A note on the Brouwer dimension of chainable spaces

A general method produces from a compact Hausdorff space S a compact Hausdorff space T with IndT=IndS+1. We show that if S is chainable, then T is also chainable while DgT<IndT, where Dg denotes dimensionsgrad, the dimension in the original sense of Brouwer. This leads to a chainable, first countable, separable space Xn with DgXn<IndXn=n for each integer n>1.     

The relationship of theory and practice in mathematics teacher professional development: an activity theory perspective

This paper describes certain interactions between the activity of “teaching” and the activity of “researching” in which the teachers participate in a 52-h professional development course aiming to introduce them to research in mathematics education as a tool for inquiry in their teaching. The teachers are involved in different research tasks such as: reading and presenting research papers; analyzing classroom dialogues and tasks; and designing, implementing, and evaluating collaboratively a classroom teaching intervention. From an activity theory (AT) perspective, and in particular Engeström’s (2001) third generation AT, distinguish two activity systems, the activity system of research and the activity system of teaching, to identify links that the participating teachers make. These links indicate the development of an inquiring stance to mathematics teaching and learning as a means of professional learning.     

Towards preparative-scale, biocatalytic alkene reductions

Simple strategies for using alkene reductase enzymes to produce gram-scale quantities of both (R)- and (S)-citronellal have been developed. The methodology is easily accessible to non-specialist laboratories, allowing alkene reductases to be added to the toolbox of routine synthetic transformations.     

Assessing Surface Permeabilities from Transient Guest Profiles in Nanoporous Host Materials

Easy come, easy go? Transport resistances on particle surfaces are important for mass transfer in nanoporous materials and bulk diffusion in crystals. Interference microscopy and IR micro‐imaging are shown to be excellent tools for determining such transport resistances. By studying short‐chain‐length alkane guest molecules in crystals of the metal–organic framework compound Zn(tbip) a data collection of surface permeabilities is established.

     

Ensemble Measurement of Diffusion: Novel Beauty and Evidence

Recording the evolution of concentration profiles in nanoporous materials opens a new field of diffusion research with particle ensembles. The technique is based on the complementary application of interference microscopy and IR micro‐imaging. Combining the virtues of diffusion measurements with solids and fluids, it provides information of unprecedented wealth and visual power on transport phenomena in molecular ensembles. These phenomena include the diverging uptake and release patterns for concentration‐dependent diffusivities, the mechanisms of mass transfer at the fluid–solid interface and opposing tendencies in local and global concentration evolution.     

Rigid continua and transfinite inductive dimension

We introduce a general method of resolving first countable, compact spaces that allows accurate estimate of inductive dimensions. We apply this method to construct, inter alia, for each ordinal number α>1 of cardinality ?c, a rigid, first countable, non-metrizable continuum Sα with . Sα is the increment in some compactification of [0,1) and admits a fully closed, ring-like map onto a metric continuum. Moreover, every subcontinuum of Sα is separable. Additionally, Sα can be constructed so as to be: (1) a hereditarily indecomposable Anderson-Choquet continuum with covering dimension a given natural number n, provided α>n, (2) a hereditarily decomposable and chainable weak Cook continuum, (3) a hereditarily decomposable and chainable Cook continuum, provided α is countable, (4) a hereditarily indecomposable Cook continuum with covering dimension one, or (5) a Cook continuum with covering dimension two, provided α>2.We also produce a chainable and hereditarily decomposable space Sω(c⁺) with , , trind₀Sω(c⁺) and trInd₀Sω(c⁺) all equal to ω(c⁺), the first ordinal of cardinality c⁺.     

Flexible working arrangements in context: An empirical investigation through self-organizing maps

This is one of the first studies to utilize Kohonen’s self-organizing maps on flexible work arrangements (FWAs), employee turnover and absenteeism within different national contexts and an array of organizational factors. While the majority of FWAs did not reduce significantly employee turnover or absenteeism, country and industry were significant contextual variables in FWA use: we deciphered six main country regions, where service and manufacturing organizations were important to FWA preferences. We found a curvilinear relationship between turnover and shift-work among manufacturing firms regardless of country: turnover decreases at low levels and increases at high levels of shift-work. We also found strong positive relationships between weekend work and turnover among manufacturing firms regardless of country and firms in the region comprising of Germany, Austria, Sweden, Finland, Denmark, Czech Republic and Belgium. Finally, we found consistently high concentration of organizations with low absenteeism throughout certain industries and countries: noteworthy are service organizations in the Netherlands and manufacturing organizations in Australia. The results demonstrate the contextuality of FWA use across countries and industries, and the usefulness of SOMs for research within human resource management.     

Coordination complexes of iron(III) with 3-hydroxy-2(1H)-pyridinone, 2,3-dihydroxybenzoic acid and 3,4-dihydroxybenzoic acid: preparation and characterization in the solid state

Summary The synthesis and study of a number of new iron(III) complexes of the ligands 3-hydroxy-2(1H)-pyridinone (3,2-opoH), 2,3-dihydroxybenzoic acid (2,3-dhbH₃) and 3,4-dihydroxybenzoic acid (3,4-dhbH₃) are described. These complexes have the formulae [Fe(3,2-opo)₂Cl]·PrⁿOH, K[Fe(2,3-dhbH)₂(H₂O)₂], [Fe(2,3-dhb)(H₂O)₂], K[Fe-(3,4-dhbH)₂(H₂O)₂], [Fe(3,4-dhb)(H₂O)₂] and K₆[Fe(3,4-dhb)₃]·3H₂O. The complexes were characterized by elemental analyses. X-ray powder patterns, t.g.a./d.t.g. techniques, magnetic susceptibilities and spectroscopic (u.v.-vis., i.r. and variable-temperature ⁵⁷Fe-M?ssbauer) studies. Monomeric octahedral structures are assigned for the 1∶2 2,3-dhbH²⁻ complex and the 1:3 3,4-dhb³⁻ compound. Dinuclear and/or oligonuclear structures are tentatively proposed for the remaining complexes in the solid state. In [FeL(H₂O)₂] (L³⁻ = 2,3-dhb³⁻ or 3,4-dhb³⁻), iron(III) appears to be 5-coordinate. Both oxygens of 3,2-opo⁻ participate in coordination, while the dihydroxybenzoato ligands exhibit various coordination modes, depending mainly on the positions of the hydroxy groups, their anionic charge and the ligand∶metal molar ratio used.     

Acceleration of the leastpth algorithm for minimax optimization with engineering applications

Over the past few years a number of researchers in mathematical programming and engineering became very interested in both the theoretical and practical applications of minimax optimization. The purpose of the present paper is to present a new method of solving the minimax optimization problem and at the same time to apply it to nonlinear programming and to three practical engineering problems. The original problem is defined as a modified leastpth objective function which under certain conditions has the same optimum as the original problem. The advantages of the present approach over the Bandler-Charalambous leastpth approach are similar to the advantages of the augmented Lagrangians approach for nonlinear programming over the standard penalty methods.This work was supported by the National Research Council of Canada under Grant A4414, and from the University of Waterloo.