Zur Aufschliessung des Chromeisensteines

Ohne Zusammenfassung     

Orders on Multisets and Discrete Cones

We study additive representability of orders on multisets (of size k drawn from a set of size n) which satisfy the condition of independence of equal submultisets (IES) introduced by Sertel and Slinko (Ranking committees, words or multisets. Nota di Laboro 50.2002. Center of Operation Research and Economics. The Fundazione Eni Enrico Mattei, Milan, 2002, Econ. Theory 30(2):265–287, 2007). Here we take a geometric view of those orders, and relate them to certain combinatorial objects which we call discrete cones. Following Fishburn (J. Math. Psychol., 40:64–77, 1996) and Conder and Slinko (J. Math. Psychol., 48(6):425–431, 2004), we define functions f(n,k) and g(n,k) which measure the maximal possible deviation of an arbitrary order satisfying the IES and an arbitrary almost representable order satisfying the IES, respectively, from a representable order. We prove that g(n,k) = n − 1 whenever n ≥ 3 and (n, k) ≠ (5, 2). In the exceptional case, g(5,2) = 3. We also prove that g(n,k) ≤ f(n,k) ≤ n and establish that for small n and k the functions g(n,k) and f(n,k) coincide.      

On Cyclic Groups of Automorphisms of Riemann Surfaces

The question of extendability of the action of a cyclic groupof automorphisms of a compact Riemann surface is considered.Particular attention is paid to those cases corresponding toSingerman's list of Fuchsian groups which are not finitely-maximal,and more generally to cases involving a Fuchsian triangle group.The results provide partial answers to the question of whichcyclic groups are the full automorphism group of some Riemannsurface of given genus g>1.     

Separation of xanthones and a biphenyl fromKielmeyera coriacea by centrifugal partition chromatography

Summary Eight xanthones and a biphenyl have been isolated from the dichloromethane extract ofKielmeyera coriacea (Guttiferae) stem bark by a combination of centrifugal partition chromatography and gel filtration on Sephadex LH-20, with HPLC-UV monitoring of fractions. The structures of the isolated compounds (Figure 1) were established by spectroscopic methods (UV, EI-MS, D/CI-MS,¹H NMR,¹³C NMR).     

Mesostructure from Hydration Gradients in Demosponge Biosilica

Organisms of the phylum Porifera, that is, sponges, utilize enzymatic hydrolysis to concatenate bioavailable inorganic silicon to produce lightweight, strong, and often flexible skeletal elements called spicules. In their optical transparency, these remarkable biomaterials resemble fused silica, despite having been formed under ambient marine biological conditions. Although previous studies have elucidated the chemical mechanisms of spicule formation and revealed the extensive hydration of these glasses, their precise composition and local and medium‐range structures had not been determined. We have employed a combination of compositional analysis, ¹H and ²⁹Si solid‐state nuclear magnetic resonance spectroscopy, and synchrotron X‐ray total scattering to characterize spicule‐derived silica produced by the demosponge Tethya aurantia. These studies indicate that the materials are highly hydrated, but in an inhomogeneous manner. The spicule‐derived silica is, on average, perfectly dense for the given extent of hydration and regions of fully condensed and unstrained Si?O networks persist throughout each monolithic spicule. To accommodate chemical strain and defects, the extensive hydration is concentrated in distinct regions that give rise to mesostructural features. The chemistry responsible for producing spicule silica resembles hydrolytic sol‐gel processing, which offers exceptional control over the precise local atomic arrangement of materials. However, the specific processing involved in forming the sponge spicule silica further results in regions of fully condensed silica coexisting with regions of incomplete condensation. This mesostructure suggests a mechanism for atomistic defect tolerance and strain relief that may account for the unusual mechanical properties of the biogenic spicules.     

Microsecond studies of layer motion in a ferroelectric liquid crystal device

Abstract

Small angle X-ray scattering has been employed to study dynamically the layer motion in a ferroelectric liquid crystal device on application of low electric fields. Microsecond time resolution was achieved and the use of an area detector in the experiment allowed the examination of layer motion in two orthogonal planes. The X-ray data show that during switching the chevron structure adopted by the layers distorts, implying a variation in the chevron angle. A rotation of the layers in the plane of the device is also observed, coincident in time with the change in chevron angle. The motion of the layers takes place on a ten microsecond time scale and the angular rotation of the layers is approximately 1°.     

