Implicit Solutions of PDE's

Further investigations of implicit solutions to non-linear partial differential equations are pursued. Of particular interest are the equations which are Lorentz invariant. The question of which differential equations of second order for a single unknown $\phi$ are solved by the imposition of an inhomogeneous quadratic relationship among the independent variables, whose coefficients are functions of $\phi$ is discussed, and it is shown that if the discriminant of the quadratic vanishes, then an implicit solution of the so-called Universal Field Equation is obtained. The relation to the general solution is discussed.Comment: 11 pages LaTeX2

Binary fluid amplifier solves stability and load problems

Digital fluid amplifier has load intensity, high stability, and operates at low reynolds numbers. It contains specially designed nozzles to provide uniform exit-velocity profiles and to ensure jets of low turbulence

Stability and sensitivity of Learning Analytics based prediction models

Learning analytics seek to enhance the learning processes through systematic measurements of learning related data and to provide informative feedback to learners and educators. Track data from Learning Management Systems (LMS) constitute a main data source for learning analytics. This empirical contribution provides an application of Buckingham Shum and Deakin Crick’s theoretical framework of dispositional learning analytics: an infrastructure that combines learning dispositions data with data extracted from computer-assisted, formative assessments and LMSs. In two cohorts of a large introductory quantitative methods module, 2049 students were enrolled in a module based on principles of blended learning, combining face-to-face Problem-Based Learning sessions with e-tutorials. We investigated the predictive power of learning dispositions, outcomes of continuous formative assessments and other system generated data in modelling student performance and their potential to generate informative feedback. Using a dynamic, longitudinal perspective, computer-assisted formative assessments seem to be the best predictor for detecting underperforming students and academic performance, while basic LMS data did not substantially predict learning. If timely feedback is crucial, both use-intensity related track data from e-tutorial systems, and learning dispositions, are valuable sources for feedback generation

The Role of Starburst-AGN composites in Luminous Infrared Galaxy Mergers: Insights from the New Optical Classification Scheme

We investigate the fraction of starbursts, starburst-AGN composites, Seyferts, and LINERs as a function of infrared luminosity (L_IR) and merger progress for ~500 infrared-selected galaxies. Using the new optical classifications afforded by the extremely large data set of the Sloan Digital Sky Survey, we find that the fraction of LINERs in IR-selected samples is rare (< 5%) compared with other spectral types. The lack of strong infrared emission in LINERs is consistent with recent optical studies suggesting that LINERs contain AGN with lower accretion rates than in Seyfert galaxies. Most previously classified infrared-luminous LINERs are classified as starburst-AGN composite galaxies in the new scheme. Starburst-AGN composites appear to "bridge" the spectral evolution from starburst to AGN in ULIRGs. The relative strength of the AGN versus starburst activity shows a significant increase at high infrared luminosity. In ULIRGs (L_IR >10^12 L_odot), starburst-AGN composite galaxies dominate at early--intermediate stages of the merger, and AGN galaxies dominate during the final merger stages. Our results are consistent with models for IR-luminous galaxies where mergers of gas-rich spirals fuel both starburst and AGN, and where the AGN becomes increasingly dominant during the final merger stages of the most luminous infrared objects.Comment: 30 pages, 19 figures, 10 tables, ApJ accepte

An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures