Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde

Multifunctional Polyoxometalate Platforms for Supramolecular Light-Driven Hydrogen Evolution

Multifunctional supramolecular systems are a central research topic in light-driven solar energy conversion. Here, we report a polyoxometalate (POM)-based supramolecular dyad, where two platinum-complex hydrogen evolution catalysts are covalently anchored to an Anderson polyoxomolybdate anion. Supramolecular electrostatic coupling of the system to an iridium photosensitizer enables visible light-driven hydrogen evolution. Combined theory and experiment demonstrate the multifunctionality of the POM, which acts as photosensitizer/catalyst-binding-site[1] and facilitates light-induced charge-transfer and catalytic turnover. Chemical modification of the Pt-catalyst site leads to increased hydrogen evolution reactivity. Mechanistic studies shed light on the role of the individual components and provide a molecular understanding of the interactions which govern stability and reactivity. The system could serve as a blueprint for multifunctional polyoxometalates in energy conversion and storage

Continuous selections of multivalued mappings

This survey covers in our opinion the most important results in the theory of continuous selections of multivalued mappings (approximately) from 2002 through 2012. It extends and continues our previous such survey which appeared in Recent Progress in General Topology, II, which was published in 2002. In comparison, our present survey considers more restricted and specific areas of mathematics. Note that we do not consider the theory of selectors (i.e. continuous choices of elements from subsets of topological spaces) since this topics is covered by another survey in this volume

Triplet-triplet annihilation upconversion for calcium sensing

Triplet-triplet annihilation upconversion is a bimolecular process converting low-energy light into high-energy one. All available calcium probes, despite their qualities, are downconverting, which leads to the autofluorescence caused by background emission of the intra- and intercellular molecules. Here we report a calcium-sensing system working via upconverted emission. The probe itself was obtained by covalent conjugation of a perylene blue emitter with a calcium-chelating moiety; it was sensitized by a red-light absorbing palladium porphyrin. Sensing was selective towards Ca2+ and occurred in the micromolar domain in aqueous solutions and methanol. The upconverted luminescence only appeared in the presence of calcium ions, with a quantum yield of up to 0.0018