The Role of Radical Bridges in Polynuclear Single-Molecule Magnets

Employing radical bridges between anisotropic metal ions has been a viable route to achieve high-performance single-molecule magnets (SMMs). While the bridges have been mainly considered for their ability to promote exchange interactions, the crystal-field effect arising from them has not been taken into account explicitly. This lack of consideration may distort the understanding and limit the development of the entire family. To shed light on this aspect, herein we report a theoretical investigation of a series of N -radical-bridged diterbium complexes. It is found that while promoting strong exchange coupling between the terbium ions, the N -radical induces a crystal field that interferes destructively with that of the outer ligands, and thus reduces the overall SMM behavior. Based on the theoretical results, we conclude that the SMM behavior in this series could be further maximized if the crystal field of the outer ligands is designed to be collinear with that of the radical bridge. This conclusion can be generalized to all exchange-coupled SMMs.     

Wechselnde Bindungen in einem Zweikörpersystem mit trockener Reibung

Übersicht Betrachtet wird ein zwangserregtes Zweikörpersystem mit wechselnden Bindungen infolge trockener Reibung. Stationäre Bewegungen werden als Grenzfall instationärer Einschwingvorgänge berechnet. Abhängig von den Systemparametern ergeben sich drei typische Bewegungsformen. Ihnen entsprechen dauernde Haftzustände, wechselnde Haft-Gleitzustände oder dauernde Gleitzustände an der Berührfläche beider Körper.

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Intermittant constraints in a two-body-system with dry friction

Summary An externally excited two-body-system with intermittant constraints due to dry friction is considered. Stationary motions are calculated as limit cases of instationary transients. Depending on the parameters of the system, three typical modes are of interest. These correspond to permanent sticking, slipstick behaviour, or to permanent slipping in the contact surface of the bodies, respectively.

     

Patterns—a fundamental idea of mathematical thinking and learning

Taking advantage of patterns is typical of our everyday experience as well as our mathematical thinking and learning. For example a working day or a morning at school displays a certain structure, which can be described in terms of patterns. On the one hand regular structures give us the feeling of permanence and enable us to make predictions. On the other hand they also provide a chance to be creative and to vary common procedures. School students usually encounter patterns in math classes either as number patterns or geometric patterns. There are also patterns that teachers can find in analyzing the errors students make during their calculations (error patterns) as well as patterns that are inherent to mathematical problems. One could even go so far as to say that identifying and describing patterns is elementary for mathematics (cf. Devlin 2003). Practising good interacting with patterns supports not only the active learning of mathematics but also a deeper understanding of the world in general. Patterns can be explored, identified, extended, reproduced, compared, varied, represented, described and created. This paper provides some examples of pattern utilization and detailed analyses thereof. These ideas serve as “hooks” to encourage the good use of patterns to facilitate active learning processes in mathematics.     

Supercritical CO2 as a superior solvent for the cyclization of diallylmalonate catalyzed by palladium-containing zeolites

Palladium-containing zeolites catalyze the cycloisomerization of diethyl diallylmalonate to dimethylcyclopentenes. When the reaction is carried out in toluene, the performance of the palladium catalyst depends on the pore size of the zeolites. At 60 °C, palladium adsorbed on large pore size Beta zeolite (pore size ∼7.4 Å) is more active than medium pore size ZSM-5 (pore size ∼5.4 Å). This lower activity of ZSM-5 compared to Beta is attributable to the restricted diffusion of reagent and products through the ZSM-5 channels as compared to Beta zeolite. However, due to the gas-like diffusion characteristic of the supercritical state, the activity of ZSM-5 increases and becomes identical to that of Beta zeolite using supercritical CO₂ as medium.     

Notiz über Parachloraldehyd

Ohne Zusammenfassung     

From a Nonlinear, Nonconvex Variational Problem to a Linear, Convex Formulation

   Abstract. We propose a general approach to deal with nonlinear, nonconvex variational problems based on a reformulation of the problem resulting in an optimization problem with linear cost functional and convex constraints. As a first step we explicitly explore these ideas to some one-dimensional variational problems and obtain specific conclusions of an analytical and numerical nature.