Theoretical and empirical differentiations of phases in the modelling process

The reconstruction of pupils modelling processes can be found in many empirical studies within the literature on modelling. The empirical differentiations of the phases, which includes putting statements and actions of the pupils in the right phase, has not been reconstructed from a cognitive psychological point of view on a micro level thus far: In this article different modelling cycles are discussed with attention to distinctions in the various phases. The «modelling cycle under cognitive psychological aspects» is specifically emphasized in contrast to the other cycles. On the basis of the results of the COM²-project (Cognitive psychological analysis of modelling processes in mathematics lessons, Borromeo Ferri) the phases of the modelling processare described empirically. Some difficulties in the process of distinguishing the various phases are also pointed out.     

Über die optimale Beleuchtung einer geraden Straße

The following problem is due toL. Fejes Tóth: For a given sort of lamps letf(x) be the intensity of brightness in each point having distancex from the foot of the lamp. How must infinitely many lamps of this kind be arranged on a both-side infinite rectilinear road, such that the infimum of the intensities of brightness, extended over the whole street, is maximal, subject to the condition that the average number of lamps per kilometer is bounded by a fixed number (“Best distributions”)? The main result of this paper is: Iff is strictly convex, the equidistant distribution is best.     

Chiral Amine Synthesis Using ω‐Transaminases: An Amine Donor that Displaces Equilibria and Enables High‐Throughput Screening

The widespread application of ω‐transaminases as biocatalysts for chiral amine synthesis has been hampered by fundamental challenges, including unfavorable equilibrium positions and product inhibition. Herein, an efficient process that allows reactions to proceed in high conversion in the absence of by‐product removal using only one equivalent of a diamine donor (ortho‐xylylenediamine) is reported. This operationally simple method is compatible with the most widely used (R)‐ and (S)‐selective ω‐TAs and is particularly suitable for the conversion of substrates with unfavorable equilibrium positions (e.g., 1‐indanone). Significantly, spontaneous polymerization of the isoindole by‐product generates colored derivatives, providing a high‐throughput screening platform to identify desired ω‐TA activity.     

Palladium‐Catalyzed Carbonylations of Aryl Bromides using Paraformaldehyde: Synthesis of Aldehydes and Esters

Carbonylation reactions represent useful tools for organic synthesis. However, the necessity to use gaseous carbon monoxide is a disadvantage for most organic chemists. To solve this problem, novel protocols have been developed for conducting palladium‐catalyzed reductive carbonylations of aryl bromides and alkoxycarbonylations using paraformaldehyde as an external CO source (CO gas free). Hence, aromatic aldehydes and esters were synthesized in moderate to good yields.     

Total Synthesis of Hapalindole‐Type Natural Products

A unified and bioinspired oxidative cyclization strategy was used in the first total syntheses of naturally occurring 12‐epi‐hapalindole Q isonitrile, hapalonamide H, deschloro 12‐epi‐fischerindole I nitrile, and deschloro 12‐epi‐fischerindole W nitrile, as well as the structural revision of the latter. Hapalindoles H and Q were also synthesized.