Systoles of Arithmetic Hyperbolic Surfaces and 3-manifolds

Our main result is that for all sufficiently large $x_0>0$, the set of commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with fixed invariant trace field $k$ and systole bounded below by $x_0$ has density one within the set of all commensurability classes of arithmetic hyperbolic 2- or 3-orbifolds with invariant trace field $k$. The proof relies upon bounds for the absolute logarithmic Weil height of algebraic integers due to Silverman, Brindza and Hajdu, as well as precise estimates for the number of rational quaternion algebras not admitting embeddings of any quadratic field having small discriminant. When the trace field is $\mathbf{Q}$, using work of Granville and Soundararajan, we establish a stronger result that allows our constant lower bound $x_0$ to grow with the area. As an application, we establish a systolic bound for arithmetic hyperbolic surfaces that is related to prior work of Buser-Sarnak and Katz-Schaps-Vishne. Finally, we establish an analogous density result for commensurability classes of arithmetic hyperbolic 3-orbifolds with small area totally geodesic $2$-orbifolds.Comment: v4: 17 pages. Revised according to referee report. Final version. To appear in Math. Res. Let

An ultra melt-resistant hydrogel from food grade carbohydrates

© 2017 The Royal Society of Chemistry. We report a binary hydrogel system made from two food grade biopolymers, agar and methylcellulose (agar-MC), which does not require addition of salt for gelation to occur and has very unusual rheological and thermal properties. It is found that the storage modulus of the agar-MC hydrogel far exceeds those of hydrogels from the individual components. In addition, the agar-MC hydrogel has enhanced mechanical properties over the temperature range 25-85 °C and a maximum storage modulus at 55 °C when the concentration of methylcellulose was 0.75% w/v or higher. This is explained by a sol-gel phase transition of the methylcellulose upon heating as supported by differential scanning calorimetry (DSC) measurements. Above the melting point of agar, the storage modulus of agar-MC hydrogel decreases but is still an elastic hydrogel with mechanical properties dominated by the MC gelation. By varying the mixing ratio of the two polymers, agar and MC, it was possible to engineer a food grade hydrogel of controlled mechanical properties and thermal response. SEM imaging of flash-frozen and freeze-dried samples revealed that the agar-MC hydrogel contains two different types of heterogeneous regions of distinct microstructures. The latter was also tested for its stability towards heat treatment which showed that upon heating to temperatures above 120 °C its structure was retained without melting. The produced highly thermally stable hydrogel shows melt resistance which may find application in high temperature food processing and materials templating

Nanocomposites and methods for synthesis and use thereof

Nanocomposite compositions and methods of synthesis of the compositions are described. In particular, liquid crystal-functionalized nanoparticles, liquid crystal-templated nanoparticles, nanocomposite compositions including the nanoparticles, and composite compositions including the nanocomposites are detailed.Board of Regents, University of Texas Syste

The meaning of charity in Locke's political thought

Copyright © 2009 by SAGE Publications. This is the authors final version, after peer-review. 12 month embargo by the publisher. Article will be released April 2010.The recent ‘religious turn’ within Locke scholarship has stressed the need to understand his theological commitments when approaching his political thought. One area of interpretation that has been completely transformed by this heightened sensitivity to the religious roots of Locke’s thought is his account of property ownership which, it is claimed, contains a ‘right to charity’—a subsistence entitlement that trumps established ownership rights. However, this increasingly accepted interpretive claim has been made without significant attention to the way in which charity is deployed throughout Locke’s writing. The aim of this article is to try and get to grips with Locke’s various usages of the term and determine whether the concept he deploys is a consistent one. After discussion of the uncertain role charity plays in his account of property, we examine how it is defined in the Essay Concerning Human Understanding, and then turn to the crucial position it occupies in his theological corpus. Though Locke’s understanding of charity seems fraught with ambiguities, the reason for these ambiguities relate to his configuration of charity as a disposition rather than a mere act, a configuration linked inextricably to his account of toleration

Eliminating Barriers: Connecting Seniors to Services in Chittenden County

Introduction. Physical activity programs for older adults help to improve physical, social, and emotional health and reduce impairments in activities of daily living1. In Chittenden county, less than 1⁄3 of older adults participate in programs, while 48% report that they would like to exercise more. Our aim was to identify barriers to participation in physical activity programs by older adults in Chittenden county, such as accessibility, transportation, health, affordability, and social isolation, and to identify strategies to overcome these barriers. Methods. 144 paper and electronic surveys were administered in Chittenden County, Vermont to assess use of group programs among older adults aged ≥ 50 years including transportation, motivation, preferences, advertisement, and barriers to access. A focus group explored aspects of ideal group activities for seniors. Results. 87.9% of respondents were active for two or more hours each week, while 46.5% had participated in group programming in the past 6 months. Group par- ticipation was significantly higher among physically active respondents (p=0.020). Motivators for participation in group activity included health benefits, social aspects, and physical activity, while the most cited barrier to attendance was timing conflicts. Respondents received information about programming via word of mouth, email, and online resources. Discussion. Overall, our findings indicate that the majority of respondents are highly active, however, they frequently experience barriers that prevent them from participating in group programming. We recommend offering flexible scheduling, advertising programming via word of mouth and email, and emphasizing program health benefits.https://scholarworks.uvm.edu/comphp_gallery/1260/thumbnail.jp

Pattern formation in crystal growth under parabolic shear flow

Morphological instability of the solid-liquid interface occuring in a crystal growing from an undercooled thin liquid being bounded on one side by a free surface and flowing down inclined plane is investigated by a linear stability analysis under shear flow. It is found that restoring forces due to gravity and surface tension is important factor for stabilization of the solid-liquid interface on long length scales. This is a new stabilizing effect different from the Gibbs-Thomson effect. A particular long wavelength mode of about 1 cm of wavy pattern observed on the surface of icicles covered with thin layer of flowing water is obtained from the dispersion relation including the effect of flow and restoring forces.Comment: 30 pages, 4 figure