Automatic Optimal Regularization for Ill-Posed Problems with Stochastical Noise without Imposing Smoothness Assumptions

We consider the compact operator A : 𝒳 → 𝒴 for the separable Hilbert spaces 𝒳 and 𝒴. The problem Ax = y is called ill-posed when the singular values s_k , k = 1, 2, … of the operator A tend to zero. Classically one assumes that y is biased with “deterministic noise”; we will also consider “stochastic noise” where the noise element is a weak Gaussian random variable. There classical stopping rules (e.g. Morozov) do not work. We will show that both for the “deterministic noise” case as well for the “stochastical noise” case we can regularize in an (asymptotically almost) optimal way without knowledge of the smoothness of the solution using Lepskij's method. Furthermore the method also works for estimated error levels and error behavior. So we can assure regularization which is just dependent on measurements obtainable in reality, e.g. satellite problems. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Overhauser DNP and EPR in a Mobile Setup: Influence of Magnetic Field Inhomogeneity

Power-dependent Overhauser dynamic nuclear polarization (DNP) enhancements and continuous-wave electron paramagnetic resonance (EPR) spectra of nitroxide radicals were measured in the magnetic field of a mobile Halbach-array permanent magnet and compared with results from a commercially available electromagnet. DNP saturation factors for varying microwave power were obtained from both measurement series and used to investigate how the increased magnetic field inhomogeneity present in the Halbach magnet affects the saturation efficiency. An EPR detection system was designed to allow continuous-wave EPR measurements at microwave power up to 20?W. Our results show that despite the lower magnetic field homogeneity, a Halbach-array magnet can be used for EPR and DNP-enhanced nuclear magnetic resonance of high quality providing almost the same performance as a more homogeneous electromagnet.     

Hydrogen determination by means of the1H(19F, αγ)16 O and1H(15N, αγ)12C resonance reactions

Hydrogen surface contamination and depth profiles can be measured by the resonant nuclear reactions¹H(¹⁹F, )¹⁶O and¹H(¹⁵N, )¹²C. The method was applied to study hydrogen-implanted silicon, amorphous silicon layers and silicon oxide films produced by anodic oxidation.     

Gerüstumlagerung eines α,β -ungesättigten γ,δ-Epoxiketons bei der Birch-Reduktion: Strukturaufklärung mittels 13C-INADEQUATE-NMR-Spektroskopie

Skeleton Rearrangement of an α-β-Unsaturated γ,δ-Epoxyketone during Birch Reduction: Structure Elucidation by Means of ¹³C-INADEQUATE-NMR Spectroscopy When the γ-epoxide 2 of β-ionone is treated under standard Birch-reduction conditions, unexpectedly a 70% combined yield of regioisomeric octalones 4 and 5 is isolated. These products unquestionably result form cleavage of the central epoxide C?C bond. The structure of compounds 4 and 5 could be determined by means of ¹³C-INADEQUATE-NMR spectroscopy.     

Advanced high-performance liquid chromatography method for highly polar nitroaromatic compounds in ground water samples from ammunition waste sites

An advanced HPLC-photodiode array detection method for the determination of 12 selected highly polar nitroaromatic compounds in ground water samples of ammunition waste sites has been developed and validated. After solid-phase extraction the limits of detection were in the range 0.1–0.5 μg/l. To prove the applicability of the method to other polar nitroaromatic compounds the retention time of another 32 polar compounds under the specified chromatographic conditions were determined and their UV spectra recorded. To review the method, interlaboratory comparisons were performed with a spiked and a real ground water sample.     

Multiphoton ionization of atoms and ions by high-intensity X-ray lasers

Coulomb corrections to the action function and rate of multiphoton ionization of atoms and ions in a strong linearly polarized electromagnetic field are calculated for high values of the Keldysh adiabaticity parameter. The Coulomb corrections significantly increase the ionization rate for atoms (by several orders of magnitude). An interpolation formula proposed for ionization rate is valid for arbitrary values of the adiabaticity parameter. The high accuracy of the formula is confirmed by comparison with the results of numerical calculations. The general case of elliptic polarization of laser radiation is also considered.