Literature

Mirskaya E. Z. Modem information and communication technologies in the professional activities of Russian scientists // Science in Russia. From the present to the future / ed. by V. S. Aru-tyunov. Moscow: URSS, 2009. P. 323-344.

Mirskaya E. Z. New information and communication technologies in the Russian academic science: history and results // Sociology of Science and Technology. 2010. T. 1. № 1. P. 127-139.

Irina V. Marshakova-Shaikevich

Institute of Philosophy RAS, Russia Adam Mickiewicz University, Poland e-mail: ishaikev@mail.ru

Russian Mathematical Journals in World and National Corpora of Scientific Journals: bibliometric analysis

In memoriam of Vladimir Arnold

The present paper is devoted to a discussion of results of the bibliometric analysis of a number of mathematical journals (more than 700) and scientific fields of knowledge (more than 50) in the JCR databases for the 1998-2010 period. An attempt is made to assess Russian journals in the mathematical sciences in the world and national corporaofscientificjournalsby the impact factor Ip and the normalized impact factor K.

Keywords: bibliometric analysis, mathematical journals, Normalized Impact Factor K, Impact factor, ranking lists, ISI Web of Knowledge: Journal Citation Reports Science Edition

Introduction

Since the beginning of the 1960-ies, a new direction in the study of science has been gaining ground — the quantitative analysis of information flows (bibliometrics). (Some precedents of bibliometric studies go back to 1917). A specific feature of bibliometrics is the use of secondary information: all kinds ofbibliographic indexes, abstracts, etc. The corresponding statistics are of substantial interest for the analysts of the development of science, they can help in the planning and management of science. The objects counted in bibliometrics are authors, journals, thematic groupings, organizations, words, etc. Bibliometrics is aimed at the quantitative analysis of documentary output in science as a whole or in specific fields of science. The bibliometric approach opens new vistas for the study of science, supplying it with an empirical base covering both the science’s past and (which is especially important) the forefront of science in the making.

Citation analysis is a standard bibliometric instrument very popular in the study of science. It is usually conducted in order to 1) retrieve documents; 2) use the corresponding information for evaluating the impact of papers, journals, countries, etc. (this is the most popular bibliometric research, it is based on citation data); 3) use co-citation information in the study of the structure of science or a scientific field. Better understanding of the development of science can be achieved with the help of such new tools as models of citation in scientific periodicals, co-citation maps of papers and authors, dynamical analysis of thematic regions, techniques of lexical monitoring of science (dynamics of word use, interrelations of keywords, etc.)

Various bibliometric methods fall into two major approaches. The first is based on the analysis of the dynamics of individual features: “plain bibliometrics”. The second is associated with the study of the correlation between objects, their clustering and classification: “structural bibliometrics”. The development of both approaches in bibliometric studies was greatly facilitated with the advent of the I SI/Thomson Reuters systems, which are a universal (world-wide and polythematic) information base.

In this study, the methods of plain bibliometrics were used for the assessment of scientific journals in the mathematical fields of science.

1. Bibliometric analysis of scientific journals

The structure of the ISI/Thomson Reuters database — Journal Citation Reports (JCR) gave rise to some fine bibliometric tools for the analysis of scientific journals. Perhaps the best example of such new indicators is the Impact Factor and Immediacy Index. The first indicator reflects the average citation of papers from a given journal (during the last two years). The immediacy index is ‘a measure of how quickly “the average cited article” in a particular journal is cited’. Both indices measure the importance and prestige of a journal with in the professional community. They rapidly became popular among librarians as guidelines for selecting the most effective journals for big libraries and information centers (see Marsha-kova-Shaikevich, 2008: 166-175). The analysis of scientific periodicals is a very popular field of study not only in Information and Library Science. Bibliometric analysis of scientific journals was always at the focus of attention of researchers from different fields of science as well as of sociologists of science. The very existence of JCR provides a unique possibility for this kind of research. E. Garfield (Garfield, 2006: 90-93) wrote that “I first mentioned the idea of impact factor in Science in 1955... In the early 1960s, Irving H. Sher and I created the journal impact factor to help select journals for the new Science Citation Index (SCI)”.

The evaluation of scientific journals was always one of the main tasks of bibliometric and webometric studies. A search of the SCI for the term “impact factor” produces 1,187 papers for the period 1996-2008. There are 48 papers, which present basic concepts, using and modifying the impact factor and also addressing critical issues in the Scientometrics Guidebook (Scientometrics Guidebook Series, 2007).

The Journal Citation Reports served as a basis for further invariant or integrative indicators, such as the ‘discipline impact factor’ of Hirst (Hirst, 1978: 171-172), or the ‘total citation influence measure’ (Narin, Pinsski, Gee, 1976). This contributed to a better understanding of the cognitive structure of the field under study and, as a rule, helped to identify the range of scientific journals of importance in particular fields. On the basis of the total

influence measure, Narin has advanced the principle of hierarchical structure of scientific periodicals within subject fields. Using JCR data for journals on human and medical genetics, A. Pudovkin and E. Garfield (Pudovkin, Garfield, 2002: 1113-1110) calculated their ‘relatedness factor’ (RF) of the leading periodicals in the field of Genetics.

The main goal of the present study is the bibliometric assessment of Russian journals of the mathematical sciences in the world and in the corpora of Russian scientific journals. Special attention in the present article is paid to the Russian Journal of Mathematical Physics (RJMP). Material for this study was drawn from DBs ISI Web of Kowledge: Journal Citation Reports Science Edition for the 1998—2010 periods (ISI Web of Knowledge: Journal Citation Reports: Science Edition, 2008-2010).

