Appropriate problems for learning and for performing—an issue for teacher training

Selecting, modifying or creating appropriate problems for mathematics class has become an activity of increaing importance in the professional development of German mathematics teachers. But rather than asking in general: “What is a good problem?” there should be a stronger emphasis on considering the specific goal of a problem, e.g.: “What are the ingredients that make a problem appropriate for initiating a learning process” or “What are the characteristics that make a problem appropriate for its use in a central test?” We propose a guiding scheme for teachers that turns out to be especially helpful, since the newly introduced orientation on outcome standards a) leads to a critical predominance of test items and b) expects teachers to design adequate problems for specific learning processes (e.g. problem solving, reasoning and modelling activities).     

Spin-trapped hydroxyl free radicals studied at low field by Field-Cycled Dynamic Nuclear Polarization

The technique of Field-Cycled Dynamic Nuclear Polarization (FC-DNP) involves the EPR irradiation of a free radical solution and the subsequent observation of the NMR signal, the experiment being carried out at a range of magnetic field strengths in order to measure the free radical’s EPR spectrum. In this work FC-DNP has been used to study the EPR spectrum of DMPO spin-trapped hydroxyl free radicals at magnetic field strengths between 0.5 mT and 13.0 mT (5–130 Gauss). The low-field EPR spectrum contains six separate EPR lines, in contrast to the well-known X-band spectrum where only four are seen. Knowledge of the spin-adduct’s EPR spectrum will be of use to workers involved in low-field EPR, especially those conducting biological or in-vivo spin-trapping experiments.     

A Tin(IV) Porphyrin with Two Axial Organometallic NCN‐Pincer Platinum Units

A tin(IV) porphyrin was combined with two axial NCN‐pincer platinum(II) fragments by utilizing the oxophilicity of the apical positions on the tin atom and the acidic nature of the NCN‐pincer platinum derived benzoic acid. The solid‐state structure determined by X‐ray crystallography revealed some close contacts between the pincer complexes and the meso‐p‐tolyl subsitutents of the porphyrin. It was shown by ¹H NMR spectroscopy that these close contacts were not present in solution and that this compound can potentially act as a novel building block for supramolecular architectures.     

Bargaining over the division of a shrinking pie: An axiomatic approach

The Bargaining Problem paradigm is extended to time-consuming conflict situations. Such a situation can be represented by a chain of bargaining domains, each representing the conflict at a different point in time. The solution function selects a point in the union of all these domains. We characterize a solution function which satisfies several requirements and explore its properties. One of the results is that an extension of the Adding requirement (Thomson-Myerson 1980) is enough, under some conditions, to yield a solution point, so there is no need to extend the stronger requirements of Independence of Irrelevant Alternatives (Nash 1950) or Monotonicity (Kalai-Smorodinsky 1975).     

Erstarrung des Fluorwasserstoffs und des Phosphorwasserstoffs,Verflüssigung und Erstarrung des Antimonwasserstoffs

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