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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Order 10 (1993), S. 105-110 
    ISSN: 1572-9273
    Keywords: 06A07 ; 06A12 ; 05E25 ; 20B25 ; Automorphism ; isotone self-map ; irreducible element
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For an ordered setP letP P denote the set of all isotone self-maps on P, that is, all mapsf fromP toP such thatx≥y impliesf(x)≥f(y), and let Aut (P) the set of all automorphisms onP, that is, all bijective isotone self-maps inP P . We establish an inequality relating ¦P P ¦ and ¦Aut(P)¦ in terms of the irreducibles ofP. As a straightforward corollary, we show that Rival and Rutkowski's automorphism conjecture is true for lattices. It is also true for ordered sets with top and bottom whose covering graphs are planar.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Bognor Regis [u.a.] : Wiley-Blackwell
    Journal of Polymer Science Part A: Polymer Chemistry 36 (1998), S. 2899-2903 
    ISSN: 0887-624X
    Keywords: cationic ring-opening polymerization ; poly(1,3-dioxepane) triol ; 2,2-bis(hydroxymethyl)butanol ; transacetalization ; activated monomer mechanism ; activated chain mechanism ; Chemistry ; Polymer and Materials Science
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: Cationic polymerization of 1,3-dioxepane (DOP) initiated by triflic acid was carried out in the presence of 2,2-bis(hydroxymethyl)butanol (BHMB). The structure and molecular weight of the products were characterized by GPC and NMR spectra. The results showed that molecular weight of the polyacetal obtained could be controlled by the initial mole ratio of DOP/BHMB. GPC showed that as the mole ratio of BHMB/DOP increased, the content of cyclic oligomers also increased. Proton, 13C and 2D HMQC-fg NMR demonstrated that no hydroxymethyl group of BHMB appeared as an end group. It was also illustrated by proton NMR that some BHMB units existed in cyclic oligomers. The mechanism of formation of cyclic oligomers was discussed. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 2899-2903, 1998
    Additional Material: 4 Ill.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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