2. Normalization of the impact factor for the assessment of journals

The impact factor (Ip) given by JCR may be regarded a measure of the mean citedness of a journal. In the annual JCR databases it is calculated as follows: the sum of cites of the current year to publications of the given journal in the two preceding years is divided by the total number of publications in that journal during those two years. To take a concrete example, in 2010 RJMP got 112 cites to the journal’s articles published in 2009 and 2008. The total number of articles published in the journal in the years 2008 and 2009 was 49 and 50, respectively. Thus the impact factor is 112 / 99 = 1.131

Cites in 2010 to items published in: 2009 = 51 Number of items published in: 2009 = 49

In the present study a special measure — the normalized impact factor (K) is also used. The JCR databases cover more than 170 fields of science and include about eight thousand scientific journals. It is well known that the level of citedness differs significantly across various fields of science: e.g. it is very high in biology and medicine and very low in mathematics or engineering. Therefore the traditional impact factor (Ip) of a journal, as it is indicated in JCR, would be valid only within large fields of science. To facilitate the cross-field evaluation of particular journals, the new measure K is introduced as follows: the Ip of a journal is divided by the standard impact factor (Ig) of the field to which this journal belongs. The technique of calculation of the standard impact factor for a field is an inherent part of the method and is of independent interest.

3. The standard impact factor for particular fields of science (Ig)

For each field of science, five journals with the highest Ip values were selected. If the total number of papers in those journals (for the two preceding years) was less than 500, the number of journals was extended until the threshold of 500 was reached. The ratio of

2008= 61 Sum: 112

2008 = 50 Sum: 99

Calculation: Cites to recentitems 112 = 1.131

Number of recentitems 99

the total number of citations (in JCR source journals) of articles in the selected journals to the total number of source items in those journals represents the field as a whole; it is called the standard impact factor of the field and is denoted by (Ig). As has been just mentioned, in the calculation of both Ip and Ig, the number (R) of current year citations is divided by the number of items (S) in the two preceding years.

The following is an example of the calculation of the standard impact factor (Ig) in the field of mathematics in 2009:

MATHEMATICS Ig = 3.06

Ip Journaltitle ER ES

4.174 ANN MATH 359 86

3.411 JAM MATH SOC 249 73

3.294 BAM MATH SOC 112 34

2.794 INVENT MATH 380 136

2.657 COMMUN PUR APPL MATH 271 102

2.619 ACTAMATH-DJURSHOLM 55 21

2.240 MEM AM MATH SOC 112 50

These calculated indicators may serve as a valuable addition to the JCR database. The standard impact factor Ig of a field can measure the rate of progress in that field. In science, fields with growing Ig might be called ‘leading’ fields. Below we follow the division of science into the research fields used in the JCR databases (the fields are called categories there).

4. Normalized impact factor of a journal

Once the standard impact factor of the field is obtained, the numerical assessment of a particular journal becomes evident. The most obvious and simple indicator is the ratio of the two measures:

K= (Ip / Ig) x 100%; this is the normalized impact factor of the journal.

If a journal belongs to two or more fields, then, instead of Ig, the arithmetic mean I’g of the two or more Ig’s must be used I’g = (Igi + Igj + ... Ign) / n, where n is number of fields of science (“categories”) in which the journal is indexed in the JCR databases. For example, in 2009 the journal CHAOS SOLITON FRACT (Ip = 3.315) was indexed in the three following JRC categories:

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS (JCR code PO): Ig = 3.27 PHYSICS, MATHEMATICAL (UR): Ig = 2.67 PHYSICS, MULTIDISCIPLINARY (UI): Ig = 17.5

The arithmetic mean is I’g = 7.8, the normalized impact factor is K = (3.27/7.8)x 100 = 42.5. We can write:

Abbr. Journal title JCR Categories I’g

CHAOS SOLITON FRACT PO, UR, UI 7.8

In the next table, this journal is compared to some journals in mathematic and physics. This procedure was applied to the JCR database (Science Edition) for 2008-2010. The normalized impact factor (K) may prove to be a better measure of journal’s impact than the traditional impact factor (Ip) of a scientific journal. The difference between the two factors in the evaluation of journals is striking. In 2009, the journals in the first two groups differ slightly in their Ip values (within the group), while the differences in K are sometimes astounding. On the other hand, the journals in the last two groups differ very much in their Ip values (JETP LETT + 1.66 and PMM-J APPL MATH MECO.36), but are quite comparable as far as K (9.50 and 9.52) is concerned:

Abbr. Journal title Ip K

RUSS J MATH PHYS 0.85 31.8

THEOR MATH PHYS + 0.80 7.9

SIAM REV 3.39 109.7

CHAOS SOLITON FRACT 3.31 42.5

JETP LETT+ 1.66 9.50

PMM-J APPL MATH MEC+ 0.36 9.52

PHYS ATOM NUCL+ 0.54 15.40

PHYS-USP+ 2.63 15.02

(In this table and in the tables below, the plus sign (+) after the title of a Russian journal indicates that it is published both in English and Russian.) The standard impact factor for particular fields of science (Ig) and the normalized impact factor K were first introduced in 1988 to evaluate Soviet scientific periodicals. Without it, the cross-disciplinary comparison of periodicals is quite impossible, owing to the exceptionally great inter-field variance of the individual impact factors. This method was first published in the author’s works in Russian (Marshakova, 1988) and later in English (Marshakova-Shaikevich, 1996: 283-290). The procedure was applied to the JCR database for 1992, then for 1998-2002 in (Marshakova-Shaikevich Irina and Heinz Michael, 2008: 37-45; Marshakova-Shaikevich, 2009). The normalized impact factor was used for the evaluation all social journals in JCR databases (Social Science Edition) for 1994—2004 by Drabek and Marshakova-Shaikevich (Drabek, Marshakova-Shaikevich, 2007: 88-104).

The normalized impact factor may be used as a standard indicator in forming particular databases. The financing of science in most countries demands great circumspection in the choice of scientific journals for subscription; the normalized measures Ig and K may be quite useful in this respect.

5. Dynamics of research fields of science

The annual calculation of the standard impact factor of particular fields (Ig) helps to monitor new tendencies in the development of science and to compare science policies of various nations. The analysis of the priority programs of the Russian ministry of science

showed that in the period of perestroika (1985-1992) the list of programs was on the whole well correlated with the list of the most dynamic fields of world science; however, the share of financial support going to specific programs was in no way connected with the significance and dynamics of the corresponding field. Even with national priorities taken into account, the correlation between bibliometric indicators and financial support should not have been violated to such an extent. The impact factor of fields could be used in systems of grant distribution financed by national or international committee scientific programs (for example, RFBR).

