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  • 42C15  (1)
  • Growth rate
  • Solid-State Physics
  • calcium
  • Springer  (2)
  • 1995-1999  (2)
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  • Springer  (2)
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    The journal of Fourier analysis and applications 5 (1999), S. 589-597 
    ISSN: 1531-5851
    Keywords: 42C15 ; 39B99 ; multivariate ; nonhomogeneous ; refinement
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We give necessary and sufficient conditions for the existence and uniqueness of compactly supported distribution solutionsf=(f 1,...,f r)T of nonhomogeneous refinement equations of the form $$f(x) = h(x) + \sum\limits_{\alpha \in A} {c_\alpha f(2x - \alpha )(x \in R^s )} $$ , where h=(h1,...,hr)Tis a compactly supported vector-valued multivariate distribution, A⊂Z+ s has compact support, and the coefficientsc α are real-valued r×r matrices. In particular, we find a finite dimensional matrix B, constructed from the coefficientsc α of the equation (I−B)q=p, where the vectorp depends on h. Our proofs proceed in the time domain and allow us to represent each solution regardless of the spectral radius of P(0):=2−s∑c α , which has been a difficulty in previous investigations of this nature.
    Type of Medium: Electronic Resource
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  • 2
    ISSN: 1573-5036
    Keywords: calcium ; plasma membrane ; root elongation ; salinity ; sodium
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract To gain a better understanding of the relations between root elongation and the amount of Ca2+ bound to the plasma membrane (PM), melon plants were grown in aerated solutions containing different concentrations of CaCl2 with various concentrations of NaCl or mannitol. With increasing external concentrations of NaCl or mannitol, root elongation was suppressed. Addition of CaCl2 to the external medium alleviated the inhibition of root elongation by high concentrations of Na+, but not of mannitol. Root elongation in media containing high concentrations of NaCl was correlated with the computed amount of Ca2+ bound to the PM. A model describing relative root elongation (RRL) under salt stress was developed. This model takes into account the osmotic potential in the growing solution (based on the mannitol experiments) and the computed amount of Ca2+ bound to the PM. Calcium binding was calculated by applying a Gouy-Chapman-Stern sorption model using the same parameters deduced from studies on PM vesicles. This model combines electrostatic theory with competitive binding at the PM surface. The model for RRL allowed the computation of a critical value for the fraction of negative sites binding Ca2+ on the PM needed for nearly optimal (95%) root elongation. Any decrease below this critical value decreased the RRL. Root elongation of Honey Dew (salt-resistant cv.) was greater than that of Eshkolit Ha'Amaqim (salt-sensitive cv.) under NaCl stress. Nearly optimal root growth for Honey Dew and Eshkolit Ha'Amaqim occurred when 40% and 51% of total membrane charged sites were bound by Ca2+, respectively. The effect of osmotic potential on the suppression of root elongation was the same for the two cultivars. To our knowledge, this report provides the first fully quantitative estimates of PM-bound Ca2+ relative to salt toxicity.
    Type of Medium: Electronic Resource
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