Homology equivalences inducing an epimorphism on the fundamental group and Quillen's plus construction

Quillen's plus construction is a topological construction that kills the maximal perfect subgroup of the fundamental group of a space without changing the integral homology of the space. In this paper we show that there is a topological construction that, while leaving the integral homology of a space unaltered, kills even the intersection of the transfinite lower central series of its fundamental group. Moreover, we show that this is the maximal subgroup that can be factored out of the fundamental group without changing the integral homology of a space.

     

New disc-shaped mesogens based on pentakis(phenylethynyl)benzene derivatives

First examples of amphiphilic alkyl pentakis(phenylethynyl)benzene ethers containing functional groups at the terminal position of their alkoxy chains were synthesized by etherification of pentabromophenol with 11-bromoundecan-1-ol and 11-bromoundecanoic acid ethyl ester, respectively, and subsequent palladium catalyzed, fivefold coupling reactions with the substituted phenylacetylene. Two undecanoic acid derivatives with different pentakis(phenylethynyl)phenoxy substituents in the ω-position were prepared by ester cleavage from the corresponding ethyl esters. The thermal behaviours of five penta-alkynes in their pure states, as well as of their charge transfer complexes formed from mixtures with 2,4,7-tri-nitrofluorenone, were examined.     

Hg2(OH)[BF4], the First Basic Mercurous Tetrafluoroborate

The first basic mercurous tetrafluoroborate, Hg₂(OH)[BF₄], was obtained through a synproportionation reaction of red mercuric oxide, HgO, and elemental mercury in a 35% solution of HBF₄ in water as colourless single crystals. The crystal structure (orthorhombic, Pbca, Z = 8, a = 985.0(1), b = 991.0(1), c = 1141.0(2) pm) contains [(HO)_1/2—Hg—Hg—(OH)_1/2]⁺ zig‐zag chains that are further connected via weak Hg—OH interchain interactions to layers between which the [BF₄]^— are located in an up and down fashion.     

Comparison of the Hartree-Fock,Møller-Plesset,and Hartree-Fock-Slater method with respect to electrostatic properties of small molecules

Summary The results of various quantum chemical calculations, the Hartree-Fock (HF) method, the Møller-Plesset perturbation theory (MP2), and the Hartree-Fock-Slater (HFS) method are compared. Atomic charges, dipole moments, topological properties of the electron density distribution and polarizabilities, and first hyperpolarizabilities are calculated. Atomic charges obtained with the HFS method are found to be very close to those calculated with the MP2 method, from which we conclude that the HFS method describes to some extent electron correlation effects. Performing an MP2 calculation after an HF calculation improves the molecular dipole moments considerably, yielding values close to the experimental ones. HFS calculations are computationally less demanding than MP2 and yield comparable results for the electron density distributions, dipole moments and polarizabilities.     

Zur Automatisierung der Auswertung bei der quantitativen Spektralanalyse

Zusammenfassung Die Eigenschaften der photoelektrischen und photographischen Registrierung von Spektren werden besprochen und die Bedeutung der photographischen Registrierung für die Verfahrensentwicklung und Routineanalyse von Proben wechselnder Zusammensetzung hervorgehoben. Das Programmsystem für den elektronischen Digitalrechner und verschiedene Möglichkeiten der Datenerfassung werden beschrieben. Durch diese Automatisierung der Auswertung wird gegenüber dem herkömmlichen Rechenbrettverfahren eine Beschleunigung um den Faktor 200 erreicht.

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Summary The characteristics of the photoelectric and photographic registration of spectra are discussed and the importance of the photographic registration for the development of methods and the routine analysis of samples of changing composition is emphasized. The program system for the electronic digitalcomputer and different possibilities of data collecting are described. Automating the evaluation has resulted in a speeding-up factor of 200 compared with the traditional computing board method.

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Die obige Arbeit wurde erwähnt von Herrn Dr. Pohl am 6. 10. 1964 in Düsseldorf in seinem Vortrag Erfassen und Verwerten von chemischen Daten. [Diese Z. 209, 19 (1965).]

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Außerdem wurde uns die Arbeit von Tunnicliff und Weaver, Analytical Chemistry 36, 2318 (1964), erst nach Abschluß unserer Arbeit bekannt. Die Autoren befassen sich mit einer ähnlichen Aufgabe, wobei allerdings das Problem der Linienauswahl eingehender behandelt wird als bei uns.     