An interesting aspect of the study of science is the analysis of the dynamics of Ig in particular categories. One should analyze the figures for specific categories, keeping in mind the growth of K for all categories in the period under consideration:

1998-2002 2003-2005 2008-2009

I’g (average Ig) 3.77 4.83 5.60

The 50 per cent growth in a decade may be explained by social aspects of the present day situation: the Internet revolution in communications facilitates access to all sources of information; the lists of cited literature grow.

The dynamics of I’g (average Ig) for three cumulative periods 1998-2009 is shown in Table 1 for some fields of science and in Figure 1 for four fields of the mathematical sciences, including the category Physics, mathematical (UR).

Table 1. I’g (average Ig) for some fields of science in 1998—2009

Code JCR categories Ig’(average Ig)

1998-2002 2003-2005 2008-2009

EX COMPUTER SCIENCE, THEORY & METHODS 1.93 2.97 3.69

IF ENGINEERING, MULTIDISCIPLINARY (Engineering) 1,29 1,97 3,36

MCB MATHEMATICAL & COMPUTATIONAL BIOLOGY — — 4,34

PQ MATHEMATICS 1,53 1,84 2,96

PN MATHEMATICS, APPLIED 1,8 2,06 3,78

PO MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 1,49 5,06 3,29

PU MECHANICS 2,26 2,93 4,91

PT MEDICAL INFORMATICS 1,59 1,83 3,16

UR PHYSICS, MATHEMATICAL 2,02 2,28 3,01

UI PHYSICS, MULTIDISCIPLINARY 6,69 7,6 12,71

XY STATISTICS & PROBABILITY 1,76 4,8 3,17

Table 2 and Figure 2 present the standard impact factor of fields (Ig) for8 categories in the last period 2008-2010.

-PQ

-PN

PO

-UR

Fig. 1. Dynamics of Ig’ for four mathematical fields of science

Table 2. Standard impact factor of fields (Ig) for 8 categories in 2008-2010

JCR categories JCR code Ig 2008 Ig 2009 Ig 2010

COMPUTER SCIENCE, THEORY & METHODS EX 3.90 3.47 3.42

STATISTICS & PROBABILITY XY 2.91 3.42 2.99

MATHEMATICS PQ 2.85 3.06 2.81

MATHEMATICS, APPLIED PN 4.48 3.09 3.49

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS PO 3.32 3.27 4.94

PHYSICS, MATHEMATICAL UR 3.36 2.67 2.42

MATHEMATICAL & COMPUTATIONAL BIOLOGY MCB 4.27 4.41 4.17

MECHANICS PU 5.34 4.48 4.04

1 r*t

L . - L . .11

FTl 11

I Ig 2008 I Ig 2009 Ig 2010

EX XY PQ PN PO UR MCB PU

Fig.2. Dynamics of Ig in 2008-2010 for 8 categories

Table 2 shows the values of Ig in 4 mathematical categories: MATHEMATICS, APPLIED (JRC code PN), MATHEMATICS, INTERDISCIPLINARY APPLICATIONS (PO), MATHEMATICS (PQ), PHYSICS, MATHEMATICAL (UR) and 4 categories related tothem: COMPUTER SCIENCE, THEORY & METHODS (EX), STATISTICS & PROBABILITY (XY), MECHANICS (PU) and MATHEMATICAL & COMPUTATIONAL BIOLOGY (MCB).

The new category (MATHEMATICAL & COMPUTATIONAL BIOLOGY, Table 2) appeared in 2008. Only two of its journals are members of the new group and of no other, while 27 journals are included in other categories as well. From time to time the classification scheme of JCR is changed. As a rule a broad (often interdisciplinary) category is split into narrower categories. This is a common procedure in biomedicine. As far as mathematical journals are concerned, one can mention the split of the MATHEMATICS, APPLIED category. In 1982 it was divided into APPLIED MATHEMATICS proper and COMPUTER APPLICATIONS&CYBERNETICS. In the 1990s, the latter category constituted a broad field, which was ultimately split into seven categories of Computer Science:

ARTIFICIAL INTELLIGENCE (EP), CYBERNETICS (ER), HARDWARE & ARCHITECTURE (ES),

INFORMATION SYSTEMS (ET), INTERDISCIPLINARY APPLICATIONS (EV), SOFTWARE ENGINEERING (EW), THEORY & METHODS (EX).

Many mathematical journals indexed in the categories PQ, PN and PO have also become part of some categories of Computer Science. For example, ACM T MATH SOFTWARE (PN, EW), SIAM J COMPUT (PN, EX), J MATH IMAGING VIS (PN, EP, EW).

The calculated values of Ig do not depend on the number of journals in the field. Two large fields of knowledge, ENGINEERING, MULTIDISCIPLINARY and PHYSICS, MULTIDISCIPLINARY, have the same number of journals (79 and 71), but their values of Ig are quite different (3.17 and 17.5). Some other examples are given below:

JRC category Number of journals Ig 2009

COMPUTER SCIENCE, THEORY & METHODS 92 3.47

STATISTICS & PROBABILITY 100 3.42

MEDICAL INFORMATICS 23 3.31

ENGINEERING, MULTIDISCIPLINARY (Engineering) 79 3.17

MATHEMATICS 255 3.06

MATHEMATICS, APPLIED 204 3.09

MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 80 3.27

PHYSICS, MATHEMATICAL 47 2.67

MATHEMATICAL & COMPUTATIONAL BIOLOGY 29 4.41

MECHANICS 123 4.48

PHYSICS, MULTIDISCIPLINARY 71 17.5

6. Bibliometric assessment of mathematical science journals in JCR

for 2008-2009

This section is devoted to discussion of calculation results of the normalized impact factor K for 615 journals included in five categories: MATHEMATICS (PQ), MATHEMATICS, APPLIED (PN), MATHEMATICS, INTERDISCIPLINARY APPLICATIONS (PO), MATHEMATICAL & COMPUTATIONAL BIOLOGY (MCB), and PHYSICS, MATHEMATICAL (UR).

