Definitizable extensions of positive symmetric operators in a Krein space

The Friedrichs extension and the Krein extension of a positive operator in a Krein space are characterized in terms of their spectral functions in a Krein space.     

A new, fast and efficient synthesis of 3-aryl indenones: intramolecular cyclization of 1,3-diarylpropynones in superacids

1,3-Diarylpropynones were cleanly converted to the corresponding 3-arylindenones in various superacidic media. This new, simple, one-pot reaction proved to be efficient (yields up to 95%) and very fast (reaction time less than 30 min).     

Kinetics and mechanism of the formation of poly[(1,1,3,3-tetramethyldisiloxanyl)ethylene] and poly(methyldecylsiloxane) by hydrosilylation

The kinetics of the formation of poly(carbosiloxane), as well as of alkyl-substituted poly(siloxane), by Karstedt's catalyst catalyzed hydrosilylation were investigated. Linear poly(carbosiloxane), poly[(1,1,3,3-tetramethyldisiloxanyl)ethylene], (PTMDSE), was obtained by hydrosilylation of 1,3-divinyltetramethyldisiloxane (DVTMDS) and 1,1,3,3-tetramethyldisiloxane (TMDS), while alkyl-substituted poly(siloxane), poly(methyldecylsiloxane), (PMDS), was synthesized by hydrosilylation of poly(methylhydrosiloxane) (PMHS) and 1-decene. To investigate the kinetics of PTMDSE formation, two series of experiments were performed at reaction temperatures ranging from 25 to 56 °C and with catalyst concentrations ranging from 7.0 × 10⁻⁶ to 3.1 × 10⁻⁵ mol Pt/mol CHCH₂. A series of experiments was performed at reaction temperatures ranging from 28 to 48 °C, with catalyst concentrations of 7.0 ×10⁻⁶ mol of Pt per mol of CHCH₂, when kinetics of PMDS formation was investigated. All reactions were carried out in bulk, with equimolar amounts of the reacting Si H and CHCH₂ groups. The course of the reactions was monitored by following the disappearance of the Si H bands using quantitative infrared spectroscopy. The results obtained showed typical first order kinetics for the PTMDSE formation, consistent with the proposed reaction mechanism. In the case of PMDS an induction period occurred at lower reaction temperatures, but disappeared at 44 °C and the rate of Si H conversion also started to follow the first-order kinetics. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 2246–2258, 2007     

A census of semisymmetric cubic graphs on up to 768 vertices

A list is given of all semisymmetric (edge- but not vertex-transitive) connected finite cubic graphs of order up to 768. This list was determined by the authors using Goldschmidt's classification of finite primitive amalgams of index (3,3), and a computer algorithm for finding all normal subgroups of up to a given index in a finitely-presented group. The list includes several previously undiscovered graphs. For each graph in the list, a significant amount of information is provided, including its girth and diameter, the order of its automorphism group, the order and structure of a minimal edge-transitive group of automorphisms, its Goldschmidt type, stabiliser partitions, and other details about its quotients and covers. A summary of all known infinite families of semisymmetric cubic graphs is also given, together with explicit rules for their construction, and members of the list are identified with these. The special case of those graphs having K_1,3 as a normal quotient is investigated in detail. Supported in part by N.Z. Marsden Fund (grant no. UOA 124) and N.Z. Centres of Research Excellence Fund (grant no. UOA 201) Supported in part by “Ministrstvo za šolstvo, znanost in šport Slovenije”, research program no. 101-506. Supported in part by research projects no. Z1-4186-0101 and no. Z1-3124-0101. The fourth author would like to thank the University of Auckland for hospitality during his visit there in 2003.     

The fixed point property in ordered sets of width two

We consider the fixed point property (FPP) in an ordered set of width two (every antichain contains at most two elements). The necessary condition of the FPP and a number of equivalent conditions to the FPP in such sets is established. The product theorem is proved, as well.     

The synthesis of 3,6-diamino-2,3,4,6-tetradeoxy-dl-threo-hexopyranose derivatives,substrates for the synthesis of negamycin

Three synthetic routes to derivatives of 3,6 - diamino - 2,3,4,6 - tetradeoxy - DL - threo - hexopyranose were investigated. Addition of sodium azide in acetic acid to 6 - phthalimido - 5,6 - dihydro - 2 - pyrone gave 4-azido compound (7) of the erythro configuration. From methyl 2,4 - dideoxy - β -dl- erythro - hexopyranoside threo 4 - phthalimido - 6 - phthalimidomethyl - tetrahydro - 2 - pyrone (17) was obtained in three steps in low overall yield. Addition of sodium azide in acetic acid to butyl 6 - oxo - 2 - hydroxy - hex - 4 - enoate followed by methylation, amonolysis of the ester group, and reduction gave methyl 3,6 - diacetamido - 2,3,4,6 - tetradeoxy - α - DL - threo - hexopyranoside (26).     

