Geometry in preduals of spaces of 2-homogeneous polynomials on Hilbert spaces

Let H be a (real or complex) Hilbert space. Using spectral theory and properties of the Schatten–Von Neumann operators, we prove that every symmetric tensor of unit norm in HoH is an infinite absolute convex combination of points of the form xox with x in the unit sphere of the Hilbert space. We use this to obtain explicit characterizations of the smooth points of the unit ball of HoH .

Improving the utilisation of University teaching space

There is a perception that teaching space in universities is a rather scarce resource. However, some studies have revealed that in many institutions it is actually chronically under-used. Often, rooms are occupied only half the time, and even when in use they are often only half full. This is usually measured by the “utilisation” which is basically the percentage of available ’seat-hours’ that are employed. In real institutions, this utilisation can often takes values as low as 20-40%. One consequence of such low utilisation is that space managers are under pressure to make a more efficient use of the available teaching space. However, better management is hampered because there does not appear to be a good understanding within space management (near-term planning) of why this happens. Nor, a good basis within space planning (long-term planning) of how best to accommodate the expected low utilisations. This motivates our two main goals: (i) To understand the factors that drive down utilisations, (ii) To set up methods to provide better space planning. Here, we provide quantitative evidence that constraints arising from timetabling and location requirements easily have the potential to explain the low utilisations seen in reality. Furthermore, on considering the decision question “Can this given set of courses all be allocated in the available teaching space?” we find that the answer depends on the associated utilisation in a way that exhibits threshold behaviour: There is a sharp division between regions in which the answer is “almost always yes” and those of “almost always no”. Our work suggests that progress in space management and planning will arise from an integrated approach; combining purely space issues with restrictions representing an aggregated or abstracted version of key constraints such as timetabling or location, and

Self-consistent geometry in the computation of the vibrational spectra of molecules

An exact and general approach to study molecular vibrations is provided by the Watson Hamiltonian. Within this framework, it is customary to omit the contribution of the terms with the vibrational angular momentum and the Watson term, especially for the study of large systems. We discover that this omission leads to results which depend on the choice of the reference structure. The self-consistent solution proposed here yields a geometry that coincides with the quantum averaged geometry of the Watson Hamiltonian and appears to be a promising way for the computation of the vibrational spectra of strongly anharmonic systems.

A systematic review protocol on the use of teaching portfolios for educators in further and higher education.

portfolio and undergraduate students have suggested that a teachingportfolio may have a benefit for educators in higher education as a means to providerelevancy and focus to their teaching.Design. The objectives of the review are to evaluate how a teaching portfolio assistseducators in teaching and learning; to evaluate the effects of maintaining a teachingportfolio for educators in relation to personal development; to explore the type ofportfolio used; to determine whether a teaching portfolio is perceived more beneficialfor various grades and professional types; and to determine any motivatingfactors or workplace incentives behind its implementation and completion. A searchof the following databases will be made MEDLINE, CINAHL, BREI, ERIC andAUEI. The review will follow the Joanna Briggs Institute guidance for systematicreviews of quantitative and qualitative research.Conclusion. The review will offer clarity and direction on the use of teachingportfolios, for educators, policymakers, supervisory managers and researchers involvedin further and higher education.