About a hundred journals belong simultaneously to two or more categories. Two journals are indexed in six categories:

Abbr. title of journal Code category Ip K

J CHEMOMETR PO, AC, EA, EP, OA, XY 1.291 33.79

OPEN SYST INF DYN UR, DT, ET, PN, PU, XY 0.935 27.18

This practice is quite common in the new category MCB. Ofthe 29 joumalsbelong-ingto MCB, only two journals are not indexed in any other category: 7 journals are covered in three categories, 3 journals, in four categories and 4 journals, in five categories. Thus the average number of categories per journals (ACJ) is 2.7. The multidisciplinary character of MCB is evident. One may expect further reclassification of the field. The PHYSICS, MATHEMATICAL

(UR) category is also highly multidisciplinary, its ACJ is 2.2.

The distribution of mathematical journals by values of K for 200 9is given below:

ZONE Values of Normalized impact factor K Number of mathematical journals in fields

PN (204) PO (80) PQ (255) UR (47) MCB (29)

1 K> 100 4 1 1 1 0

2 100 < K > 50 27 9 12 17 2

3 < 50 K > 20 111 43 125 19 20

4 < 20 K > 10 56 20 99 6 4

5 < 10K>0 6 7 18 4 1

6 K=0 0 0 0 0 0

Table 3 below includes 32 mathematical journals (PN, PO, PQ, and MCB) with K>50 ranked by normalized impact factor.

Table 3. Mathematical (PQ, PN, PO, MCB) journals with K > 50 (JCR database for 2009)

Rank Abbreviated Journal Title Code JCR category Impact Factor K 2009

1 INT J NONLIN SCI NUM PN, PU, IF, UR 5.276 157.49

2 ANN MATH PQ 4.174 136.40

3 ECONOMETRICA PO, XY 4.000 119.76

4 SIAM REV PN 3.391 109.74

5 B AM MATH SOC PN 3.294 106.60

6 JAM MATH SOC PN, EX 3.411 103.99

7 STRUCT EQU MODELING PO 3.153 96.42

8 BMC SYST BIOL MCB 4.064 92.15

9 INVENT MATH PQ 2.794 91.31

10 COMMUN PUR APPL MATH PQ, PN 2.657 86.55

11 ACTA MATH-DJURS HOLM PQ 2.619 85.59

12 PLOS COMPUT BIOL MCB, CO 5.759 85.57

13 BIOSTATISTICS MCB, XY 3.246 83.23

14 SIAM J MATRIX ANAL A PN 2.411 78.02

15 NONLINEAR ANAL-REAL PN 2.381 77.05

16 MULTISCALE MODEL SIM PO, UR 2.198 74.01

17 MEM AM MATH SOC PQ 2.240 73.20

18 ABSTR APPL ANAL PN 2.221 71.88

19 MULTIVAR BEHAV RES PO, XY 2.328 69.70

20 STAT METHODS MED RES MCB, HL, PT, XY 2.569 68.87

21 MATH MOD METH APPL S PN 2.095 67.80

22 INVERSE PROBL PN, UR 1.900 65.97

23 MATH PROGRAM PN, EW, PE 2.048 65.22

24 APPL COMPUT HARMON A PN, UR 1.854 64.37

25 FUZZY SET SYST PN, XY, EX 2.138 64.20

26 INVERSE PROBL IMAG PN, UR 1.831 63.57

27 FOUND COMPUT MATH PQ, PN, EX 1.905 63.08

28 INT J NUMER METH ENG PO, IF 2.025 62.89

29 CHAOS PN, UR 1.795 62.33

30 SIAM J APPL DYN SYST PN, UR 1.786 62.01

31 J CRYPTOL PN, EX, IQ 2.297 61.42

32 ARCH RATION MECH AN PO, PU 2.331 60.23

The 13 leading Russian journals in the same categories occupy very modest ranks (239-488) in this list (which contains 491 journals).

RUSSIAN JOURNALS

239 MOSC MATH J PQ, PN 0.712 23.30

280 REGUL CHAOTIC DYN PN, PU,UR 0.725 21.26

292 IZV MATH + PQ 0.635 20.75

380 ALGEBR LOG+ PQ 0.479 15.65

385 RUSS J NUMER ANAL M PN, IF 0.485 15.49

387 SIBERIAN MATH J + PQ 0.475 15.47

413 RUSS MATH SURV + PQ 0.425 13.88

440 PROBL INFORM TRANSM+ PM, EX 0.393 11.98

457 DIFF EQUAT+ PQ 0.339 11.08

458 MATH NOTES + PQ 0.337 11.0

476 PMM-J APPL MATH MEC+ PN, PU 0.360 9.52

477 FUNCT ANAL APPL + PQ PN 0.289 9.32

488 DOKLMATH PQ 0.162 5.29

In the Physics, mathematical (UR) category, there were 47 journals in 2009. The ranking of the 18 journals which have of values K greater than 50 is presented in Table 4 below. Here again the ranks of the three leading Russian journals in that category (including the Russian Journal of Mathematical Physics) are quite modest.