Arylesters of alkylsulfonic acids in sediments Part III of organic compounds as contaminants of the Elbe River and its tributaries

Sediments from the Elbe River and from its major tributaries are shown to be contaminated with arylesters of alkylsulfonic acids. Here we report on the structure elucidation and quantification of aryl esters of alkylsulfonic acids. Chromatographic separation and mass spectrometric properties are discussed. Congener-specific analyses revealed a highly similar pattern throughout the area investigated. Alkylsulfonic acid phenylesters were present at almost all sampling locations. Amounts ranged from 33 000 μg/kg near the industrial region of Bitterfeld to 15 μg/kg in wadden sea sediments. Concentrations of alkylsulfonic acid cresylesters were between 10–40% of the phenylesters, and fell below the detection limit only in the Elbe estuary. The presence of aryl esters of alkylsulfonic acids in all sediment samples analyzed indicates a widespread distribution of these compounds in the environment. Previous literature described these compounds erroneously as phenoxyalkanes. Received: 5 August 1997 / Accepted: 21 August 1997     

A concise synthesis of β-lactam-sulfonamide hybrids

Using ring closing metathesis (RCM) as the key operation, a rapid access to β-lactams fused to a sultam moiety of variable ring size was developed from low cost, commercially available starting materials. An efficient RCM of 4-vinyl-azetidin-2-ones to give 1-aza-bicyclo[4.2.0]oct-4-en-8-ones is also reported.     

Syntheses and X-Ray Crystal Structures of 2-Aminoindenes and Aminocymantrenes

Substituted 2-aminoindenes have been synthesized in almost quantitative yields by reactions of amines such as methylpiperazine, trimethylethylenediamine, 1,4-diaza-cycloheptane and N,N′-dimethylethylenediamine with 2-indanone. The 2-aminoindenes can be deprotonated and reacted with BrMn(CO)₃(Py)₂ to produce the respective aminoindenyl-cymantrenes in yields between 55–70%. The X-ray crystal structures of 2-(methylpiperazine)indenyl-cymantrene 5 (P1 , a = 12.667(3) Å, b = 16.630(3) Å, c = 17.382(3) Å, α = 72.70(3)°, β = 74.59(3)°, γ = 88.66(3)°, V = 3364.1(12) Å ³, Z = 8, R1(2σ(I)) = 4.02%, wR2(2σ(I)) = 10.30%) and the HClO₄ adduct of 2-(trimethylethylenediamine)-indenyl-cymantrene 6 (Cc, a = 23.722(5) Å, b = 6.9080 Å, c = 13.264 Å, β = 111.77(3)°, V = 2018.6(7) Å 3, Z = 4, R1(2σ(I)) = 2.94%, wR2(2σ(I)) = 7.90%) were determined. In both complexes the indenyl-carbon bonded to nitrogen displays significantly longer bonds to manganese [223.5(3)–225.8(3) pm] than the other four carbon atoms [213.3(3)–219.1(3) pm]. The short indenyl-nitrogen bonds of 136.2(4) and 137.8(4) pm are indicative of a substantial multiple bond character. The complexation of Zn²⁺ by the nitrogen atoms of 6 results in significant shifts of the CO stretching frequencies.     

Farbe und Konstitution bei anorganischen Feststoffen, 11. Mitt.: Die Lichtabsorption des oktaedrisch koordinierten Co2+-Ions in der Mischkristallreihe Mg1−x Co x O und anderen oxidischen Wirtsgittern

Zusammenfassung Für das oktaedrisch koordinierte Co²⁺-Ion werden ein Termschema und Energiegleichungen für zwei charakteristischeDq/B-Werte angegeben und mit deren Hilfe aus den Spektren der Co²⁺-haltigen Ilmenite MgTiO₃ und CdTiO₃ ¹ die Zuordnung des intensitätsstärksten Quartett-Dublett-Überganges ( _a ⁴ T_{1g b} ² T_1g) auf eindeutige Weise ermöglicht.Weiter wird das spektrale Verhalten der Mg_1–x CO _x O-Mischkristalle (0,05x1,0) in Abhängigkeit von der Co²⁺-Konzentration untersucht. Die Änderungen der Bandenintensitäten und desRacah-ParametersB werden wie in der analogen MgO-NiO-Mischkristallreihe² auf Spin-Spin-Wechselwirkungen der über Sauerstoff benachbarten Co²⁺-Ionen zurückgeführt.

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The energy levels of the octahedrally coordinated Co²⁺-ion and energy equations for two characteristicB-values are given, which allow to identify the quartet-doublet-transition ( _a ⁴ T_{1g b} ² T_1g) of the highest intensity from the spectrum of the Co²⁺ containing ilmenites MgTiO₃ and CdTiO₃ ¹.In addition, the variation of the spectra of the Mg_1–x Co _x O-mixed crystals (0.05x1.0) with the Co²⁺ concentration is investigated. The changes in the intensities of the absorption bands and of theRacah-parameterB are (as for the corresponding MgO-NiO-mixed crystals² interpreted as being caused by spin-spin-interactions between Co²⁺ ions bonded to the same oxygen.

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Mit 3 Abbildungen     

Surface roughening for two-dimensional percolation abovepc

The surfaces of large clusters above the critical concentrationp _c were Monte Carlo-simulated on a 2-dimensional square lattice. We study the widthW of the interface separating the interior of very large clusters from the outside region. The results show clearly surface roughening (at least in the simulated range). Even in the high concentration limitp1 the interface widthW increases with the lengthL of the simulated interface, following (presumably) a square root law.