Spectral Gap and Edge Excitations of dd-dimensional PVBS models on half-spaces

We analyze a class of quantum spin models defined on half-spaces in the $d$-dimensional hypercubic lattice bounded by a hyperplane with inward unit normal vector $m\in\mathbb{R}^d$. The family of models was previously introduced as the single species Product Vacua with Boundary States (PVBS) model, which is a spin-$1/2$ model with a XXZ-type nearest neighbor interactions depending on parameters $\lambda_j\in (0,\infty)$, one for each coordinate direction. For any given values of the parameters, we prove an upper bound for the spectral gap above the unique ground state of these models, which vanishes for exactly one direction of the normal vector $m$. For all other choices of $m$ we derive a positive lower bound of the spectral gap, except for the case $\lambda_1 =\cdots =\lambda_d=1$, which is known to have gapless excitations in the bulk

Product Vacua and Boundary State Models in d Dimensions

We introduce and analyze a class of quantum spin models defined on d-dimensional lattices Lambda subset of Z^d, which we call `Product Vacua with Boundary States' (PVBS). We characterize their ground state spaces on arbitrary finite volumes and study the thermodynamic limit. Using the martingale method, we prove that the models have a gapped excitation spectrum on Z^d except for critical values of the parameters. For special values of the parameters we show that the excitation spectrum is gapless. We demonstrate the sensitivity of the spectrum to the existence and orientation of boundaries. This sensitivity can be explained by the presence or absence of edge excitations. In particular, we study a PVBS models on a slanted half-plane and show that it has gapless edge states but a gapped excitation spectrum in the bulk

Self monitoring of blood glucose - a survey of Diabetes UK members with type 2 diabetes who use SMBG

Background: aim - to survey members of Diabetes UK who had Type 2 diabetes and who used self monitoring of blood glucose (SMBG), to elicit their views on its usefulness in the management of their diabetes, and how they used the results. A questionnaire was developed for the Diabetes UK website. The questionnaire was posted on the Diabetes UK website until over 500 people had responded. Questions asked users to specify the benefits gained from SMBG, and how these benefits were achieved. We carried out both quantitative analysis and a thematic analysis for the open ended free-text questions.Findings: 554 participants completed the survey, of whom 289 (52.2%) were male. 20% of respondents were recently diagnosed (&lt; 6 months). Frequency of SMBG varied, with 43% of participants testing between once and four times a day and 22% testing less than once a month or for occasional periods.80% of respondents reported high satisfaction with SMBG, and reported feeling more 'in control' of their diabetes management using it. The most frequently reported use of SMBG was to make adjustments to food intake or confirm a hyperglycaemic episode.Women were significantly more likely to report feelings of guilt or self-chastisement associated with out of range readings (p = &lt; .001).Conclusion: SMBG was clearly of benefit to this group of confirmed users, who used the results to adjust diet, physical activity or medications. However many individuals (particularly women) reported feelings of anxiety and depression associated with its use.<br/

a. Taboo or Trivial: Women Adult Educators with Visible Tattoos and the Effect on Learners

The purpose of this session is to discuss a future research project which examines the effect on adult learning conducted by a woman instructor with visible tattoos

Marshall University Music Department Presents Amanda Young, Senior Percussion Recital, with Marshall University Percussion Ensemble

https://mds.marshall.edu/music_perf/1256/thumbnail.jp

Quantum Spin Systems

This work provides an overview of gapped quantum spin systems, including concepts, techniques, properties, and results. The basic framework and objects of interest for quantum spin systems are introduced, and the main ideas behind methods for proving spectral gaps for frustration-free models are outlined. After reviewing recent progress on several spectral gap conjectures, we discuss quasi-locality of the Heisenberg dynamics and its utility in proving properties of gapped quantum spin systems. Lieb-Robinson bounds have played a central role in establishing exponential decay of ground state correlations, an area law for one-dimensional systems, a many-body adiabatic theorem, and spectral gap stability. They also aided in the development of the quasi-adiabatic continuation, which is a useful for investigating gapped ground state phases, both of which are also discussed.Comment: 12 pg. 1 fig. Review paper. This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physic

Exploring the Revenue Mix of Nonprofit Organizations -- Does it Relate to Publicness

Nonprofit organizations offer a wide range of goods and services and seek funding from a variety of revenue sources. Our working theory n this paper is that the sources of funding are related to the services a nonprofit provides - specifically whether services are public, private, or mixed in the nature of their benefits. Using multiple subfields from three major fields in the National Taxonomy of Exempt Entities (NTEE), this study divides nonprofits according to service type, and estimates the impact of service character on particular revenue streams and overall level of revenue diversification. Generally, the proportion of revenues generated by program fees is lowest for the category deemed public, highest for those with mostly private benefits, and midway for "mixed" services which are private in character but entail substantial public benefits. Similarly, the more public a nonprofit's services, the greater the proportion of revenues it generates through donations. However, we also identify some puzzling results that suggest the need for continued investigation of the determinants of the sources and mixes of nonprofit income. Working Paper 07-3