A Neural Network-Based Policy Iteration Algorithm with Global $$H^2$$ -Superlinear Convergence for Stochastic Games on Domains

In this work, we propose a class of numerical schemes for solving semilinear Hamilton–Jacobi–Bellman–Isaacs (HJBI) boundary value problems which arise naturally from exit time problems of diffusion processes with controlled drift. We exploit policy iteration to reduce the semilinear problem into a sequence of linear Dirichlet problems, which are subsequently approximated by a multilayer feedforward neural network ansatz. We establish that the numerical solutions converge globally in the \(H^2\)-norm and further demonstrate that this convergence is superlinear, by interpreting the algorithm as an inexact Newton iteration for the HJBI equation. Moreover, we construct the optimal feedback controls from the numerical value functions and deduce convergence. The numerical schemes and convergence results are then extended to oblique derivative boundary conditions. Numerical experiments on the stochastic Zermelo navigation problem are presented to illustrate the theoretical results and to demonstrate the effectiveness of the method.

     

WITCH: A Penning Trap Retardation Spectrometer Combination for Precision Studies of the Weak Interaction

We present data from three seasons of experimental field work designed to recreate ancient Andean coastal ceramic firing techniques. Based on the recent discovery of two different archaeological ceramic production sites in the La Leche river valley of northern coastal Peru, the opportunity arose to apply Mössbauer spectroscopy and other analytical methods to reconstruct ancient firing procedures. Two sets of firings took place in 1993 and 1997 in Batán Grande using a partially restored Formative kiln from about 800 BC, local hardwood and cow dung as fuel. A third experiment followed in 2000 after the discovery of a Middle Sicán ceramics workshop in use between ca. AD 950 and 1050 at Huaca Sialupe, where an exact replica of an ancient kiln was built from local clay, and fired with local wood and cow dung. Additionally, inverted urns found at Huaca Sialupe were tested for their potential use as furnaces for metal working. Mössbauer spectroscopy was used to compare the physical and chemical state of specimens produced in the field experiments with ancient ceramics and with specimens produced in controlled laboratory experiments.     

Physical boundaries within aggregates – differences between amorphous,para‐crystalline,and crystalline Structures

The structural properties of finely divided inorganic materials such as metal and metalloid oxides, silicates or carbonates of both synthetic and natural origin are compared by means of electron microscopy and tomography. The structure of the outer surfaces of various compact or compacted agglomerates may suggest some striking similarities between various amorphous silica on the one hand and crystalline titania and alumina on the other however the details of the interior fine structure are completely different. Inside of the crystalline aggregates of, for example, alumina and titania distinct grain boundaries between the inter‐grown primary crystallites exist. Also physical boundaries between different solid phases and crystalline/amorphous transitions in core/shell structures can occur. No physical grain or phase boundaries were found inside of synthetic amorphous silica or para‐crystalline carbon black thus, the aggregate is the constituent particle. Synthetic amorphous silica from different production technologies (fumed/pyrogenic, precipitated, aerogel, gel) may exhibit different macro‐morphology but distinct similarities of the amorphous silica networks. Computational studies on silica and titania underline the stability of constituent particles and aggregates as observed by means of TEM after dispersing the original materials by ultra‐sonication.     

Epitaxially grown zinc oxide films for electro-optic and acousto-optic interactions

Measurements of acoustic surface waves (ASW) and optical guided waves (OGW) wave properties have been carried out on chemical vapor deposited (CVD) epitaxial zinc oxide (ZnO) films on sapphire (Al₂O₃) substrates of different orientations. Surface preparation and orientation effects have been studied. Untuned acoustic insertion loss of 40 dB at 160 MHz and optical propagation loss of better than 5 dB/cm at 6328Å for the TE₀ mode were obtained in a 2μm thick (11$\text{2}$4) ZnO film deposited on a (0001) sapphire substrate.     

2-Quinolyl- and 1-isoquinolylnitrenes: ring expansion and ring opening in heteroarylnitrenes

Argon matrix photolysis of tetrazolo[1,5-a]quinoline 8 and tetrazolo[5,1-a]isoquinoline 7 causes nitrogen elimination and ring expansion to 1,3-diazabenzo[d]cyclohepta-1,2,4,6-tetraene 13. The photolysis of tetrazolo[5,1-a]isoquinoline 7 also causes ring opening to o-cyanophenylketenimine 22. Mechanisms of ring opening of heteroarylnitrenes are discussed.     

Struktur/wirkung-Beziehungen bei Geruchsstoffen mit dem Bicyclo[2.2.2.]octan-Gerüst

Structure-Activity Relationships of Odorants with a Bicyclo[2.2.2]octane System The synthesis of the olfactory interesting homonojigikualcohol 2 and of its epimer 10 leads to the keto alcohols 6a, b and 7a, b as intermediates. The latter have OH and C?O groups (an AH/B system) fixed at the rigid bicyclic nucleus at different distances (2.8 and 4.7 Å) and confirm Ohloff's rule for odoriferous properties which is based on this distance.     

A simple clean-up procedure for the quantitative determination of PCBs in complex materials

Summary A simple, rapid, low cost and uniform single-step clean-up procedure with a column containing two silica gel packings of different mesh size for the quantitative determination of PCBs by capillary gas chromatography (ECD) is reported. Its application to 9 complex matrices, among them a transformer oil, a waste motor oil, and an oil from a tempering bath, shows that in contradiction to other clean-Up methods nearly all accompanying substances can be separated. The reproducibility of 4.7% and the recovery rate of 92.7% for the PCBs are comparable with data found in literature.

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Einfaches Clean-up-Verfahren zur quantitativen Bestimmung von PCBs in komplexen Materialien