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					                             Dr. W.B.VASANTHA KANDASAMY
                                      Department of Mathematics
                                    Indian Institute of Technology
                                        Chennai 600 036, India
                      web: http://mat.iitm.ac.in/~wbv, http://www.vasantha.in
                               e-mail: vasanthakandasamy@gmail.com
                          mobile: +9198847 75009, phone: +914422570517



Date of Birth         :         24 December 1951
Residential Address   :         D-3/1, First Link Road
                                (Near State Bank of India)
                                Indian Institute of Technology
                                Chennai – 600 036
Father‘s Name         :         Worathur Balasubramaniam
                                (Ex-Headmaster, Thondaimandala
                                Thuluva Vellala Higher
                                Secondary School, Chennai)
Mother‘s Name         :         Krishnaveni Balasubramaniam
Community             :         Backward Class
Martial Status        :         Married to Dr. K. Kandasamy
Children              :         Two daughters


Educational Qualification

Degree                    Institute                                  Year

Ph.D.                     University of Madras                        1980
                          (Guide: Prof. Dr. Mrs.Iqbal Unnissa) (highly commended
                                                               by both examiners)

M.Sc. Mathematics         Stella Maris College, Chennai              1974
                                                                   (First Class)

B.Sc. Mathematics         Stella Maris College, Chennai              1972
                                                                   (First Class)

PUC                       Vaishnava College for Women, Chennai       1969
                                                                   (First Class)

SSLC                      Christ King Girls High School, Chennai     1968
                                                                   (First Class)
Professional Experience

Institute                              Post                           Year

Indian Institute of Technology   Assistant Professor               1988- till date
(IIT Madras)

University of Madras             Research Associate                   1983-1988

Ethiraj College                  Lecturer                             1981-1983

University of Madras             Ph.D (UGC Junior Research Fellow) 1975-1981

Auxilium College, Katpadi        Lecturer                             1974-1975


Area of specialization:                 Pure and Applied Algebra
                                        Coding/Communication Theory
                                        Fuzzy Theory
Teaching & Research
           Experience:                 36 years

Research Guidance:                     13 Ph.Ds
                                       (13 have completed).
                                       76 post-graduate research projects
                                       (72 have completed, 4 currently working).


Research Books published:              50 (47 books published in the USA)
                                                                3 books on AIDS,
                                       Publisher: Tamil Nadu AIDS Control Society)

Papers presented in National
& International Conferences:           351
Research Papers published in
National & International Journals:     211
(Authored individually)
Research Papers published in
National and International Journals:   106
(Co-authored with students)
                                              Total Research papers: 668
Editor, Board Member of Journals :     10
Sponsored Research Projects:           Indian Space Research Organization
                                       Tamil Nadu State AIDS Control Society
                                       Board of Research in Nuclear Sciences

                                        2
Research Contributions for the
Development of Society
A major part of my research work has been devoted to the use of fuzzy and
neutrosophic mathematical tools to the study of sociological problems.

Though my earlier specialization was in pure algebra, in keeping with my
research philosophy, I decided that mathematics could be made of immense
significance in finding a solution to the real world's everyday problems.

I have published hundreds of papers and more than 15 books in Pure
Mathematics, yet I always had an urge and a frustration that mathematics must
be used in the service of the suffering humanity.

Some of the socially relevant issues which will benefit humanity to which I have
applied fuzzy and neutrosophic mathematics are:


Service to HIV/AIDS through research

   1.    Socio-psychological problems of migrant labourers with HIV/AIDS
   2.    Dissemination of information and awareness about AIDS
   3.    Street Children and HIV/AIDS prevalence
   4.    Allocation of funds for HIV/AIDS prevention and cure
   5.    Community Mobilization for HIV/AIDS and Women Empowerment
   6.    Teaching about AIDS to school-children in non-school environment

Study of school dropouts and child labourers

   7.    School dropouts and the child-labour problem
   8.    School dropouts in primary education
   9.    School dropouts and its relation to migration
   10.   Performance aspects of school children
   11.   School dropouts among female children
   12.   Plight of rag-picking children in Chennai

Research about living conditions of bonded labourers

   13. Study of bonded labourers in rice-mills
   14. Brick-makers working as bonded labourers
   15. Tribals in Kodaikanal forests who are bonded labourers


                                       3
Study of the ill-effects of chemical pollution

   16.   Control of atmospheric pollution by chemical industries
   17.   Development of long-range planning for chemical plants
   18.   Occupational hazards in textile industries
   19.   Health hazards associated with solid waste disposal

Mathematical Analysis of the suffering of Cancer Patients

   20. Prevalence of tobacco-related cancer among rural men
   21. Socio-economic problems of cervical cancer patients
   22. Pollution related cancers
   23. Depression in terminally ill patients
   24. Personality-disease model in homeopathy
   25. Determination of hidden pattern in diseases

Research about the cruelty of female infanticide

   26. Socio-economic analysis of reasons for female infanticide and foeticide

Solutions to problems faced in public transport

   27. Passenger transportation problems
   28. Alternative for urban mass transportation project

Study of socially relevant current student issues

   29. Problems due to rapid increase of technical educational institutions
   30. Internet addiction and its effect on student behaviour
   31. E-mail hacking by college students
   32. Children as victims of cyber-crime
   33. Influence of media and television on crime

Research into the sufferings of transsexuals and sex workers

   34. Socio-economic, physical and psychological problems of sex workers

Analysis of Periyar's thoughts on the eradication of untouchability

   35. Analysis of Periyar‘s views on Untouchability


                                       4
1. Socio-psychological problems                       faced      by     migrant
labourers as HIV/AIDS patients *
Volunteers who were interested in serving HIV/AIDS patients were absent in the
years 2001 or earlier. The social stigma associated with the disease was so strong
that no volunteer would work for them.

So, in the year 2001 I took up a project with TNSACS (Tamil Nadu State
AIDS Control Society) and under this project I met over 100 migrant
labourers affected with HIV/AIDS in the Tambaram Sanatorium. I
discussed their problems, came to know their histories and authored
the book: "Love. Life. Lust. Loss : 101 Real Life Stories of Migration and
AIDS." The book is enclosed.

We studied the levels of knowledge and awareness relating to STD/HIV/AIDS
existing among the migrant labourers in Tamil Nadu; and their attitude, risk
behavior and promiscuous sexual practice of migrant labourers. This study was
mainly motivated from the data collected by us of 100 HIV/AIDS infected persons
who belonged to the category that comes to be defined as migrant labourers.
Almost all of them were natives of (remote) villages and had migrated to the city,
typically, ―in search of jobs‖. We have noticed in our study as to how,
starting from small villages with hopes and dreams these people had
set out to the city, only to succumb to various temptations, and finally
all their dreams turned into horrid nightmares. Our research included
probing into areas like: patterns and need of migration to get work,
vulnerabilities and risk exposure in an alien surrounding, ‘new’ sexual
practices/ attitudes, access to health services, experiences and
understanding of stigma and discrimination, effect of displacement,
coping mechanism etc.

We also study how the new economic policies of liberalization and globalization
has affected people to lose their traditional livelihood and sources of local
employment, forcing them into migration. Our study has been conducted
among this informal sector mainly because migrant labourers are more
vulnerable to HIV/AIDS infection, when compared to the local
population for reasons which include poverty, powerlessness,
inaccessibility to health services, unstable lifestyles such as insecurity
in jobs, lack of skills, alienation from hometown, lack of family
binding. Moreover, migrant labourers are also not organized into trade unions, as
a result of which, they are made victims of horrendous exploitation: they are paid
less than the minimum wages, they don‘t receive legal protection, they are unaware
of worker‘s rights issues, and essentially lack stability.




