Some light on Littlewood-Paley theory

The purpose of this note is to correct an error in a paper of M. Cowling, G. Fendler and J.J.F. Fournier, and to give a counterexample to a conjecture of J.-L. Rubio de Francia.Comment: 3 pages, no figures; submitted to Math Annale

Toward future 'mixed reality' learning spaces for STEAM education

Digital technology is becoming more integrated and part of modern society. As this begins to happen, technologies including augmented reality, virtual reality, 3d printing and user supplied mobile devices (collectively referred to as mixed reality) are often being touted as likely to become more a part of the classroom and learning environment. In the discipline areas of STEAM education, experts are expected to be at the forefront of technology and how it might fit into their classroom. This is especially important because increasingly, educators are finding themselves surrounded by new learners that expect to be engaged with participatory, interactive, sensory-rich, experimental activities with greater opportunities for student input and creativity. This paper will explore learner and academic perspectives on mixed reality case studies in 3d spatial design (multimedia and architecture), paramedic science and information technology, through the use of existing data as well as additional one-on-one interviews around the use of mixed reality in the classroom. Results show that mixed reality can provide engagement, critical thinking and problem solving benefits for students in line with this new generation of learners, but also demonstrates that more work needs to be done to refine mixed reality solutions for the classroom

Teaching complex theoretical multi-step problems in ICT networking through 3D printing and augmented reality

This paper presents a pilot study rationale and research methodology using a mixed media visualisation (3D printing and Augmented Reality simulation) learning intervention to help students in an ICT degree represent theoretical complex multi-step problems without a corresponding real world physical analog model. This is important because these concepts are difficult to visualise without a corresponding mental model. The proposed intervention uses an augmented reality application programmed with free commercially available tools, tested through an action research methodology, to evaluate the effectiveness of the mixed media visualisation techniques to teach ICT students networking. Specifically, 3D models of network equipment will be placed in a field and then the augmented reality app can be used to observe packet traversal and routing between the different devices as data travels from the source to the destination. Outcomes are expected to be an overall improvement in final skill level for all students

Piloting mixed reality in ICT networking to visualize complex theoretical multi-step problems

This paper presents insights from the implementation of a mixed reality intervention using 3d printed physical objects and a mobile augmented reality application in an ICT networking classroom. The intervention aims to assist student understanding of complex theoretical multi-step problems without a corresponding real world physical analog model. This is important because these concepts are difficult to conceptualise without a corresponding mental model. The simulation works by using physical models to represent networking equipment and allows learners to build a network that can then be simulated using a mobile app to observe underlying packet traversal and routing theory between the different devices as data travels from the source to the destination. Outcomes from usability testing show great student interest in the intervention and a feeling that it helped with clarity, but also demonstrated the need to scaffold the use of the intervention for students rather than providing a freeform experience in the classroom

The Levi Decomposition of a Graded Lie Algebra

We show that a graded Lie algebra admits a Levi decomposition that is compatible with the grading

On derivations of subalgebras of real semisimple Lie algebras

Let g be a real semisimple Lie algebra with Iwasawa decomposition k+a+n. We show that, except for some explicit exceptional cases, every derivation of the nilpotent subalgebra n that preserves its restricted root space decomposition is of the form ad( W), where W belongs to m+a

Assessing mobile mixed reality affordances as a comparative visualization pedagogy for design communication

Spatial visualisation skills and interpretation are critical in the design professions but are difficult for novice designers. There is growing evidence that mixed reality visualisation improves learner outcomes, but often these studies are focused on a single media representation and not on a comparison between media and the underpinning learning outcomes. Results from recent studies highlight the use of comparative visualisation pedagogy in design through learner reflective blogs and pilot studies with experts, but these studies are limited by expense and designs familiar to the learner. With increasing interest in mobile pedagogy, more assessment is required in understanding learner interpretation of comparative mobile mixed reality pedagogy. The aim of this study is to do this by evaluating insights from a first-year architectural design classroom through studying the impact and use of a range of mobile comparative visualisation technologies. Using a design-based research methodology and a usability framework for accessing comparative visualisation, this paper will study the complexities of spatial design in the built environment. Outcomes from the study highlight the positives of the approach but also the improvements required in the delivery of the visualisations to improve on the visibility and visual errors caused by the lack of mobile processing