's and Colitis Organisation CONFER [COllaborative Network For Exceptionally Rare case reports] project. Clinical data were recorded in a standardized case report form. RESULTS: A total of 40 patients were reported [22 males, mean (±SD, range) age at oesophageal CD diagnosis: 25 (±13.3, 10-71) years and mean time of follow-up: 67 (±68.1, 3-240) months]. Oesophageal involvement was established at CD diagnosis in 26 patients (65%) and during follow-up in 14. CD was exclusively located in the oesophagus in 2 patients. Thirteen patients (32.2%) were asymptomatic at oesophageal disease diagnosis. Oesophageal strictures were present in 5 patients and fistulizing oesophageal disease in one. Eight patients exhibited granulomas on biopsies. Proton-pump inhibitors (PPIs) were administered in 37 patients (92.5%). Three patients underwent endoscopic dilation for symptomatic strictures and none oesophageal-related surgery. Diagnosis in pre-established CD resulted in treatment modifications in 9/14 patients. Clinical remission of oesophageal disease was seen in 33/40 patients (82.5%) after a mean time of 7 (±5.6, 1-18) months. Follow-up endoscopy was performed in 29/40 patients and 26/29 (89.7%) achieved mucosal healing. CONCLUSION: In this case series the endoscopic and histologic characteristics of isolated oesophageal CD were similar to those reported in other sites of involvement. Treatment was primarily conservative, with PPIs administered in the majority of patients and modifications in pre-existing IBD-related therapy occurring in two thirds of them. Clinical and endoscopic remission was achieved in more than 80% of the patients.info:eu-repo/semantics/publishedVersio

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

Measuring Outcome after Wrist Injury: Translation and Validation of the Swedish Version of the Patient-Rated Wrist Evaluation (PRWE-Swe)

<p>Abstract</p> <p>Background</p> <p>There is a need for outcome measurement instruments for evaluation of disability after trauma. The Patient-Rated Wrist Evaluation (PRWE) is a self-administered region-specific outcome measuring instrument developed for use in evaluating disability and pain of the wrist. The aim of this study is to translate and to cross-culturally adapt the PRWE for use in a Swedish patient population. Moreover, we aim at investigating the PRWE in terms of validity, reliability and responsiveness.</p> <p>Methods</p> <p>We performed a translation and cross-cultural adaptation of the PRWE to Swedish (PRWE-Swe), utilising the process recommended by the American Association of Orthopedic Surgeons. A total of 124 patients with an injury to the wrist were included in the study. They filled in the PRWE and the DASH questionnaires at two separate occasions.</p> <p>Results</p> <p>Reliability of the PRWE in terms of internal consistency (Cronbach's alpha 0.97) and test-retest stability (intraclass correlation coefficient 0.93) were excellent. Face validity and content validity were judged as good. Criterion validity assessed as the correlation between the PRWE and the DASH was also good (Spearman's rho = 0.9). Responsiveness measured by the standardized response mean (SRM) was good with an SRM_PRWEof 1.29.</p> <p>Conclusion</p> <p>This Swedish version of the PRWE is a short and easily understood self-administered questionnaire with good validity, reliability, and responsiveness. Our results confirm that the PRWE is a valuable tool in evaluating the results after treatment of a wrist injury.</p

Elemental Abundances in M31: Iron and Alpha Element Abundances in M31’s Outer Halo

We present [Fe/H] and [α/Fe] abundances, derived using spectral synthesis techniques, for stars in M31's outer stellar halo. The 21 [Fe/H] measurements and 7 [α/Fe] measurements are drawn from fields ranging from 43 to 165 kpc in projected distance from M31. We combine our measurements with existing literature measurements, and compare the resulting sample of 23 stars with [Fe/H] and 9 stars with [α/Fe] measurements in M31's outer halo with [α/Fe] and [Fe/H] measurements, also derived from spectral synthesis, in M31's inner stellar halo (r < 26 kpc) and dSph galaxies. The stars in M31's outer halo have [α/Fe] patterns that are consistent with the largest of M31's dSph satellites (And I and And VII). These abundances provide tentative evidence that the [α/Fe] abundances of stars in M31's outer halo are more similar to the abundances of Milky Way halo stars than to the abundances of stars in M31's inner halo. We also compare the spectral synthesis–based [Fe/H] measurements of stars in M31's halo with previous photometric [Fe/H] estimates, as a function of projected distance from M31. The spectral synthesis–based [Fe/H] measurements are consistent with a large-scale metallicity gradient previously observed in M31's stellar halo to projected distances as large as 100 kpc