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  • 39B99  (1)
  • Al3+  (1)
  • Springer  (2)
  • 2005-2009
  • 1995-1999  (1)
  • 1990-1994  (1)
  • 1920-1924
  • 1905-1909
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  • Springer  (2)
Years
  • 2005-2009
  • 1995-1999  (1)
  • 1990-1994  (1)
  • 1920-1924
  • 1905-1909
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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
    Electronic Resource
    Electronic Resource
    Springer
    Plant and soil 134 (1991), S. 167-178 
    ISSN: 1573-5036
    Keywords: Al3+ ; aluminium ; hydroxy-aluminium ; phytotoxicity ; polynuclear aluminium ; rhizotoxicity ; roots ; toxicity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Agriculture, Forestry, Horticulture, Fishery, Domestic Science, Nutrition
    Notes: Abstract The aluminium (III) released from soil minerals to the soil solution under acid conditions may appear as hexaaquaaluminium (Al(H2O)6 3+, or Al3+ for convenience) or may react with available ligands to form additional chemical species. That one or more of these species is rhizotoxic (inhibitory to root elongation) has been known for many decades, but the identity of the toxic species remains problematical for the following reasons. 1. Several Al species coexist in solution so individual species cannot be investigated in isolation, even in artificial culture media. 2. The activities of individual species must be calculated from equilibrium data that may be uncertain. 3. The unexpected or undetected appearance of the extremely toxic triskaidekaaluminium (AlO4Al12(OH)24(H2O)12 7+ or Al13) may cause misatribution of toxicity to other species, especially to mononuclear hydroxy-Al. 4. If H+ ameliorates Al3+ toxicity, or vice versa, then mononuclear hydroxy-Al may appear to be toxic when it is not. 5. The identity and activities of the Al species contacting the cell surfaces are uncertain because of the H+ currents through the root surface and because of surface charges. This article considers the implications of these problems for good experimental designs and critically evaluates current information regarding the relative toxicities of selected Al species. It is concluded that polycationic Al (charge 〉2) is rhizotoxic as are other polyvalent cations.
    Type of Medium: Electronic Resource
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