A cyclographic approach to the vertices of plane curves

For a closed plane curve the centers of distance functions are considered satisfying the condition that the function attains at least two absolute minima along. From the topology of the closure of this set some information on specific vertices of the curve can be obtained. If a simply closed curve has a finite number of vertices only, then the structure of this set is given by a tree, composed from regular arcs, such that the end points of this tree belong to minimal osculating circles of, which entirely are located in the interior of. Furthermore, the curve can be reconstructed from this set as the envelope of a suitable family of circles. These relations are used to give alternative proofs and extensions of several known vertex theorems for closed curves.Dedicated to N. Stephanidis on occasion of his 65. birthday     

The job-shop problem and immediate selection

The job-shop problem is one of the most difficult NP-hard scheduling problems. A 10×10-problem published in 1963 has been solved only recently by Carlier and Pinson using a branch and bound method. Other branch and bound algorithms have been developed recently. The efficiency of all these branch and bound methods relies on the concept of immediate selection which allows to introduce order relations on the setI of all operations to be processed on the same machine before branching. We present new algorithms for immediate selection. Among them are

1. anO(max {n logn,f})-algorithm for fixing all disjunctions induced by cliques;
2. anO(n ²)-algorithm based on concepts which are different from those used by Carlier and Pinson.

Here,n is the number of operations inI andf is the number of induced order relations.     

On pasting -weights

Theorem 3 gives a condition when two -weights can be ``pasted' together to yield another -weight. It is subsequently used in Example 6 to give an example that shows that a necessary condition by Gohberg, Krupnik, and Spitkovsky is not sufficient.

     

Fibre cycles of holomorphic maps

This and the second part of the paper are to a great extent parts of my thesis [Si] which also appeared as preprint Mathematica Gottingensis 5/92. This work was partly supported by the S7B170 Geometrie und Analysis in Göttingen     

Mechanism of Reppe's nickel-catalyzed ethyne tetramerization to cyclooctatetraene: a DFT study

In this B3 LYP model study, homoleptic nickel(0) ethyne complexes have been predicted as the catalyst resting state for the title reaction. Ethyne ligand coupling of Ni(C(2)H(2))(3) yields monoethyne nickelacyclopentadiene in the rate-determining step. Ethyne coordination is followed by insertion of an ethyne ligand into the Ni--C sigma bond. A highly strained monoethyne trans-nickelacycloheptatriene is formed. This trans intermediate is unable to reductively eliminate benzene without prior isomerization to a cis-structure. Instead, it rapidly collapses to a nickelacyclononatetraene. Ethyne coordination induces reductive elimination to the cyclooctatetraene complex Ni(eta(2)-C(2)H(2))(eta(2)-C(8)H(8)), followed by facile ligand exchange. Other ethyne coupling pathways have been computed to be less favored. The cyclooctatetraene ligand binds significantly weaker to nickel(0) than ethyne, both for mononuclear, and for dinuclear species. For this reason, C--C bond formation steps at Ni(2)(micro-cot) fragments have been predicted to feature prohibitively high overall reaction barriers.     

Two-electron-transfer redox systems,part 7: two-step electrochemical oxidation of the boron subhalide cluster dianions B6X 2- 6 (X = Cl,Br, I)

Boron subhalide cluster dianions B6X 2- 6 (X = Cl, Br, I) are electrochemically oxidized in two steps. According to cyclic voltammograms, the first step is chemically reversible and yields the corresponding radical anions B6X .- 6. The electron transfer is nearly diffusion controlled. The second, slower electron-transfer step leads to a species which we assume to be the hitherto not yet described neutral compounds B6X 2- 6. The voltammograms indicate a coupled fast catalytic reaction, producing the radical anions in a reduction by an electrolyte component. Computer simulations of the cyclic voltammograms reveal mechanistic details of the redox reactions, as well as quantitative values for formal potentials, rate constants, and diffusion coefficients. The results are compared to other BnXn redox systems.     

carbon-carbon bond formation between 1,3-dienes and electron deficient alkenes

1,3-Dienes and electron deficient alkenes are coupled in a one pot carbon-carbon bond formation reaction under mild conditions.     

Surface chemistry of nanoscale Fe_3O_4 dispersed in magnetic fluids

The interaction between stabilizers and nanoparticles is one of the important factors to prepare stable magnetic fluids. The magnetic nano-size Fe3O4 core with single domain and the average grain size around 8-12 nm were prepared by chemical precipitation method. The O/Fe molar ratio of the particle surface was measured by X-ray photoelectron spectroscopy (XPS). The heat effects of stabilizers ad- sorption on nanoparticles were measured by solution calorimetry. The excess amount of oxygen was possibly the result of the hydroxygen formed on the surface of the nanoparticles. The heat effects showed that compounds containing carboxyl groups can be adsorbed chemically on magnetite by forming chemical bonds. The other stabilizers involving NH-groups, such as polyethylene-imine, can be adsorbed physically. The exothermic value is about half of the former case.