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  • 1995-1999  (1)
  • 1970-1974  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Discrete & computational geometry 20 (1998), S. 307-331 
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. This paper considers the following problem, which we call the largest common point set problem (LCP): given two point sets P and Q in the Euclidean plane, find a subset of P with the maximum cardinality that is congruent to some subset of Q . We introduce a combinatorial-geometric quantity λ(P, Q) , which we call the inner product of the distance-multiplicity vectors of P and Q , show its relevance to the complexity of various algorithms for LCP, and give a nontrivial upper bound on λ(P, Q) . We generalize this notion to higher dimensions, give some upper bounds on the quantity, and apply them to algorithms for LCP in higher dimensions. Along the way, we prove a new upper bound on the number of congruent triangles in a point set in four-dimensional space.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 0018-019X
    Keywords: Chemistry ; Organic Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Four analogs of the acetylenic alkaloid, histrionicotoxin (C19H25NO) and the allenic alkaloid, isodihydrohistrionicotoxin have been isolated from extracts of skins of the arrow poison frog, Dendrobates histrionicus and characterized as neodihydrohistrionicotoxin, tetrahydrohistrionicotoxin, isotetrahydrohistrionicotoxin and octahydrohistrionicotoxin. These spiropiperidine (8-hydroxy-1-azaspiro[5.5]undecane) alkaloids differ only in the degree of unsaturation in the five carbon atoms (position 2) and four carbon atoms (position 7) side chains. A fifth compound, HTX-D, corresponds in empirical formula to a tetrahydrohistrionicotoxin with a 7-(cis-1-butenyl-3-ynyl) side chain, but the major mass spectral fragmentation with loss of C2H5O is not characteristic of the histrionicotoxins. Reduction of histrionicotoxin with hydrogen and Lindlar catalyst affords an isomeric dihydrohistrionicotoxin with the terminal acetylene of the five carbon atoms side chain reduced, tetrahydrohistrionicotoxin and hexahydrohistrionicotoxins, while reduction with hydrogen and palladium on charcoal affords dodecahydrohistrionicotoxin which is readily methylated to the tertiary amine by methyl iodide.
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
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