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     

Conformational analysis by LIS. II. 2-and 3-alkyl substituted 1-indanones

The preferred conformations of the alkyl groups relative to the cyclopentenone ring of 2-ethyl-, 2-benzyl-, 2-isopropyl-, and 3-isopropyl-1-indanone were determined by means of the lanthanide-induced-shift technique (LIS). Two different models were used in the calculation of LIS. Coupling data-where available-were compatible with the conformations derived from LIS data. O. Hofer, Mh. Chem.109, 405 (1978).     

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.     

Absolute configurations and circular dichroism of sesquiterpene-coumarin ethers

The absolute stereochemistry of 14 naturally occurring sesquiterpenecoumarin ethers is discussed. In 13 cases the coumarin moiety is isofraxidin (7-hydroxy-6,8-dimethoxycoumarin), in one case scopoletin (7-hydroxy-6-methoxycoumarin). The sesquiterpene moieties belong either to the bicyclic drimenole series or to its consecutive products (methyl migration, ring opening). The CD spectra of all compounds are given. The assignments of the absolute configurations are based on the method ofHoreau, chemical correlation by degradation reactions, extensive comparison of CD data, and biogenetic considerations.

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Absolute Konfigurationen und Circulardichroismus von Sesquiterpen-Cumarin-Ethern

Zusammenfassung Es wird die absolute Stereochemie von 14 natürlich vorkommenden Sesquiterpen-Cumarin-Ethern diskutiert. In 13 Fällen wird die Cumarineinheit von Isofraxidin (7-Hydroxy-6,8-dimethoxycumarin) repräsentiert, in einem Fall von Scopoletin (7-Hydroxy-6-methoxycumarin). Der Sesquiterpenteil ist entweder von Drimenol oder Folgeprodukten (Methylgruppenwanderung, Ringöffnung) abgeleitet. Die CD-Spektren aller Verbindungen sind angegeben. Die Zuordnung der absoluten Konfigurationen basiert auf der Methode vonHoreau, chemischer Korrelation über Abbaureaktionen, Vergleich der CD-Spektren und biogenetischen Überlegungen.

     

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.

     

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).     

Shape-Aware Matching of Implicit Surfaces Based on Thin Shell Energies

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane energy measuring the rate of tangential distortion when deforming the reference shell into the template shell, and a bending energy measuring the bending under the deformation in terms of the change of the shape operators from the undeformed into the deformed configuration. The variational method applies to surfaces described as level sets. It is mathematically well-posed, and an existence proof of an optimal matching deformation is given. The variational model is implemented using a finite element discretization combined with a narrow band approach on an efficient hierarchical grid structure. For the optimization, a regularized nonlinear conjugate gradient scheme and a cascadic multilevel strategy are used. The features of the proposed approach are studied for synthetic test cases and a collection of geometry processing examples.