Compact Ovoids in Quadrangles II: the Classical Quadrangles

In this second part we consider ovoids in the classical compact connected quadrangles. We solve the problem whether closed ovoids or spreads exist in these quadrangles. In fact we prove a slightly more general result: we determine whether the normal sphere bundles of the point- or line space admit sections, or whether they are topologically trivial. We also give explicit geometric constructions for spreads and ovoids. Some of these spreads are apparently new.     

Compact Ovoids in Quadrangles III: Clifford Algebras and Isoparametric Hypersurfaces

In this third part, we consider those compact quadrangles which arise from isoparametric hypersurfaces of Clifford type and their focal manifolds. Sections 9–11 give a comprehensive introduction to these quadrangles from the incidence-geometric point of view. Section 10 contains also a new (algebraic) proof that these geometries are quadrangles.We determine which of these quadrangles have ovoids or spreads and also whether the normal sphere bundles of the focal manifolds admit sections, or whether they are topologically trivial. We give explicit geometric constructions for spreads, ovoids, and sections.     

Eigenvalue estimates for the Dirac operator on quaternionic K?hler manifolds

We consider the Dirac operator on compact quaternionic K?hler manifolds and prove a lower bound for the spectrum. This estimate is sharp since it is the first eigenvalue of the Dirac operator on the quaternionic projective space. Received April 21, 1998; in final form June 16, 1998     

Tevatron-hera colour-octet charmonium anomaly versus higher-order QCD effects

Approximately taking into account the higher-order effects due to multiple-gluon initial-state radiation, we extract from the latest Tevatron data of prompt hadroproduction the leading colour-octet matrix elements within the nonrelativistic-QCD (NRQCD) factorization formalism proposed by Bodwin, Braaten, and Lepage. We find that the matrix elements which describe the formation of mesons from colour-octet pairs in the angular-momentum states and , with , which are responsible for the excess of the predicted cross section of inelastic photoproduction over the existing HERA data at high values of the inelasticity variable , are significantly reduced. We conclude that it is premature to proclaim a discrepancy between the Tevatron and HERA measurements of inclusive production in the NRQCD framework. We also consider mesons originating from the radiative feed down of promptly produced mesons. Received: 10 March 1998 / Revised version: 22 April 1998 / Published online: 30 July 1998     

The preparation of a certified reference material of polar pesticides in freeze-dried water (CRM 606)

The preparation of a certified reference material of polar pesticides in freeze-dried water is described. The pesticides selected were atrazine, simazine, carbaryl, propanil, linuron, fenamiphos and permethrin which were added to 6000 litres of tap water at 50–80 μg · L^–1 (200–320 μg · L^–1 for permethrin) level in presence of NaCl (2.5 g · L^–1) prior lyophilization. After the freeze-drying process the residue was rehomogenized, filled into amber glass bottles and stored at –20?°C, +4?°C and +20?°C. All pesticides were determined by HPLC/diode array detector, except permethrin which was determined by GC/ECD. The results obtained for atrazine, simazine, carbaryl, propanil, linuron and fenamiphos showed no within- or between-bottle inhomogeneity, however the material was non-homogeneous for permethrin and therefore this was withdrawn from further studies. With respect to the stability for over one year, all pesticides were stable at –20?°C. At +4?°C all pesticides were stable for at least 9 months and at +20?°C the stability was demonstrated only during the first month of storage. The content (mass fractions) of atrazine, simazine, carbaryl, propanil and linuron in freeze-dried water (CRM 606) was certified by an interlaboratory testing and a certification campaign.     

Organic contaminants in water - conceptual considerations for the production of liquid reference materials in support of the new water framework directive

The lack of suitable certified reference materials for the determination of organic pollutants in water has become a major problem within the framework of the new European water policy. This paper highlights approaches towards the production of certified reference materials and their drawbacks. On the basis of experience gained from proficiency-testing schemes, analytical practice, and reference material production a new concept for the production of liquid reference materials to be used in support of European legislation is presented and discussed briefly. The concept is based on a standard-addition approach and the simulation of effects interfering with the analytical process by use of individual matrix constituents or matrix-mimicking substances in combination with water-miscible solvents. The concept enables quantification of dissolved organic compounds in unknown water samples and evaluation of the analytical process with the help of a reconstituted sample. Open questions for further research are also outlined.     