*For more refer: Books Sl. No. 11 and 13, Combined Research Papers No. 63 and 67,
Conference Papers No. 183, 207, 212, 224, 274, 293 and 307
                                        5
2. Dissemination of information and awareness of AIDS*
Today’s biggest challenge in the health sector faced by the nation is the
control of the spread of HIV/AIDS infection among its citizens. We
should not neglect this threat like Africa did. Currently it faces a
terrible crisis on all fronts because of this problem of uncontrollable
spread of HIV/AIDS. So it is important that the government takes strong
measures to prevent the spread of HIV/AIDS. One of the basic method of
prevention lies in making the people aware of this dangerous disease, which has no
cure at all. The awareness can be made through use of alternative media and
regular features like advertisement in dailies, T. V. shows, skits and dramas,
posters in buses and other forms of transport. We have analysed the best methods
using fuzzy theory. As a first part, to tackle this problem we formulated a linguistic
questionnaire. We made 150 people, mainly from rural areas, including NGOs,
doctors and social workers from that area to fill in the questionnaire. The
questionnaires of illiterate respondents was filled out by us. As a result of our
study, we derived the following conclusions.

Out of the 150 interviewed 123 of them felt that the awareness of HIV/AIDS should
be through small skits in television. Some 115 of them felt that street theatre and
puppet shows can aid a lot in the dissemination of information pertaining to
HIV/AIDS. A large section of them emphasized that the whole presentation must
not be in a serious or gloomy/threatening way, but the message should be said in a
lighter vein. They feel that instead of immediately provoking a negative response,
comedy could elicit them to think it over again and again. Around 88% of the
respondents felt that if popular actors/ actresses conveyed the message
of safe habits in cinema/ television, the effect on the viewers would be
more significant. Over 65% felt that songs about HIV/AIDS could also
help a great deal in making the rural masses knowledgeable about
these diseases.




*For more refer: Books Sl. No. 23 and 24, Combined Research Paper No. 77 and
Conference Papers No. 183, 200, 212, 224, 294, 308 and 323
                                         6
3. Street children and AIDS prevalence*
It is estimated that there are 60,000 street children in Vijayawada. Further
statistics from the Andhra Pradesh State AIDS Control Society indicate that 3.6%
of the HIV positive cases occur in children under 14 years of age. Several spine-
chilling information about their general life and habits are narrated.

In our study we are not interested in going into their lives or behaviour
or their ignorance. We are mainly interested in analysing, what has
driven them out of their homes? What is the role of the nation/
politicians? Why does the law remain imperfect in rehabilitation of
these children? What is the problem in the functioning and modelling
of the Juvenile homes that causes these children not to stay there?
Does it confirm that children are not vote banks?

These children are innoncent lot who have inherited the stigmatised disease from
their parents and for no fault of theirs, they suffer discrimination and ill-treatment
from others. Also, some of these children become infected by HIV/AIDS due to
their bad habits even before they reach the age of 20.




*   For more refer: Conference Papers No. 200, 224 and 235
                                          7
4. Allocation of funds for HIV/AIDS prevention and cure*
The allocation of funds for the benefit of the HIV/AIDS patients is a sensitive issue.
For, the expert cannot arbitrarily allot money to several heads like
creating awareness programs for uneducated rural women, drivers
and agriculturists, HIV/AIDS affected children, children orphaned due
to HIV/AIDS parents and so on and so forth. Also the type of programs
scheduled to be given in radio or T.V or posters on buses, autos etc., or
advertisement through newspapers or awareness education etc., what should be
adapted to which group must be decided. We for the first time use the
transportation model to analyse the allocation of funds to HIV/AIDS patients.

Using the Vogel‘s Approximation Method we arrive at the following conclusions. In
rural areas maximum amount is allotted to create awareness among uneducated
women through T.V and radio only. For this will benefit 1,92,000 women if
Rs. 24 lakhs is spent on awareness by T.V/radio. Likewise by spending
Rs.22 lakhs for HIV/AIDS affected children, 1,76,000 children will be
benefited. Here we give the amount to be spent, the mode of awareness
program and the number of people who are benefited by it.




*For more refer: Ph.D. Thesis of T. Johnson, Conference Papers No. 200, 294 and
303.
                                         8
5. Community Mobilization for HIV/AIDS and Women's
Empowerment*
This analysis deals with the study of generating Women‘s Empowerment as the
right force behind an active community mobilization using Fuzzy Associative
memories (FAM) model. We further look into the aspects of how such a social and
economic empowering of women could give rise to better prevention and care
programs relating to the AIDS epidemic.

In this study also a field work was carried out by me with my students.
We visited the hospital in Tambaram for HIV/AIDS patients and met
the women patients and gathered their problems which is used in our
study. It is very sad to note that most of these women patients lived like
orphans with no one to take care of them. Several of them were
terminally ill.

Out of the 100 women patients interviewd by us, 97 of them were infected by their
husbands who were HIV/AIDS patients, which only brings to light two factors: first
the careless attitude of men and second, the ignorance among women about the
disease.

These information was analysed using fuzzy models and published as a
book by TNSACS (Tamil Nadu State AIDS Control Society) entitled
"Women.Work. Worth. Womb" enclosed with this. This book is for free
distribution.




*For more refer: Books Sl. No. 16 and 18, Combined Research Papers No.32,
Conference Papers No. 195, 303 and 308.
                                        9
6. Teaching about AIDS to school-children in a non-school
environment*
The issue of HIV/AIDS is a much talked about and several of the educators have
agreed that it should be taught in schools as part of the school curriculum. The
question is how much of this is mentioned and discussed in schools? The subject
may crop up in the language classes as a topic for essay writing. It may be in the
Biology class as a research topic and how much of it is mentioned in the Health
science lessons? Teachers are inhibited when it comes to mentioning this issue let
alone discuss it.

Thus to make school children aware of HIV/AIDS is very difficult in the classroom
or in the school atmosphere. Meeting youths and youth leaders of some schools
and representatives of classes above eight standard we derived these suggestions
from them.

The meeting with them was analyzed using fuzzy theory as this concept is a delicate
one involving a lot of emotions or feelings and the following suggestions are
derived:

      1. Youth participants were not inhibited and willing to learn about
         HIV/AIDS only in non-school environment with the classes
         handled by an expert and not by a teacher of the same school.

      2. The absence of their teachers gave more involvement and free
         expression of these students.

      3. Group discussion with experts made them free to ask their
         doubts regarding HIV/AIDS.

      4. Most of them felt that interactions in the non-school
         environment like regular lectures, workshops, seminars, talk
         and video shows can educate them about HIV/AIDS.

      5. Devoted teachers can alone bring out the best from these school
         children.




*   For more refer: Conference Papers No. 200 and 207
                                          10
7. School dropouts and the child labour problem*
The child labour problem is the highest form of slavery and the first human rights
issues to arouse international concern. Yet according to the latest census
reports of 200 million Indian children in the age group of 5 to 14 about
11.3 million are labourers. In fact, over 60 million child labourers in
India work in carpet, bangle, matches, firework, and pottery making
industries and as a domestic helps. The carpet industry alone has
3,00,000 children working in it. A close look at the child labour
situation in Delhi show that of the 3 million children in the age group of
6-14 years, a million are child labourers of which 2,00,000 work, as
domestic help and almost an equal number are bonded labourers. To
everyone‘s knowledge, no proper measure is taken legally or even humanly to save
these children. A major reason is that because of the lack of political will and
inaction mainly because children are not vote banks. The motivation for the
application of fuzzy set theory to the design of databases and information storage
lies in the need to handle imprecise information. The database can accommodate
imprecise information, can store and manipulate not only precise facts, but also
subjective expert opinions, judgements and values specified in linguistic terms.

