Wiener's lemma for twisted convolution and Gabor frames

We prove non-commutative versions of Wiener's Lemma on absolutely convergent Fourier series (a) for the case of twisted convolution and (b) for rotation algebras. As an application we solve some open problems about Gabor frames, among them the problem of Feichtinger and Janssen that is known in the literature as the ``irrational case'.

     

Semivolatile organic compounds — polychlorinated dibenzo-p-dioxins (PCDD), dibenzofurans (PCDF), biphenyls (PCB), hexachlorobenzene (HCB), 4,4'-DDE and chlorinated paraffins (CP) — as markers in sewer films

A municipal sewer system has been investigated for the sources of a set of semivolatile compounds, such as polychlorinated dibenzo-p-dioxins (PCDD), polychlorinated dibenzofurans (PCDF), polychlorinated biphenyls (PCB), hexachlorobenzene (HCB), 1,1-dichloro-2,2-bis(p-chlorophenyl)-ethene (4,4'-DDE), and chlorinated paraffins (CP), using sewer films as the sampling medium. A cleanup method for these semivolatile compounds in sewer films is described. The project has been undertaken for the differentiation and localization of specific inputs of xenobiotics from defined regions of the city. A unique pattern of PCDD/PCDF found in sewage sludge has led to the search for a specific source within the sewer system, which has finally been localized as a distinct plant. Other organochlorine compounds proved to be significant indicators for industrial and domestic sewers. PCB appeared as an industry correlated parameter, while 4,4'-DDE indicated domestic sewers. Chlorinated paraffins have been detected in the mg/kg range and are markers and indicators for metal-working industries. Finally, the release of CP by the sewage treatment plant, into the nearby river, has been investigated.     

Isomer-specific determination of 79 polychlorinated diphenyl ethers (PCDE) in cod liver oils, chlorophenols and in a fly ash

The occurrence of polychlorinated diphenyl ethers (PCDEs) has been investigated in two different cod liver oils produced in 1985 and 1993, respectively, from North-Atlantic fish. These samples mirror the distribution of PCDEs among other persistent organochlorine compounds in the marine environment. To elucidate the input of PCDEs in the environment, five possible sources of PCDEs have been analyzed, namely two wood preserving formulations containing approximately 10% pentachlorophenol, two technical chlorophenol products, and one fly ash from a municipal waste incinerator. The determination has been based on 106 available PCDE congeners. During sample preparation a 2-(l-pyrenyl)ethyldimethylsilylated silica column has been used in the normal phase mode to separate the PCDEs from possible PCDF interferences. The PCDEs have been quantified by high resolution gas chromatography/mass spectrometry on a SE 54 capillary column using electron ionization and selected ion monitoring. The total amount of PCDEs in 2,3,4,6-tetrachlorophenol have been determined to be 213 mg/kg. The lowest concentrations of PCDEs have been found in the more recently produced cod liver oil (sum PCDEs: 49 g/kg) and in the fly ash sample (sum PCDEs: 93 µg/kg), respectively. The isomer-specific analysis has been employed to characterize the relationship between possible sources and the PCDEs found in the environment. PCDEs, like PCBs, can be indicator molecules for the global pollution of the environment.Dedicated to Professor Dr. Dieter Klockow on the occassion of his 60th birthday     

Long chain alkyl-polysiloxanes as non-polar stationary phases in capillary gas chromatography

Summary A new methyl-octadecyl polysiloxane phase with a distinct selectivity in PCB separation and a significantly improved temperature range has been developed. The basic structural element of the separation of PCBs on methyl-octadecyl-polysiloxane is the elution according to the number of the substituents in the ortho-positions 2,2 and 6,6. The 2,2,6,6-substituted congeners are eluted first, while the non-2,2,6,6-substituted coplanar PCB are eluted last. As compared to methyl-phenyl (5%) polysiloxane (SE 54) the standard stationary phase used for the separation of the PCBs, the methyl-octadecyl-polysiloxane has several unique features in an improved PCB separation. The Sil 5–50% C18 column resolves the pair PCB 31/28 and also the sets PCB 5/8, PCB 16/15/32, PCB 25/53, PCB 48/47, PCB 56/60, PCB 118/149, PCB 105, 132, 153, and PCB 170/190. All these separations are not achieved with a SE 54 column. No separation is observed for the pair PCB 138/163 on Sil 5–50% C18. The order of elution of the Cl_xB congeners reveals a rather stringent structure correlation. If the structure/retention correlation is extended to all 209 Cl_xB congeners, 20 groups with one ring fixed / one ring variable substitution can be distinguished.Dedicated to Prof. Dr. V. Krivan on the occasion of his 60th birthday.Presented at 14th International Symposium on Capillary Chromatography, May 25–29, Baltimore, USA.     

