A new skew-elliptical distribution and its properties

This article generalizes a multivariate skew-elliptical distribution and describes its many interesting properties. The univariate version of the new distribution is compared with two other currently used distributions. The use of the new distribution is illustrated with a real data example suitable for regression modelling. The new model provides a better model fit than its two rivals as evaluated by some suitable Bayesian model selection criteria

Multivariable Repetitive-predictive Controllers using Frequency Decomposition

Repetitive control is a methodology for the tracking of a periodic reference signal. This paper develops a new approach to repetitive control systems design using receding horizon control with frequency decomposition of the reference signal. Moreover, design and implementation issues for this form of repetitive predictive control are investigated from the perspectives of controller complexity and the effects of measurement noise. The analysis is supported by a simulation study on a multi-input multi-output robot arm where the model has been constructed from measured frequency response data, and experimental results from application to an industrial AC motor

A transport model of the turbulent scalar-velocity

Performance tests of the third-order turbulence closure for predictions of separating and recirculating flows in backward-facing steps were studied. Computations of the momentum and temperature fields in the flow domain being considered entail the solution of time-averaged transport equations containing the second-order turbulent fluctuating products. The triple products, which are responsible for the diffusive transport of the second-order products, attain greater significance in separating and reattaching flows. The computations are compared with several algebraic models and with the experimental data. The prediction was improved considerably, particularly in the separated shear layer. Computations are further made for the temperature-velocity double products and triple products. Finally, several advantages were observed in the usage of the transport equations for the evaluation of the turbulence triple products; one of the most important features is that the transport model can always take the effects of convection and diffusion into account in strong convective shear flows such as reattaching separated layers while conventional algebraic models cannot account for these effects in the evaluation of turbulence variables

Applying Graph Theory to Examine the Dynamics of Student Discussions in Small-Group Learning.

Group work in science, technology, engineering, and mathematics courses is an effective means of improving student outcomes, and many different factors can influence the dynamics of student discussions and, ultimately, the success of collaboration. The substance and dynamics of group discussions are commonly examined using qualitative methods such as discourse analysis. To complement existing work in the literature, we developed a quantitative methodology that uses graph theory to map the progression of talk-turns of discussions within a group. We observed groups of students working with peer facilitators to solve problems in biological sciences, with three iterations of data collection and two major refinements of graph theory calculations. Results include general behaviors based on the turns in which different individuals talk and graph theory parameters to quantify group characteristics. To demonstrate the potential utility of the methodology, we present case studies with distinct patterns: a centralized group in which the peer facilitator behaves like an authority figure, a decentralized group in which most students talk their fair share of turns, and a larger group with subgroups that have implications for equity, diversity, and inclusion. Together, these results demonstrate that our adaptation of graph theory is a viable quantitative methodology to examine group discussions