Approximate estimation of the degree of lanthanide tetrad effect from the data potentially involving all lanthanides

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Abstract

Here is presented a mathematical method which enables us to evaluate the degrees of lanthanide tetrad effects from the data involving all of REE. Each of the four spans corresponding to four subgroups, La-Nd, Pm-Gd, Gd-Ho, and Er-Lu, is approximately fitted to a quadratic function and the resultant quadratic coefficient is employed as a numerical indicator for the tetrad effect. For the purpose of approximation by a quadratic function, the least-squares method is used under the constraint that the first and second quadratic curves intersect at the middle point between Pm and Sm, and that the third and fourth ones intersect at the middle point between Ho and Er. Since, mathematically, the subject is a problem on the conditional extremum, the method of Lagrange undetermined multipliers should be used. It is noted that the degrees of four tetrad effects can be evaluated simultaneously. This method can lead us to the mathematically well-defined estimation of the tetrad effect.

Journal

  • GEOCHEMICAL JOURNAL

    GEOCHEMICAL JOURNAL 31(3), 125-133, 1997-06-01

    GEOCHEMICAL SOCIETY OF JAPAN

References:  20

Codes

  • NII Article ID (NAID)
    10008801504
  • NII NACSIS-CAT ID (NCID)
    AA00654975
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00167002
  • NDL Article ID
    4231173
  • NDL Source Classification
    ZM41(科学技術--地球科学)
  • NDL Call No.
    Z53-R488
  • Data Source
    CJP  NDL  J-STAGE 
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