Table 4. PHYSICS, MATHEMATICAL category journals in 2009

Rank Abbreviated Journal Title Code Ig Impact Factor K 2009

1 INT J NONLIN SCI NUM UR, PN, PU, IF 5.276 157.49

2 COMMUN COMPUT PHYS UR 2.077 77.79

3 COMMUN MATH PHYS UR 2.067 77.41

4 QUANTUM INF COMPUT UR, EX, UP 2.980 77.40

5 J STAT MECH-THEORYE UR, PU 2.670 74.79

6 J COMPUT PHYS UR, EV 2.369 74.26

7 MULTISCALE MODEL SIM UR, PO 2.198 74.01

8 PHYS REVE UR, UF 2.400 70.80

9 INVERSE PROBL UR, PN 1.900 65.97

10 APPL COMPUT HARMON A UR, PN 1.854 64.37

11 INVERSE PROBL IMAG UR, PN 1.831 63.57

12 CHAOS UR, PN 1.795 62.33

13 SIAM J APPL DYN SYST UR, PN 1.786 62.01

14 COMPUT PHYS COMMUN UR, EV 1.958 61.38

15 INT J GEOM METHODS M UR 1.612 60.37

16 J NONLINEAR SCI UR, PN, PU 1.816 53.25

17 J STAT PHYS UR 1.390 52.06

18 ADV THEOR MATH PHYS UR, UP 2.034 50.35

RUSSIAN JOURNALS

26 RUSS J MATH PHYS UR 0.850 31.83

35 REGUL CHAOTIC DYN UR, UP 0.725 21.26

44 THEOR MATH PHYS + UR, UI 0.796 7.90

The geographical distribution of the 47 journals of the Physics, mathematical category is as follows: USA — 16, The Netherlands — 8, Singapore — 7, England — 6, Russia and Switzerland — 3, Germany, Poland, China and Ukraine — 1. Two Russian journals in this field - REGUL CHAOTIC DYN and RUSS J MATH PHYS are published only in English, THEOR MATH PHYS+ is published in Russian and translated into English.

7. Russian mathematical journals in the world corpus of scientific journals

In 20102 the Russian corpus of scientific journals included 147 journals (the corresponding figure for 2008 is 108, and for 2009, it is 123.1n the list of Russian journals for 2010, there

2 The JCR database (Science Edition) for 2010 has become accessible only in July 2011.

are 19 journals dealing with the mathematical sciences. Among them there are three new mathematical science journals:

COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS (COMP MATH MATH PHYS+),

PROCEEDINGS OF THE STEKLOY INSTITUTE OF MATHEMATICS (P STEKLOYI MATH),

ST PETERSBURG MATHEMATICAL JOURNAL (ST PETERSB MATH+).

Data on thel9 journals in the mathematical sciences are presented in Table 5 below.

Table 5. Russian Mathematical Journals in JCR databases for 2008-2010

Journal abbreviation Category code 2008 2009 2010

Ip K Ip K Ip K

ALGEBR LOG+ PQ — — 0.479 15.65 0.455 16.19

COMP MATH MATH PHYS+ PN, UR — — — — 0.380 12.88

DIFF EQUAT+ PQ 0.437 15.33 0.339 11.08 0.369 13.13

DOKLMATH PQ 0.222 7.79 0.162 5.29 0.204 7.26

FUNCT ANAL APPL + PQ, PN 0.449 12.25 0.289 9.32 0.688 21.84

IZV MATH + PQ 0.494 17.3 0.635 20.8 0.494 17.58

MATH NOTES + PQ 0.270 9.5 0.337 11.0 0.344 12.24

MOSC MATH J PQ, PN — — 0.712 23.3 0.721 22.89

P STEKLOVI MATH+ PQ, PN — — — — 0.276 8.76

PMM-J APPL MATH MEC+ PN, PU 0.348 7.09 0.360 9.52 0.352 9.36

PROBL INFORM TRANSM+ PM, EX — — 0.393 11.98 0.418 12.11

REGUL CHAOTIC DYN PN, PU,UR 0.568 12.94 0.725 21.26 0.529 15.93

RUSS J MATH PHYS UR 0.944 28.09 0.850 31.83 1.131 46.73

RUSS J NUMER ANAL M PN, IF 0.305 7.60 0.485 15.49 0.592 18.97

RUSS MATH SURV + PQ 0.430 15.08 0.425 13.9 0.496 17.65

SIBERIAN MATH J + PQ 0.445 15.61 0.475 15.5 0.388 13.81

ST PETERSB MATH J+ PQ — — — — 0.347 12.35

THEOR MATH PHYS+ UR, UI 0.721 11.52 0.796 7.90 0.748 13.50

THEOR PROBAB APPL+ XY 0.698 23.97 0.827 24.18 0.318 10.63

The values of the standard impact factor Ig of some JCR categories in the mathematical sciences in 2008-2009 are shown in Table 6 below.

Table 6. Standard impact factor Ig for some JCR categories

Code Categories in JCR Standard impact factor

2008 2009 2010

EX COMPUTER SCIENCE, THEORY & METHODS 3.90 3.47 3.42

IF ENGINEERING, MULTIDISCIPLINARY (Engineering) 3.54 3.17 2.75

PN MATHEMATICS, APPLIED 4.48 3.09 3.49

PO MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 3.32 3.27 4.94

PQ MATHEMATICS 2.85 3.06 2.81

PU MECHANICS 5.34 4.48 4.04

PT MEDICAL INFORMATICS 3.01 3.31 2.69

UR PHYSICS, MATHEMATICAL 3.36 2.67 2.42

UI PHYSICS, MULTIDISCIPLINARY 9.16 15.50 8.66

XY STATISTICS & PROBABILITY 2.91 3.42 2.99

The dynamics of the normalized impact factor K for Russian journals in the mathematical sciences for the three years 2008-2009-2010 are presented in Figure 3 below. Note that RJMP has the highest values of K and the rate of growth of its normalized impact factor is quite substantial.

Fig. 3. Dynamics of K of the Russian journals in the mathematical sciences in 2008—2010

Let us examine changes in the values of the normalized impact factor K of Russian journals in the mathematical sciences in 2008, 2009 and 2010 (Fig. 3). We see that only three journals: RUSS J MATH PHYS, RUSS J NUMER ANALM and MATH NOTES+ had a stable growth of K; on the other hand, we see that two new journals: ALGEBR LOG+ and PROBL INFORM TRANSM+ had insignificant growth.

Figure 4 below shows the ranks of these journals according to their values of K in 2010.

K10

Fig. 4. Rankings by K of Russian journals in the mathematical sciences in 2010

This figure shows that only two journals have values of Kbetween 20 and 40: RJMP and MOSC MATH J. Most Russian journals (14) have values of Kbetween 10 and 20, while three have values of K less than 10.This is confirmed by Table 7 below, which also shows K’, the average values of K in 2008-2010.This list is headed by three journals: RJMP, MOSC MATH J, and FUNCT ANAL APPL + with values of K in 2010 between 20 and 50.

