Meeting infinitely many cells of a partition once

We investigate several versions of a cardinal characteristic defined by Frankiewicz. Vojtáš showed , and Blass showed . We show that all the versions coincide and that is greater than or equal to the splitting number. We prove the consistency of and of . Received: 2 October 1996 / Revised version: 22 May 1997     

Circular dichroism of sesquiterpene-umbelliferone ethers and structure elucidation of a new derivative isolated from the gum resin “Asa Foetida”

The CD spectra of 16 naturally occurring sesquiterpene-umbelliferone ethers, including the complete set of farnesiferol A isomers with all acetates and 6-oxoderivatives, are reported over the significant wavelength range of 350–200 nm. 11 compounds were isolated from an Asa Foetida sample and 5 further derivatives, already known as natural products, were obtained by acetylation orJones oxidation. In addition, a new compound — kamolonol (14) — was isolated. Its structure is characterized by twofold methyl migration in the drimenol derived sesquiterpene moiety.¹H-NMR, MS, IR, UV, and CD data of the new compound are discussed.Herrn Prof. Dr.K. Schlögl mit den besten Wünschen zum 60. Geburtstag gewidmet.     

Lanthanide induced shifts of aromatic 1,2,3-trimethoxy compounds: Conformational analysis of tetrahydrofurofuran-lignans in solution

Summary The solution conformations of 1,4-diaryl-tetrahydro-1H,3H-furo[3,4-c]furans were determined by means of the LIS technique using a modified LIS-simulation program specially designed for the requirements of the aromatic 1,2,3-trimethoxy arrangement as a bidentate coordination site for the NMR shift reagent. The resulting geometries were confirmed by force field calculations (MM2-87) and compared with X-ray derived structures. Reliable data for the conformations in solution allowed a quantitative estimation of the circular dichroism based on the coupled oscillator model.

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Lanthanideninduzierte Verschiebungen von aromatischen 1,2,3-Trimethoxy-Verbindungen: Konformationsanalyse von Tetrahydrofurofuran-Lignanen in Lösung

Zusammenfassung Es wurden mittels der LIS-Technik die Konformationen von 1,4-Diaryl-tetrahydro-1H,3H-furo[3,4-c]furanen in Lösung bestimmt. Dazu mußte ein modifiziertes LIS-Simulationsprogramm entworfen werden, das auf die besonderen Verhältnisse der aromatischen 1,2,3-Trimethoxy-Gruppierung eingeht, welche in den untersuchten Verbindungen als zweizähnige Koordinationsstelle für das NMR-Verschiebungsreagens fungiert. Die resultierenden Geometrien wurden mittels Kraftfeldrechnungen (MM2-87) überprüft und soweit vorhanden auch mit Röntgenstrukturdaten verglichen. Für die Lösungskonformationen wurde eine quantitative Abschätzung des Circulardichroismus auf der Basis des Modells für gekoppelte Oszillatoren durchgeführt.

     

Dipole strengths in the chlorophylls

Measurements of dipole strengths of chlorophylls in solution are reviewed and correlated. The refractive index dependence is found to be expressible in a simple empirical fashion that does not rely on the concept of vacuum dipole strength. The index dependence in some respects contradicts the dependence expected on the basis of effective field theories.     

New amides fromSpilanthes oleracea

In addition to the well known affinin [=spilanthol, (2E,6Z,8E)-deca-2,6,8-trienoic acid isobutylamide (1)], the corresponding 2-methyl-butylamide (2), and two new acetylenic alkamides were isolated fromSpilanthes oleracea L. by reversed phase medium pressure chromatography: (Z)-non-2-en-6,8-diynoic acid isobutylamide (3) and (Z)-dec-2-en-6,8-diynoic acid isobutylamide (4). The structures and their stereochemistries were elucidated by¹H-NMR,¹³C-NMR (2 and3), MS, UV, IR, and CD (2). The chemotaxonomic significance of the distribution of alkamides within theCompositae tribeHeliantheae is briefly discussed.

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Neue Amide ausSpilanthes oleracea (Kurze Mitteilung)

Zusammenfassung AusSpilanthes oleracea wurden neben dem seit langem bekannten Affinin [=Spilanthol, (2E,6Z,8E)-Deca-2,6,8-triensäureisobutylamid (1)] durch Umkehrphasen-Mitteldruckchromatographie das entsprechende 2-Methylbutylamid (2) und zwei neue acetylenische Alkamide isoliert: (Z)-Non-2-en-6,8-diinsäure-isobutylamid (3) und (Z)-Dec-2-en-6,8-diinsäure-isobutylamid (4). Die Strukturen und deren Stereochemie wurden mittels¹H-NMR,¹³C-NMR (2 und3), MS, UV, IR und CD (2) aufgeklärt. Die chemotaxonomische Bedeutung der Verbreitung von Alkamiden innerhalb der Compositen-TribusHeliantheae wird kurz diskutiert.

     

Structural basis for the highly selective inhibition of MMP-13

Inhibitors for matrix metalloproteinases (MMPs) are under investigation for the treatment of cancer, arthritis, and cardiovascular disease. Here, we report a class of highly selective MMP-13 inhibitors (pyrimidine dicarboxamides) that exhibit no detectable activity against other MMPs. The high-resolution X-ray structures of three molecules of this series bound to MMP-13 reveal a novel binding mode characterized by the absence of interactions between the inhibitors and the catalytic zinc. The inhibitors bind in the S1' pocket and extend into an additional S1' side pocket, which is unique to MMP-13. We analyze the determinants for selectivity and describe the rational design of improved compounds with low nanomolar affinity.     

Beiträge zur chemie der Pyrrolpigmente, 10. Mitt.: Elektronenspektrometrische Untersuchungen über die Struktur von Quadratsäurederivaten

The structure of squaric acid derivatives was investigated on the basis of the PPP—SCF—LCAO—MO—CI method utilizing the π-electron densities and bond orders. The parameters used in the calculations were modified to fit the experimental data for representative compounds. The data were obtained by X-ray photoelectron spectrometry and electron absorption spectroscopy (including the polarization of the bands as determined by liquid crystal induced circular dichroism measurements).     

Diversity-oriented synthesis of biaryl-containing medium rings using a one bead/one stock solution platform

Diversity-oriented synthesis of structurally complex and diverse small molecules can be used as the first step in a process to explore cellular and organismal pathways. The success of this process is likely going to be dependent on advances in the synthesis of small molecules having natural product-like structures in an efficient and stereoselective manner. The development, scope, and mechanism of the oxidation of organocuprates was investigated and exploited in the atropdiastereoselective synthesis of biaryl-containing medium rings (9-, 10-, and 11-membered rings). The methodology was performed on high-capacity, large polystyrene beads by metalating aryl bromides with i-PrBu(2)MgLi, followed by transmetalating with CuCN x 2LiBr and then oxidizing with 1,3-dinitrobenzene, and was used in a diversity-oriented synthesis of biaryl-containing medium rings (library total theoretical maximum 1412 members). The high capacity beads were arrayed into 384-well plates and, using a process optimized during the development of a one bead/one stock solution technology platform, converted into arrays of stock solutions, with each stock solution containing largely one compound. These stock solutions were used in numerous phenotypic and protein-binding assays. The process described outlines a pathway that we feel will contribute to a comprehensive and systematic chemical approach to exploring biology (chemical genetics).