The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning.     

Normal forms for nonlinear control systems with scalar output

We propose a normal form for nonlinear control systems with scalar output. We follow an approach proposed by Poincaré and adapted for control systems by Kang and Krener which consists of analyzing, step-by-step, the action of the change of coordinates on the system. To cite this article: I.A. Tall, M. Balde, C. R. Acad. Sci. Paris, Ser. I 341 (2005).     

Anodic Stripping Voltammetry of Heavy Metals at Nanocrystalline Boron‐Doped Diamond Electrode

Boron‐doped Diamond (BDD) electrode has become one of the important tools for heavy metal detection. By studying some analytical parameters of DPASV method, like deposition time and potential in different electrolyte concentrations (acetate buffer), the conditions for detecting very low metal ion levels (Zn, Cd, Pb, and Cu) could be chosen. Diluted electrolyte (0.01 M buffer) was one of the factors favoring low detection and quantification limits, but its quantification range is short in comparison to more concentrated media. For ?1.7 V deposition potential, the detection of single metal at ppb levels was reached in 60 s deposition time. Understanding different metal‐metal interactions shows the limits to the simultaneous determination of heavy metals at BDD. Quantification was possible for the simultaneous determination of Zn, Cd and Pb despite the overlapping of Zn and Cd peaks. The performance of the BDD was compared with that of another C‐based solid electrode: the glassy carbon electrode (without mercury plating). A lower base line current, wider potential range, higher sensitivity (3 to 5 times higher than GC) and longevity of the material were noticed for the BDD.     

In situ assembled ZIF superstructures via an emulsion-free soft-templating approach

Assembling well-defined MOF superstructures remains challenging as it requires easily removable hard templates or readily available immiscible solutions for an emulsion-based soft-template approach. In this work, a single-step emulsion-free soft templating approach is reported to spontaneously prepare hollow ZIF-8 and ZIF-67 colloidosomes with no further purification. These superstructures can load different enzymes regardless of the size and charge with a high encapsulation efficiency of 99%. We envisage that this work will expand the repertoires of MOF superstructures by the judicious selection of precursors and the reaction medium.

An emulsion-free approach for the preparation of hollow ZIF-8 superstructures in a single step is established based on metal sulfate hydrates in methanol.     

Perfectly normal non-metrizable non-Archimedean spaces are generalized Souslin lines

In this paper we prove the equivalence between the existence of perfectly normal, non-metrizable, non-archimedean spaces and the existence of ``generalized Souslin lines", i.e., linearly ordered spaces in which every collection of disjoint open intervals is -discrete, but which do not have a -discrete dense set. The key ingredient is the observation that every first countable linearly ordered space has a dense non-archimedean subspace.

     

Compact spaces, elementary submodels, and the countable chain condition, II

Given a space 〈X,T〉 in an elementary submodel of H(θ), define XM to be X∩M with the topology generated by . It is established that if XM is compact and satisfies the countable chain condition, while X is not scattered and has cardinality less than the first inaccessible cardinal, then X=XM. If the character of XM is a member of M, then “inaccessible” may be replaced by “1-extendible”.     

Indestructibility of compact spaces

In this article we investigate which compact spaces remain compact under countably closed forcing. We prove that, assuming the Continuum Hypothesis, the natural generalizations to _ω1${\omega }_1$-sequences of the selection principle and topological game versions of the Rothberger property are not equivalent, even for compact spaces. We also show that Tall and Usuba?s “_ℵ1${\aleph }_1$-Borel Conjecture” is equiconsistent with the existence of an inaccessible cardinal.     

An algorithm for unimodular completion over Laurent polynomial rings

We present a new and simple algorithm for completion of unimodular vectors with entries in a multivariate Laurent polynomial ring over an infinite field K. More precisely, given n?3 and a unimodular vector V=^t(v₁,…,v_n)∈Rⁿ (that is, such that 〈v₁,…,v_n〉=R), the algorithm computes a matrix M in M_n(R) whose determinant is a monomial such that MV=^t(1,0,…,0), and thus M^-1 is a completion of V to an invertible matrix.     

Enhanced rigidity of recycled polypropylene from packaging waste by compounding with talc and high‐ crystallinity polypropylene

Polypropylene (PP) constituted 30% of the collected material in a Swedish collection system for rigid plastic packaging waste. The PP fraction was however a complex mixture of grades with widely different properties. In order to enhance the rigidity of the recycled PP, modified grades were prepared by compounding with talc and/or a virgin high‐crystallinity PP grade. Adding 20–40% of high‐crystallinity PP enhanced the stiffness and yield strength without impairing the impact resistance. A composite material consisting of 20% of this grade, 20% talc and 60% recycled PP gave mechanical properties similar to those of a commercial talc‐filled PP compound used for demanding engineering applications. The present study demonstrates that recycled PP derived from post‐consumer packaging waste can also be made useful for demanding engineering applications. Copyright © 2001 John Wiley & Sons, Ltd.     

Flexible thinking and met-befores: Impact on learning mathematics

In this paper we study the difficulties resulting from changes in meaning of the minus sign, from an operation on numbers, to a sign designating a negative number, to the additive inverse of an algebraic symbol on students in two-year colleges and universities. Analysis of the development of algebra reveals that these successive meanings that the student has met before often become problematic, leading to a fragile knowledge structure that lacks flexibility and leads to confusion and long-term disaffection. The problematic aspects that arise from changes in meaning of the minus sign are identified and the iconic function machine is utilized as a supportive strategy, along with formative assessment to encourage teachers and learners to seek more flexible and effective ways of making sense of increasingly sophisticated mathematics.