The approach to child labour is often status-quoist, and at other times
casteist, and no political group is willing to divert its energies towards
the solution of this problem. While India’s communist parties blame
child labour solely on poverty, the right-wing parties have at times
expressed the view that child labour is essentially skilled labour that
has to be utilized. NGOs and other volunteer organizations, of course, have their
intervention and rescue programs; but unfortunately not all NGOs working
towards the eradication of child labour are above board, some of them pump up
the figures, in order to obtain substantially greater amounts of funds. While this
haunts the child labour problem, we decided to study the lives of child labourers, in
order to comprehend the larger social problem, i.e. child labour. We chose to study
child labourers who are employed in restaurants, hotels, teashops and other eatery
joints. For the purpose of our study, we have selected a sample of 29
children from the age group of 11 to 14 years who are employed in small
teashops and mini-hotels in Kasimedu in Tamil Nadu. We queried into
their backgrounds, their ambivalence towards education etc. We found out among
our sample that only five of the children weren‘t interested in reading; for the rest
of them education was stopped due to poverty. The children, on an average, work
for ten hours a day. They also mentioned pathetically that their earning was crucial
for the sustenance of their families. Among the 29 children interviewed, 27
belonged to the oppressed dalit community and 2 were from the Most Backward
Castes (MBC). Their earnings were meager and ranged from Rs.20 to Rs. 50 per
day. We have used Fuzzy Associative Memories to analyse this problem and
derived interesting conclusions.


*For more refer: Post-graduate Research Project No.30, Combined Research Papers
No. 40, 45, 48 and 64, Conference Papers No. 128, 197, 269, 273, 304 and 315
                                        11
8. School dropouts in primary education*
We use Fuzzy Cognitive Maps to study the dropouts in primary education. We
construct a teacher-student-model in primary education using some basic nature
of teachers-like devoted teacher, trained teacher, untrained teacher, friendly
approach of the teacher towards the student etc. In primary education,
teachers play a major role, in not only creating interest in small
children but also vitally affect the dropouts in primary education. By
using the Fuzzy Cognitive Maps we obtain the hidden pattern of the cause for the
dropouts in primary education. The hidden pattern cannot be found out using any
other method.

Secondly we also construct a parent-children model to study dropouts
in primary education using Fuzzy Cognitive Map. We have constructed
this model using the following concepts: namely, the educational status
of the parents, economical status of the parents, fee structure and
inability of parents to teach their children in a language alien to them
and analyze how they affect dropouts in primary education. We present
the opinion of two experts. The main aim of the study is to find the cause of
dropouts in primary classes, which seems to be a major problem, as it largely
affects the literary percentage of our nation. We analyse the cause of dropouts and
the parents role in denying a child even a primary education. To achieve this we
construct a FRM model; as the data under analysis is an unsupervised one we felt
only FRM can give us the hidden pattern of the situation. The main causes for the
dropouts in primary schools are:

1. Poor economic condition of the parents.
2. No school in the neighbourhood with less fees.
3. Language problems
4. Uneducated parents who are unaware of the value of education.
5. No proper counselling given to the poor and uneducated parents by the teachers
or social workers about the need of the basic primary education and the unknown
harm they are doing to their children by denying them education.

We suggest that education should be made free at least for the very poor in the
schools in their locality.

The motivation for the application of fuzzy set theory to the design of databases
and information storage lies in the need to handle imprecise information. The
database that can accommodate imprecise information can store and manipulate
not only precise facts, but also subjective expert opinions, judgements and values
that can be specified in linguistic terms. This type of information which is quite
useful is for the first time applied by us to study the child labour problem, as this
problem is one of the vital problems of the nation as one is not able to precisely say

*For more refer: Post-graduate Research Project No. 43, Combined Research Papers
No. 30, 59, 65 and 80, Conference Papers No. 128, 130, 197, 238, 269, 273, 292, 299,
304 and 315
                                         12
why children are used to do work when they should be given basic education and
should be free to enjoy life. The various reasons spoken for child labour are
very vague like poverty, lack of motivation in parents, absence of
school, hereditary job, uneducated parents, drop outs in schools and so
on and so forth, but one is not able to precisely pinpoint the cause of child labour.

This fuzzy database model and its associated fuzzy relation algebra obtained by us
contain opinions of a group of experts about child labour. We use Computer coding
(SQL statements) to program the tables using fuzzy relational equations. As our
approach to study the child labour problem is using fuzzy database and since our
results are derived not only using the statistical data but also equal weightage is
given to the ‗feelings‘ as to why child labour is practiced we think that our
conclusions would be better than the ones found out by analyzing only the
statistical data. We see that school dropout rates and child labour go hand in hand.




                                        13
9. School dropouts and its relation to migration*
By the term dropout we mean children who discontinue their studies in the middle
from the standards 1 to 8. The increase in school dropouts is very steady, many
reasons can be attributed for it. The major reasons for school dropouts is
the poverty that the family faces and no proper motivation about
studies to children by the teachers. Further no necessary action is taken by
the government to stop or even lessen the number of school dropouts. Now we
view the school dropouts and its relation to migration. For we see majority of the
school dropouts (also school goers who drop from school and go to work) in
Mudianur village near Kallakurichi, Villupuram district migrate to Kerala for
labour. They labour in summer and come back to their village in the rainy season
because they do not have any work in the rainy season. These school dropouts who
are in the age group from 10 to 15 are vulnerable to several bad habits which will
directly affect their health. After migration they find it difficult to adjust with their
society and family for they lose respect when they work in different states.

The rate of school dropouts in rural India is only in the steady increase.
The major reasons attributed for this are globalisation,
industrialization, modernization and above all commercialisation of
school education. The schools and school education in Tamil Nadu have become
centres of investment of black money and a place of easy earning. Majority of
individuals become rich overnight by establishing a school. These schools in urban
areas are mainly for rich and people shun building schools in rural areas for these
schools with their fee structure cannot survive in rural areas. Thus private schools
in rural areas are rare and the government schools in rural areas function with
least number of teachers. The government does not take steps to educate the rural
poor, for rural poor are expected to work for the rural landowners. Thus the
dropouts in rural areas are very high, that too among the poor. This is established
using the fuzzy relational equations and neural networks.

The major observation from our analysis reveals the dropout has a strong impact
on the classroom atmosphere teacher‘s attitude and the school mission.




* For more refer: Combined Research Papers No.40, 59 and 80, Conference Papers No.
115, 208, 238, 292, 299 and 333
                                          14
10. Study of performance aspect of the school children*
A rule-based control system depends largely on the availability and the
performance of the rule base. When there are no experts available at hand to
supply knowledge about any problem, rule based control system can be used. We
are the first one to apply rule based control system to study the performance aspect
of the school students. By performance aspects of school students we don‘t mean a
student getting full or good percentage of marks or becoming eligible for a
professional course.

By performance aspects we mean the students life after the completion of his
education and later his position in society, i.e. his overall personality like moral
integrity, love for the nation etc. The teacher is used as the controller or control
actions (i.e. how best a teacher should be, bad and good nature of the teacher is
used) to mould a student to possess atleast more good qualities than the evil ones,
i.e. whether the students presence is advantageous to society or disadvantageous to
the society or is it indeterminable. To achieve this the input is taken as the
student nature and teacher is taken as the control process and the
outputs give the student’s position in society after he is settled in life.
The output seems to be heavily dependent on the teacher who is used as
the control process.

We infer from this study that a devoted teacher with good moral values and
understanding of the student‘s nature can certainly produce in future responsible
citizens in contrast to teachers who have no devotion to work and no interest in the
profession who works solely for money can at large produce citizens who could be
dangerous to society.




*For more refer: Post-graduate Research Projects No. 32 and 43, Combined Research
Paper No. 65, Conference Papers No. 130, 269, 315 and 334.
                                        15
11. School dropouts among female children*
We studied the cause for the school dropouts among female children using Fuzzy
Associative Memories (FAM). This study is carried out by taking a sample of 100
female children from 40 villages near Kallakurichi. They are in the age group from
5 to 13 at the time when they were stopped from their school education. Most of
them claim that the major reasons for this are: poverty, no school
facility in the nearby area, family circumstances, responsibilities at
home, uneducated parents who do not know the value of education, no
stable job for parents and the consequent migration for the sake of
livelihood, a feeling after all why should a female be educated as the
parents are basically uneducated and orthodox; and they do not know
the value of education. Because of male ego, they think that women are
inferior and they do not need education and so on.




