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  • Articles  (4)
  • 4.22  (2)
  • numerical taxonomy  (2)
  • Springer  (4)
  • 2020-2020
  • 1970-1974  (4)
  • 1945-1949
  • 1971  (4)
  • Mathematics  (4)
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  • Articles  (4)
Publisher
  • Springer  (4)
Years
  • 2020-2020
  • 1970-1974  (4)
  • 1945-1949
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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    BIT 11 (1971), S. 107-119 
    ISSN: 1572-9125
    Keywords: Recursive Function ; Recursive Proceduré ; ALGOL-60 ; ALGOL W ; PL/I ; SIMULA-67 ; Automatic Formula Manipulation ; SYMBAL ; APL ; 5.20 ; 5.23 ; 4.22
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Ackermann's function is of highly recursive nature and of two arguments. It is here treated as a class of functions of one argument, where the other argument defines the member of the class. The first members are expressed with elementary functions, the higher members with a hierarchy of primitive recursive functions. The number of calls of the function needed in a straightforward recursive computation is given for the first members. The maximum depth in the recursion during the evaluation is investigated. Results from tests with the Ackermann function of recursive procedure implementations in ALGOL-60, ALGOL W, PL/I and SIMULA-67 on IBM 360/75 and CD 6600 are given. A SYMBAL formula manipulating program, that automatically solves recurrence relations for the first members of the function class and for the number of calls needed in their straightforward computation, is given. The Ackermann rating of programming languages is discussed.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    BIT 11 (1971), S. 84-93 
    ISSN: 1572-9125
    Keywords: arithmetic expression ; compiler design ; dependency tree ; programming ; storage minimization ; 4.12 ; 4.22 ; 6.32
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The question of how many temporary storage registers are needed to evaluate compiled arithmetic and masking expressions is discussed. It is assumed that any combination of left-to-right, right-to-left, top-to-bottom, and bottom-to-top techniques may be used to evaluate an expression, but that no factoring or re-arranging of the expression may occur. On this basis, the maximum number of registers needed to evaluate nonparenthesized expressions isN+1, withN the number of dyadic operator precedence levels. For parenthesized expressions with a maximum ofK nested parenthetical subexpressions, the maximum number of registers needed is (K+1)N+1.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 3 (1971), S. 297-311 
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; discriminant analysis ; numerical taxonomy ; paleontology
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Eighty-eight specimens of Eocene nummulitids from the Yellow Limestone Formation of northwestern Jamaica are classified according to quantitative measurements of morphologic parameters that are generally considered to be taxonomically useful. The specimens are grouped into homogeneous classes by the computer screening of differently oriented data projections. By this method, the use of similarity coefficients and the question of a priori weighting of characters, for which numerical taxonomy has been heavily criticized, are both avoided. The stability of the classes thus obtained is validated by discriminant analysis. These techniques provide an objective view of phenetic differences among specimens and show how the measured characters produce those differences. Tightness of coiling and total number of whorls, prove to be the most useful features in discriminating between groups but seem to have taxonomic value only at the specific and not at the generic level. This suggests that the generaOperculinoides andNummulites are synonymous.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    Springer
    Mathematical geology 3 (1971), S. 1-14 
    ISSN: 1573-8868
    Keywords: classification ; cluster analysis ; principal components analysis ; numerical taxonomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Geosciences , Mathematics
    Notes: Abstract Numerical methods for the examination of multivariate soil samples are presented in geometric terms. Techniques of coordinate representation by principal components, by nonmetric scaling, and by a new method are discussed, as are techniques for agglomerative hierarchic cluster analysis. These are illustrated by two sets of previously published data.
    Type of Medium: Electronic Resource
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