Using Goffman's concepts to explore collaborative interaction processes in elementary school mathematics

The present paper describes the combined implementation of two approaches which are based on the work of Erving Goffman and focus on the analysis of the interactional participation structures. Our aim is to examine the ways that differing interpretations of the ongoing interactions may lead the students to adopt differing roles, which in turn affects the process of negotiating and establishing shared meanings. For this purpose we analyse the interaction processes in one ‘expert’ group within the ‘Jigsaw’ form of cooperation (Aronson, 1978 Aronson, E. 1978. The jigsaw classroom, Beverly Hills, CA: Sage.  [Google Scholar]), decomposing the participants’ roles according to their interactional status and their interpersonal effect. Our analysis points out the different roles that emerge in the process of collaborative interaction, and the influence of these roles on group achievement and individual learning possibilities.     

Spectrum and analyticity of semigroups arising in elasticity theory and hydromechanics

Cauchy problems for a second order linear differential operator equation

The Transitive Minimum Manhattan Subnetwork Problem in 3 dimensions

We consider the Minimum Manhattan Subnetwork (MMSN) Problem which generalizes the already known Minimum Manhattan Network (MMN) Problem: Given a set P of n points in the plane, find shortest rectilinear paths between all pairs of points. These paths form a network, the total length of which has to be minimized. From a graph theoretical point of view, a MMN is a 1-spanner with respect to the L₁ metric. In contrast to the MMN problem, a solution to the MMSN problem does not demand L₁-shortest paths for all point pairs, but only for a given set R⊆P×P of pairs. The complexity status of the MMN problem is still unsolved in ≥2 dimensions, whereas the MMSN was shown to be NP-complete considering general relations R in the plane. We restrict the MMSN problem to transitive relations R_T (Transitive Minimum Manhattan Subnetwork (TMMSN) Problem) and show that the TMMSN problem in 3 dimensions is NP-complete.     

Desch‐Schappacher perturbation of one‐parameter semigroups on locally convex spaces

We prove a Desch‐Schappacher type perturbation theorem for strongly continuous and locally equicontinuous one‐parameter semigroups which are defined on a sequentially complete locally convex space.     

Multiresolution schemes for conservation laws

Summary. In recent years a variety of high–order schemes for the numerical solution of conservation laws has been developed. In general, these numerical methods involve expensive flux evaluations in order to resolve discontinuities accurately. But in large parts of the flow domain the solution is smooth. Hence in these regions an unexpensive finite difference scheme suffices. In order to reduce the number of expensive flux evaluations we employ a multiresolution strategy which is similar in spirit to an approach that has been proposed by A. Harten several years ago. Concrete ingredients of this methodology have been described so far essentially for problems in a single space dimension. In order to realize such concepts for problems with several spatial dimensions and boundary fitted meshes essential deviations from previous investigations appear to be necessary though. This concerns handling the more complex interrelations of fluxes across cell interfaces, the derivation of appropriate evolution equations for multiscale representations of cell averages, stability and convergence, quantifying the compression effects by suitable adapted multiscale transformations and last but not least laying grounds for ultimately avoiding the storage of data corresponding to a full global mesh for the highest level of resolution. The objective of this paper is to develop such ingredients for any spatial dimension and block structured meshes obtained as parametric images of Cartesian grids. We conclude with some numerical results for the two–dimensional Euler equations modeling hypersonic flow around a blunt body. Received June 24, 1998 / Revised version received February 21, 2000 / Published online November 8, 2000     

Numerical Investigation of Shock Wave Interference Heating in Chemical Nonequilibrium

A Navier‐Stokes solver is extended by a nonequlibrium gas model to investigate heat transfer rates in hypersonic flow. The nonequlibrium model is shortly discussed and results for a type IV interaction on a cylinder are presented and compared to experimental measurements. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Pupils’ attitudes towards mathematics: a comparative study of Norwegian and English secondary students

Comparing English and Norwegian pupils’ attitude towards mathematics, in this article I develop a deeper understanding of the factors that may shape and influence ‘pupil attitude towards mathematics’, and argue for it as a socio-cultural construct embedded in and shaped by students’ environment and context in which they learn mathematics. The theoretical framework leans on work by Zan and Di Martino (The Montana Mathematics Enthusiast, Monograph 3, pp. 157–168, 2007) to elicit Norwegian and English pupils’ attitude of mathematics as they experience it in their respective environments. Whilst there were differences which could be seen to be accounted for by differently ‘figured’ environments, there are also many similarities. It was interesting to see that, albeit based on a small statistical sample, in both countries students had a positive attitude towards mathematics in year 7/8, which dropped in year 9, and increased again in years 10/11. This result could be explained and compared with other larger scale studies (e.g. Hodgen et al. in Proceedings of the British Society for Research into Learning Mathematics. 29(3), 2009). The analysis of pupils’ qualitative comments (and classroom observations) suggested seven factors that appeared to influence pupil attitude most, and these had ‘superficial’ commonalities, but the perceptions that appeared to underpin these mentions were different, and could be linked to the environments of learning mathematics in their respective classrooms. In summary, it is claimed that it is not enough to identify the factors that may shape and influence pupil attitude, but more importantly, to study how these are ‘lived’ by pupils, what meanings are made in classrooms and in different contexts, and how the factors interrelate and can be understood.     

From workplace air measurement results toward estimates of exposure? Development of a strategy to assess exposure to manufactured nano-objects

In the past few years, an increasing number of studies on workplace air measurements on manufactured nano-materials and -objects have been published. Most of the studies had a more explorative character, so a direct interpretation to workers” exposure for a given exposure situation, activity, or process is not a straight-forward process. In general, the studies use a quite similar package of devices for near real-time monitoring of particle number- and mass concentration in size ranges <100 nm up to 10 μm, and the collection of samples for off-line characterization of air samples. Various approaches for addressing background concentrations and its use to indicate the potential for exposure to nano-objects could be observed. Within the EU-sponsored NANOSH project, a harmonized approach for measurement strategy, data analysis and reporting was developed. In addition to time/activity–concentration profiles as reported by most studies, this approach enables a first step to estimate the potential for exposure to manufactured nano-objects, more quantitatively. The NANOSH data will be collated into a base, which may form the starting point for a harmonized database facilitating overall analysis in near future, to derive estimates for exposure for several exposure situations.     

Enantioselective Hydrolysis of Phenyl Glycidyl Ether Catalyzed by Newly Isolated Bacillus Megaterium ECU1001

Microbial epoxide hydrolases from bacterial and fungal sources?1? are hi ghly versatile catalysts for the asymmetric hydrolysis of chiral epoxides which are extensively employed as useful building blocks for the synthesis of various biologically active products in the pharmaceutical and agrochemical industries. Microorganism means allows an unlimited supply of these enzymes for preparative -scale applications. Phenyl glycidyl ether (PGE), an aryl epoxide, is a potenti ally useful compound in the synthesis of chiral amino alcohols and bioactive com pounds such as ?blockers. No suitable biocatalyst with sufficiently high enan tioselectivity (E?20) for the kinetic resolution of this compound was previ ously found among bacteria and fungi. This prompted us to screen epoxide hydrola se-producing microorganisms with higher enantioselectivity toward phenyl glycid yl ether from soil samples.     

Admissible control and observation operators for Volterra integral equations

The admissibility of observation operators and control operators for linear Volterra systems is studied by means of the theory of composition operators on Hardy spaces.Under certain assumptions it is shown to be equivalent to admissibility for the classical Cauchy problem. A duality between control and observation operators is also established,extending known results for the Cauchy problem,which is a special case.