*For more refer: Post-graduate Research Project No. 19, Combined Research Paper
No. 29 and 80, Conference Paper No. 111 and 292
                                       16
12. The plight of rag picking children working in Chennai*
The immense increase in the number of rag pickers in the Madras city
is alarming. Even in a particular area of the city we find over 3000 rag
pickers. (The number of rag pickers is dependent on the area: residential or
otherwise). We have interviewed over 100 rag pickers from north Madras. It is
unfortunate to note that rag pickers are not only small children who are runaways
but several families do the job of rag picking. We are worried more about the risks,
which they are exposed to while doing this job. Further these rag pickers suffer
from several diseases because of their profession. They sleep in dingy pavements,
on the roadsides, amidst sewers, with pigs, and dogs and live a life in the
wretchedness of poverty deprived of any material comforts. This has forced us to
analyze their problem.

The difficulties faced by rag pickers in Madras city are multifold. They
choose this profession for their livelihood due to acute poverty or run
away from home or no education, or frustration or it is the only self
employment etc. Once they are in the profession of rag picking they face still
more problems by the police, by the public, by the middle men, by the other rag
pickers and so on. Apart from these problems they face acute health
hazards, no proper place of sleep, exposure to evils of society (like
ganja addiction, alcohol, smoke, sex, etc.), which are forcefully
imposed or thrust upon them due to their profession as rag pickers. All
the problems associated with them be it social or economic or psychological no one
can attribute a specific cause for it, we see the very problem involves lots of
uncertainties and ambiguities so the data associated with this is only an
unsupervised one; we are at the outset justified in using fuzzy technique in general
and FCM in particular. We derive 10 attributes by interviewing over 100 rag
pickers and these attributes are divided into overlapping blocks of size 4 and then
we adopt the overlap block FCM to obtain the following conclusions.

      1. The police exploit the rag pickers, for they find it easy to register petty cases
         of theft etc., falsely.
      2. The health hazards faced by them is very acute. Most of them suffer from
         seasonal fever, malaria (due to mosquito bite) and other skin ailments due
         to very bad hygiene and sanitary conditions.
      3. These children become easy victims of all bad habits and become real
         criminal due to misuse and bad company.

Unless some sympathetic/understanding social workers help them
with good guidance and protection they will die at an early age for they
are unaware of any health problems they face due to their profession.
They do not know the means to save or use properly the money they
earn by rag picking. Unless public and government take a sympathetic stand
and help them nothing much can be achieved.


*   For more refer: Conference Papers No. 282, 302, 306, 327, 330 and 336
                                            17
13. Study of bonded labourers in rice-mills*
The freedom of every individual is his fundamental right. The freedom
from not being slave to another individual is still more important and
we, in the 21st century after over 60 years of independence, see bonded
labour not only of individuals but also shockingly as families. So, we
have taken up the study of the problem of bonded labour using the tool of fuzzy
relational equations. We choose to use fuzzy theory mainly to bring out the
unscrupulous nature of the individuals who have enslaved several families, mainly
their mental make up, socioeconomic and cultural identities and above all their
ethical values.

On the other hand, we also take into account the mental, physical and
psychological suffering inhibited in the minds of the labourers. We have taken
as the sample from over 1000 families of bonded labourers living and
working as bonded labourers in rice mills in and around the Red Hills
Area. It is a shocking information to see that roughly 1630 children
work in rice mill industry of which 40% are in the age group 6-14 years
and even basic primary education is denied to them. It is sympathetic
to note that these families have become bonded labourers for cost as
less as Rs. 5000. So the children have become slaves and possession of
them in true sense.

Thus bonded labourers breed child labourers in an exponential way. It is a pity that
the Government only frees some bonded labourers but never gives them any form
of alternate employment which leads them to die of starvation.




* For more refer: Combined Research Paper No. 62, Conference Papers No. 272
and 283.
                                        18
14. Study of brick-makers working as bonded labourers*
The study of brick makers who work as bonded labourers in places around Chennai
viz. Ponneri, Koyambedu, Chengelpet and Cuddalore has been carried. For this
purpose we interviewed 105 bonded labourers. They have been bonded only
for a six-month period (January to July) with an entire family working
for Rs.7, 000 to Rs.10, 000. This money is not paid back to their
owners, but instead they do an indentured labour for a period of six
months.

The interest rate for the above sum is collected by making extra bricks, i.e., for
every 1000 bricks they have to make an extra of 50 bricks. The main reason for
them to have become bonded/indentured labourers is agricultural failure, poverty,
illiteracy, family debts and unemployment/under employment. They labour for
over 10 to 12 hours, including the night duty from 11 p.m. to 6 a.m. with
Sundays and Mondays as holidays. They suffer from skin ailments,
fever, cold and allergic diseases, which remain untreated. We use six
experts’ opinions and use weighted multi-expert neural networks and
arrive conclusions based on our study.

Governmental neglect is the root-cause for bonded labour. If the government
ensures that these labourers are provided with some kind of job security and
ensures that the gap between the haves and the have-nots is reduced, certainly a
better situation will be faced by these bonded labourers.




* For more refer: Conference Papers No. 301 and 333
                                       19
15.Tribals in          Kodaikanal            forests    who      are     bonded
labourers*
The bonded labourers near Kodaikanal (Mulayur) are tribals, who were once the
owners of the forest. Due to untold reasons these lands are being owned by Nadars
and Chettiyars, under whom these tribals work as bonded labourers. We
interviewed 80 families from this village. Of these only 50% of them
had government given huts, which comprised of a single room. These
bonded labourers worked over 8 hours a day. Their main duty was to
work in the farms and forests owned by chettiyars and nadars, none of them
have entered the school premises and the child labour is at its peak. Their work was
at odd places, which prevented them from having lunch. They ate twice a day,
which was not a square meal in the morning and in the night. Their pay as daily
wage was partly less than Rs.50, which was insufficient to make both, ends meet.
As the data is an unsupervised one we are justified in using fuzzy theory in
studying their living conditions.

The only solution for the problem would be to study how the
landowners and sons of the soil, the tribals became bonded labourers
and how the Chettiars and Nadars became the owners of the land of the
tribals.




* For more refer: Conference Papers No. 206, 305, 324 and 337
                                        20
16. Control          of    atmospheric          pollution       by     chemical
industries*
The main source of pollution of the environment is chemical plants. Carbon
monoxide, nitric oxide, etc. are some of the factors of pollution from chemical
industries. The maintenance of clean and healthy atmosphere makes it
necessary to keep pollution under control. We use fuzzy control to
minimize the waste gas pollution in environment by oil refineries,
cement industries, dyeing industries, leather industries.

The main observation is that the owners of these industries are least bothered
about the environmental pollution but they are only interested in making
maximum profit. In most cases, while planning the industries, no importance is
given about the wastes produced by it. This is one of the reasons for the high
percentage of pollution.




* For more refer: Ph.D. Thesis No. 6 and 7, Combined Research Papers No. 27, 28,
31, 42, 51, 58 and 73, Conference Papers No. 129, 139, 150, 151, 166, 178, 184, 194,
201, 214, 233, 298, 322 and 338
                                        21
17. Development of long-range planning for a chemical
plant*

The productivity of chemical plants depends greatly on their
production schedules. But the production schedule is mainly
dependent on production time. So the scheduling of production time is
particularly important in chemical plants. Chemical plants can be divided
into two categories from the viewpoints of their production schedule, they are 1,
Multiproduct chemical plants and 2, Multipurpose chemical plants. Here we
model and study only production in multi purpose chemical plants.

