An analysis of quantitative data on the incidence of phase relations associated
with mathematical sciences is presented. It has been found that application and bias
phase relations have high percentage of incidence. Physical sciences show a greater
tendency for phase relations wittr mathematics. It is also observed that intra-subject
phase relations with mathematics is fairly frequent

Gopinath, M.A.

Lakshmanamoorthy, A.

English

Librarians' Digital Library

Lib. Sc. 20; 1983; Paper B. 
PHASE RELATIONS ASSOCIATED WITH 
MATHEMATICAL SCIENCES: A Case Study 
M A GOPINATH AND A LAKSHMANAMOORTHY,* 
Documentation Research and Training Centre, Indian Statistical Institute, 
31 Church Street, Bangalore 560 001. 
An analysis of quantitative data on the incidence of phase relations associated 
with mathematical sciences is presented. It has been found that application and bias 
phase relations have high percentage of incidence. Physical sciences show a greater 
tendency for phase relations wittr mathematics. It is also observed that intra-subject 
phase relations with mathematics is fairly frequent. 
I 
0 introduction 
Complex subjekts have been identified as one of the important 
features in the structure and development of universe of subjects. 
They arise out of the mode of 'loose assemblage" (3). The resulting 
relation is called "Phase Relation (5). In phase relation, two or more 
subjects arc combined by a variety of relations such as Bias, 
Application, Influence and also Comparison, Difference and General 
(5). Detqiled deftnitions of this typology has been presented in Colon 
Classification (-- CC) and also in same papers (1,2,4). However to get 
data on the frequency of inadence of phase relations in different 
subject fields, we have to identity a large collection of documents, 
principally in a library. In this paper, we have attempted to find out 
the types of phase relations incident in documents collected in a large 
scientific library. We have further restricted our study to the phase 
relations of subjects associated with Mathematical Sciences. 
* Student of DRTC Course (1982-84) 
18 Lib Sc 
 Library Science With a slant to Documentation, 1983, 20(1), 18-30. (Revised version of the paper presented in the 20th DRTC Annual Seminar
on Classification and Indexing in Science & Technology, 21-25 February 1983, Bangalore. DRTC, Bangalore, 1983. pp. BDI-BD19).
PHASE RELATIONS WITH hWTHEMATICAL SCIENCES B2 
1 The nature of Mathematical Sciences 
Mathematical Sciences is .a field which generates a kind of 
absmct logic. It attempts to find patterns from empirical situations 
and generalize them into a principle or a function Such generalisa- 
tions are helpfbl for applications to solve problems in different 
contexts. In a sense, specialists express difficult concepts and 
multivariate relational complexities with the help of mathematical 
Language. The field of mathematics is an ancient one. It has developed 
from Arithmetics, Algebra and Geometry to the current developments 
of Statistical analysis, Operations Research and Topology. In fact, it is 
said that mathematics is a discipline whose structure is ever changing 
and developing. Mathematics has been used as a general input 
discipline to the study of the relations and critical factors in these 
relations in various subject fields. Such studies aid prediction and 
improve the rigour of the field of study for hrther development. 
In order to get a feel of the ramifications of the use of 
mathematics in different fields, we have attempted to get a sample set 
of documents from a large library for analysis. 
2 Methodology by collecting the samples 
To get an empirical sample of documents which embody 
complex subjects associated with mathematics, we selected a large 
science library in Bangalore, namely the Indian Institute of Science 
Library. This library has a collection of books which range 1,15,000. 
Amidst these documents mathematics has around 7000 documents. 
Of these documents, 3000 documents are those published during 
1960 to 1980. From this collection, we selected a sample of subjects 
which have phase relations with Mathematical Sciences. The 
procedure of the selection of the documents for the purpose of study is 
as follows: 
1) The alphabetical part of the catalogue, containing subject 
entries were scanned. The entry term normally used was mathematics 
or any of its associated fields such as Algebra, Geometry, Statistics, 
Calculus etc. From this part call numbers for various documents 
indicating phase relations were selected. 
2) Using the call numbers selected, the classified pan was 
searched for the specific main entries representing documents having 
complex subjects. In this process, the entire classified part was 