Table 7. Normalized impact factor K (and its average K’ for 2008-2010)

for the same journals

Journal abbr. K 08 K09 K10 Average K’

RUSS J MATH PHYS 28.09 31.83 46.73 35.55

MOSC MATH J — 23.3 22.89 23.09

FUNCT ANAL APPL + 12.25 9.32 21.84 14.47

RUSS J NUMER ANAL M 7.60 15.49 18.97 14.02

RUSS MATH SURV + 15.08 13.9 17.65 15.54

IZV MATH + 17.3 20.8 17.58 18.56

ALGEBR LOG+ — 15.65 16.19 15.92

REGUL CHAOTIC DYN 12.94 21.26 15.93 16.71

SIBERIAN MATH J + 15.61 15.5 13.81 14.97

THEOR MATH PHYS+ 11.52 7.90 13.50 10.97

DIFF EQUAT+ 15.33 11.08 13.13 13.18

COMP MATH PHYS+ — — 12.88 12.88

ST PETERSB MATH J+ — — 12.35 12.35

MATH NOTES + 9.5 11.0 12.24 10.91

PROBL INFORM TRANSM+ — 11.98 12.11 12.04

THEOR PRO BAB APPL+ 23.97 24.18 10.63 19.59

PMM-J APPL MATH MEC+ 7.09 9.52 9.36 8.66

P STEKLOVI MATH+ — — 8.76 8.76

DOKL MATH 7.79 5.29 7.26 6.78

8. Russian mathematical journals in the national corpus of scientific journals

The rankings of 50 Russian scientific journals by impact factor Ip and by normalized impact factor K are presented in Tables 8 and 9.The leader of the journals in the mathematical sciences comes 13th in the Ip list (Table 8), yet among the 10 leaders in the list ranked by the normalized impact factor K (T able 9), we find five (!) mathematical journals with K more than 20. In these two tables, the journals in the mathematical sciences are displayed in bold font.

Table 8. Ranking of Russian scientific journals by impact factor Ip in 2009

Rank Abbreviated Journal Title Impact Factor K 2009

1 PHYS-USP+ 2.628 15.02

2 RUSS CHEM REV+ 2.073 14.17

3 JETP LETT+ 1.662 9.50

4 BIOCHEMISTRY-MOSCOW+ 1.327 4.73

5 GEOTECTONICS+ 1.000 23.64

6 RUSS GEOL GEOPHYS+ 1.000 17.42

7 COMP CYTOGENET 0.973 5.03

8 ASTRON LETT+ 0.943 12.12

9 PHYS PART NUCLEI+ 0.935 17.28

10 STRATIGR GEO CORREL+ 0.915 30.35

11 PETROLOGY+ 0.912 15.89

12 J EXP THEOR PHYS+ 0.871 5.62

13 RUSS J MATH PHYS 0.850 31.83

14 THEOR PROBAB APPL+ 0.827 24.18

15 THEOR MATH PHYS+ 0.796 7.90

16 QUANTUM ELECTRON+ 0.791 10.37

17 MENDELEEV COMMUN 0.769 5.26

18 ASTRON REP+ 0.759 9.75

19 J RUSS LASER RES 0.748 19.63

20 REGUL CHAOLIC DYN 0.725 21.26

21 ASLROPHYS BULL 0.723 9.29

22 PHYS SOLID SLALE+ 0.721 6.23

23 MOSCMALH J 0.712 23.19

24 KINEL CALAL+ 0.691 5.92

25 POLYM SCI SER A+ 0.688 13.62

26 LASER PHYS 0.676 9.37

27 APPL BIOCHEM MICRO+ 0.670 4.40

28 LOWLEMP PHYS+ 0.662 6.23

29 MICROBIOLOGY+ 0.638 4.55

30 SEMICONDUCLORS+ 0.637 5.50

31 IZVMALH+ 0.635 20.75

32 RUSS J COORD CHEM+ 0.605 12.52

33 PALEONLOL J+ 0.604 20.68

34 J ANAL CHEM+ 0.604 13.16

35 COLLOID J+ 0.588 5.04

36 PLASMA PHYS REP+ 0.584 14.17

37 LECH PHYS LELL+ 0.580 5.46

38 HIGH LEMP+ 0.578 5.44

39 MOL BIOL+ 0.570 2.03

40 CRYSLALLOGR REP+ 0.559 9.24

41 REV ADV MALER SCI 0.558 3.14

42 COMBUSL EXPLO SHOCK+ 0.547 6.81

43 PHYS ALOM NUCL+ 0.539 15.40

44 ACOUSL PHYS+ 0.534 22.44

45 RUSS J ORG CHEM+ 0.525 9.46

46 OPLSPECLROSC+ 0.505 13.25

47 GEOCHEM INL+ 0.502 11.87

48 RUSS JGENEL+ 0.501 2.59

49 RUSS J PLANE PHYSL+ 0.500 4.80

50 HIGH ENERG CHEM+ 0.498 4.27

The ranking of the same journals according to K looks quite different.