In multipurpose chemical plants each operate for multiple products carried out
with their own distinct equipments model sequences through the chemical plants.
But the production time, period of production schedules of
multipurpose chemical plants is more complicated, because the time
period of production may vary, hence the time period of production
scheduling is an uncertainty. As the model is a complicated one and
uncertainty of both time and productivity prevails we are justified in adopting fuzzy
set theory in general and fuzzy linear programming in particular in scheduling of
the chemical plants.

The acceptable production flexibility and acceptable production time are
determined by fuzzy set theory based on equipment models. By this approach we
maximize the flexibility of production and minimize the production time.

Chemicals include raw materials, intermediates and products that may be
purchased from and or sold to different markets. The main decision problem is the
selection of process from among competing technologies and subsequent timing of
process expansions. Also it is important to determine the optimal production levels
for the installed process. The decision maker would like to maximize the net
present value of the project over a long-range horizon consisting of a finite number
of time periods. The net present value dependent on demands of chemicals,
investments and operating cost of the processes, material costs, product prices,
product demands and market demands. The demands of chemicals material cost
etc., can vary from time to time. So we consider these as uncertainties and
use fuzzy linear programming techniques and obtain a model and study
the long range planning process for the chemical industries with a view
to maximize the net present value of the project. By this method, we are
able to overcome the usual problem viz., the inability to predict tight bounds.




* For more refer: Ph.D. Thesis No. 6 and 7, Combined Papers No. 21, 24, 41 and
50, Conference Papers No. 82, 83, 98, 105, 106, 118, 120, 137, 147, 155, 169 and 170
                                        22
18. Occupational hazards in textile industries*
With an ever-increasing demand for a comfortable living in recent days the
number of industries are on the increase. Several industries like cement industries,
chemical industries, textile industries etc., serve mainly for comfortable living. The
transition from manually built hut to multistoried buildings and like changes have
not only increased the number of industries but also increased the occupational
hazards faced. We only concentrate on the occupational hazards faced by
workers at the textile industries; by conducting a sample survey of the
health problems faced by the workers and their family members. A
survey was done by collecting the data from 50 families mainly weavers in textile
industry; to this collected data Fuzzy Cognitive Maps (FCM) were applied. Equal
weightage was given to everyone by taking the combined FCMs.

The survey consisted of not only the workers but also all the family members who
lived with him. From the survey the following results were derived:

    1.   Most of the workers and their family members suffer from either Asthma
         or Allergy cold or TB or from frequent attacks of Cold,

    2. Only a very few or negligible less people suffer from Lung cancer. Here if
       they had the habit of smoking we did not take their problem due to working
       in the factory,

    3. Another strange ailment was nose block and throat infections, which were
       also a frequent problem, faced by them.

    4. The external problems faced by them were skin ailments.

The number who suffered from skin problems among weavers was less
than the number of weavers who faced respiratory problems. Thus our
sample study made it clear that the major occupational hazard faced by
weavers was respiratory problems. We suggest that the employers give
information before hand, to the workers about the occupational hazard so that they
can take precautionary methods before they become a victim of the occupational
hazard.

In our society, the employers never give the employee any health advice of the
hazards which they will be prone to because of doing the job. This is very special to
India. The nation must respect the poor employee only then such health hazards
can be prevented.




* For more refer: Post-graduate Research Projects No. 35 and 47, Combined
Research Paper No. 34, Conference Papers No. 166, 168, 181, 184, 205, 332 and
338
                                         23
19. Health hazards associated with solid waste disposal*
The solid wastes disposed from hospitals, chemical industries, plastic industries
and leather industries can create chronic disease, accidents and infections if not
disposed properly. But in India nobody bothers about the disposal of the
solid wastes from these five primary sources. Further the first and foremost
affected persons because of these improperly disposed wastes are children whose
living is by rag-picking.

Secondly the government employed scavengers whose job is to dispose these solid
wastes from one destination to another. Recycling of these solid wastes too
carry health risks if proper precautions are not taken. Workers
working with wastes may experience toxic reactions. Disposal of health
care waste requires special attention since it can create major health hazards like
Hepatitis B and C, through wounds caused by discarded syringes as the children
may sustain injuries and come in direct contact with these infectious items. Certain
chemicals if released untreated can cause death. Some studies show these
chemicals can cause cancer to residents exposed to hazardous waste.
Many studies have been carried out about the influence of the hazardous waste on
the health.

We adopt multi-fuzzy neural network method to study these problems, as the most
affected by these wastes are the poor, the poor children employed, as rag pickers in
contrast to these persons who produce the hazardous wastes are industrialists and
rich class people. Since it involves lots of inexpressible concepts and feelings, we
feel it appropriate to use neural networks to analyze them.




* For more refer: Combined Research Papers No. 34, 42 and 51, Conference
Papers No. 152, 158, 181, 178, 184, 201, 204, 205, 214, 228, 293, 298, 314, 322 and
332
                                        24
20. Study of the prevalence of tobacco related cancers
among rural men*
Howard K. Koh, Christine Kannler and Alan G. Geller have studied about tobacco
related cancers in the United States of America. They claim that tobacco and
tobacco smoke contains at least 4000 chemicals of which 55 are known
carcinogens identified by the International Agency for Research on Cancer.

In our research study we have investigated the relation between use of
tobacco and cancers of tongue, salivary gland, pharynx, larynx and
lungs of 121 male patients from rural areas who belong to an
economically poor status. Of these 121 male patients, 36 suffer from tongue
cancer, 8 suffer from salivary gland cancer, 24 from pharynx cancer, 40 from lung
cancer and 13 from larynx cancer. All the 121 of them had used tobacco both as
cigar and spit tobacco (The term spit tobacco is used for both snuff and chewing of
tobacco as it requires continual expectoration. We also call snuff and chewing
tobacco as smokeless tobacco). Of the 121, 60 of them acknowledged that they had
used tobacco and snuff. These men were agricultural coolies from the near-by
villages of Tanjore; they were taking treatment from the Tanjore Medical College
Hospital. The use of tobacco by them is social and psychological problem as there
is no rhyme or reason for using tobacco products we are at the outset justified in
using Fuzzy Cognitive Maps (FCMs) to analyse it. Now using FCM we analyse the
types of cancer they suffer due to use of tobacco. Also we analyse the cause for
using smokeless tobacco and cigars. The smokeless tobacco is mainly used
as an addiction to keep themselves dazed and free from hunger (due to
poverty they cannot afford even a square meal a day) and do the work
mechanically without any problem. On the other hand the agricultural
coolies who use cigars do it as a masculine identification and they are
mostly persons with all bad habits.

Further from our study we suggest that these persons must be tested for other
types of cancer also. For these cases were reported to suffer only from one type of
cancer but it may be most likely they may certainly suffer from more than one type
of cancer. So it is suggested that they are scanned for all the tobacco related
cancers though they only suffer from one of them. Further the tobacco related
cancer can be completely eradicated by banning the use of tobacco.




* For more refer: Combined Research Paper No. 84, Conference Paper No. 314
                                        25
21. Socio-economic problems of cervical cancer patients*
We analyse the socio economic problems related with the cervical cancer patients
using Bi-directional Associative Memories Model (BAM model). We have
interviewed over 260 cervical cancer patients using a linguistic questionnaire from
the Tanjore Medical College Hospital. This linguistic questionnaire was
transformed into BAM model.

From the BAM model we see the major reason for the cervical cancer is
due to lack of genital hygiene in both partners, social and economical
conditions, several sex partners, early marriage and poverty. We, using
the same attributes form the Fuzzy Relational Maps (FRM) and compare them with
BAM and derive the following conclusions and results. Our sample study is mainly
based on economically and socially backward women. Further most of them were
coolies married at a very young age and we could conjecture that due to their
profession and social set-up they must have had prolonged period of sexual
activity. Unless women are economically and socially empowered the increase in
the number of cervical cancer patients cannot be reduced. Further only economic
empowerment can make them self-sufficient and insist on genital hygiene of their
partner.

