Neutral-pion photoproduction off protons in the energy range 0.3 GeV<E(gamma)<3 GeV

Single pi(0) photoproduction has been studied with the CB-ELSA experiment at Bonn using tagged photon energies between 0.3 and 3.0 GeV. The experimental setup covers a very large solid angle of approximately 98% of 4pi. Differential cross sections dsigma/dOmega have been measured. Complicated structures in the angular distributions indicate a variety of different resonances being produced in the s channel intermediate state gammap-->N(*)(Delta(*))-->ppi(0). A combined analysis including the data presented in this letter along with other data sets reveals contributions from known resonances and evidence for a new resonance N(2070)D15.     

Synthesis of a tin-functionalized cyclopentadiene derivative

A 3-tert-butyl-1-(stannylpropyl)-functionalized cyclopentadienyl ligand precursor 6 is readily available in 64% overall yield from allylic alcohol 1 by a three-step reaction sequence including Pd-catalyzed hydrostannylation with Ph₃SnH. Treatment with FeCl₂ and ZrCl₄ · 2THF afforded corresponding ferrocene and zirconocene derivatives. Transmetallation of Sn-Ph with Li-Bu was observed under these reaction conditions by using BuLi as a base.     

Capillary gas chromatography-mass spectrometry of all 93 acyclic octenes and their identification in fluid catalytic cracked gasoline

The Kováts retention indices of all 93 acyclic octenes on polydimethylsiloxane and squalane as stationary phases as well as their mass spectra were measured. The means of gas chromatography-mass spectrometry (GC-MS) were used for confirmation of GC identification as well as for mass spectrometric deconvolution of the majority of gas chromatographic unseparated isomeric octene peaks. The distinction between corresponding E and Z acyclic octenes, that is either difficult or even impossible by means of GC-MS, was obtained on the basis of larger temperature coefficients of retention indices for Z isomeric octenes than for corresponding E isomers. The retention data expressed as homomorphy factors were correlated with the degree of branching, position of double bond, and position of alkyl group with respect to the double bond of acyclic octenes, and the structure-retention relationships were formulated. The 81 acyclic octenes were identified in FCC gasoline.     

Degrees of logics with Henkin quantifiers in poor vocabularies

We investigate some logics with Henkin quantifiers. For a given logic L, we consider questions of the form: what is the degree of the set of L–tautologies in a poor vocabulary (monadic or empty)? We prove that the set of tautologies of the logic with all Henkin quantifiers in empty vocabulary L* is of degree 0. We show that the same holds also for some weaker logics like L(H) and L(E). We show that each logic of the form L^(k)(Q), with the number of variables restricted to k, is decidable. Nevertheless – following the argument of M. Mostowski from [Mos89] – for each reasonable set theory no concrete algorithm can provably decide L^(k)(Q), for some (Q). We improve also some results related to undecidability and expressibility for logics L(H₄) and L(F₂) of Krynicki and M. Mostowski from [KM92].Mathematics Subject Classification (2000): 03C80, 03D35, 03B25Revised version: 28 August 2003     

Fiber-assisted detection with photon number resolution

We report the development of a photon-number-resolving detector based on a fiber-optical setup and a pair of standard avalanche photodiodes. The detector is capable of resolving individual photon numbers and operates on the well-known principle by which a single-mode input state is split into a large number (eight) of output modes. We reconstruct the photon statistics of weak coherent input light from experimental data and show that there is a high probability of inferring the input photon number from a measurement of the number of detection events on a single run.     

Direct measurement of the spatial Wigner function with area-integrated detection

We demonstrate experimentally a novel technique for characterizing transverse spatial coherence by using the Wigner distribution function. The method is based on the measurement of interference between a pair of rotated and displaced replicas of the input beam with an area-integrating detector, and it provides an optimal signal-to-noise ratio in regimes when array detectors are not available. We analyze the quantum-optical picture of the presented measurement for single-photon signals and discuss possible applications in quantum information processing.     

Photon counting with a loop detector

We propose a design for a photon-counting detector that is capable of resolving multiphoton events. The basic element of the setup is a fiber loop, which traps the input field with the help of a fast electro-optic switch. A single weakly coupled avalanche photodiode is used to detect small portions of the signal field extracted from the loop. We analyze the response of the loop detector to an arbitrary input field and discuss both the reconstruction of the photon-number distribution of an unknown field from the count statistics measured in the setup and the application of the detector in conditional-state preparation.     

Empirisch begründete Idealtypenbildung. Ein methodisches Prinzip zur Theoriekonstruktion in der interpretativen mathematikdidaktischen Forschung

How does the development of ideal types contribute to an empirically based construction of theories in the interpretative research of mathematics education? Before answering this question I clarify what is meant by the termstheory andideal type. Personal ideal types, ideal types of actions andsituational ideal types are going to be distinguished. Representing research examples. I show that forming ideal types can be considered as a methodical principle for empirically grounded theory construction with common features and different heuristics.