H2 molecule in strong magnetic fields

The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant magnetic field is asymptotic, in norm-resolvent sense, to an effective Hamiltonian which has the form of a multi-particle Schr\"odinger operator with interactions given by one-dimensional \delta-potentials. We study this effective Hamiltonian in the case of the H2 -molecule and establish existence of the ground state. We also show that the inter-nuclear equilibrium distance tends to 0 as the field-strength tends to infinity

The Phenion (R) Full-Thickness Skin Model for Percutaneous Absorption Testing

In recent years many efforts have been made to replace dermal toxicity testing of chemicals in the animal by in vitro assays. As a member of a German research consortium, we have previously contributed to the validation of an in vitro test protocol for percutaneous absorption studies on the basis of reconstructed human epidermis and both human and pig skin ex vivo. Aiming to assess the barrier properties of a newly developed reconstructed skin model, this protocol has now been transferred to the Phenion (R) Full-Thickness Skin Model (FT model). The permeation of testosterone and caffeine was quantified in parallel to that of pig skin using Franz-type diffusion cells. In addition, the permeation of benzoic acid and nicotine was studied. As expected, the FT model is more permeable than pig skin, yet its barrier properties are well in accordance with those of reconstructed human epidermis when compared to previous data. In fact, the FT model most efficiently retards testosterone as the compound of highest lipophilicity, which can be explained by an additional uptake by a reservoir formed by the dermis equivalent. Thus, the structure closely parallels human skin. In consequence, the Phenion FT model appears to be suitable for percutaneous absorption studies in hazard analysis and should be subjected to a catch-up validation study. Copyright (C) 2009 S. Karger AG, Base

The role of oxygen vacancies on the structure and the density of states of iron doped zirconia

In this paper we study, both with theoretical and experimental approach, the effect of iron doping in zirconia. Combining density functional theory (DFT) simulations with the experimental characterization of thin films, we show that iron is in the Fe3+ oxidation state and accordingly that the films are rich in oxygen vacancies (VO). VO favor the formation of the tetragonal phase in doped zirconia (ZrO2:Fe) and affect the density of state at the Fermi level as well as the local magnetization of Fe atoms. We also show that the Fe(2p) and Fe(3p) energy levels can be used as a marker for the presence of vacancies in the doped system. In particular the computed position of the Fe(3p) peak is strongly sensitive to the VO to Fe atoms ratio. A comparison of the theoretical and experimental Fe(3p) peak position suggests that in our films this ratio is close to 0.5. Besides the interest in the material by itself, ZrO2:Fe constitutes a test case for the application of DFT on transition metals embedded in oxides. In ZrO2:Fe the inclusion of the Hubbard U correction significantly changes the electronic properties of the system. However the inclusion of this correction, at least for the value U = 3.3 eV chosen in the present work, worsen the agreement with the measured photo-emission valence band spectra.Comment: 24 pages, 8 figure

A tight lower bound instance for k-means++ in constant dimension

The k-means++ seeding algorithm is one of the most popular algorithms that is used for finding the initial $k$ centers when using the k-means heuristic. The algorithm is a simple sampling procedure and can be described as follows: Pick the first center randomly from the given points. For $i > 1$, pick a point to be the $i^{th}$ center with probability proportional to the square of the Euclidean distance of this point to the closest previously $(i-1)$ chosen centers. The k-means++ seeding algorithm is not only simple and fast but also gives an $O(\log{k})$ approximation in expectation as shown by Arthur and Vassilvitskii. There are datasets on which this seeding algorithm gives an approximation factor of $\Omega(\log{k})$ in expectation. However, it is not clear from these results if the algorithm achieves good approximation factor with reasonably high probability (say $1/poly(k)$). Brunsch and R\"{o}glin gave a dataset where the k-means++ seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability that is exponentially small in $k$. However, this and all other known lower-bound examples are high dimensional. So, an open problem was to understand the behavior of the algorithm on low dimensional datasets. In this work, we give a simple two dimensional dataset on which the seeding algorithm achieves an $O(\log{k})$ approximation ratio with probability exponentially small in $k$. This solves open problems posed by Mahajan et al. and by Brunsch and R\"{o}glin.Comment: To appear in TAMC 2014. arXiv admin note: text overlap with arXiv:1306.420

Typhoid fever: clinical features

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