Page 303 - Becoming Metric Wise

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The Informetric Laws

In practice, worldwide studies do not exist but are replaced by (large)
database-dependent studies.
Next we provide an example of a synchronous study, recalling that
other studies are performed in a similar way. Decreasing use over time or
obsolescence can be measured as follows. Consider a set of articles pub-
lished in the year Y e.g., published in the same journal. We consider their
references and determine the age of each item, where a reference pub-
lished in the year Y-3 has age 3. The number of references of age t is
denoted as c(t). Consider now the ratio
ct 1 1Þ
ð
atðÞ 5 (9.1)
ctðÞ
If we assume that a(t) is a constant function: a(t) 5 a, then c(1)/c(0) 5
2
a, hence c(1) 5 c(0)a.Now, c(2)/c(1) 5 a and hence c(2) 5 c(1)a 5 c(0)a .
Continuing in this way we find that for each t:
ctðÞ 5 c 0ðÞa t (9.2)
where c(0) 5 c is constant. This function is an exponential function. Note
that decrease in use only occurs if 0 , a , 1. If a 5 1 then use stays constant,
while for a . 1 we have an increasing exponential function. The general
form of an exponential function with 0 , a , 1 is shown in Fig. 9.1.
The parameter a is called the aging rate. When a is small, aging goes
fast and when a is larger (but strictly smaller than 1), aging goes slow.
t
Note that we will always use the form a for an exponential function,
t kt
but remark that a may also be written in the form e 5 exp(kt), with

Figure 9.1 Graph of an exponential function (0 , a , 1).