It is further suggested that the government should take steps to offer
women in the age group 30-65 free periodic screening tests for
deduction of cervical cancer so that they do not become chronic
patients, and enable them to take treatment at the appropriate time.




* For more refer: Conference Papers No. 297 and 232
                                        26
22. Analysis of the various pollution-related cancers*
Over-crowded vehicles, industries like cement industries, chemical industries, oil
refineries and cotton/textile industries form a basic pollutants of atmosphere in
Tamil Nadu. Modernization has resulted in pollution of atmosphere due to heavy
traffic. These pollutions lead to lung cancer, pleura, oral cavity, skin and bladder
cancer. Tobacco, smoke-pollution includes all the types of cancer expect skin
cancer. Now we using the data collected from Tanjore Government
General Hospital find the gradations of pollutions associated with each
type of cancer using Fuzzy Associative Memories (FAM) model for this is
the model which gives the resultants which can be graded in comparison with other
fuzzy models which give the ON or OFF state of an attribute.

It is surprising to see that from our analysis we are made to include the
pollution due to the spray of pesticides and insecticides that is also one
of the reasons for all types of cancer. For some of these agricultural labourers
who are not exposed to any form of pollution who are not Tobacco users are
affected by these types of cancers. So the chemicals sprayed as pesticides or as
manure must also be analyzed for the analysis of the blood samples of the
agricultural labourers to find the chemicals present is to tested for some of them
are carcinogenic.




* For more refer: Combined Research Papers No. 42, 73 and 84, Conference
Papers No. 214, 184, 233, 280, 295, 298, 314, 322, 332 and 338
                                        27
23. Study of depression in terminally ill patients*
In recent medical literature several authors have expressed the views
that many terminally ill patients are depressed or suicidal. Depressed
patients may be irrational. In most cases, doctors miss the presence of depression
and so do not realize these patients need special management. Since the very study
involves feelings that too very strong feeling and depression, we felt it essential to
model their problem using Fuzzy Cognitive Map (FCM). We have chosen 15
important attributes to study, some of the important ones are mentioned here as
follows: constant fear or anxiety of death of terminally ill, physical suffering, mercy
killing as a solution, right to die of terminally ill, counseling, loss of dignity and
independence, religion as an escape, unconcern of doctors or nurses, 6 to 58% face
depression, role of relatives, large doses of medicine which hastens death etc.
These are taken as conceptual nodes of FCM. The connection matrix acts as the
dynamical system and the hidden pattern of our study was obtained and we
derived the following conclusions:

    1.   Over 90% of terminally ill patients longed for solace from
         religion. Religious people could reduce the percentage of depression and
         expressed that such facility was not available it was highly costly. A
         mediocre person had no reach and only very few hospitals had such
         facilities.

    2. Very few sympathetic doctors showing concern for terminally ill were able
       to relieve depression and reassure peace temporarily.

    3. Their inability to be free and dependence on others and loss of
       dignity was the major cause of depression more than physical
       pain.

    4. Some of the medicines given to these patients may cause
       depression that angle must be analysed by doctors and necessary
       steps must be taken by them for the side-effects.

From the doctors view, several of them felt that to give the patients a peaceful
death and save them from the agony of pain they often had to administer large
doses of medicine which brought the patients closer to death.




* For more refer: Conference Paper No.196
                                         28
24. Personality-disease model in Homeopathy*
Homoeopathic medicines are given to persons largely depending on
their personality traits. For there may be several medicines for a
particular symptom/ disease but it is based on the personality, the
particular medicine is chosen. Personality does not imply only the physical
outlook but it also includes the total nature of the person like jovial, social,
temperamental, harsh, kind etc. In this dissertation we construct and study the
Personality Medicine model of a patient for Homeopathic medicine using Fuzzy
associative memories. The very term personality is an attribute and is a quality that
cannot be very precisely assigned a value for it varies from person to person, time
to time and circumstance to circumstance. For a person say a peon by profession,
behaviour at home would be entirely different from the office. At home he is a
bread-winner, at the office he is a peon.

To study the personality medicine relationship we have used fuzzy
theory in general and Fuzzy Associative memories (FAM) in particular
to analyze the problem. We have specifically chosen this for it is the
only tool which can give gradations between preferences. This research is
a very beneficial one if for each symptom each of these medicines are graded
depending on the personalities of patients.

But it is pertinent to mention only a good expert doctor alone can treat
because many of the medicines if given wrongly can create the disease
itself in otherwise healthy patients, so it is very very important to see
that before using a medicine if confirmation of the medcine and their
personality is made.




* For more refer: Post-graduate Research Project No.20, Conference Paper No. 112
                                        29
25. Use of fuzzy evidence theory to determination of
hidden patterns in diseases*
We study the symptom-disease model in children. We use Fuzzy Cognitive Maps to
obtain the hidden pattern existing between symptom and diseases.

We apply this mathematical tool because it allows experts to represent
factual and evaluative concepts in an interactive framework. Experts
can dissent or consent to the local causal structure and perhaps the
global equilibrations. It also allows us to encode the experts knowledge
or ignorance, wisdom or prejudice. We thus study the various
symptoms, and the corresponding diseases they indicate.

This study is mainly taken because children below 5 years do not know how to
properly express their health problems, they experience at the time of sickness. So,
it is the ardent duty of the doctors to spend lot of their time to find the symptoms/
disease in them for in several cases the wrong medicine/ diagnosis may lead to
death or kidney failure or liver problems.

The study is free from any prejudice as all experts are given equal weightage.




* For more refer: Post-graduate Research Project No.17, Combined Research
Paper No. 14, Conference Paper No.100 and 136
                                        30
26. Underlying reasons for female infanticide and
foeticide: A socio-economic analysis*
In our research we have analyzed and studied the cause of female infanticide in
India. Since the cause cannot be pin-pointed out for a particular reason or for some
reason we felt that the cause is mainly a vague one varying from people to people,
society to society and also depending on the social and economic conditions. Since
the data involved in this study can only be an unsupervised one we are at the outset
justified in analyzing them using fuzzy theory in general and Bidirectional
Associative Memories in particular.

We study and apply the BAM model to the problem of female infanticide. The main
conclusions derived from our study are:

   1.   The number of children seems to have no impact on the various sections as
        long as they are male children.

   2. In poor society, female infanticide is both direct and indirect i.e.
      the poverty plays a major role and these female babies die of malnutrition,
      starvation and lack of proper medical care: though they are born as
      very healthly children. Principally people consider the girl child
      as a burden to them and hence decide against bringing up the
      girl child.

   3. Women having inferiority complex is also one of the major reasons for
      female infanticide. The main suggestions are

                  i. The attitude of men towards woman must drastically change.

                  ii. Constitutional amendments should be made to protect and
                      empower the girl child.

                  iii. Women should be educated equally as men so as to
                       bring down the feeling of inferiority complex
                       prevalent among women.

                  iv. If the death of the female child is proved due to
                      unnatural reasons the parents and in laws must be
                      given severe punishment.

                  v. If the girl children are given some monetary benefit by the
                     state then certainly for the sake of money they may not kill
                     the girl child.



* For more refer: Post-grduate Research Project No. 19, Combined Research Paper
No.29, Conference Paper No. 111
                                        31
27. Passenger transportation problem*
We had studied the Passenger Transportation Problem using Fuzzy Mathematical
Tools and Java Programming with specific reference to the Metropolitan
Transportation Corporation of the Chennai city. We study the transportation
problem of passengers traveling in a bus between two fixed points under varying
constraints. We assume that the approximate number of passengers traveling
between every origin-destination pair, along any route in all services is given. To
determine the choice of the services, we develop a fuzzy reasoning algorithm
where, the fuzzy phrases are represented by the membership function as fuzzy sets.
A preference index value is chosen to determine the frequency of the services. We
model the problem where the basic input data are treated as Triangular fuzzy
numbers. Fuzzy optimization techniques are used to solve this problem.

