Kinematic geometry of mass-triangles and reduction of Schrödinger’s equation of three-body systems to partial differential equations solely defined on triangular parameters

Schrödinger’s equation of a three-body system is a linear partial differential equation (PDE) defined on the 9-dimensional configuration space, ℝ9, naturally equipped with Jacobi’s kinematic metric and with translational and rotational symmetries. The natural invariance of Schrödinger’s equation with respect to the translational symmetry enables us to reduce the configuration space to that of a 6-dimensional one, while that of the rotational symmetry provides the quantum mechanical version of angular momentum conservation. However, the problem of maximizing the use of rotational invariance so as to enable us to reduce Schrödinger’s equation to corresponding PDEs solely defined on triangular parameters—i.e., at the level of ℝ6/SO(3)—has never been adequately treated. This article describes the results on the orbital geometry and the harmonic analysis of (SO(3),ℝ6) which enable us to obtain such a reduction of Schrödinger’s equation of three-body systems to PDEs solely defined on triangular parameters.

Mapping the parameters of prion-induced neuropathology

We present a theoretical framework that enables us to dissect out the parametric dependencies of the pathogenesis of prion diseases. We are able to determine the influence of both host-dependent factors (connectivity, cell density, protein synthesis rate, and cell death) and strain-dependent factors (cell tropism, virulence, and replication rate). We use a model based on a linked system of differential equations on a lattice to explore how the regional distribution of central nervous system pathology in Creutzfeldt-Jakob disease, Gerstmann-Sträussler-Scheinker syndrome, and fatal familial insomnia relates to each of these factors. The model then is used to make qualitative predictions about the pathology for two possible hypothetical triggers of neuronal loss in prion diseases. Pathological progression in overexpressing mouse models has been shown to depend on the site of initial infection. The model allows us to compare the pathologies resulting from different inoculation routes.

Measuring cosmological parameters

In this review, the status of measurements of the matter density (Ωm), the vacuum energy density or cosmological constant (ΩΛ), the Hubble constant (H0), and the ages of the oldest measured objects (t0) are summarized. Three independent types of methods for measuring the Hubble constant are considered: the measurement of time delays in multiply imaged quasars, the Sunyaev–Zel’dovich effect in clusters, and Cepheid-based extragalactic distances. Many recent independent dynamical measurements are yielding a low value for the matter density (Ωm ≈ 0.2–0.3). A wide range of Hubble constant measurements appear to be converging in the range of 60–80 km/sec per megaparsec. Areas where future improvements are likely to be made soon are highlighted—in particular, measurements of anisotropies in the cosmic microwave background. Particular attention is paid to sources of systematic error and the assumptions that underlie many of the measurement methods.

Educating a New Cadre of Experts Specializing in Digital Collections and Digital Curation: Experiential Learning in Digital Library Curriculum

Integration of experiential learning into the library and information science (LIS) courses has been a theme in LIS education, but the topic deserves renewed attention with an increasing demand for professionals in the digital library field and in light of the new initiative announced by the Library of Congress (LC) and the Institution of Museum and Library Services (IMLS) for national residency program in digital curation. The balance between theory and practice in digital library curricula, the challenges of incorporating practical projects into LIS coursework, and the current practice of teaching with hands on activities represent the primary areas of this panel discussion.

(Table 1) Conditions of vertical near-bottom profiling and the main parameters of the benthic boundary layer in several regions of the Black Sea shelf

Measurements of 14 vertical profiles of currents and hydrological parameters in the near-bottom layer with depth resolution of 0.1 m were carried out in several regions of the Black Sea shelf, at five points over the continental slope, and in three deep water regions. The upper boundary of the benthic boundary layer (BBL) was reliably determined at a point at distance from 5-7 to 35-40 m from the bottom where the gradients of density and current velocity changed. Experimental data obtained were used to determine the coefficient of bottom friction, friction velocity, coefficients of vertical diffusion of momentum and density, and vertical fluxes of temperature and salinity in the BBL.

Vertical profiles of environmental parameters measured on discrete water samples collected with Niskin bottles during the Tara Oceans expedition 2009-2013

The present data publication provides permanent links to original and updated versions of validated data files. The data files include properties of seawater, particulate matter and dissolved matter that were measured from discrete water samples collected with Niskin bottles during the 2009-2013 Tara Oceans expedition. Properties include pigment concentrations from HPLC analysis (10 depths per vertical profile, 25 pigments per depth), the carbonate system (Surface and 400m; pH (total scale), CO2, pCO2, fCO2, HCO3, CO3, Total alkalinity, Total carbon, OmegaAragonite, OmegaCalcite, and dosage Flags), nutrients (10 depths per vertical profile; NO2, PO4, N02/NO3, SI, quality Flags), DOC, CDOM, and dissolved oxygen isotopes. The Service National d'Analyse des Paramètres Océaniques du CO2, at the Université Pierre et Marie Curie, determined CT and AT potentiometrically (Edmond 1970; DOE 1994) on samples preserved according to Dickson et al. (2007). More than 250 vertical profiles of these properties were made across the world ocean. DOC, CDOM and dissolved oxygen isotopes are available only for the Arctic Ocean and Arctic Seas (2013).

Pedestrian injury causation parameters. Phase II. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Methods for integrating alcohol education into existing curriculum. Volume II. Part 7. Final report.

National Highway Traffic Safety Administration, Office of Alcohol Countermeasures, Washington, D.C.

Improvements of methods for determining pre-crash parameters from skid marks. Final report.

Mode of access: Internet.

Guidelines for a K-12 traffic safety education curriculum. Volume I: procedures and findings. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Guidelines for a K-12 traffic safety education curriculum. Volume II: curriculum content and instructional approach. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Surface water quality parameters for monitoring oil shale development /

Mode of access: Internet.

Instructor training institute for NHTSA curriculum package: emergency medical technician-dispatcher. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Statistical analysis of preliminary data for the safe performance curriculum driving knowledge test. Interim report.

DeKalb County School System, Decatur, Ga.

Calibration of a 90 V̊-notch weir using parameters other than upstream head /

Mode of access: Internet.