Absolutely continuous spectrum for the Anderson model on a product of a tree with a finite graph

We prove the almost sure existence of absolutely continuous spectrum at low disorder for the Anderson model on the simplest example of a product of a regular tree with a finite graph. This graph contains loops of unbounded size.     

Mesoscale and clusters of synchrony in networks of bursting neurons

We study the role of network architecture in the formation of synchronous clusters in synaptically coupled networks of bursting neurons. We give a simple combinatorial algorithm that finds the largest synchronous clusters from the network topology. We demonstrate that networks with a certain degree of internal symmetries are likely to have cluster decompositions with relatively large clusters, leading potentially to cluster synchronization at the mesoscale network level. We also address the asymptotic stability of cluster synchronization in excitatory networks of Hindmarsh-Rose bursting neurons and derive explicit thresholds for the coupling strength that guarantees stable cluster synchronization.     

Zur Leistungsf?higkeit der energiedispersiven R?ntgenspektralanalyse

Zusammenfassung Am Beispiel eines schwierigen Analysenproblems wird gezeigt, was die energiedispersive Methode der Röntgenspektralanalyse hinsichtlich Genauigkeit, Richtigkeit, Nachweisvermögen und Aufwand zu leisten vermag. Das Analysenproblem besteht darin, Ag und Cu als Hauptbestandteile und weitere 25 Elemente als mögliche Begleiter in mehr als 200 römischen Silbermünzen (Denare, Quinare, Antoniniane) zerstörungsfrei zu bestimmen. Historischer Hintergrund ist der Stoffwertverfall im römischen Kaiserreich.

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On the efficiency of energy dispersive X-ray spectrometryMultielement analysis of Roman silver coins

Summary The efficiency of the energy dispersive method of X-Ray spectral analysis with regard to its precision, accuracy, detecting power and expenditure is shown by means of a difficult analytical problem: Ag and Cu as major constituents together with other 25 elements as possible minor constituents are to be determined non-destructively in more than 200 Roman silver coins (Denarii, Quinarii, Antoniniani). Historical background is the depreciation of the coins during the Roman Empire.

     

The development of a fully automated solid-phase radioimmunoassay for digoxin

A radioimmunoassay for using antibody coated tubes and a unique radiotracer is described. The assay was designed specifically for use with the fully automated instrument Micromedic Systems «Concept 4 Automatic Radioassay». Antisera to digoxigenin-3-succinyl-BSA were raised in rabbits, purified by ammonium sulfate precipitation, and coated onto polypropylene tubes. An iodinated histamine derivative of digoxigenin which is insensitive to serum variability is utilized. The standard curve is linear for digoxin concentrations between 0.4 and 6.4 ng/ml and is parallel for two different sample sizes. Recovery of added digoxin was quantitative. Sample values obtained by this method correlate well with values obtained by other methods. The assay can either be performed manually or fully automated on Concept 4. The advantages provided by total automation are discussed.     

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and non-relativistic electrons that are coupled to the UV-cutoff quantized radiation field in the dipole approximation. If the lowest point of the energy spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this eigenvalue is an analytic function of the nuclear coordinates and of α^3/2, α being the fine structure constant. A suitably chosen ground state vector depends analytically on α^3/2 and it is twice continuously differentiable with respect to the nuclear coordinates. Submitted: November 24, 2008. Accepted: March 4, 2009.     

Wegner Estimate and Anderson Localization for Random Magnetic Fields

We consider a two dimensional magnetic Schrödinger operator with a spatially stationary random magnetic field. We assume that the magnetic field has a positive lower bound and that it has Fourier modes on arbitrarily short scales. We prove the Wegner estimate at arbitrary energy, i.e. we show that the averaged density of states is finite throughout the whole spectrum. We also prove Anderson localization at the bottom of the spectrum.     

Models for capacitated lot-sizing problem with backlogging,setup carryover and crossover

Setup operations are significant in some production environments. It is mandatory that their production plans consider some features, as setup state conservation across periods through setup carryover and crossover. The modelling of setup crossover allows more flexible decisions and is essential for problems with long setup times. This paper proposes two models for the capacitated lot-sizing problem with backlogging and setup carryover and crossover. The first is in line with other models from the literature, whereas the second considers a disaggregated setup variable, which tracks the starting and completion times of the setup operation. This innovative approach permits a more compact formulation. Computational results show that the proposed models have outperformed other state-of-the-art formulation.