Determination of thallium and lead in cadmium salts by anodic stripping voltammetry with addition of surfactants to suppress the cadmium peaks

Conditions have been found which make possible the determination of thallium and/or lead in cadmium and its salts without preliminary separation. The electrochemical activity of the cadmium, which usually interferes in the determination of thallium, is inhibited by the addition of 0.01% of polyethylene glycol of M.W. 4000. Thallium is determined by electrolysis at ?0.74 V vs. SCE, in 0.1M EDTA solution: 10^?1M thallium can be determined in the presence of 0.1M cadmium, while copper and lead at 10^?2M and 10^?5M respectively do not interfere. Lead is determined in 0.1M acetic acid containing 0.1% cetyltrimethylammonium bromide (CTAB). The addition of CTAB shifts the cadmium peak, as well as the optimum deposition potential for cadmium, to more negative values, making it possible to determine lead in the presence of cadmium as long as the deposition potential lies in the range between ?0.50 and ?0.56 V vs. SCE. Lead can be determined in the presence of ten times as much thallium.     

Application of the ring oven method to the determination of dyestuffs

Summary The Weisz ring oven method has been applied to the semiquantitative determination of indigo carmine, erythrosin A, amaranth O, new coccine, Victoria blau B, tartrazine, azorubin S, alizarin S, eosin, light green SF, Guinea green B, fuchsin, eriochrome black T, saphranine, ponceau 3 R, cyanine, gelborange S, and methyl violet 6 B. The amount of dye needed ranges from 0.5 to 20g, and the error is generally less than 5%. The method has been used for the determination of azorubin S, methyl violet 6 B, tartrazine, and amaranth O in various materials.

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Zusammenfassung Die Ringofenmethode vonWeisz wurde für die semiquantitative Bestimmung folgender Farbstoffe angewendet: Indigocarmin, Erythrosin A, Amaranth O, Neucoccin, Viktoria blau B, Tartrazin, Azorubin S, Alizarin S, Eosin, Lichtgrün SF, Guineagrün B, Fuchsin, Eriochromschwarz T, Saphranin, Ponceau 3 R, Cyanin, Gelborange S und Methylviolett 6 B. Die dazu nötige Farbstoffmenge beträgt 0,5 bis 20g, der Fehler ist im allgemeinen geringer als 5%. Die Methode wurde für die Bestimmung von Azorubin S, Methylviolett 6 B, Tartrazin und Amaranth O in verschiedenen Materialien angewendet.

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Résumé On a appliqué la méthode du four annulaire deWeisz au dosage semi-quantitatif du carmin d'indigo, de l'érythrosine A, de l'amaranthe O, de la coccine nouvelle, du bleu Victoria B, de la tartrazine, de l'azorubine S, de l'alizarine S, de l'éosine, du vert lumière SF, du vert Guinée B, de la fuchsine, du noir ériochrome T, de la safranine, du ponceau 3 R, de l'orangé jaune, de la cyanine S et du violet de méthyle 6 B. La quantité de colorant nécessaire va de 0,5 à 20g et l'erreur est généralement inférieure à 5%. On a appliqué la méthode au dosage de l'azorubine S, du violet de méthyle 6 B, de la tartrazine et de l'amaranthe O dans diverses substances.

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We wish to thank Mrs.Lidija Pfendt of the Faculty of Sciences in the University of Belgrade for doing the spectrophotometric analyses.     

Synthesis, crystal structure, and nonlinear optical behavior of beta-unsubstituted meso-meso E-vinylene-linked porphyrin dimers

[structure: see text] A vinylene-linked porphyrin dimer, with no substituents at the beta-positions, has been synthesized by CuI/CsF promoted Stille coupling. In the crystal structure of this dimer, the C(2)H(2) bridge is twisted by 45 degrees relative to the plane of the porphyrins. The absorption, emission spectra, and electrochemistry reveal substantial porphyrin-porphyrin pi-conjugation. The triplet excited-state absorption spectrum of this dimer makes it suitable for reverse saturable absorption at 710-900 nm.