Automatic Dantzig–Wolfe reformulation of mixed integer programs

Mathematical Programming - Dantzig–Wolfe decomposition (or reformulation) is well-known to provide strong dual bounds for specially structured mixed integer programs (MIPs). However, the...     

Sufficient conditions for Willmore immersions in \mathbb{R }^3 to be minimal surfaces

We provide two sharp sufficient conditions for immersed Willmore surfaces in $\mathbb{R }^3$ to be already minimal surfaces, i.e. to have vanishing mean curvature on their entire domains. These results turn out to be particularly suitable for applications to Willmore graphs. We can therefore show that Willmore graphs on bounded $C^4$ -domains $\overline{\varOmega }$ with vanishing mean curvature on the boundary $\partial \varOmega $ must already be minimal graphs, which in particular yields some Bernstein-type result for Willmore graphs on $\mathbb{R }^2$ . Our methods also prove the non-existence of Willmore graphs on bounded $C^4$ -domains $\overline{\varOmega }$ with mean curvature $H$ satisfying $H \ge c_0>0 \,{\text{ on }}\, \partial \varOmega $ if $\varOmega $ contains some closed disc of radius $\frac{1}{c_0} \in (0,\infty )$ , and they yield that any closed Willmore surface in $\mathbb{R }^3$ which can be represented as a smooth graph over $\mathbb{S }^2$ has to be a round sphere. Finally, we demonstrate that our results are sharp by means of an examination of some certain part of the Clifford torus in $\mathbb{R }^3$ .     

Beitrag zum qualitativen Tartratnachweis

Ohne Zusammenfassung     

Investigations of nitrogen diffusion in austenitic CrNi steels

Parameters of the diffusion of N (up to 0.3 wt.%) in austenitic stainless steels (12 to 19 wt.% Cr, 12 to 16 wt.% Ni, up to 2 wt.% Mo) were determined within the temperature range of 1283–1573K. The small concentration gradients of N were successfully investigated using (1) mechanical serial sectioning technique in combination with either chemical N analysis or X-ray precision lattice parameter determination, and (2) measurements on microsections by means of either electron probe microanalysis or Kossel technique.The diffusion coefficients of N were found to be independent of its concentration. The alloying elements Cr and Mo reduce the N diffusivity in austenitic stainless steels which on the other hand is increased by Ni.     

JRQ and JPA irradiated and annealed reactor pressure vessel steels studied by positron annihilation

The paper is focused on a comprehensive study of JRQ and JPA reactor pressure vessel steels from the positron annihilation lifetime spectroscopy (PALS) point of view. Based on our more than 20 years’ experience with characterization of irradiated reactor steels, we confirmed that defects after irradiation start to grow and/or merge into bigger clusters. Experimental results shown that JPA steel is more sensitive to the creation of irradiation-induced defects than JRQ steel. It is most probably due to high copper content (0.29?wt.% in JPA) and copper precipitation has a major impact on neutron-induced defect creation at the beginning of the irradiation. Based on current PALS results, no large vacancy clusters were formed during irradiation, which could cause dangerous embrittlement concerning operation safety of nuclear power plant. The combined PALS, small angle neutron scattering and atomic probe tomography studies support the model for JRQ and JPA steels describing the structure of irradiation-induced clusters as agglomerations of vacancy clusters (consisting of 2–6 vacancies each) and are separated from each other by a distribution of atoms.     

Investigations of precipitates in heat treated AgPd30/CuSn6 layers

The subject of the investigations are precipitation zones, which grew as a result of chemical diffusion in AgPd30/CuSn6 bimetals. These precipitation zones have been characterized by metallography, electron probe microanalysis and x-ray diffraction. The growth of precipitation zones in the plating layer and in the substrate layer in dependence on time have been determined. The use of x-ray diffraction alone for the identification of the precipitates could not supply satisfying results in every case. This problem was solved by the application of electron probe microanalysis using a correction method, which allows the estimation of the chemical composition of small particles.Dedicated to Professor Dr. rer. nat. Dr. h. c. Hubertus Nickel on the occasion of his 65th birthday     

Quantitative detection of C-deuterated drugs by CARS microscopy and Raman microspectroscopy

The introduction of carbon-deuterium (C-D) bonds into drug compounds by organic synthesis is a non-invasive labelling approach, which does not alter the chemical and physiological properties of the drug itself. C-deuterated drugs exhibit characteristic vibrational signatures in the C-D stretching region around 2100-2300 cm(-1), which avoids spectral interference with contributions from a complex biological environment. In this paper, the quantitative detection of C-deuterated drugs by Raman microspectroscopy and single-band CARS microscopy is examined. Concentration-dependent studies on drugs with aliphatic and aromatic C-D moieties were performed in a two-channel microfluidic chip, using the corresponding non-deuterated (C-H) isotopologues as an internal reference.     

Spin-State Variations of Iron(III) Complexes with Tetracarbene Macrocycles

Starting from their six-coordinate iron(II) precursor complexes [L^8RFe(MeCN)]²⁺, a series of iron(III) complexes of the known macrocyclic tetracarbene ligand L^8H and its new octamethylated derivative L^8Me, both providing four imidazol-2-yliden donors, were synthesized. Several five- and six-coordinate iron(III) complexes with different axial ligands (Cl⁻, OTf⁻, MeCN) were structurally characterized by X-ray diffraction and analyzed in detail with respect to their spin state variations, using a bouquet of spectroscopic methods (NMR, UV/Vis, EPR, and ⁵⁷Fe Mößbauer). Depending on the axial ligands, either low-spin (S=1/2) or intermediate-spin (S=3/2) states were observed, whereas high-spin (S=5/2) states were inaccessible because of the extremely strong in-plane σ-donor character of the macrocyclic tetracarbene ligands. These findings are reminiscent of the spin state patterns of topologically related ferric porphyrin complexes. The ring conformations and dynamics of the macrocyclic tetracarbene ligands in their iron(II), iron(III) and μ-oxo diiron(III) complexes were also studied.     

Group actions on Segal operads

We give a Quillen equivalence between model structures for simplicial operads, described via the theory of operads, and Segal operads, thought of as certain reduced dendroidal spaces. We then extend this result to give a Quillen equivalence between the model structures for simplicial operads equipped with a group action and the corresponding Segal operads.