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  • 1
    Electronic Resource
    Electronic Resource
    A simple method for the preparation of various 1-oxo-hydrindene-2-acetic and -propionic acids. Valuable precursors of strigol and its analogues
    Amsterdam : Elsevier
    Tetrahedron 50 (1994), S. 2895-2906 
    Details
    ISSN: 0040-4020
    Keywords: 5-Nitropentan-2-one ; Annulation ; Cyclopent-2-enone derivatives ; Michael reaction ; Strigol
    Source: Elsevier Journal Backfiles on ScienceDirect 1907 - 2002
    Topics: Chemistry and Pharmacology
    Type of Medium: Electronic Resource
    URL: http://linkinghub.elsevier.com/retrieve/pii/S0040-4020(01)87001-0
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  • 2
    Electronic Resource
    Electronic Resource
    Highly saturated packings and reduced coverings (1998)
    Springer
    Monatshefte für Mathematik 125 (1998), S. 127-145 
    Details
    ISSN: 1436-5081
    Keywords: 52C17 ; packing ; covering ; saturated ; reduced ; convex ; body
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We introduce and study certain notions which might serve as substitutes for maximum density packings and minimum density coverings. A body is a compact connected set which is the closure of its interior. A packingP with congruent replicas of a bodyK isn-saturated if non−1 members of it can be replaced withn replicas ofK, and it is completely saturated if it isn-saturated for eachn≥1. Similarly, a coveringC with congruent replicas of a bodyK isn-reduced if non members of it can be replaced byn−1 replicas ofK without uncovering a portion of the space, and its is completely reduced if it isn-reduced for eachn≥1. We prove that every bodyK ind-dimensional Euclidean or hyperbolic space admits both ann-saturated packing and ann-reduced covering with replicas ofK. Under some assumptions onK⊂E d (somewhat weaker than convexity), we prove the existence of completely saturated packings and completely reduced coverings, but in general, the problem of existence of completely saturated packings, and completely reduced coverings remains unsolved. Also, we investigate some problems related to the the densities ofn-saturated packings andn-reduced coverings. Among other things, we prove that there exists an upper bound for the density of ad+2-reduced covering ofE d with congruent balls, and we produce some density bounds for then-saturated packings andn-reduced coverings of the plane with congruent circles.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01332823
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  • 3
    Electronic Resource
    Electronic Resource
    Synthesis and stereochemistry of 8-methyl-5-nitro-1-octalones (1995)
    Springer
    Monatshefte für Chemie 126 (1995), S. 1011-1019 
    Details
    ISSN: 1434-4475
    Keywords: Precursors of strigol analogues ; Michael reaction ; NMR ; Molecular modelling
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Description / Table of Contents: Zusammenfassung BasenkatalysierteMichael-Addition von 5-Nitropentan-2-on-ethylenketal (1) und Cyclohex-2-enon (2), anschließende Entfernung der Schutzgruppe und darauffolgende Aldolkondensation liefert isomer 8-Methyl-5-nitro-1-octalone (5a,b). Struktur, relative Konfiguration und Konformation von5a und5b wurden mittels1H- und13C-NMR-Spektroskopie aufgeklärt.
    Notes: Summary Base catalyzedMichael addition of 5-nitropentan-2-one ethylene ketal (1) and cyclohex-2-enone (2), subsequent deprotection, and intramolecular aldol condensation yields the 8-methyl-5-nitro-1-octalone isomers (5a,b). The structure, relative configuration, and conformation of5a and5b were elucidated utilizing the results of1H and13C NMR investigations
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00811021
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  • 4
    Electronic Resource
    Electronic Resource
    Blichfeldt's density bound revisited (1993)
    Springer
    Mathematische Annalen 295 (1993), S. 721-727 
    Details
    ISSN: 1432-1807
    Keywords: 52C17
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01444913
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    Paper (German National Licenses)
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