Table 9. Ranking by K of Russian scientific journals in 2009

Rank Abbreviated Journal Litle Impact Factor K 2009

1 RUSS J MALH PHYS 0.850 31.83

2 SLRALIGR GEO CORREL+ 0.915 30.35

3 LHEOR PRO BAB APPL+ 0.827 24.18

4 GEOLECLONICS+ 1.000 23.64

5 MOSC MALH J 0.712 23.19

6 ACOUST PHYS+ 0.534 22.44

7 REGUL CHAOTIC DYN 0.725 21.26

8 IZVMATH+ 0.635 20.75

9 PALEONTOL J+ 0.604 20.68

10 J MIN SCI+ 0.352 20.00

11 J RUSS LASER RES 0.748 19.63

12 PHYS MET METAT T OGR+ 0.477 18.42

13 RUSS GEOL GEOPHYS+ 1.000 17.42

14 PHYS PART NUCLEI+ 0.935 17.28

15 PETROLOGY+ 0.912 15.89

16 ALGEBR LOG+ 0.479 15.65

17 SIBERIAN MATH J+ 0.475 15.52

18 RUS S J NUMER ANAL M 0.485 15.49

19 PHYS ATOM NUCL+ 0.539 15.40

20 PHYS-USP+ 2.628 15.02

21 PLASMA PHYS REP+ 0.584 14.17

22 RUSS CHEM REV+ 2.073 14.17

23 RUSS MATH SURV+ 0.425 13.89

24 POLYM SCI SERA+ 0.688 13.62

25 PROT MET+ 0.347 13.40

26 OPT SPECTROSC+ 0.505 13.25

27 J ANAL CHEM+ 0.604 13.16

28 RUSS J COORD CHEM+ 0.605 12.52

29 ASTRON LETT+ 0.943 12.12

30 PROBL INFORM TRANSM+ 0.393 11.98

31 GEOCHEM INT+ 0.502 11.87

32 DIFF EQUAT+ 0.339 11.08

33 MATH NOTES+ 0.337 11.01

34 GEOL ORE DEPOSIT+ 0.331 10.47

35 QUANTUM ELECTRON+ 0.791 10.37

36 RUSS J NONDESTRUCT+ 0.195 10.37

37 RUSS J MAR BIOL+ 0.346 10.12

38 ASTRON REP+ 0.759 9.75

39 INSTRUM EXP TECH+ 0.331 9.54

40 PMM-J APPL MATH MEC+ 0.360 9.52

41 JETP LETT+ 1.662 9.50

42 RUSS J ORG CHEM+ 0.525 9.46

43 FUNCT ANAL APPL+ 0.289 9.41

44 LASER PHYS 0.676 9.37

45 ASTROPHYS BULL 0.723 9.29

46 RUSS J ELECTROCHEM+ 0.347 9.25

47 CRYSTALLOGR REP+ 0.559 9.24

48 J VOLCANOL SEISMOL+ 0.386 9.12

49 IZV ATMOS OCEAN PHY+ 0.371 9.09

50 OCEANOLOGY+ 0.307 8.95

It is interesting to compare the ranks of journals by the normalized impact factor K for K > 15 and by the impact factor Ip (Table lObelow). The two well-known journals JETP LETT and J EXP THEOR PHYS do not appear in this table, because they have smaller values of K (9.50 and 5.62, respectively). Their ranks by K are 41 and 67 in the Russian national corpus.

Table 10. Ranks by K and by Ip of Russian scientific journals with K> 15

Rank by K Russian journals JCR:2009SE Ip K 2009 Rank by Ip 2009

1 RUSS J MATH PHYS 0.850 31.83 13

2 STRATIGR GEO CORREL+ 0.915 30.35 10

3 THEOR PRO BAB APPL+ 0.827 24.18 14

4 GEOTECT ONICS+ 1.000 23.64 5.5

5 MOSC MATH J 0.712 23.19 23

6 ACOUST PHYS+ 0.534 22.44 5

7 REGUL CHAOTIC DYN 0.725 21.26 22

8 IZVMATH+ 0.635 20.75 31

9 PATEONTOT ,T+ 0.604 20.68 33.5

10 J MIN SCI+ 0.352 20.00 71

11 J RUSS LASER RES 0.748 19.63 19

12 PHYS MET METALLOGR+ 0.477 18.42 54

13 RUSS GEOL GEOPHYS+ 1.000 17.42 5.5

14 PHYS PART NUCLEI+ 0.935 17.28 9

15 PETROLOGY+ 0.912 15.89 11

16 ALGEBR LOG+ 0.479 15.65 53

17 SIBERIAN MATH J+ 0.475 15.52 55

18 RUSS J NUMER ANAL M 0.485 15.49 52

19 PHYS ATOM NUCL+ 0.539 15.40 43

20 PHYS-USP+ 2.628 15.02 1

Further, it is interesting to compare the bibliometric indicators (and ranks) off our Russian journals from the Physics, Mathematical (UR) category with the two Russian journals, J EXP THEOR PHYS+ and JETP LETT + from the Physics, Multidisciplinary (UI) category (Table 11).

Table 11. Bibliometric indicators for 6 Russian journals: 2008—2010

Journal abbr Category code 2008 2009 2010

Ip K Ip K Ip K

COMP MATH MATH PHYS+ PN, UR — — — — 0.380 12.88

REGUL CHAOTIC DYN PN, PU,UR 0.568 12.94 0.725 21.26 0.529 15.93

RUSS J MATH PHYS UR 0.944 28.09 0.850 31.83 1.131 46.73

THEOR MATH PHYS+ UR, UI 0.721 11.52 0.796 7.90 0.748 13.50

J EXP THEOR PHYS+ UI 0.892 9.74 0.871 4.98 0.946 10.92

JETP LETT + UI 1.418 15.48 1.662 9.5 1.557 17.98

We see that in 2010 RJMP is in first place among six Russian journals in the physical fields. The journal JETP LETT is in second place in 2008 and 2010 by values K.

In Figure 8 below, we show the dynamics of the values of the normalized impact factor K for the same six Russian journals in the physical sciences.

Fig. 8. Dynamics of the normalized impact factor K for six Russian physics journals

Thus Figures 3 and 8, together with Table 10, show that RJMP is in first place by normalized impact factor K not only among Russian journals in the physical and mathematical sciences, but also among all the Russian scientific journals appearing in the JCR databases in 2008-2010.

In conclusion of this section, it is interesting to compare, on the one hand, the ranks of live important physics journals indexed in the categories Physics, Mathematical (UR) and Physics, Multidisciplinary (UI) (by two bibliometric indicators: the normalized impact factor K and the impact factor Ip) in the entire Russian scientific corpus ( 123 journals) with, on the other hand, the ranks of those journals in the appropriate categories by the impact factor Ip from the JCR database for 2009 (Table 12).

