Synthesis and structural characterization of cationic rhenium(V) and technetium(V) dioxo complexes containing four N-heterocyclic carbene ligands

Cationic dioxorhenium and dioxotechnetium complexes of the composition [MO(2)(L(1))(4)](+) (L(1) = 1,3-diisopropyl-4,5-dimethylimidazol-2-ylidene) have been prepared from various starting materials and studied spectroscopically and by X-ray crystallography. The metal-carbon distances range from 2.216(4) to 2.232(4) A indicating mainly sigma-bonding.     

Temperature-dependent crystal structure of the isopropanol clathrate of Dianin's compound

The title compound undergoes two order-disorder transitions between 15 and 299 K, dictated by ordering of the guest molecules in the host cages, and resulting in three related crystal structures. We anticipate behaviour of this kind to be widespread, and speculate that the concept of "the crystal structure" for individual Dianin's clathrates may be elusive.     

The Site‐Assembly Determines Catalytic Activity of Nanoparticles

Heterogeneous catalysts are often designed as metal nanoparticles supported on oxide surfaces. Here, the relation between particle morphology and reaction kinetics is investigated by scaling relation kinetic Monte Carlo simulations using CO oxidation over Pt nanoparticles as a model reaction. We find that different particle morphologies result in vastly different catalytic activities. The activity is strongly affected by kinetic couplings between sites, and a wide site distribution generally enhances the activity. The present study highlights the role of site‐assemblies as a concept that, in addition to isolated active sites, can be used to understand catalytic reactions over nanoparticles.     

Exceptions and counterexamples: Understanding Abel's comment on Cauchy's Theorem

It may seem odd that Abel, a protagonist of Cauchy's new rigor, spoke of “exceptions” when he criticized Cauchy's theorem on the continuity of sums of continuous functions. However, when interpreted contextually, exceptions appear as both valid and viable entities in the early 19th century. First, Abel's use of the term “exception” and the role of the exception in his binomial paper is documented and analyzed. Second, it is suggested how Abel may have acquainted himself with the exception and his use of it in a process denoted critical revision is discussed. Finally, an interpretation of Abel's exception is given that identifies it as a representative example of a more general transition in the understanding of mathematical objects that took place during the period. With this interpretation, exceptions find their place in a fundamental transition during the early 19th century from a formal approach to analysis toward a more conceptual one.     

Polyhedral approximation and practical convex hull algorithm for certain classes of voxel sets

In this paper we introduce an algorithm for the creation of polyhedral approximations for certain kinds of digital objects in a three-dimensional space. The objects are sets of voxels represented as strongly connected subsets of an abstract cell complex. The proposed algorithm generates the convex hull of a given object and modifies the hull afterwards by recursive repetitions of generating convex hulls of subsets of the given voxel set or subsets of the background voxels. The result of this method is a polyhedron which separates object voxels from background voxels. The objects processed by this algorithm and also the background voxel components inside the convex hull of the objects are restricted to have genus 0. The second aim of this paper is to present some practical improvements to the discussed convex hull algorithm to reduce computation time.     

Effect of particle size on carburization of Fe-Co alloy catalysts

Bimetallic Fe-Co alloy catalysts supported on silica have been studied by use of combined Mössbauer absorption and emisson spectroscopy. Effects of carburization on samples with different particle size are discussed.