Synthesis of Surface-Modified Nanoparticles via Cycloaddition-Reactions

Summary. The surface modification of nanoparticles via azide/alkine-1,3-dipolar cycloaddition-reactions is described. Ligand exchange onto various nanoparticles was monitored by ¹H NMR spectroscopy and formed the basis for the attachment of ligands onto the nanoparticles and their subsequent modification by dipolar cycloaddition reactions. Nanoparticle-surfaces were monitored by binding onto self-assembled monolayers derivatized with matching supramolecular interactions after derivatization.     

Innately transitive subgroups of wreath products in product action

A permutation group is innately transitive if it has a transitive minimal normal subgroup, which is referred to as a plinth. We study the class of finite, innately transitive permutation groups that can be embedded into wreath products in product action. This investigation is carried out by observing that such a wreath product preserves a natural Cartesian decomposition of the underlying set. Previously we classified the possible embeddings in the case where the plinth is simple. Here we extend that classification and identify several different types of Cartesian decompositions that can be preserved by an innately transitive group with a non-abelian plinth. These different types of decompositions lead to different types of embeddings of the acting group into wreath products in product action. We also obtain a full characterisation of embeddings of innately transitive groups with diagonal type into such wreath products.

     

The influence of the oxygen exposure on the thermal faceting of W[1 1 1] tip

The oxygen induced faceting of the macroscopic W[1 1 1] tip has been studied for oxygen exposures in the range 0.5-31 L and annealing temperatures 800-1800 K using the field ion microscopy (FIM) technique. After annealing at temperatures lower than 800 K, higher than 1850 K or for exposures lower than 0.5 L faceting was not observed. For exposures 0.5-1.9 L and annealing temperatures 800-1600 K well developed {1 1 2} facets with sharp edges formed. For exposures higher than 2.0 L edges of the {1 1 2} facets were broadening and disappearing, what has been attributed to the formation of three-dimensional tungsten oxides. The oxides could be easily removed by annealing the tip at 1700 K, what leads to formation of sharp facet edges. On the basis of these results a modified procedure of the ultrasharp tip fabrication has been proposed.     

Lattice theory,quadratic spaces,and quantum proposition systems

A quadratic space is a generalization of a Hilbert space. The geometry of certain kinds of subspaces (closed, splitting, etc.) is approached from the purely lattice theoretic point of view. In particular, theorems of Mackey and Kaplansky are given purely lattice theoretic proofs. Under certain conditions, the lattice of closed elements is a quantum proposition system (i.e., a complete orthomodular atomistic lattice with the covering property).     

On the slowness of phase boundary motion in one space dimension

We study the limiting behavior of the solution of with a Neumann boundary condition or an appropriate Dirichlet condition. The analysis is based on “energy methods”. We assume that the initial data has a “transition layer structure”, i.e., u^? ≈ ±+M 1 except near finitely many transition points. We show that, in the limit as ? → 0, the solution maintains its transition layer structure, and the transition points move slower than any power of ?.     

On false branch points of incompressible branched immersions

We prove that a branched immersion of a surface with boundary into a differentiable manifold has no false branch points (in fact, no ramified points) if the immersion induces an isomorphism of fundamental groups and some other natural hypotheses are satisfied. This result has immediate applications to Plateau's problem.Work done while the first author was a visiting member of the Max-Planck-Institut für Mathematik at Bonn. Both authors acknowledge the support of Max-Planck-Institut für Mathematik, Bonn and Schwerpunkt Geometrie at Mathematisches Institut, University of Heidelberg