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  • 06A10  (2)
  • Effect of pressure  (1)
  • Springer  (3)
  • Periodicals Archive Online (PAO)
  • 2015-2019
  • 1985-1989  (2)
  • 1975-1979
  • 1970-1974  (1)
  • 1955-1959
  • 1925-1929
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  • Springer  (3)
  • Periodicals Archive Online (PAO)
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  • 2015-2019
  • 1985-1989  (2)
  • 1975-1979
  • 1970-1974  (1)
  • 1955-1959
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Year
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of solution chemistry 1 (1972), S. 309-327 
    ISSN: 1572-8927
    Keywords: Effect of pressure ; ionization of water ; molal volume
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The apparent molal volumes of dilute (0.002 to 1.0m) aqueous HCl and NaOH solutions have been determined at 0, 25, and 50°C and NaCl solutions at 50°C. The partial molal volumes ( $$\bar V$$ ) of HCl, NaOH, and NaCl solutions have been determined from these apparent molal volumes and other reliable data from the literature. The partial-molal-volume changes ( $$\Delta \bar V_1 $$ ) for the ionization of water, H2O→H++OH−, have been determined from 0 to 50°C and 0 to 1m ionic strength from the partial molal volumes of HCl, NaOH, NaCl, and H2O. The partial molal compressibilities ( $$\bar K$$ for HCl, NaOH, NaCl, and H2O have been estimated from data in the literature and used to determine the partial molal compressibility changes ( $$\Delta \bar K_1 $$ ) for the ionization of water from 0 to 50°C and 0 to 1m ionic strength. The effect of pressure on the ionization constant of water has been estimated from partial-molal-volume and compressibility changes using the relation $$RTln(K^P /K) = - \Delta \bar V(P - 1) + \tfrac{1}{2}\Delta \bar K(P - 1)^2 $$ from 0 to 50°C and 0 to 2000 bars. The results agree very well with the directly measured values.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Order 3 (1986), S. 15-20 
    ISSN: 1572-9273
    Keywords: 06A10 ; Partially ordered set
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Order 5 (1988), S. 17-20 
    ISSN: 1572-9273
    Keywords: 06A10 ; 06A23 ; Lattice ; order dimension ; least size
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: 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→∞.
    Type of Medium: Electronic Resource
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