Hamilton's theory of turns revisited

We present a new approach to Hamilton's theory of turns for the groups SO(3) and SU(2) which renders their properties, in particular their composition law, nearly trivial and immediately evident upon inspection. We show that the entire construction can be based on binary rotations rather than mirror reflections.

Tetragonal bismuth bilayer: A stable and robust quantum spin hall insulator

Topological insulators (TIs) exhibit novel physics with great promise for new devices, but considerable challenges remain to identify TIs with high structural stability and large nontrivial band gap suitable for practical applications. Here we predict by first-principles calculations a two-dimensional (2D) TI, also known as a quantum spin Hall (QSH) insulator, in a tetragonal bismuth bilayer (TB-Bi) structure that is dynamically and thermally stable based on phonon calculations and finite-temperature molecular dynamics simulations. Density functional theory and tight-binding calculations reveal a band inversion among the Bi-p orbits driven by the strong intrinsic spin-orbit coupling, producing a large nontrivial band gap, which can be effectively tuned by moderate strains. The helical gapless edge states exhibit a linear dispersion with a high Fermi velocity comparable to that of graphene, and the QSHphase remains robust on a NaCl substrate. These remarkable properties place TB-Bi among the most promising 2D TIs for high-speed spintronic devices, and the present results provide insights into the intriguing QSH phenomenon in this new Bi structure and offer guidance for its implementation in potential applications.

Predicting single-layer technetium dichalcogenides (TcX2, X = S, Se) with promising applications in photovoltaics and photocatalysis

One of the least known compounds among transition metal dichalcogenides (TMDCs) is the layered triclinic technetium dichalcogenides (TcX2, X = S, Se). In this work, we systematically study the structural, mechanical, electronic, and optical properties of TcS2 and TcSe2 monolayers based on density functional theory (DFT). We find that TcS2 and TcSe2 can be easily exfoliated in a monolayer form because their formation and cleavage energy are analogous to those of other experimentally realized TMDCs monolayer. By using a hybrid DFT functional, the TcS2 and TcSe2 monolayers are calculated to be indirect semiconductors with band gaps of 1.91 and 1.69 eV, respectively. However, bilayer TcS2 exhibits direct-bandgap character, and both TcS2 and TcSe2 monolayers can be tuned from semiconductor to metal under effective tensile/compressive strains. Calculations of visible light absorption indicate that 2D TcS2 and TcSe2 generally possess better capability of harvesting sunlight compared to single-layer MoS2 and ReSe2, implying their potential as excellent light-absorbers. Most interestingly, we have discovered that the TcSe2 monolayer is an excellent photocatalyst for splitting water into hydrogen due to the perfect fit of band edge positions with respect to the water reduction and oxidation potentials. Our predictions expand the two-dimensional (2D) family of TMDCs, and the remarkable electronic/optical properties of monolayer TcS2 and TcSe2 will place them among the most promising 2D TMDCs for renewable energy application in the future.

The impact of the public library as a creative place in the community: A contextual review

This review examines recent literature on the public library as a creative place and the ways in which socio-cultural impact is being measured in assessments of cultural value. Inputs such as funding and staffing are frequently measured against outputs such as visitor numbers and lending frequencies, but qualitative measures (outcomes and impacts) are minimal in the literature because of the lack of persuasive evaluative frameworks and the difficulty of designing and facilitating the evaluations at local and national levels. Nevertheless, when combined with data about outputs and outcomes, the impact on individuals and their communities can be measured effectively and reported persuasively (Poll 2012, p.124). This contextual review provides an overview of current thinking about public libraries and creative spaces with particular attention paid to the rise of so-called makerspaces and Fab Labs. This includes discussion on the types of creative activities that are occurring in the public library context, and an outline of the rhetoric and reality of the public library as a community space. These outlines are reconsidered in a discussion of the evaluative frameworks that have been employed by libraries in the past, followed by an account of some prominent creative spaces that have been formally evaluated. The existence of creative spaces in public libraries is in a state of constant flux, and the development and redevelopment of evaluative frameworks will ensure that published reports will continue to appear throughout 2015 and beyond. This review provides a brief snapshot of the state of the field as it is in the first quarter of 2015.