Metal-Assisted Oxidative Cyclization of Arylamidrazones I. Synthesis of 3-Acetyl-1,4-dihydro-1-phenyl-1,2,4-benzotriazine

In the presence of RuCl₃, N-phenylamidrazone underwent oxidative cyclization into 1,4-dihydro-1-phenyl-1,2,4-benzotriazine, the structure of which is established by spectral and X-ray diffraction data.     

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.     

Algebraic properties of discrete box splines

The central objective of this paper is to discuss linear independence of translates of discrete box splines which we introduced earlier as a device for the fast computation of multivariate splines. The results obtained here allow us to draw conclusions about the structure of such discrete splines which have, in particular, applications to counting the number of nonnegative integer solutions of linear diophantine equations.     

A characterization of the \Sigma_1-definable functions of KP\omega + (uniform\; AC)

The subject of this paper is a characterization of the -definable set functions of Kripke-Platek set theory with infinity and a uniform version of axiom of choice: . This class of functions is shown to coincide with the collection of set functionals of type 1 primitive recursive in a given choice functional and . This goal is achieved by a G?del Dialectica-style functional interpretation of and a computability proof for the involved functionals. Received October 9, 1996     

Two Ergodic Sample-Path Properties of the Poisson Process

For increasing sequences of real numbers we consider two types of asymptotic behavior that remind of the defining property of a (homogeneous) Poisson process according to which the numbers of points in disjoint intervals are independent and follow Poisson distributions with specified parameters. We prove that almost all paths of a Poisson process show this asymptotic behavior, and characterize the Poisson process by these properties. Further we discuss the connection to equidistribution notions.