Browsing by Subject "Support"

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  • Chen, Lifeng; Dong, Zhao; Jiang, Jifa; Niu, Lei; Zhai, Jianliang (2019)
    Motivated by the remarkable works of Busse and his collaborators in the 1980s on turbulent convection in a rotating layer, we explore the long-run behavior of stochastic Lotka-Volterra (LV) systems both in pull-back trajectories and in stationary measures. A decomposition formula is established to describe the relationship between the solutions of stochastic and deterministic LV systems and the stochastic logistic equation. By virtue of this formula, it can be verified that every pull-back omega limit set is an omega limit set of the deterministic LV system multiplied by the random equilibrium of the stochastic logistic equation. The formula is also used to derive the existence of a stationary measure, its support and ergodicity. We prove the tightness of stationary measures and that their weak limits are invariant with respect to the corresponding deterministic system and supported on the Birkhoff center. The developed theory is successfully utilized to completely classify three dimensional competitive stochastic LV systems into 37 classes. The expected occupation measures weakly converge to a strongly mixing measure and all stationary measures are obtained for each class except class 27 c). Among them there are two classes possessing a continuum of random closed orbits and strongly mixing measures supported on the cone surfaces, which weakly converge to the Haar measures of periodic orbits as the noise intensity vanishes. The class 27 c) is an exception, almost every pull-back trajectory cyclically oscillates around the boundary of the stochastic carrying simplex characterized by three unstable stationary solutions. The limit of the expected occupation measures is neither unique nor ergodic. These are consistent with symptoms of turbulence. (C) 2019 Elsevier Masson SAS. All rights reserved.
  • Splichal, Jin Michael; Oshima, Jun; Oshima, Ritsuko (2018)
    Many studies attempt to effectively support student regulation of collaboration using CSCL tools to enrich learning outcomes. However, few studies are aimed at facilitating development of students' internal scripts for regulation of collaboration. This study focuses on developing and evaluating a computer-mediated learning environment for project-based learning to facilitate student internal scripts for regulation by designing external scripts for effective reflection. Forty- eight first-year university students participated in this study as part of their curriculum. Our analyses of their internal scripts before and after PBL participation revealed that significantly more students who encountered an unfamiliar situation during collaboration constructed new regulation scripts. Moreover, in case studies, we found that students augmented their scripts for socially shared regulation when recognizing socio-cognitive challenges, whereas they augmented co-regulation and self-regulation scripts when recognizing socio-emotional challenges.