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  • 06A10  (2)
  • 06A23  (1)
  • Electrochemical oxidation  (1)
  • Springer  (3)
  • Periodicals Archive Online (PAO)
  • 2015-2019
  • 1985-1989  (3)
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  • Springer  (3)
  • Periodicals Archive Online (PAO)
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  • 2015-2019
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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Order 3 (1986), S. 15-20 
    ISSN: 1572-9273
    Schlagwort(e): 06A10 ; Partially ordered set
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Let P be a partially ordered set. Define k = k (P) = max p∈ |{x ∈ P : p 〈 x or p = x}|, i.e., every element is comparable with at most k others. Here it is proven that there exists a constant c (c 〈 50) such that dim P 〈 ck(log k)2. This improves an earlier result of Rödl and Trotter (dim P ≤2 k 2+2). Our proof is nonconstructive, depending in part on Lovász' local lemma.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Order 5 (1988), S. 17-20 
    ISSN: 1572-9273
    Schlagwort(e): 06A10 ; 06A23 ; Lattice ; order dimension ; least size
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We investigate the behavior of f(d), the least size of a lattice of order dimension d. In particular we show that the lattice of a projective plane of order n has dimension at least n/ln(n), so that f(d)=O(d) 2 log2 d. We conjecture f(d)=θ(d 2 ), and prove something close to this for height-3 lattices, but in general we do not even know whether f(d)/d→∞.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 3
    ISSN: 1572-879X
    Schlagwort(e): Electrochemical oxidation ; alkenoic acids on platinum
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Abstract Studies of the electrochemical oxidation of a series of straight-chain terminal alkenoic acids adsorbed at a Pt(111) electrode surface are reported. Compounds adsorbed were: propenoic acid (acrylic acid, PPA); 3-butenoic acid (vinylacetic acid, 3BTA); 4-pentenoic acid (allylacetic acid, 4PTA); 6-heptenoic acid (6HPA); and 10-undecenoic acid (10UDA). Vibrational spectra of adsorbed layers were obtained by use of electron energy-loss spectroscopy (EELS). Molecular packing densities were measured by use of Auger spectroscopy. Electrochemical oxidation of each adsorbed layer was explored by means of cyclic voltammetry in aqueous inert electrolyte (KF/HF). As the analogous aliphatic acids are not chemisorbed at Pt under the same conditions, the alkenoic acids evidently adsorb at Pt(111) predominantly through the C=C double bond. Molecular packing densities indicate that the carboxylic acid moiety is in contact with the Pt surface only in the case of PPA. EELS spectra also indicate that the carboxylate groups (other than in PPA) are present as pendants. The carboxylic acid O-H stretching bands of most of the adsorbed acids are red-shifted and broadened, evidently due to extensive intermolecular hydrogen bonding; the exceptions are PPA, for which the interaction is primarily with the Pt surface, and 3BTA, for which intermolecular interaction between the carboxylic acid pendants is apparently prevented by steric considerations. The surface-attached carboxylic acid moieties react with KOH solution, leading to retention of K+ ions, detected by Auger spectroscopy, and to changes in the vibrational spectra indicative of carboxylate anions; reactivity toward KOH decreases with chain length. Adsorbed alkenoic acids at Pt(111) surfaces are stable in water and in vacuum. Oxidation of the adsorbed short-chain acids PPA and 3BTA proceeds to completion, forming CO2 as the principal product. Oxidation of the adsorbed long-chain acids converts the C=C moiety to 2CO2, and transforms the remainder of the molecule to an unadsorbed diacid (likely possibilities are malonic acid from 4PTA; glutaric acid from 6HPA; and heptane-1,7-dioic acid from 10UDA).
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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