A quasiconformal dynamic property of the disk

It is known that every conformai embedding of the disk into the extended complex plane possesses a r²-quasiconformal extension across eachr-level line (the r²-property of a domain). We show here that this is a characteristic property of the disk: any simply connected domain which is not a disk does not admit ther ²-property. Supported by the RiP-program of the Volkswagen-Stiftung in the Mathematisches Forschungsinstitut Oberwolfach.     

Free arrangements and rhombic tilings

Let Z be a centrally symmetric polygon with integer side lengths. We answer the following two questions:

1. When is the associated discriminantal hyperplane arrangementfree in the sense of Saito and Terao?
2. When areall of the tilings of Z by unit rhombicoherent in the sense of Billera and Sturmfels?

Surprisingly, the answers to these two questions are very similar. Furthermore, by means of an old result of MacMahon on plane partitions and some new results of Elnitsky on rhombic tilings, the answer to the first question helps to answer the second. These results then also give rise to some interesting geometric corollaries. Consideration of the discriminantal arrangements for some particular octagons leads to a previously announced counterexample to the conjecture by Saito [ER2] that the complexified complement of a real free arrangement is aK (π, 1) space.     

Analysis of an intermediate in a 1,3-dipolar cycloaddition of methylsulfonyl azide

MNDO-PM3 calculations, carried out on an experimentally determined structure of an intermediate in the cycloaddition of an electrophilic azide and a nucleophilic 1,3-dipolarophile, show that the semiempirical MO scheme models this structure closely. Transition structures for formation of the intermediate and ring closure of the latter are described.     

Gas chromatographic/mass spectrometric determination of 3-methoxy-1,2-propanediol and cyclic diglycerols, by-products of technical glycerol, in wine: interlaboratory study

The aim of the present study was to provide the official wine control authorities with an internationally validated method for the determination of 3-methoxy-1,2-propanediol (3-MPD) and cyclic diglycerols (CycDs)-both of which are recognized as impurities of technical glycerol-in different types of wine. Because glycerol gives a sweet flavor to wine and contributes to its full-body taste, an economic incentive is to add glycerol to a wine to mask its poor quality. Furthermore, it is known that glycerol, depending on whether it is produced from triglycerides or petrochemicals, may contain considerable amounts of 3-MPD in the first case or CycDs in the second. However, because these compounds are not natural wine components, it is possible to detect glycerol added to wine illegally by determining the above-mentioned by-products. To this end, one of the published methods was adopted, modified, and tested in a collaborative study. The method is based on gas chromatographic/mass spectrometric analysis of diethyl ether extracts after salting out with potassium carbonate. The interlaboratory study for the determination of 3-MPD and CycDs in wine was performed in 11 laboratories in 4 countries. Wine samples were prepared and sent to participants as 5 blind duplicate test materials and 1 single test material. The concentrations covered ranges of 0.1-0.8 mg/L for 3-MPD and 0.5-1.5 mg/L for CycDs. The precision of the method was within the range predicted by the Horwitz equation. HORRAT values obtained for 3-MPD ranged from 0.8 to 1.7, and those obtained for CycDs ranged from 0.9 to 1.3. Average recoveries were 104 and 109%, respectively.     

Measurement of PCDDs, PCDFs, and non-ortho-PCBs by comprehensive two-dimensional gas chromatography-isotope dilution time-of-flight mass spectrometry (GC x GC-IDTOFMS)

Comprehensive two-dimensional gas chromatography with isotope-dilution time-of-flight mass spectrometry (GC × GC-IDTOFMS) was used to measure polychlorinated dibenzo-p-dioxin (PCDD), polychlorinated dibenzofuran (PCDF), and coplanar polychlorinated biphenyl (cPCB) concentrations in ash, sediment, vegetation, and fish samples. The GC × GC capability was achieved by using a quad jet, dual stage, thermal modulator. Zone compression of the GC peaks from modulation resulted in a significant increase of the signal intensity over classical GC-IDTOFMS. The GC × GC column set used an Rtx-Dioxin 2 phase as the first dimension (¹D) and an Rtx-500 as the second dimension (²D). The chromatographic separation of the 17 PCDD/Fs and the 4 cPCBs was attained in ¹D except for 2,3,7,8-TCDD and CB126 for which deconvoluted ion currents (DIC) were required to be reported separately. The Rtx-500 phase separated the bulk matrix interfering compounds from the target analytes in ²D. The instrumental limit of detection (iLODs) was 0.5 pg for 2,3,7,8-TCDD. The calibration curves showed good correlation coefficients for all the compounds investigated in the concentration range of 0.5–200 pg. GC × GC-IDTOFMS results compared favorably to those from conventional isotope-dilution one-dimensional gas chromatography-high resolution mass spectrometry (GC-IDHRMS). The comprehensive mass analysis of the TOFMS further permitted the identification of other contaminants of concern in the samples.     

The effect of pressure on hydrogen transfer reactions with quinones

The effect of pressure on the oxidation of hydroarenes 3-9 with 2,3-dichloro-5,6-dicyano-1,4-quinone (DDQ; 1 a) or o-chloranil (10), leading to the corresponding arenes, has been investigated. The activation volumes were determined from the pressure dependence of the rate constants of these reactions monitored by on-line UV/Vis spectroscopic measurements in an optical high-pressure cell (up to 3500 bar). The finding that they are highly negative and only moderately dependent on the solvent polarity (DeltaV( not equal ) = -13 to -25 in MTBE and -15 to -29 cm(3) mol(-1) in MeCN/AcOEt, 1:1) rules out the formation of ionic species in the rate-determining step and is good evidence for a hydrogen atom transfer mechanism leading to a pair of radicals in the rate-determining step, as was also suggested by kinetic measurements, studies of kinetic isotope effects, and spin-trapping experiments. The strong pressure dependence of the kinetic deuterium isotope effect for the reaction of 9,10-dihydroanthracene 5/5-9,9,10,10-D(4) with DDQ (1 a) can be attributed to a tunneling component in the hydrogen transfer. In the case of formal 1,3-dienes and enes possessing two vicinal C--H bonds, which have to be cleaved during the dehydrogenation, a pericyclic hydrogen transfer has to considered as one mechanistic alternative. The comparison of the kinetic deuterium isotope effects determined for the oxidation of tetralin 9/9-1,1,4,4-D(4)/9-2,2,3,3-D(4)/9-D(12) either with DDQ (1 a) or with thymoquinone 1 c indicates that the reaction with DDQ (1 a) proceeds in a stepwise manner through hydrogen atom transfer, analogously to the oxidations of 1,4-dihydroarenes, whereas the reaction with thymoquinone 1 c is concerted, following the course of a pericyclic hydrogen transfer. The difference in the mechanistic courses of these two reactions may be explained by the effect of the CN and Cl substituents in 1 a, which stabilize a radical intermediate better than the alkyl groups in 1 c. The mechanistic conclusions are substantiated by DFT calculations.