We have mainly taken this problem as only middle class and poor people use this
mode of transportation.

Our aim is to achieve the goal or more precisely the fuzzy goal viz. To
maximize the comfort of the passengers in the Metropolitan Transport
Corporation (MTC). We try to analyze the fuzziness inherent in the
goals and in the constraints of the system under the following five
heads:

Maximizing the comfort.
Minimizing the cost.
Minimizing the travel time.
Maximizing the revenue and
Maximizing the frequency of the services.

Here, we treat our main goal namely maximizing the comfort of the passengers as
the core of the problem. We analyze this problem in two ways: First, by using Fuzzy
Cognitive Maps and then by using Fuzzy optimization techniques. In the first case
expert opinions are obtained by taking the main objective as the passengers
comfort. Using Fuzzy Cognitive Maps (FCMs), results are derived from the opinion
of the experts and the cumulative FCM is taken as the ultimate opinion. In the
second part, we use Fuzzy linear programming to obtain the optimal value bearing
in mind, the goal as to maximize the comfort of the passengers subject to certain
constraints. Finally, we derive our results by giving weightage to both the methods.

Specially written Java program for this fuzzy model makes the calculations
simple and easy. We have taken the direct help of the M.T.C. of Tamil Nadu
the public and several others which had made our research a success.


* For more refer: Ph.D. Thesis No. 4, Post-graduate Research Project No.22,
Combined Research Papers No. 10, 19, 20, Conference Papers No. 40, 43, 54, 57,
66, 75, 77, 80, 92, 110
                                        32
28. Alternative for an urban mass transportation project *
We study the potential benefit assessment and identification of the best alternative
of an urban mass transportation project. The vehicle miles produced by each of the
individual alternatives are given as constants. The basic input data are the capital
costs and the user savings. These numbers are often impossible to be estimated
with enough precision. Also there is uncertainty in the estimation of the future
benefits.

Fuzzy set theory is a convenient mathematical device with which we are able to
solve problems that involve uncertainty, ambiguity and indetermination. We
represent these input data as fuzzy numbers. Triangular Fuzzy Number (TFN) is an
easy way of expressing the input data.

On the basis of the economic criteria we identify the best alternative
from the examined ones as that which yield the maximum difference
between the total benefits and the costs; or alternatively, the system for
which the marginal benefits and the marginal costs are equal. By
varying the width of the triangular fuzzy numbers that represent the
user savings and the capital costs, both individually and
simultaneously, we obtain the best alternatives for every system of user
savings and capital costs.




* For more refer: Ph.D. Thesis No. 4, M.Sc. Research Project No. 22, Combined
Research Papers No.10, 19, 20, Conference Papers No. 40, 54, 57, 77, 92
                                        33
29. Large-scale problems arising out of the rapid increase
of technical education institutions*
At present there are over 2280 technical education institutions functioning under
the All India Council of Technical Education (AICTE). Every year several new
engineering institutions have been approved to admit new students. Thus the
increase in the number of engineering graduates is very disproportionate to the
need. The rate of increase in engineering graduates is alarming. In India alone
every single year roughly about 2,32,000 engineering graduates are produced apart
from 1,88,000 diploma engineers. All these 4 lakhs engineers are just fresh
out of college. Nobody among India’s education planners seem to have
thought about the following: Who is going to employ them? What are
their job opportunities? Are 4 lakh new jobs created every year?
Certainly not! If they remain unemployed, what will be their contribution to
society? How many of these frustrated persons will turn into educated criminals
and anti-socials? How many of them would become drug and alcohol addicts? etc.
Our policy makers of education have confused the concepts of technological
development and technical institutions. If we need to be a technologically
developed country, we can achieve that by producing a lesser quantity and higher
quality of students who will contribute to the growth of the nation. Large number
of engineering students is only a sheer waste of manpower. Thus the hazardous
increase in engineering colleges and polytechnics is going to be only a problem to
the nation.

Developed countries like U.S. have manpower departments that
estimate the number of job vacancies to be created over the years, the
fields pertaining to the vacancies and the number of foreign labor that
can be used to cope up etc. But our technical education system has not made
any such studies. In fact in the year 1998, there were 571 Engineering colleges and
1134 Polytechnics but as of today there are 838 Engineering colleges and 1224
Polytechnics. In these three years there is no need to have such a sharp increase in
the number of Engineering colleges because there is no corresponding increase in
the number of job opportunities. Privatization of education and several other
factors have made the running of engineering colleges into highly lucrative
businesses. The failed technical educational system is not going to provide any kind
of employment to these engineers. So based on all these data we have taken the
opinion of vice-chancellors, directors and engineering students themselves who are
employed and we use fuzzy model to study them. The important facts derived are:

   1. Suggestions are made that new engineering colleges must not be given
      approval by AICTE.
   2. There must be a larger restriction and restraint on the number of student
      sanction allowed to these Engineering colleges and Polytechnics.


* For more refer: Combined Research Paper No. 61, Conference Papers No. 194,
199, 271, 284 and 320
                                        34
   3. Technical Educational Institutions with political backing and those, which
      are run with the primary intention of making money, must not be
      encouraged.

According to the editorial dated 2nd August 2003 in the Economic and
Political Weekly (EPW), in Tamil Nadu alone over 21000 Engineering
seats will remain unfilled this academic year and over 30 colleges in the
private sector are in danger of being forced to close down. The editorial
further states that in April 2003, the Supreme Court had directed the state
government to create additional seats in medical and engineering to accommodate
those meritorious students in the open category affected by the 69% reservation
policy. According to the EPW there is an all too evident absence of coherent and
comprehensive policy direction. Taking these facts into account, we analyse the
situation of Engineering Education in Tamil Nadu using Fuzzy Theory.

We also further studied the present scenario of Technical/ engineering education
in the context of Government i.e. state controlled regulatory body, the All India
Council for Technical Education (AICTE) versus the Managements, which runs the
privately owned engineering institutions. The main attributes taken relative to the
Government regulatory body i.e., AICTE are

   1.   No proper scrutiny of the infrastructure of the institution is assessed by the
        body of inspectors from AICTE.

   2. Reports have often surfaced about how corruption rules the roost in this
      council and how bribes are taken in order to grant sanction for technical
      education institutions which are often run by politically or economically
      powerful.

   3. No proper assessment about the teaching faculty is done by the experts
      who visit from AICTE (untrained, just engineering graduates are employed
      as teachers).

   4. The cost spent by most students is disproportionate to their job
      opportunities (This concept is never discussed or given importance by the
      AICTE).

   5. Non-existence of Manpower Corporations/ Departments and no steps to
      give any information regarding any type of job opportunities.

   6. There is no equity in the distribution opportunities in a higher education by
      Government in general and Engineering education in particular.

   7. The AICTE has blindly given sanction to new Engineering institutions has
      made both students and the owners of the institutions in highly erratic
      condition.

   8. Several other points can also be taken under this head.
                                         35
The main attributes related with the persons who start the Engineering colleges:

           i.        Most of the persons who start the college are persons with
                     least knowledge on Engineering education.

           ii.       Their sole motive is profit. The institutional cost is minimal
                     and personal cost is maximal leading to degeneration in
                     quality maintenance.

           iii.      They cheat the government/AICTE by showing false quality
                     manpower to get sanction.

           iv.       As they have spent substantial money as bribe to
                     government/AICTE their main motive is to get back that cost
                     from students or run the college with minimum or non-
                     faculty that in turn has brought down the results drastically.

           v.        When results are poor the colleges do not get even enough
                     students to run the institution. For instance, there are over
                     two dozen engineering colleges in which the admission
                     hovers at the single digit level.

           vi.       We could also observe that government-run colleges function
                     better than the private owned colleges. This is sharp contrast
                     to the lame argument which supports privatization on the
                     basis that it creates better quality.




