Condensation of all-cis-tetraphenylcyclotetrasiloxanetetraol in ammonia: new method for preparation of ladder-like polyphenylsilsesquioxanes

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On Series of Ordinals and Combinatorics

This paper deals mainly with generalizations of results in finitary combinatorics to infinite ordinals. It is well-known that for finite ordinals ∑_bT<αβ is the number of 2-element subsets of an α-element set. It is shown here that for any well-ordered set of arbitrary infinite order type α, ∑_bT<αβ is the ordinal of the set M of 2-element subsets, where M is ordered in some natural way. The result is then extended to evaluating the ordinal of the set of all n-element subsets for each natural number n ≥ 2. Moreover, series ∑_β<αf(β) are investigated and evaluated, where α is a limit ordinal and the function f belongs to a certain class of functions containing polynomials with natural number coefficients. The tools developed for this result can be extended to cover all infinite α, but the case of finite α appears to be quite problematic.     

Numerical solutions of the shallow water equations with discontinuous bed topography

A simple scheme is developed for treatment of vertical bed topography in shallow water flows. The effect of the vertical step on flows is modelled with the shallow water equations including local energy loss terms. The bed elevation is denoted with z_b^‐ for the left and z_b⁺ for the right values at each grid point, hence exactly representing a discontinuity in the bed topography. The surface gradient method (SGM) is generalized to reconstruct water depths at cell interfaces involving a vertical step so that the fluxes at the cell interfaces can accurately be calculated with a Riemann solver. The scheme is verified by predicting a surge crossing a step, a tidal flow over a step and dam‐break flows on wet/dry beds. The results have shown good agreements compared with analytical solutions and available experimental data. The scheme is efficient, robust, and may be used for practical flow calculations. Copyright © 2002 John Wiley & Sons, Ltd.     

A finite model property for RMImin

It is proved that the variety of relevant disjunction lattices has the finite embeddability property. It follows that Avron's relevance logic RMI _min has a strong form of the finite model property, so it has a solvable deducibility problem. This strengthens Avron's result that RMI _min is decidable. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Black-hole horizon and metric singularity at the brane separating two sliding superfluids

An analogue of a black hole can be realized in the low-temperature laboratory. The horizon can be constructed for “relativistic” ripplons (surface waves) living on the brane. The brane is represented by the interface between two superfluid liquids, ³He-A and ³He-B, sliding along each other without friction. A similar experimental arrangement was recently used for the observation and investigation of the Kelvin-Helmholtz type of instability in superfluids [1]. The shear-flow instability in superfluids is characterized by two critical velocities. The lowest threshold measured in recent experiments [1] corresponds to the appearance of the ergoregion for ripplons. In the modified geometry, this will give rise to the black-hole event horizon in the effective metric experienced by ripplons. In the region behind the horizon, the brane vacuum is unstable due to interaction with the higher-dimensional world of bulk superfluids. The time of the development of instability can be made very long at low temperature. This will allow us to reach and investigate the second critical velocity—the proper Kelvin-Helmholtz instability threshold. The latter corresponds to the singularity inside the black hole, where the determinant of the effective metric becomes infinite.     

Investigation of multicomponent fluoride optical materials in the UV spectral region: I. Single crystals of Ca1−x R xF2+x (R = Sc, Y, La, Yb, Lu) solid solutions

Crystalline materials that are transparent in the vacuum UV spectral region and currently used have been reviewed. Transmission of crystals of solid solutions with the fluorite structure Ca_1?x R _xF_2+x (R = Sc, Y, La, Yb, Lu) in the UV and vacuum UV spectral regions has been investigated. It is shown that application of different methods of purification of fluorides from some impurities can significantly improve the optical quality of fluoride multicomponent crystals in the short-wavelength spectral region.     

Vascular morphology by three-dimensional magnetic resonance imaging

A three-dimensional examination of blood vessels is provided using MR data from seven cases. The vascular surfaces are constructed with an algorithm that automatically follows the selected artery or vein and generates a projected three-dimensional gradient shaded image. Fast 3DFT pulse sequences were optimized to enhance the time-of-flight contrast of the intravascular region. By increasing the surface threshold value in a three-dimensional head study, the flesh of a patient's face was peeled away to demonstrate the superfacial temporal artery. Gated cardiac images show the great vessels and cardiac chambers. A three-dimensional view of the aorta shows an irregular surface in the vicinity of an adrenal tumor. 3D MR exams provide a non-invasive technique for assessing vascular morphology in a clinical setting.     

Untersuchungen zur Wechselwirkung von gasf?rmigem molekularem Iod mit Silberoberfl?chen mittels XPS und AES

Summary The adsorption of gaseous molecular iodine on clean silver surfaces proceeds in the first stage by dissociative chemisorption. After the formation of half a monolayer of chemisorbed iodine atoms the formation of silver iodide begins, which forms a very regular overlayer on top of the substrate. Both iodine species can be distinguished due to a difference in chemical shift of the M₄N₄, ₅N₄, ₅-Auger transitions. After completion of this overlayer further iodine uptake is slowed down significantly. Above an overlayer thickness of about 10 nm a further progress of the reaction cannot be followed anymore due to the limited information depth of XPS.