Quotients, exactness, and nuclearity in the operator system category

We continue our study of tensor products in the operator system category. We define operator system quotients and exactness in this setting and refine the notion of nuclearity by studying operator systems that preserve various pairs of tensor products. One of our main goals is to relate these refinements of nuclearity to the Kirchberg conjecture. In particular, we prove that the Kirchberg conjecture is equivalent to the statement that every operator system that is (min,er)-nuclear is also (el,c)-nuclear. We show that operator system quotients are not always equal to the corresponding operator space quotients and then study exactness of various operator system tensor products for the operator system quotient. We prove that an operator system is exact for the min tensor product if and only if it is (min,el)-nuclear. We give many characterizations of operator systems that are (min,er)-nuclear, (el,c)-nuclear, (min,el)-nuclear and (el,max)-nuclear. These characterizations involve operator system analogues of various properties from the theory of C*-algebras and operator spaces, including the WEP and LLP.

Hypercyclic and mixing operator semigroups

We describe a class of topological vector spaces admitting a mixing uniformly continuous operator group $\{T_t\}_{t\in\C^n}$ with holomorphic dependence on the parameter $t$. This result covers those existing in the literature. We also
describe a class of topological vector spaces admitting no supercyclic strongly continuous operator semigroups $\{T_t\}_{t\geq 0}$.

Group work in elementary science:Towards organisational principles for supporting pupil learning

Group work has been promoted in many countries as a key component of elementary science. However, little guidance is given as to how group work should be organised, and because previous research has seldom been conducted in authentic classrooms, its message is merely indicative. A study is reported, which attempts to address these limitations. Twenty-four classes of 10-12-year-old pupils engaged in programmes of teaching on evaporation and condensation, and force and motion. Both programmes were delivered by classroom teachers, and made extensive use of group work. Pupil understanding progressed from pre-tests prior to the programmes to post-tests afterwards, and results suggest that group work played a critical role. Organisational principles are extrapolated from the findings, which could be readily adopted in classrooms. © 2007 Elsevier Ltd. All rights reserved.

A randomized trial of paired tutoring in elementary schools:effects on self-esteem

This paper reports data on self-esteem collected during a large-scale randomized trial of paired reading and Duolog Maths with primary school children (The Fife Peer-Learning Project). Self-report measures were analysed to assess the effect of a range of organisational variables on measured self-esteem. The presentation reports findings from a sample of reading-only schools in the first year of the project. Statistically significant gains in self-esteem were found across a range of conditions. Patterns of scores pointed to differences between same-age and cross-age conditions, and highlighted the influence of role played (tutor v tutee). In addition to the findings summarized here, it is hoped that preliminary findings from year two of the project - with an increased sample size - will also be shared. © 2009.

Experimental Evaluations of Elementary Science Programs: A Best-Evidence Synthesis

This article presents a systematic review of research on the achievement outcomes of all types of approaches to teaching science in elementary schools. Study inclusion criteria included use of randomized or matched control groups, a study duration of at least 4 weeks, and use of achievement measures independent of the experimental treatment. A total of 23 studies met these criteria. Among studies evaluating inquiry-based teaching approaches, programs that used science kits did not show positive outcomes on science achievement measures (weighted ES=+0.02 in 7 studies), but inquiry-based programs that emphasized professional development but not kits did show positive outcomes (weighted ES=+0.36 in 10 studies). Technological approaches integrating video and computer resources with teaching and cooperative learning showed positive outcomes in a few small, matched studies (ES=+0.42 in 6 studies). The review concludes that science teaching methods focused on enhancing teachers’ classroom instruction throughout the year, such as cooperative learning and science-reading integration, as well as approaches that give teachers technology tools to enhance instruction, have significant potential to improve science learning.

Manual mapping of drumlins in synthetic landscapes to assess operator effectiveness

Mapped topographic features are important for understanding processes that sculpt the Earth’s surface. This paper presents maps that are the primary product of an exercise that brought together 27 researchers with an interest in landform mapping wherein the efficacy and causes of variation in mapping were tested using novel synthetic DEMs containing drumlins. The variation between interpreters (e.g. mapping philosophy, experience) and across the study region (e.g. woodland prevalence) opens these factors up to assessment. A priori known answers in the synthetics increase the number and strength of conclusions that may be drawn with respect to a traditional comparative study. Initial results suggest that overall detection rates are relatively low (34–40%), but reliability of mapping is higher (72–86%). The maps form a reference dataset.

Operator Synthesis and Tensor Products

We show that Kraus' property $ S_{\sigma }$ is preserved under taking weak* closed sums with masa-bimodules of finite width and establish an intersection formula for weak* closed spans of tensor products, one of whose terms is a masa-bimodule of finite width. We initiate the study of the question of when operator synthesis is preserved under the formation of products and prove that the union of finitely many sets of the form $ \kappa \times \lambda $, where $ \kappa $ is a set of finite width while $ \lambda $ is operator synthetic, is, under a necessary restriction on the sets $ \lambda $, again operator synthetic. We show that property $ S_{\sigma }$ is preserved under spatial Morita subordinance.