Irradiation-dependent equilibrium between open and closed form of UV absorbers of the 2-(2-hydroxyphenyl)-1,3,5-triazine type

2-(2-Hydroxyphenyl)-4,6-diaryl-1,3,5-triazines (HPTs) bearing one or more intramolecular hydrogen bonds (IMHBs) show phosphorescence in polar solvents at 77 K which increases in intensity with UV-irradiation time (λ_irr = 333 nm) until an equilibrium value is reached (phosphorescence evolution). Phosphorescence emission is produced from open conformers of the molecules with intermolecular rather than intramolecular hydrogen bonds, which are formed in polar solvents under the influence of UV radiation. All IMHBs of an individual molecule must be broken to enable triplet state population. Reformation of the closed form is observed for HPTs after dark periods resulting in a lower initial phosphorescence intensity upon renewed irradiation (relaxation). The methoxy derivatives (MPTs), where the OH groups are replaced by methoxy groups, can be employed as spectroscopic models for the open form; they emit phosphorescence independent of irradiation time. For the equilibrium between open and closed form of M-OH-P (2-(2-hydroxy-4-methoxyphenyl)-4,6-diphenyl-1,3,5-triazine) under constant irradiation (λ_irr = 333 nm, 100 W-HBO lamp) a proportion of 5% of open form was evaluated.     

Enantioselective synthesis of the antiinflammatory agent (-)-acanthoic acid.

An enantioselective synthesis of the potent antiinflammatory agent (-)-acanthoic acid (1) is described. The successful strategy departs from (-)-Wieland-Miescher ketone (10), which is readily available in both enantiomeric forms and constitutes the starting point toward a fully functionalized AB ring system of 1. Conditions were developed for a regioselective double alkylation at the C4 center of the A ring, which produced compound 32 as a single stereoisomer. Construction of the C ring of 1 was accomplished via a Diels-Alder reaction between sulfur-containing diene 43 and methacrolein (36), which after desulfurization and further functionalization yielded synthetic acanthoic acid. The described synthesis confirms the proposed stereochemistry of the natural product and represents a fully stereocontrolled entry into an underexplored class of biologically active diterpenes.     

Breakdown of Layering in Frustrated Smectic‐A Elastomers

Smectic‐A elastomers combine the positional long‐range order of mesogenic molecules in one dimension with the rubber elasticity of a polymer network. Upon mechanical deformation, completely different responses of the phase structure have been reported. We present a highly distorted system which shows a breakdown of smectic layering but no reorientation under deformation along the layer normal, while the phase structure stays unaffected under uniaxial stress in the perpendicular direction. The thermoelastic properties, macroscopic dimensions and stress–strain behaviour are investigated parallel and perpendicular to the layer normal. SAXS measurements supply evidence for a breakdown of the macroscopically ordered layer structure indicated by the small angle intensities and correlation length, whereas the orientational order is preserved. We propose defects in the smectic layer structure to be the origin of the different responses of different smectic elastomers.

     

Stochastic immersed boundary method incorporating thermal fluctuations

We give a brief introduction to the stochastic immersed boundary method which allows for simulation of small length-scale physical systems in which elastic structures interact with a fluid flow in the presence of thermal fluctuations. The conventional immersed boundary method is extended to account for thermal fluctuations by introducing stochastic forcing terms in the fluid equations. This gives a system of stiff SPDE's for which standard numerical approaches perform poorly. We discuss a numerical method derived using stochastic calculus to overcome the stiff features of the equations. We then discuss results which indicate that the method captures physical features predicted by statistical mechanics for small length-scale systems. The stochastic immersed boundary method holds promise as a numerical approach in simulating microscopic mechanical systems in which thermal fluctuations play a fundamental role. A more detailed discussion of this work is given in [1, 2, 3]. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)