V20 Nl: 1983 MARCH 19 
searched. Fields in Natural Sciences and Social Sciences were looked 
into for co~ec t ions  with nmathematical sciences. 
3) For each main entry selected as a sample for the study of 
phase relations, the following items of information were collected: 
a) DDC call number of the docbk'nen~ 
b) Title of the document; 
c) Edition andlor the year of publication of the document; 
d) - Subject headmgs wherever they were provided. 
4) The collected samples totalled to 576. Of these 223 were 
published chning 1960's (1 960-1 969) and 293 were published during 
1970's (1970-198 1). T1 ey were analysed as follows: 
a) The actual documents on the shelf were also consulted for 
determining the specific subject embodied in it; 
b) Each of these specific subjects was analysed using 
postulational approach to classification. 
c) The type of phase relations involved was identified and noted 
on each slip; 
d) The component subjects involved in the phase relations were 
also noted. For this purpose, the classification schemes such 
as the Dewey Decimal Classification (DDC), C.C. and the 
Broad System of Ordering (BSO) were used, for recognising 
the subjects. 
e) The total data collected from the samples was consolidated in 
the following manner: 
i) By types of phase relations namely General, Bias, 
Application and Influence; 
ii) By subjects involved in phase relation; 
iii) By the date of publication of documents. For this 
purpose, we selected documents which were published 
after 1960 upto 1980's. 
The consolidated data and inferences that can be drawn from 
this data are presented in this paper. 
Lib Sc 
PHASE RELATIONS WITH MA'l'l I li.\M11CAL SCIENCES B3 
3 Subjects involved in the phwe relations 
From the samples collected, it was found that a fairly wide 
spec- of subjects have phase relations involving Mathematid 
Sciences. This spectrum ranges from Physical Sciences, Natural 
Sciences to Social Saences. The following tables present the quanti- 
tative data on inadence of various types of phase relations with 
 lathema ma tical Sciences. 
TABLE 1. Main subject fields and the number of phase relations in it. 
- 
S1. No. Main, Subject Divisions No. of phase 
relations 
Sciences (In General) 
Mathematical Sciences 
Physical Sciences 
Chemical Sciences 
Biological and Medical Sciences 
Social Sciences 
Management Sciences 
Computer Science * 
Total Phase Relations 636 
TABLE 2. Subjects having phase relations with Mathematical Sciences 
S1. No. Name of the Subject No. of phase 
relation 
Information and communication theory 
Computer Science 
Science (General) 
Mathematics 
Statistics 
Astronomy 
Physics 
Engineering 
Chemistry 
Chemical Technology 
Biological Sciences 
Earth Sciences 
Agriculture 
hledicine 
V20 N 1 : 1983 MARCH 
B2 GOI'INATH AND LNCSHMANAMOORTHY 
S1. No. - Name of Subject 
- - -- - - - - - - 
Behavioural Sciences 
Philosophy 
Psychology 
Social Sciences 
Education 
Political Science 
Economics 
Management Science 
Commerce/Busincss 
No. of Phase 
relation 
Total 
Note for the Tabks::It is important here to note that a single document 
having more than one complex subject has been counted seprately, 
hence resulting 636 phase relations out of the sample contaning 5 16 
entries. 
Annotation: 
It is evident from the above two tables that the complex subjects 
going with mathematical sciences has a fairly high incidence, namely 
178 instances out of 636 relations.This indicates that interrelations in 
mathematics have a high internal incidence, that is a subfield in 
Mathematics is used for the study of another subfield. Physical 
sciences have ranked second in phase relations with Mathematics (it 
has 174 phase relations). Here again, it is found that Engineering has 
the highest incidence (105). The third field which uses mathematics 
is Management Science. Social sciences rank fourth in having 
interrelations with mathematical sciences. Ranked in discending 
sequence of their interrelations, we can list the following subjects 
namely, Computer Science, Sciences in general, Biological and 
Medical Science and Chemical Sciences. It is obvious that the 
Physical and Natural Science sector uses mathematics more than 
Social Sciences Sector. It may be cautioned that the data is collected 
h m  a predominantly Science and Technology library and hence 
there is slant in the incidence of phase relations. 
4 Analysis of data by phore reladons 
The phase relations incident in the sample subject chosen for 
study are General, Bias,-Application and Influence. There was no 
22 Lib Sc 
PHASE RELhnONS WITH .MATHWfATiCAL SCIENCES EM1 
incidence of comparison and difTerence phase relations in the sample. 
