Lie algebra and invariant tensor technology for g2

Proceeding in analogy with su(n) work on lambda matrices and f- and d-tensors, this paper develops the technology of the Lie algebra g2, its seven dimensional defining representation gamma and the full set of invariant tensors that arise in relation thereto. A comprehensive listing of identities involving these tensors is given. This includes identities that depend on use of characteristic equations, especially for gamma, and a good body of results involving the quadratic, sextic and (the non-primitivity of) other Casimir operators of g2.Comment: 29 pages, LaTe

Districts Taking Charge of the Principal Pipeline

Six urban school districts received support from The Wallace Foundation to address the critical challenge of supplying schools with effective principals. The experiences of these districts may point the way to steps other districts might take toward this same goal. Since 2011, the districts have participated in the Principal Pipeline Initiative, which set forth a comprehensive strategy for strengthening school leadership in four interrelated domains of district policy and practice:Leader standards to which sites align job descriptions, preparation, selection, evaluation, and support.Preservice preparation that includes selective admissions to high-quality programs.Selective hiring, and placement based on a match between the candidate and the school.On-the-job evaluation and support addressing the capacity to improve teaching and learning, with support focused on needs identified by evaluation.The initiative also brought the expectation that district policies and practices related to school leaders would build the district's capacity to advance its educational priorities. The evaluation of the Principal Pipeline Initiative has a dual purpose: to analyze the processes of implementing the required components in the participating districts from 2011 through 2015; and then to assess the results achieved in schools led by principals whose experiences in standards-based preparation, hiring, evaluation, and support have been consistent with the initiative's requirements. This report addresses implementation of all components of the initiative as of 2014, viewing implementation in the context of districts' aims, constraints, and capacity

Simulation and measurement of hts josephson heterodyne oscillator

We report continuing investigations into practical applications of the ac Josephson effect as the basis for a voltage-tunable radio-frequency oscillator. We have previously demonstrated experimentally that useful power levels (10 s of nW) and linewidths of a few kHz can be achieved in the heterodyne output from a High-Temperature-Superconducting Resistive SQUID (HTS-RSQUID) operating in the frequency range 1-50 MHz. Those results were achieved with 2-junction R-SQUIDs incorporating current-biased shunt resistors of a few micro-ohms. We have now modified the fabrication procedures, and adjusted the shunt resistors and bias current values so that higher frequencies can be achieved. The Josephson junctions are of step-edge type, rather than the bi-crystal type used in our earlier work. The step-edge technique permits much more flexibility in the geometrical lay-out and utilizes the more cost-effective single-crystal MgO substrates. In the present paper, we report numerical simulations and experimental measurements on these devices in the frequency range up to 2 GHz

Six Districts Begin the Principal Pipeline Initiative

This first report of an ongoing evaluation of The Wallace Foundation's Principal Pipeline Initiative describes the six participating school districts' plans and activities during the first year of their grants. The evaluation, conducted by Policy Studies Associates and the RAND Corporation, isintended to inform policy makers and practitioners about the process of carrying out new policies and practices for school leadership and about the results of investments in the Principal Pipeline Initiative. This report is based on collection and analysis of qualitative data, including the districts' proposals, work plans, and progress reports and semi-structured interviews in spring 2012 with 91 administrators employed by districts and their partner institutions. Leaders in all districts report wanting to enlarge their pools of strong applicants for principal positions and to identify and cultivate leadership talent as early as possible in educators' careers.Districts are actively working on allrequired pipeline components: (1) with stakeholder participation, they have developed standards and identified competencies for principals, which they plan to use to guide principal training, hiring, evaluation, and support; (2) they are initiating or strengthening partnerships with university training programs; (3) for hiring, they have standard performance tasks and are developing systems to capture data on candidates' experience; (4) they have diagnostic evaluation tools and are working to build the capacity of principals' supervisors and mentors to support principals' skill development. In addition, all are also bolstering district-run training programs for graduates of university training programs who aspire to become principals

Investigations of Optical Coherence Properties in an Erbium-doped Silicate Fiber for Quantum State Storage

