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  • 1
    Electronic Resource
    Electronic Resource
    Proof of a conjecture on the Sperner property of the subgroup lattice of an abelianp-group (1998)
    Springer
    Annals of combinatorics 2 (1998), S. 85-101 
    Details
    ISSN: 0219-3094
    Keywords: 05A05 ; 05D05 ; 06A07 ; Sperner property ; poset ; subgroup lattice
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let $$L_{\left( {k^n } \right)}$$ (p) denote the subgroup lattice of the abelianp-group $$(Z/p^k Z) \times \cdots \times (Z/p^k Z)(ntimes).$$ . It is conjectured that the lattice has the Sperner property. Whenk=1, the conjecture is true since it is isomorphic to the subspace lattice, and Stanley has confirmed it fork=2. In this paper, we prove that the conjecture is generally true.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01626030
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  • 2
    Electronic Resource
    Electronic Resource
    Influence of the Brönsted and Lewis Acid Sites in Platinum/Solid Acid Catalysts on the Hydrogenation of Benzene and Toluene (2000)
    Springer
    Reaction kinetics and catalysis letters 69 (2000), S. 277-284 
    Details
    ISSN: 1588-2837
    Keywords: Aromatic hydrogenation ; Brönsted acid ; Lewis acid ; platinum
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The hydrogenation of benzene and toluene was investigated over US-SSY, γ-Al2O3, and Ha1-MCM-41 supported platinum catalysts. The acidity of catalyst supports was measured by IR spectra of pyridine adsorption. On the Brönsted acid supported catalyst, both the hexacyclic saturation product and the pentacyclic one, the hydroisomerization product, were observed, and these two products were revealed to be primary reaction products. The two products were proposed to be formed competitively on Brönsted acid sites with carbonium ions as the reaction intermediate. By contrast, no hydroisomerization product was found on Lewis acid supported catalysts. It was inferred that the electron-deficient reaction intermediate formed on Lewis acids could not undertake any skeletal isomerization process to give a pentacyclic saturation product.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1005695715788
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