Further it can be stated that the dominant phase relations were bias 
phase relations and application phase relations. The succeding sec- 
tions discuss the details of the various phase relations. 
41 ' General Phase Rehation 
The following table presents details about the incidence of 
general phase relation of the complex subjects associated with 
mathematical sciences. By genetal relation it is meant that the two 
subjects are yet to get into any kinds of dynamic relations such as Bias, 
Applications and Influence. For example the following title is 
considered to have general phase relation 'Algebraic methods in the 
global theory of complex spaces. 1976". 
TABLE 3. Complex Subjects having general phase relations with Mathematical 
Sciences 
S1. Number of General Phase 
No. Subject Relation 
Information and communication theory 
Computer Science 
Mathematics 
Statistics 
Physics 
Engineering 
Chemistry 
Agriculture 
Social Science 
Politic& Science 
Economics 
Management Science 
Cornmerce/Busintss 
Total 
Annotation: 
146 instances of general phase relations have been found out of 
the sample of 516 documents. The 1970's indicate slightly higher 
V20.Nl: 1983 MARCH 23 
f341 GO131NATH AND LAKSHMANAMOORTHY 
r incidence than &at in the 1960s. The mathematics itself has a f&ly 
high incidence of gened phase relation with rm&cmaticat scienccs. 
Apart ftam Ws the field of statistics hs o high incidence of general 
phase relations. The social sciences appcar to have very low incidence 
of general phase relation 
Bias phase relation appears to be one of the commonest 
incidences of phase relations. In this relations the subject appearing 
in the first phase is oriented to the needs of the subjects appearing in 
the second phase. For example %he following subject is said to have 
bias phase relation. 
"Numerical Methods for Engineers and Scientists. 1977." The 
following table presents quantitative data on the incidence of bias 
phase relation of difTerent subject fields with Mathematical Sciences. 
TABLE 4. Complex Subjtcts having Bias Phase relation with mathematical sciences. 
si. 
No. Sub j tct 
No. of bias phase 
relations 
Computer Science 
Science (General) 
Mathematics 
Statistics 
Physics 
Engineering 
Chemistry 
Biological Sciences 
Agriculture 
Medicine 
Behavioural Sciences 
Psychology 
Social Sciences 
Education 
Economics 
Management Science 
Commerce/Business 
Total 
24 Lib Sc 
PHASE RELATIONS WITH MAW E.'\1A'I'lCAL SCIENCES 
Bias phase relation has a fairly large incidence in the complex 
subjects studied in the sample. There arc about 191 instances of bias 
phase relations out of 5 1 6 documents. The 1970's indicates a slight 
increase of bias phase relations. Engineering fields appear to have 
fairly high percentage of incidence of bias phase relation Sciences 
(General) comes next in order. Social sciences have a sprinkling of 
bias phase with economics having a large share in this. It can also be 
observed that computer sciences have a large incidence of bias phase 
relations in 1970s. 
43 Application Phase Relcuiun 
Mathematics is an important field for the study of many 
disciplines. This is well borne out in the sample chosea Almost all 
the fields of knowledge have fairly good incidence of application 
phase relation with mathematical sciences. For example, the 
following document illustrates the nature of applied phase relation 
with krthematics. "Group theory and its applications to Physical 
Problems". 8 
The following table presents the quantitative data of the 
complex subjects associated with mathematics. 
TABLE 5. Complex Subjects having Application Phase Relations with Mathematical 
Sciences. 
S1. 
No. Subject 
No. of Application 
phase relation 
1 Information 8t Communication theorg 
2 Computer Science 
3 Science (General) 
4 Mathematics 
5 Statitstics 
6 Astronomy 
7 Physics 
8 &gineering 
9 Chcmimistrg 
10 Chemical Technology 
1 1 Biologicd Sciences 
12 Earth Sciences 
i720 N1: 1983 MARCH 
B42 GOPINATH AND LAKSHMANAA"00RTHY 
SL 
No. 
No. of Application 
phase relation 
- --- 
13 Agriculture 1 - 
14 Medicine 1 3 
15 Behaviowal Sciences 1 
16 Philosophy 1 - 
17 Psychology 2 - 
18 Social Sciences - 3 
19 Education 2 2 
20 Political Science 1 - 
21 Economics 3 6 
22 Management Science 5 17 
23 Commerce/Business 3 6 
Total 110 144 
Annotation: 
Application phase relation has the highest incidence - that is 
above 250 instance out i f  516 documents chosen as sample. The 
1970's show slight increase in the percentage of applicatibn phase 
relation of complex subjects with mathetical sciences. Engineering 
and Physics apqears to have high incidence of application phase 
relation Social sciences also have good incidence of the phase 
relation. Apart from this the computer sciences appear to have a good 
