Simple Synthesis of a Heterocyclophane Exhibiting Anti-c-Met Activity by Acting as a Hatch Blocking Access to the Active Site**

A simple approach to the synthesis of heterocyclophane consisting of two 4,4’-bithiazoles has been developed in mild conditions. The heterocyclophane with two short chains was conveniently prepared by Hantzsch thiazoles synthesis using the reaction of 3-tert-butoxycarbonyl-3-azapentanethiocarboxamide with 1,4-dibromobutane-2,3-dione in methanol under reflux for only 15 min. Amino groups at the linkers of this heterocyclophane can be functionalized to give acylated and carbamate derivatives. Their properties as protein kinase inhibitors were investigated, and one of the heterocyclophanes exhibited specific anti-activity for c-mesenchymal epithelial transition factor (IC₅₀=603 nm ), among seven types of protein kinases investigated. The computational site identification by ligand competitive saturation method was used to determine why the one heterocyclophane exhibited strong anti-activity for c-mesenchymal epithelial transition factor.     

Vibrations of a continuous web on elastic supports

We consider an infinite, homogenous linearly elastic beam resting on a system of linearly elastic supports, as an idealized model for a paper web in the middle of a cylinder-based dryer section. We obtain closed-form analytical expressions for the eigenfrequencies and the eigenmodes. The frequencies increase as the support rigidity is increased. Each frequency is bounded from above by the solution with absolutely rigid supports, and from below by the solution in the limit of vanishing support rigidity. Thus in a real system, the natural frequencies will be lower than predicted by commonly used models with rigid supports.     

Lewis Acids as Activators in CBS‐Catalysed Diels–Alder Reactions: Distortion Induced Lewis Acidity Enhancement of SnCl4

The effect of several Lewis acids on the CBS catalyst (named after Corey, Bakshi and Shibata) was investigated in this study. While ²H NMR spectroscopic measurements served as gauge for the activation capability of the Lewis acids, in situ FT‐IR spectroscopy was employed to assess the catalytic activity of the Lewis acid oxazaborolidine complexes. A correlation was found between the Δδ(²H) values and rate constants k_DA, which indicates a direct translation of Lewis acidity into reactivity of the Lewis acid–CBS complexes. Unexpectedly, a significant deviation was found for SnCl₄ as Lewis acid. The SnCl₄–CBS adduct was much more reactive than the Δδ(²H) values predicted and gave similar reaction rates to those observed for the prominent AlBr₃–CBS adduct. To rationalize these results, quantum mechanical calculations were performed. The frontier molecular orbital approach was applied and a good correlation between the LUMO energies of the Lewis acid–CBS–naphthoquinone adducts and k_DA could be found. For the SnCl₄–CBS–naphthoquinone adduct an unusual distortion was observed leading to an enhanced Lewis acidity. Energy decomposition analysis with natural orbitals for chemical valence (EDA‐NOCV) calculations revealed the relevant interactions and activation mode of SnCl₄ as Lewis acid in Diels–Alder reactions.     

Symmetry justification of Lorenz’ maximum simplification

In 1960 Edward Lorenz (1917–2008) published a pioneering work on the ‘maximum simplification’ of the barotropic vorticity equation. He derived a coupled three-mode system and interpreted it as the minimum core of large-scale fluid mechanics on a ‘finite but unbounded’ domain. The model was obtained in a heuristic way, without giving a rigorous justification for the chosen selection of modes. In this paper, it is shown that one can legitimate Lorenz’ choice by using symmetry transformations of the spectral form of the vorticity equation. The Lorenz three-mode model arises as the final step in a hierarchy of models constructed via the component reduction by means of symmetries. In this sense, the Lorenz model is indeed the ‘maximum simplification’ of the vorticity equation.     

On the model of non-holonomic billiard

In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.