Levels of polychlorinated biphenyls in the lower troposphere of the North- and South-Atlantic Ocean

Summary Fourteen polychlorinated biphenyl (PCB) congeners were quantified in air samples of the tropospheric boundary layer of the Atlantic Ocean. The samples were taken on the German research vessel Polarstern during north-south cruises across the Atlantic Ocean (1990, 1991), and on the Capo Verde islands in the North Atlantic Ocean (1992). Values for the sum of PCB were between 48 pg/m³ (values for the seven indicator congeners were [in pg/m³]: PCB 28: 1.3; PCB 52: 5.0; PCB 101: 3.0; PCB 118: 0.5; PCB 138: 1; PCB 153: 1; PCB 180: <0.2) in the Westwind Belt of the eastern North Atlantic and 22 pg/m³ (values for the seven indicator congeners were [in pg/m³]: PCB 28: 2.3; PCB 52: 3.4; PCB 101: 0.5; PCB 118: <0.2; PCB 138: <0.2; PCB 153: <0.2; PCB 180: <0.2) in the Westwind Belt of the central South Atlantic. Up to 385 pg/m³ (values for the seven indicator congeners were [in pg/m³]: PCB 28: 2.6; PCB 52: 11.7; PCB 101: 28.4; PCB 118: 9; PCB 138: 21; PCB 153: 18; PCB 180: 5.5) were measured of the coast of South Patagonia. A difference depending on latitude and on terrestrial influenced air masses between the lower and the higher chlorinated congeners was observed. The levels of three- and tetrachlorinated congeners were highest in the Trade Wind regions. The contents of the higher chlorinated congeners had maxima in samples influenced by continental air masses. A correlation of the levels of the lower chlorinated congeners in air over the South Atlantic with the surface water temperature and thus with the temperature dependent gas/water partition coefficient K_gw was observed. Part XVI: Fischer RC, Krämer W, Ballschmiter K (1991) Chemosphere 23:889–900     

Heterocyclic Spiro-naphthalenones. Part II. Synthesis and reactions of some spiro [tetrahydrofuran-2,1′-(2′H-naphthalene)]-2′,5-diones and Spiro [tetrahydrofuran-2,2′-(1′H-naphthalene)]-1′,5-diones

The spiro-lactone 3 was obtained by N-bromosuccinimide (NBS) oxidation of the carboxylate 2 at ? 20°. When 2 was oxidized at 10° the spiro-lactone 4 was the main product. Compound 4 was rearranged with triethylamine to the spiro-lactone 9 whereas the stereoisomeric spiro-lactones 14 and 15 were obtained by NBS oxidation of the carboxylate 13 . The ketones 3, 4, 9, 14 and 15 were reduced with NaBH₄ to the corresponding alcohols 5, 6, 10, 16 and 18 respectively; these were hydrogenated to the alcohols 7, 8, 11 and 20 . The allylic alcohols 5 and 6 gave the benzochromanone 1 when heated in polyphosphoric acid whereas the benzochromanones 12 and 21 were obtained from the alcohols 10 and 16 respectively.     

Heterocyclic Spiro-naphthalenones. Part I: Synthesis and reactions of some spiro [(1 H-naphthalenone)-1,3′-piperidines]

The title compounds 14–16 were obtained via an intramolecular Mannich condensation by treating 11–13 with CH₂O at RT. The unsaturated ketones 14 and 15 were reduced to the allylic alcohols 18 and 19 respectively. Ring cleavage of compound 18 on treatment with 2N HCl gave the substituted aminopropanol 20 . The allylic alcohols 18 and 19 were hydrogenated to 22 and 23 respectively. With CH₂O, the amino-alcohol 23 gave the methano-naphthoxazocine 24 , whereas 22 and 23 , on heating in polyphosphoric acid (PPA), afforded the naphthazepines 25 and 26 respectively. With organolithium compounds, the unsaturated ketones 14 and 16 gave the teriary allylic alcohols 27–29 , which were hydrogenated and dehydrated to the olefins 36–40 ; these were cyclized via an intramolecular alkylation to the methanodibenzo-octahydrocyclooctapyridines 41–43 . On heating in PPA, the allylic alcohol 29 was converted into the naphthazepine 44 . With CH₂O, the naphthol 49 gave the naphthoxazocine 50 , in equilibrium with the spiro-naphthalene-pyrrolidinone 51 in solution. Finally, in the presence of CH₂O, the naphthazepine 57 afforded the methano-naphthazepinone 58 , which, by a 4-stage degradation, was transformed to the benzisoquinoline 62 .