THE NUCLEAR ZONE OF A LEIMKUHLER CURVE
| DOI | https://doi.org/10.1108/eb026814 |
| Published date | 01 April 1987 |
| Pages | 322-333 |
| Date | 01 April 1987 |
| Author | RONALD ROUSSEAU |
| Subject Matter | Information & knowledge management,Library & information science |
DOCUMENTATION NOTE
THE NUCLEAR ZONE OF A LEIMKUHLER CURVE
RONALD ROUSSEAU
Universitaire Instelling
Antwerp
Universiteitsplein
1, 2610
Wilrijk,
Belgium
and
Katholieke Industriële Hogeschool West-Vlaanderen
Zeedijk 101, 8400
Oostende,
Belgium
JOURNAL OF DOCUMENTATION Vol.
43,
no. 4
A new definition of the nuclear zone of
a
Bradford or Leimkuhler curve
is
propos-
ed. A p-nucleus is defined within which the gradient of the curve is less than the
proportion p of
its
maximum value. This definition is invariant of scale and so is
widely applicable. Using Egghe's fitting method it is shown how one can find
a
p-
nucleus for data which may deviate from a strict Bradford-Leimkuhler curve (e.g.
having a Groos droop or being heavily truncated). A 0·75-nucleus is proposed for
practical applications.
INTRODUCTION
IN THE PAPER1 where he introduced his famous law Bradford wrote 'The law
of distribution of papers on a given subject in scientific periodicals may thus be
stated: if scientific journals are arranged in order of decreasing productivity of ar-
ticles on a given subject, they may be divided into a nucleus of periodicals more
particularly devoted to the subject and several groups or zones containing the
same number of articles as the nucleus, when the numbers of periodicals in the
nucleus and succeeding zones will be as l:n:n2 . . .'. In this way also the term
'nucleus' was introduced in the literature on information science. For Bradford
the term nucleus clearly coincided with the first group. Later Brookes2 saw Brad-
ford's law
as
consisting of two
parts:
a
first, describing
a
nuclear zone, which does
not have to coincide with the first group only, and a second, describing a log-
linear zone (see Figure 1). Since then people have estimated the nucleus from the
Bradford graph on semi-logarithmic paper (see, for instance, Lipatov and
Denisenko3 for a recent example).
However, in 1967, Leimkuhler4 showed that the part which previously had
been called the log-linear part, should be expressed in the form
R(r) = a log
(1 + br)
(1)
where R(r) is the cumulative total of items in the first r sources and a and b are
parameters to be evaluated from the data. The logarithm in Leimkuhler's formula
can be taken with respect to any base. In this paper we will use logarithms with
respect to the base 10. Leimkuhler's approach made it difficult to use the term
'nucleus' as there is a gradual transition between the two parts of the curve.
Journal of Documentation, Vol. 43, No. 4, December 1987, pp. 322-333.
322
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