We studied optical coherence properties of the 1.53 $\mu$m telecommunication transition in an Er$^{3+}$-doped silicate optical fiber through spectral holeburning and photon echoes. We find decoherence times of up to 3.8 $\mu$s at a magnetic field of 2.2 Tesla and a temperature of 150 mK. A strong magnetic-field dependent optical dephasing was observed and is believed to arise from an interaction between the electronic Er$^{3+}$ spin and the magnetic moment of tunneling modes in the glass. Furthermore, we observed fine-structure in the Erbium holeburning spectrum originating from superhyperfine interaction with $^{27}$Al host nuclei. Our results show that Er$^{3+}$-doped silicate fibers are promising material candidates for quantum state storage

Time-frequency analysis of ship wave patterns in shallow water: modelling and experiments

A spectrogram of a ship wake is a heat map that visualises the time-dependent frequency spectrum of surface height measurements taken at a single point as the ship travels by. Spectrograms are easy to compute and, if properly interpreted, have the potential to provide crucial information about various properties of the ship in question. Here we use geometrical arguments and analysis of an idealised mathematical model to identify features of spectrograms, concentrating on the effects of a finite-depth channel. Our results depend heavily on whether the flow regime is subcritical or supercritical. To support our theoretical predictions, we compare with data taken from experiments we conducted in a model test basin using a variety of realistic ship hulls. Finally, we note that vessels with a high aspect ratio appear to produce spectrogram data that contains periodic patterns. We can reproduce this behaviour in our mathematical model by using a so-called two-point wavemaker. These results highlight the role of wave interference effects in spectrograms of ship wakes.Comment: 14 pages, 7 figure

Photo- and solvatochromic properties of nitrobenzospiropyran in ionic liquids containing the [NTf2]- anion

The photo-, thermo- and solvatochromic properties of 2,3-dihydro-10,30,30-trimethyl-6-nitrospiro- [1-benzopyran-2,20-1H-indole] (BSP-NO2) were studied in ILs containing the anion [NTf2]- by UV-Vis absorption spectroscopy, ab initio molecular orbital theory and density functional theory (DFT) calculations. It was found that the kinetics and thermodynamics of the BSP-NO2 MC (merocyanine) equilibrium was sensitive to the nature of the cation. It was also observed that the imidazolium cation can form a through-space orbital interaction with the MC isomer, rather than a simple electrostatic interaction, thus preventing the MC conversion back to the BSP-NO2 isomer. The BSP-NO2 MC equilibrium thus serves as a model system for studying modes of interaction of the cations in ionic liquids

Quantum mechanics over a q-deformed (0+1)-dimensional superspace

We built up a explicit realization of (0+1)-dimensional q-deformed superspace coordinates as operators on standard superspace. A q-generalization of supersymmetric transformations is obtained, enabling us to introduce scalar superfields and a q-supersymmetric action. We consider a functional integral based on this action. Integration is implemented, at the level of the coordinates and at the level of the fields, as traces over the corresponding representation spaces. Evaluation of these traces lead us to standard functional integrals. The generation of a mass term for the fermion field leads, at this level, to an explicitely broken version of supersymmetric quantum mechanics.Comment: 11 pages, Late

Geometrical foundations of fractional supersymmetry

A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra of a $q$-deformed boson. The limit of this algebra when $q$ is a $n$-th root of unity is also studied in detail. By means of a chain rule expansion, the left and right derivatives are identified with the charge $Q$ and covariant derivative $D$ encountered in ordinary/fractional supersymmetry and this leads to new results for these operators. A generalized Berezin integral and fractional superspace measure arise as a natural part of our formalism. When $q$ is a root of unity the algebra is found to have a non-trivial Hopf structure, extending that associated with the anyonic line. One-dimensional ordinary/fractional superspace is identified with the braided line when $q$ is a root of unity, so that one-dimensional ordinary/fractional supersymmetry can be viewed as invariance under translation along this line. In our construction of fractional supersymmetry the $q$-deformed bosons play a role exactly analogous to that of the fermions in the familiar supersymmetric case.Comment: 42 pages, LaTeX. To appear in Int. J. Mod. Phys.