Hexagon-free subgraphs of hypercubes

It is shown (for all n ≥ 3) that the edges of the n-cube can be 3-colored in such a way that there is no monochromatic 4-cycle or 6-cycle. © 1993 John Wiley & Sons, Inc.     

A routine accredited method for the analysis of polychlorinated biphenyls,organochlorine pesticides,chlorobenzenes and screening of other halogenated organics in soil,sediment and sludge by GCxGC-μECD

The analysis of persistent organic pollutants is a real challenge due to the large number of compounds with varying chemical and physical properties. Gas chromatography with electron capture detection or mass spectrometry has been the method of choice for the past 50 years. Comprehensive two-dimensional gas chromatography (GCxGC) coupled with micro-electron capture detector (μECD) is a new method that can analyze polychlorinated biphenyls (PCBs), organochlorine pesticides (OCs) and chlorobenzenes (CBz) in a single analytical run with enhanced selectivity and sensitivity over single column methods and can also be used to screen for other halogenated organics in environmental samples. An accredited routine method using commercially available LECO GCxGC-μECD and a column combination DB-1 × Rtx-PCB has been developed to analyse PCBs/OCs/CBz in soils, sediments and sludges. The method provides quantification of Aroclors and Aroclor mixtures to within 15% of target values and sub-nanogrammes per gramme detection limits.     

Cavitation structures formed during the rebound of a sphere from a wetted surface

We use high-speed imaging to observe the dynamics of cavitation, caused by the impact and subsequent rebound of a sphere from a solid surface covered with a thin layer of highly viscous liquid. We note marked qualitative differences between the cavitation structures with increase in viscosity, as well as between Newtonian and non-Newtonian liquids. The patterns observed are quite unexpected and intricate, appearing in concentric ring formations around the site of impact. In all cases, we identify a distinct radius from which the primary bubbles emanate. This radius is modelled with a modified form of Hertz contact theory. Within this radius, we show that some fine cavitation structure may exist or that it may be one large cavitation bubble. For the non-Newtonian fluids, we observe foam-like structures extending radially with diminishing bubble sizes with increase in radial position. Whereas for the Newtonian fluids, the opposite trend is observed with increasing bubble size for increasing radial position. Finally, we compare our experimental observations of cavitation to the maximum tension criterion proposed by Joseph (J Fluid Mech 366:367–378, 1998) showing that this provides the lower limit for the onset of cavitation in our experiments.     

Ordering double perovskite hydroxides by kinetically controlled aqueous hydrolysis

The precipitation of crystals with stoichiometric and ordered arrangements of distinct metal cations often requires carefully designed molecular precursors and/or sufficient activation energy in addition to the necessary mass transport. Here, we study the formation of ordered double perovskite hydroxides, MnSn(OH)(6) and CoSn(OH)(6), of the generic chemical formula, BB'(OH)(6) (no A site), using kinetic control of aqueous hydrolysis from simple metal salt solutions. We find that the precipitation yields ordered compounds only when the B ion is Mn(II) or Co(II), and not when it is any other divalent transition metal ion, or Zn(II). The key step in forming the compounds is the prevention of rapid and uncontrolled hydrolysis of Sn(IV), and this is achieved by a fluoride counteranion. The two compounds, MnSn(OH)(6) and CoSn(OH)(6), are studied by high-resolution synchrotron X-ray diffraction and from the temperature dependence of magnetic behavior. From maximum entropy image restoration of the electron density and from Rietveld analysis, the degree of octahedral distortion and tilting and the small extent of anti-site disorder are determined. From the nonoverlapping electron density, we infer strongly ionic character of bonding. As the first magnetic study of such materials, we report simple paramagnetic behavior with no long-range magnetic order down to 2 K for the Mn(II) compound, while the cobalt compound presents uncompensated antiferromagnetic interactions, attributed to the single-ion anisotropy of octahedral Co(II).