One-radius results for supermedian functions on {\mathbb R^d} , d ≤ 2

A classical result states that every lower bounded superharmonic function on ${\mathbb{R}^{2}}$ is constant. In this paper the following (stronger) one-circle version is proven. If ${f : \mathbb{R}^{2} \to (-\infty,\infty]}$ is lower semicontinuous, lim inf_|x|→∞ f (x)/ ln |x| ≥ 0, and, for every ${x \in \mathbb{R}^{2}}$ , ${1/(2\pi) \int_0^{2\pi} f(x + r(x)e^{it}) \, dt \le f(x)}$ , where ${r : \mathbb{R}^{2} \to (0,\infty)}$ is continuous, ${{\rm sup}_{x \in \mathbb{R}^{2}} (r(x) - |x|) < \infty},$ , and ${{\rm inf}_{x \in \mathbb{R}^{2}} (r(x)-|x|)=-\infty}$ , then f is constant. Moreover, it is shown that, assuming r ≤ c| · | + M on ${\mathbb{R}^d}$ , d ≤ 2, and taking averages on ${\{y \in \mathbb{R}^{d} : |y-x| \le r(x)\}}$ , such a result of Liouville type holds for supermedian functions if and only if c ≤ c ₀, where c ₀ = 1, if d = 2, whereas 2.50 < c ₀ < 2.51, if d = 1.     

Untersuchungen Über die Veresterung unsymmetrischer zwei- und mehrbasischer Säuren

Ohne Zusammenfassung     

Extraction inductively coupled plasma-optical emission spectrometry (ICP-OES) determination of traces of phosphorus in tungsten

A method for the separation and preconcentration of traces of phosphorus from tungsten was developed. Solid phase extraction of the phosphovanadomolybdate complex performed on a micro-column was applied. Phosphorus was determined by optical emission spectroscopy (OES) with inductively coupled plasma (ICP) excitation. A limit of detection of 0.4 g/g P with respect to the solid phase is obtained. By directly coupling the extraction/elution step to the ICP instrument a detection limit of 0.06 g/g P in W was achieved. Besides, the complexity of spectral evaluation in ICP-OES determinations of traces in spectralline-rich matrices is discussed.Presented in part at the 1989 European Winter Conference on Plasma Spectrochemistry, Reutte, Austria     

Photochemische Reaktionen. 83. Mitteilung. Verbindungen der 3,4-Dihydrojonon-Reihe als Modelle zur Photochemie γ, δ- bzw. δ, ϵ-ungesättigter Ketone und Aldehyde

Compounds of the 3,4-dihydro-ionone series as models for the photochemistry of γ, δ- and δ,?- unsaturated ketones and aldehydes . The photochemistry of γ, δ- and δ,?-unsaturated carbonyl compounds of the dihydro-ionone series has been studied, with special attention to the investigation of oxetane formation versus hydrogen abstraction. UV.-irradiation of the dihydro-β-ionone compounds with structure A ( 1 , 7 , 14 , 18 , 24 , 29 ) led to isomeric ethers with structures B ( 2 , 8 , 15 , 19 , 25 , 30 ), C ( 3 , 9 , 16 , 20 , 26 , 31 ) and D ( 4 , 21 , 27 ), isomeric bicyclic alcohols with structure E ( 5 , 10 , 17 , 22 , 28 ), and photoreduction products with structure F ( 6 , 11 , 12 , 13 ). Photolysis of dihydro-γ-ionone ( 32 ) gave a complex mixture containing fragmentation product 35 , hydrocarbon 36 , β-ambrinol ( 34 ), oxetane 33 , as well as dihydro-β-ionone ( 1 ) and three of its photoproducts ( 2 , 3 , 5 ). The dihydro-α-ionone compounds 37 and 40 gave mixtures of fragmentation products and the oxetanes 38 and 41 . Irradiation of the side-chain homologues 42 and 45 yielded 43 , which photo-cyclizes to 44 . In contrast, 3 , 4 -dihydro-3′,4′-dehydro-β-ionone ( 46 ) gave merely the isomeric open-chain triene-ketone 47 . The structures assigned to the ethers 2 , 3 , 33 , 38 and to the alcohols 5 , 10 , 13 could be confirmed by chemical reactions and mutual interconversions. The structure of the ether 21 had to be established by X-ray analysis, details of which are described. A novel intramolecular hydrogen transfer is involved in formation of ethers B . The photocyclization A → D probably proceeds by addition of the carbonyl-C atom to the double bond ( A → h ), followed by methyl (1 → 2)-shift ( h → i ). Process A → h may also be involved in formation of compounds of type C and E .     

Implementation of proficiency testing schemes for a limited number of participants

A metrological background for the selection and use of proficiency testing (PT) schemes for a limited number N of laboratories-participants (less than 20–30) is discussed. The following basic scenarios are taken into account: (1) adequate matrix certified reference materials (CRM) or in-house reference materials (IHRM) with traceable property values are available for PT use as test items; (2) no appropriate matrix CRM is available, but a CRM or IHRM with traceable property values can be applied as a spike or similar; (3) only an IHRM with limited traceability is available. The discussion also considers the effect of a limited population of PT participants N _p on statistical assessment of the PT results for a given sample of N responses from this population. When N _p is finite and the sample fraction N/N _p is not negligible, a correction to the statistical parameters may be necessary. Scores suitable for laboratory performance assessment in such PT schemes are compared. Presented at the 3rd International Conference on Metrology, November 2006, Tel Aviv, Israel.     

Über das Phenylhydrazon und Oxim des Protocatechualdehyds

Ohne Zusammenfassung     

Über die Darstellung ders-Tribrombenzoësäure auss-Tribromanilin

Ohne Zusammenfassung     

Circular photogalvanic effect at inter-band excitation in semiconductor quantum wells

We observed a circular photogalvanic effect (CPGE) in GaAs quantum wells at inter-band excitation. The spectral dependence of the CPGE is measured together with that of the polarization degree of the time-resolved photoluminescence. A theoretical model takes into account spin splitting of conduction and valence bands.