Since recently there has been much ado invoked in science by incessant attempts at replacing expertise with numerical manipulations. Of especial relevance to the Russian mathematical community are the following indices:
These indices are calculated for each journal one by one. Let Q_{N,k} be the number of citations in year N of the articles published in the journal in year Nk. By P_{N} we denote the number of the articles published by the journal in year N. Note in passing that N is the number of a year in the Gregorian calendar, and so N is at least six since N is greater than thousand. In this notation MCQ_{N}, the MCQ of the journal in year N, is calculated as follows:

Denote the impact factor in year N by IF_{N}. By definition

Thus, MCQ and IF are defined by the same scheme covering the different time spans of the relevant databases. The first takes the citations of the previous five years; whereas the second, of the last two years. The RISC and MNRU impact factors are calculated by the classical twoyear formula for IF suggested by Eugene Garfield, the founder of the Institute for Scientific Information. It is worth observing that all four indices use different although intersecting databases.
Let us assume that all articles in some journal are of the same high quality and has the same number of citations. Assume further that the number of articles in any volume is the same every year. In other words, suppose that Q_{N,k} and P_{N} are independent of N and k. In this model case, the MCQ and IF of the journal must coincide with one another as well as with the remaining two indices. Fluctuations are inevitable in practical situations, but the trend to coincidence should prevail for sufficiently full databases. However, we observe nothing like this for the real indices. The discrepancies in their actual values for a particular journal seem improbable for random fluctuations. For instance, IF is twice as much as MCQ for a few outstanding mathematical journals.
By way of illustration let us compare the current impact factors of the two pairs of prestigious journals on algebra and logic:
IF  MCQ  

J. Algebra  0. 630  0. 64 
J. Pure Appl. Algebra  0. 666  0. 59 
J. Symbol. Logic  0. 609  0. 31 
J. Pure Appl. Logic  0. 613  0. 30 
Using MCQ it is possible to conclude that the two logical journals are twice as “feeble” as their algebraic counterparts. In fact, the practical coincidence of the IF and MCQ of the two algebraic journals demonstrates most likely that the articles of these journals primarily attracts the scientists that publish their papers in the journals covered by MR. At the same time, more than a half of the citations of the two logical journals appears in the sources that are not scanned by MR. Therefore, the scope of influence of the logical pair on the flux of scientific information is substantially broader than that of the other pair. Moreover, the narrow audience is hardly a merit of any scientific journal.
The differences in databases greatly effect the calculation of the indices of Russian periodicals. Let us take a look at the current values of the abovementioned indices for a few authoritative journals of the Russian Academy of Sciences. The first four of them publish papers in all areas of mathematics, and the fifth is interdisciplinary.
IF  MCQ  RISC  MNRU  Year of Foundation  

Sb. Math.  0.359  0.44  0.113  0.399  1886 
Russ. Math. Surv.  0.309  0 35  0.103  0.382  1936 
Sib. Math. J.  0.208  0.18  0.108  0.269  1960 
Math. Notes  0.251  0.18  0.030  0.244  1967 
Theoret. Math. Phys.  0.622  0.12  0.107  0.601  1969 
The obvious conclusion is in order that, taken per annum, all indices under consideration primarily characterize the respective databases, slightly reflecting a minor part of few phenomena of the real functioning of science.
The dynamics of citation indices may be more informative. For instance look at the impact factors IF and MCQ of the Russian Journal of Mathematical Physics:
IF  MCQ  

2003  0.291  0.23 
2004  0.348  0.19 
2005  0.394  0.26 
2006  0.493  0.34 
2007  1.012  0.35 
Viktor Maslov, EditorinChief of this journal, indicates that a few publications on economic applications of the ideas of mathematical physics might be a reason for the almost twotimes raise of IF in 2007. Incidentally, MCQ neglects this phenomenon completely.
Traffic congestion never reflects the artistic gifts of jammed drivers. By analogy, there are insufficient grounds to correlate rather arbitrary numerical indices of the dynamics of scientific information in a particular database with the quality of publications, all mystical hypotheses of the bureaucracy of science notwithstanding.
Science is not the glass bead game despite whatever ciphers.
May 20, 2009
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