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.     

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.     

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.     

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.     

Transfer matrices, hyperbolic geometry and absolutely continuous spectrum for some discrete Schrödinger operators on graphs

We prove the existence of absolutely continuous spectrum for a class of discrete Schrödinger operators on tree like graphs. We consider potentials whose radial behaviour is subject only to an ?^∞ bound. In the transverse direction the potential must satisfy a condition such as periodicity. The graphs we consider include binary trees and graphs obtained from a binary tree by adding edges, possibly with weights. Our methods are motivated by the one-dimensional transfer matrix method, interpreted as a discrete dynamical system on the hyperbolic plane. This is extended to more general graphs, leading to a formula for the Green's function. Bounds on the Green's function then follow from the contraction properties of the transformations that arise in this generalization. The bounds imply the existence of absolutely continuous spectrum.     

Conjugated Biradical Intermediates: Spectroscopic,Kinetic, and Trapping Studies of 2,2-Dimethyl-1,3-perinaphthadiyl

The biradical 2,2-dimethyl-1,3-perinaphthadiyl ( a ) was generated from two different precursors, the naphthocyclopropane 1 and the azo compound 2 , and from each by three different pathways (pyrolysis, direct photolysis, and triplet sensitization, Scheme 1). The combined evidence from flash photolysis, low-temperature spectroscopy, and product analyses provides a detailed mechanistic picture of the formation and decay of this reactive intermediate which is persistent at 77 K in the triplet ground state (³ a ) and rather long-lived (400 μs) at room temperature. When formed in its lowest singlet state (¹ a ), the biradical is too short-lived to undergo intersystem crossing to ³ a or bimolecular reactions. Thus, ³ a is formed exclusively from the excited triplet state of the precursor compounds, ³ 1 * or ³ 3 *. The monomolecular decay of ³ a is retarded by the spin barrier; ³ a initiates the polymerization of acrylonitrile and is trapped by ³O₂.     

Absolutely Continuous Spectrum for the Anderson Model on a Tree: A Geometric Proof of Klein’s Theorem

We give a new proof of a version of Klein’s theorem on the existence of absolutely continuous spectrum for the Anderson model on the Bethe Lattice at weak disorder.     

Bestimmung von Plasma-Kallikrein mit einem chromogenen Peptid-Substrat: Methodik und klinische Anwendung

Ohne Zusammenfassung

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Determination of plasma kallikrein with a chromogenic peptide substrate: Method and clinical evaluation