Table 12. Bibliometric indicators for 6 Russian journals: 2009

Abbr. journal title K Ip Rank in Russian national corpus (123 journals) Rank in category UR (47 journals) Rank in category UI (71 journals)

byK bylp bylp bylp

RUSS J MATH PHYS 31.83 0.850 1 13 33 —

REGUL CHAOTIC DYN 22.60 0.725 7 20 37

JETP LETT + 9.50 1.662 41 3 — 24

THEOR MATH PHYS+ 7.90 0.796 53 15 34

J EXP THEOR PHYS+ 5.62 0.871 67 12 — 40

9. The citations of V. I. Arnold

To conclude this study, the author would like to analyze the citations of the work of the famous Russian mathematician Vladimir Arnold, to whom this article is dedicated. We present the citation of V. I. Arnold in the period 1945-2011 below.

The JCR database Web of Science (ISI Web of Science: 1945-2011) includes 3248 cites to Arnold’s publications in a total of 2012 records (documents). We analyze cites by (1) categories, (2) countries, and (3) authors.

(1) References to Arnold appear in 29 Web of Science categories, but more than 50 % of them are in the following 9 categories:

MATHEMATICS (562)

MATHEMATICS APPLIED (468)

PHYSICS, MATHEMATICAL (364)

PHYSICS MULTIDISCIPLINARY (312)

MECHANICS (245)

PHYSICS FLUIDS PLASMAS (130)

MULTIDISCIPLINARY SCIENCES (95)

MATHEMATICS INTERDISCIPLINARY APPLICATIONS (83)

ASTRONOMY ASTROPHYSICS (74)

(2)Almost one fourth of the references to Arnold are from the USA (507), Russia holds second place with 290 cites, with France (241), England (156), USSR (104), Germany (102), Canada (90), Italy (85), China (71), Israel (59) and others. Total statistics by countries shows that references to Arnold’s papers were done by authors from 57 countries.

(3) The 2012 cites to Arnold belong to 742 authors, 29 of them cited Arnold in more than seven publications:

Authors Record- Count % of2012 Authors Record- Count % of2012

MARSDENJE 28 1.392 GLASS L 8 0.398

HOLM DD 24 1.193 GUCKENHEIMER J 8 0.398

SHEPHERD TG 22 1.093 MAHALOVA 8 0.398

ARNOLD VI 18 0.895 NICOLAENKO B 8 0.398

MOSEKILDE E 15 0.746 SAGDEEV RZ 8 0.398

GRAMMATICOS B 13 0.646 SPERL M 8 0.398

RAMANIA 13 0.646 VLADIMIROV VA 8 0.398

RATIU TS 12 0.596 BRENIER Y 7 0.348

GOTZEW 11 0.547 GAETA G 7 0.348

IEEE 11 0.547 KARPENKOVON 7 0.348

JANECZKO S 11 0.547 KHESIN B 7 0.348

CHERNIKOV AA 10 0.497 KOZLOVW 7 0.348

CHERNIKOV AA 10 0.497 KRAUSKOPF B 7 0.348

MUM 10 0.497 MARCHIORO C 7 0.348

CHIRIKOV BV 9 0.447 OSINGAHM 7 0.348

MARMIS 9 0.447 PUTAM 7 0.348

ZASLAVSKY GM 9 0.447 RATIU T 7 0.348

SOSNOVTSEVA OV 7 0.348

Conclusion

1. The bibliometric analysis of scientific journals, based on the JCR databases, shows that the impact factor of fields of science (Ig) is growing in science as a whole. The growth of the number of citations is due both to the progress of science proper and of the means of communication facilitating access to information.

2. The normalized impact factor (K) is a tool for the comparison of journals across fields of knowledge, and it is very important in assessing national contributions to world science.

3. The traditional impact factor (Ip) favors such disciplines as biology and medicine and can hardly be used in reference to fields with lower level of citedness (such as mathematics or technology). The introductions of the normalized impact factor K will help remedy that injustice.

4. The bibliometric analysis of Russian mathematical journals shows that they occupy only a modest place in the world list of 609 mathematical journals (see Tables 3 and 4). However, within the national Russian corpus of scientific journals, they fare much better. Measured by the normalized impact factor, eight mathematical journals (RJMP, THEORPROBABAPPL+, MOSCMATHJ, REGULCHAOTICDYN, ALGE-BRLOG+, SIBERIANMATHJ+, RUSSJNUMERANALM) appear among the twenty leaders of the list of 140 journals. In 2009 and 2010, the list is headed by the Russian Journal of Mathematical Physics, published in English by MAIKNAUKA/ INTERPE-RIODICA/SPRINGER.

Acknowledgements

The author is grateful to A. B. Sossinsky for translating the author’s poor English into clear idiomatic American English. This study was supported by the RFBR grant № 10-06-0018a.

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Irina G. Dezhina,

Head of Economics of Science and Innovations Division,

Institute of World Economy and International Relations,

Russian Academy of Sciences

Creating Linkages: Government Policy to Stimulate R&D through University-Industry Cooperation in Russia

The article analyzes new government measures aimed at the creation of linkages between universities and companies in Russia to strengthen R&D and make them more effective in terms of practical applications. Three measures are assessed — programs of innovation development of large government-controlled companies, technology platforms, and cooperative R&D projects. It is shown that all measures are important and interconnected though there are some flaws in their implementation. At the same time application of these measures caused a number of positive side effects for Russian R&D complex.

Keywords: R&D, universities, companies, financing, workforce, technology platforms, programs of innovative development, joint R&D projects

State of R&D in Russia

The R&D complex inherited to a large extent Soviet traditions and organization. It is still highly hierarchical, and centralized. The federal government dominates both in terms of financing and control over organizations involved in R&D. Federal budget is the major source of support for R&D in Russia and the share of federal budget among the sources of support is increasing while business plays an insufficient role in financing R&D. Moreover, government in a way substitutes private funds creating in this way disincentives for business. All these characteristics are especially noticeable from international perspective (tables 1 and 2).