On intersection multigraphs of hypergraphs

The sum of the cardinalities of all the edges of a hypergraph is computed in two different ways. This result is used to treat the generalisation of the notion of cyclomatic number for hypergraphs. Among others the following result is obtained: The cyclomatic number of the hypergraph H vanishes if and only if some maximum forest of the weighted intersection graph of H has the property that for every vertex of H the subgraph of the forest induced by those edges containing that vertex is connected.     

The semi-classical limit of large fermionic systems

We study a system of N fermions in the regime where the intensity of the interaction scales as 1 / N and with an effective semi-classical parameter \(\hbar =N^{-1/d}\) where d is the space dimension. For a large class of interaction potentials and of external electromagnetic fields, we prove the convergence to the Thomas–Fermi minimizers in the limit \(N\rightarrow \infty \). The limit is expressed using many-particle coherent states and Wigner functions. The method of proof is based on a fermionic de Finetti–Hewitt–Savage theorem in phase space and on a careful analysis of the possible lack of compactness at infinity.     

The de-Rham theorem and Shapiro lemma for Schwartz functions on Nash manifolds

In this paper we continue our work on Schwartz functions and generalized Schwartz functions on Nash (i.e. smooth semi-algebraic) manifolds. Our first goal is to prove analogs of the de-Rham theorem for de-Rham complexes with coefficients in Schwartz functions and generalized Schwartz functions. Using that we compute the cohomologies of the Lie algebra g of an algebraic group G with coefficients in the space of generalized Schwartz sections of G-equivariant bundle over a G-transitive variety M. We do it under some assumptions on topological properties of G and M. This computation for the classical case is known as the Shapiro lemma.     

The 2-center problem in three dimensions

Let P be a set of n points in ${\mathbb{R}}^3$. The 2-center problem for P is to find two congruent balls of minimum radius whose union covers P. We present a randomized algorithm for computing a 2-center of P that runs in $O(\beta (r^{?})n^2{\log }^{4}n\log \log n)$ expected time; here $\beta (r)=1/{(1?r/r_0)}^3$, $r^{?}$ is the radius of the 2-center balls of P, and $r_0$ is the radius of the smallest enclosing ball of P. The algorithm is near quadratic as long as $r^{?}$ is not too close to $r_0$, which is equivalent to the condition that the centers of the two covering balls be not too close to each other. This improves an earlier slightly super-cubic algorithm of Agarwal, Efrat, and Sharir (2000) [2] (at the cost of making the algorithm performance depend on the center separation of the covering balls).     

Hypernuclear physics legacy and heritage of Dick Dalitz

The major contributions of Richard H. Dalitz to hypernuclear physics, since his first paper in 1955 to his last one in 2005 covering a span of 50 years during which he founded and led the theoretical study of hypernuclei, are reviewed from a personal perspective. Topical remarks on the search for quasi-bound -nuclear states and on kaon condensation are made.     

Derivation of Hartreeʼs theory for generic mean-field Bose systems

In this paper we provide a novel strategy to prove the validity of Hartree?s theory for the ground state energy of bosonic quantum systems in the mean-field regime. For the known case of trapped Bose gases, this can be shown using the strong quantum de Finetti theorem, which gives the structure of infinite hierarchies of k-particles density matrices. Here we deal with the case where some particles are allowed to escape to infinity, leading to a lack of compactness. Our approach is based on two ingredients: (1) a weak version of the quantum de Finetti theorem, and (2) geometric techniques for many-body systems. Our strategy does not rely on any special property of the interaction between the particles. In particular, our results cover those of Benguria–Lieb and Lieb–Yau for, respectively, bosonic atoms and boson stars.     

Optische Methoden

Analytical and Bioanalytical Chemistry -     

Studies on the migration in PA6‐OMMT nanocomposites: effect of annealing on migration as evidenced by ARXPS (angle resolved X‐ray photoelectron spectroscopy)

The present paper deals with experiments in which the angle resolved X‐ray photoelectron spectroscopy (ARXPS) technique was applied to investigate the phenomenon of migration in polyamide 6 with organically modified montmorillonite (PA6‐OMMT) nanocomposites. This is the first time ARXPS was used, to gain a more detailed insight into the migration process. Curve‐fitting analyses are reported which enable the differentiation between a manual mixture of PA6 with OMMT at room temperature from a nanocomposite structure. The ARXPS technique was applied to annealed samples at 250, 275, and 285°C, for 2 hr, and with three take of angles, α, of 90, 60, and 30°. The depth of the layer investigated is 9 nm in case the sample surface is well defined. By tilting the take‐off angle of the beam‐out electrons one can determine the intensity of the signals at various distances from the surface within the investigated layer. The concentration gradient of the Si signals is observed. The rate of migration is found to be more rapid in the layer closest to the surface. The intensity of the Si signals in the investigated layer is found to be 1.8 to 9.1 times that of the same composite sample at room temperature. This ratio determines the extent of migration. At temperatures higher than 250°C and times of annealing greater than 30 min a decrease in the extent of migration is observed. This decrease is explained by the gradual decomposition of the surfactant and the consequent removal of the polymeric matrix molecules from the migrating exfoliated units, culminating in denuded alumino‐silicate layers. These layers aggregate to noncolloidal microcomposite particles which do not migrate. The concentration of the exfoliated units decreases with consequent decrease in migration. A gradient of decreasing concentration of Si2p signals was observed after various times of annealing, where the gradient becomes more uniform with increase in time. Copyright © 2008 John Wiley & Sons, Ltd.