Harmonic morphisms as unit normal bundles¶of minimal surfaces

Let be an isometric immersion between Riemannian manifolds and be the unit normal bundle of f. We discuss two natural Riemannian metrics on the total space and necessary and sufficient conditions on f for the projection map to be a harmonic morphism. We show that the projection map of the unit normal bundle of a minimal surface in a Riemannian manifold is a harmonic morphism with totally geodesic fibres. Received: 6 February 1999     

Singular superspaces

We introduce a wide category of superspaces, called locally finitely generated, which properly includes supermanifolds, but enjoys much stronger permanence properties, as are prompted by applications. Namely, it is closed under taking finite fibre products (i.e. is finitely complete) and thickenings by spectra of Weil superalgebras. Nevertheless, in this category, morphisms with values in a supermanifold are still given in terms of coordinates. This framework gives a natural notion of relative supermanifolds over a locally finitely generated base. Moreover, the existence of inner homs, whose source is the spectrum of a Weil superalgebra, is established; they are generalisations of the Weil functors defined for smooth manifolds.     

Some equilibrium problems under uncertainty and random variational inequalities

In this paper we describe some nonlinear equilibrium problems under uncertainty arising from economics and operations research. In particular we treat Wardrop equilibria in traffic networks. We show how the theory of monotone random variational inequalities, where random variables occur both in the operator and the constraint set, can be applied to model these problems. Therefore in this contribution we introduce the topic of random variational inequalities and present some of our recent results in this field. In particular, we treat the more structured case where a finite Karhunen-Loève expansion leads to a separation of the random and the deterministic variables. Here we describe a norm convergent approximation procedure based on averaging and truncation. We illustrate this procedure by means of some small sized numerical examples.     

Ethan D. Bolker und Maura B. Mast: Common Sense Mathematics,Second Edition

Mathematische Semesterberichte -     

A primal-dual interior-point algorithm for nonsymmetric exponential-cone optimization

Mathematical Programming - A new primal-dual interior-point algorithm applicable to nonsymmetric conic optimization is proposed. It is a generalization of the famous algorithm suggested by Nesterov...     

Dual Metastability in Electroless Plating: Complex Inertness Enabling the Deposition of Composition-Tunable Platinum Copper Alloy Nanostructures

Autocatalytic deposition represents a facile, versatile, and scalable wet-chemical tool for nanofabrication. However, the intricate component interplay in plating baths containing multiple metal species impedes alloy deposition. We resolved this challenge in the bimetallic copper-platinum system by exploiting the kinetic stability of platinum complexes, which allows adjusting their ligand sphere and thus reactivity independently from the present copper ions in a preceding, thermally activated ligand exchange step. By using metastable Pt^IV precursors of varying degrees of complexation, copper-platinum alloys of adjustable atomic ratio were plated from solutions of identical composition and concentration, but differing local coordination environment. Due to its excellent conformity and nanoscale homogeneity, the reaction is compatible with ambitious 3D substrate morphologies, as demonstrated in the template-assisted fabrication of nanotubes with high aspect ratio. The ability to generate additional synthetic degrees of freedom by decoupling the metal complex speciation from the solution composition is of large interest for redox-chemical synthesis techniques, such as electrodeposition or nanoparticle colloid production.     

Daniel Grieser: Mathematisches Problemlösen und Beweisen – Eine Entdeckungsreise in die Mathematik. 2. Auflage

Mathematische Semesterberichte -     

Methanol-Assisted Autocatalysis in Catalytic Methanol Synthesis

Catalytic methanol synthesis is one of the major processes in the chemical industry and may grow in importance, as methanol produced from CO₂ and sustainably derived H₂ are envisioned to play an important role as energy carriers in a future low-CO₂-emission society. However, despite the widespread use, the reaction mechanism and the nature of the active sites are not fully understood. Here we report that methanol synthesis at commercially applied conditions using the industrial Cu/ZnO/Al₂O₃ catalyst is dominated by a methanol-assisted autocatalytic reaction mechanism. We propose that the presence of methanol enables the hydrogenation of surface formate via methyl formate. Autocatalytic acceleration of the reaction is also observed for Cu supported on SiO₂ although with low absolute activity, but not for Cu/Al₂O₃ catalysts. The results illustrate an important example of autocatalysis in heterogeneous catalysis and pave the way for further understanding, improvements, and process optimization of industrial methanol synthesis.