share of this phase relation with mathematics. Further the 1970's 
indicate larger incidence with computer science. 
# 1-e Phase Relation 
Influence phase relation is a relation in which the subject field in 
the hrst phase is influenced by the structure and development of the 
subject in the second phase. For example, 'Selecting and Ordering of 
Population: Influence of Statistical Methods. 1976". 
The followhg table presents data on the incidences of influence 
phase relation in the cornpiex subjects associated with mathematical 
sciences. 
Lib Sc 
PHASE RELATIONS \YrlTH MATHEtMATICAL SCIENCES B5 
TABLE 6 Complex Subjects having Influence Phase Relations with Mathematical 
Sciences. 
- 
SL 
No. Subject 
No. of influence 
phase relations 
Computcr Science 
Mathematics 
Statistics 
Physics 
Engineering 
Chemistry 
Economics 
Management Science 
Commerce/Business 
Total 11 34 
Annotation: 
The data indicates that the influence phase relation is internal to 
mathematics. The large percentage of influence phase relation is 
shared by mathematical sciences themselves. Engineering and 
Management Sciences rank next in the sequence. It may also be 
observed that influence phase relation is on the increase in its 
incidence in the 1970s. 
5 Overall Analysis 
The incidence of phase relations in the complex subjects 
associated with Mathematical Sciences appears to be significant 
though not dominate one. Roughly out of the 3000 mathematical 
documents (published after 196(Ys), we find 516 documents having 
phase relations. Even there we find application phase relation has a 
dominant position followed by bias phase relation (See tables 7 and 8 
in the Annexwe). It may be observed &at this may be due to the 
abstract nature of mathematics and its utility for application in 
different contexts. In fact mpthematics in general is used as an 
objective language for analysis of the problems in various fields of 
knowledge. 
V20 N1: 1983 MARCH 27 
This paper presents a case study to analyse empirically the 
ioddence o f . d o ~ e n t s  with phase relations in the collecdm of 
libraries. It is obviaus that we annot gencnlise the infmnces on the 
buis of the sample data provided in this paper. But it is an attempt to 
apply a methodology ro find the d c a t i o n s  in the incidences of 
complex subjects and the type of phase relations. It may be helpful to 
coilcct data from the coliections of other large libraries oriented to 
science and technology as well as social sciences. Such dam collection 
may help us to develop a quantitative pattern ofincidence ofcomplex 
subjects in the universe of subjects. - 
7 Bit,liographic References 
1 JAYARAJAN (P) and GOPI'NATW (MA).  Ussification of complex subjects in 
CC and UDC. (DRTC Annual Semmnar. 2; 197 1; Paper CCj. 
2 N N E W G H A N  (A; and GOPINATH (M A). Subjects presenting relanons 
between two subjecss with particular reference to phase retation: Case Stud.. 
(DRTC Annual Seminar 7; 1969; Paper BB). 
4 lUNGANI4THAN (S R). Kinds of bonds between w a  subjects including f v s c t ~ ~  
bond. (DRTC Annual Seminar 5;  1967; Paper B). 
5 WGANA'l 'HAK (S R). Phase and inaa-facet relation. (In his Colon Classification. 
Ed. 6. 1960. Chapter 6:. 
TABLE 7. Phase relations in Mathematical Sciences (Total No. of 
documents 5 1 6). 
Phase Relation Number of Documents 
Geaersl 
Bias 
Application 
influence 
XU. I )  DitTcntrccditions ofthc wme document by rhc same author in rhe same period 
8rc ac8d as one docummt. 
(2) When mort thao one GonferencelSeminar caking place on a subject 
suaasively in the same period, it is also treated as one Conference. (eg. 
Confkrcnce on Applicafan of Logic to Aigebn md Arirhmetic, 1979; 
P r d g s ) .  
TABLE 8. Phase Relations in Mathematical Sciences 
S1. Phase Relation General Bias Application Influence Total 
No. 
Phase relation with 1960's 1970's 1960's 1970's 1960's 1970's 1960's 1970's 
1 Information and Communication theory 
2 Computer Sciences 
3 Science (Gtncml) 
4 Mathematic8 
5 Strtisdcs 
6 Aattonomy 
7 Physics 
8 Engineering 
9 Chemistry 
10 Chemical Ttcbnology 
1 1 Biological Sciences 
12 Earth Sciences 
1 3 Agriculture 
14 Medicine , 
15 Behrviounl Sciencea 
16 Philorophy 
17 Paychololty 
18 Socid Scicnceb 
19 Education 
21 Economics 
22 Management Science 
23 Comme~:e/Business 
Total . 69 77 80 111 1 44 11 34 636 
GOPNATH AND LAKSHMANAMOORTHY 
93 Types of Phase Relations with Mathematics 
Totar 
v 
Total 
General Bias Application Influence 
Phase Relations 
Lib Sc 


Phase relations associated with mathematical sciences

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Phase relations associated with mathematical sciences

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