                                        36
30. Internet addiction and its effect on student behaviour*
Today‘s biggest hazard faced in the life of student community at large is the evil
effects of the Internet. When we use the term behaviour we are using it only as
attribute. Any sort of addictions in a student‘s life is a certain impediment to
improvement in any form. When visiting cyber café as customer we made a survey
and observed the following facts. First the cyber cafes promise ―100% privacy‖
anyone can be sure that intellectual pursuit or researching for study material by a
student needs no privacy. Secondly the key words in all these cafes is the fact the
customer is the king. So these two securities for the students have lead to do evil in
a most conducive atmosphere. Most of them come to the cyber café or Internet
parlour informing their parents that they had to send email or for chatting but in
reality they are busy over surfing the pornographic sites. The proof is seen from the
exponential increase of cyber cafes. The high rates of addictions of student’s
community to porn sites has led to a exponential increase in the
number of porn sites. Also this very increase in addiction among the
students causes several more perverted minds and accelerates the
decay in moral values. Police say putting conditions on these Internet cafes is
like wild goose chase. Parents and teachers must accept their helplessness.

Here we use fuzzy analysis and derive the following conclusions – The student‘s
behaviour changes with poor performance in studies, looks as if under hypnotic
spell or dream fantasy world, eye-ailment increase in eve-teasing, drug abuse,
sadomasochism, crime against female children, including rape and degradation of
the marital relationship. It also increases the condemnable activities like stealing
and misusing money and above all violence. The study suggests that as
Government cannot make any law to prevent it, this can however be stopped by
teachers, religious groups, educators, public administrators, youth themselves and
the public. For example, the public can stop such cafes from existing in their
locality if abuses of the Internet are sensed.




* For more refer: Conference Paper No. 193
                                         37
31. Study of E-mail hacking by college students*
One major problem in today‘s world of information technology that is faced by one
and all is: How safe are the messages that are sent by E-mail? Is there enough
privacy?

For if a letter is sent by post one can be certain that it cannot be read by other
person, other than the receiver. Even telephone conversations are most of the time
subject to a good deal of privacy. Even tapping or listening (overhearing) of phone
calls from an alternate location/ extension is only a very uncommon problem.

However compared to these modes of communication even though E-
mail guarantees a lot of privacy it is highly common practice to hack E-
mail. Hacking is legally a cyber crime but it is also one of the crimes
that does not leave any trace. The additional factor which makes hacking E-
mails one of the easiest work is the fact that it requires very less technical
knowledge and few details of the person whose E-mail account is being hacked.
Hacking of another person‘s E-mail account can be carried out for a variety of
purposes. We research and find out the factors that are the root cause for such
cyber crimes.

Some students do this merely for fun, some do it on inquisteness about their
classmates (mainly opposite sex) and some do it to entangle their own classmates
and there by hold some sort of power on them. Some students do it to retrieve
question papers from their teacher‘s/ department‘s computer. But whatever be the
reason it is an heinous crime should be tackled in a rationalistic and reasonable
way!




* For more refer: Conference Paper No. 193
                                        38
32. Study of children as victims of cyber-crime*
There has been an alarming increase in crimes over the internet. While it took 38
years for radio to reach 50 million people and television reached the same number
in 13 years; the internet touched this point in just four years. By the end of
2002, there are expected to be 800 million internet subscribers in the
world. According to predictions by the NASSOM, by 2003 there would
be approximately 23 million internet users in India alone. However, it
is unfortunate that on parallel lines there has been a rapid increase in
cyber crimes. A vast majority of the targets are women and children. So
we analyze the evils affected on children due to the unchecked rise in
the number of cyber criminals. We also deal with the consequences of
pornography, for studies have shown that over 60% of the websites have explicit
sexual content. An estimated 1,00,000 pornographic websites generate revenue in
the region of $1 billion annually. The worst affected by these sites are children who
not only become addicted to such sites but are also easily vulnerable to internet
stalkers and pedophiles.

Secondly women with education also fall a easy trap. They are blackmailed and
misused even by their own classmates and at times by their professors.

Crimes in the virtual world affect day-to-day life in the real world and
we find that often it is very difficult to recoup from the consequences of
cyber-crime for it causes disruption of lives. It is also clear that part of these
problems are caused because of various factors such as lack of parental
supervision/ guidance and at times because children themselves succumb to peer
pressure. Further, there is an urgent need for law to tackle the cyber-
criminals for as such the existing penal code is outmoded in its
application.




* For more refer: Conference Paper No.229
                                        39
33. Influence of media on crime*
The term media represents both print and electronic media. The effect of media
in committing crimes is analyzed in our research. For almost all the
movies and in television serials we see the murder, abduction, extra-
martial affairs etc. are done in a simple way without deep reason or
rhyme. An innocent but desperate person on seeing these crimes may
think he can commit the crime and go scot-free. For instance a MBA college
boy from Andhra Pradesh surrendered in Chennai for murdering his classmate due
to love failure. Two days later in the same style a college girl in Tiruchi was
murdered by a boy who wanted to marry her. Thus the media effect is seen from
Andhra Pradesh to Tiruchi. We analyze the effect of media's influence to
indulgence in crime using FRMs. For FRMs are the best tools when the data can be
partitioned and applying FRM to this problem we obtain the hidden pattern.

Further, we also see that media in many a case has played a role of havoc—for
when certain criminal acts are published the student's community instead of
feeling ashamed to practice violence, blindly imitates it, which results in loss of life.
The main reason which can be attributed to these crimes is that the
education does not impose in the minds of the students values in life so
they easily become victims who mainly act without reason.




* For more refer: Conference Paper No.325
                                          40
34. Socio-economic, physical and psychological problems
of sex workers
A study and analysis of the socio-economic, physical and psychological problems of
sex-workers had become very essential because of the prevalent myth in our society
that HIV/AIDS spreads mainly because of CSWs.

This was very clearly revealed when we made an analysis of the migrant labourers
affected by HIV/AIDS. Further, the men living with HIV/AIDS speak of the
CSWs not with sympathy or consideration or aloofness rather with a
kind of hatred. All the time they spoke not only ill of CSWs but bluntly blamed
the CSWs for infecting them with HIV/AIDS. Now, a very natural question arises—
how many of the CSWs were infected with HIV/AIDS because of the men (with
HIV/AIDS) who visited them?

The answer to this question is very sensitive, for when we interviewed migrant
labourers we could get a clear feedback that most of the men infected with
HIV/AIDS suffer from an odd psychological ailment, namely they wish to infect as
many women as possible with HIV/AIDS, that is why they don't go for protected
sex. The first person whom they experiment and willfully infect is their wife! This is
very clear from our study because 97% of rural women were only infected by their
husband. When these men are so vengeful and irrational with their own wives,
what will be their behaviour with the CSWs?

So we wanted to know the problems faced by CSWs. Most of the CSWs
continue in that trade against their wishes for the sake of livelihood.
They cannot refuse sex even to men with HIV/AIDS because they fear
the middlemen to whom they are accountable or entangled. So we have
ventured to study their problems.




                                         41
35. Analysis of Periyar’s Views on Untouchability *
For the first time, the social problem of untouchability, which is peculiar to India,
was studied mathematically. We used Fuzzy Cognitive Maps and
Neutrosophic Cognitive maps to analyse the views of the revolutionary
Periyar who relentlessly worked for more than five decades to secure
the rights of the oppressed people who were considered untouchables.
Our study is of great interest to human rights activists, socio-scientist, historians,
and above all, mathematics. This has been published as a book entitled ―Fuzzy and
neutrosophic analysis of Periyar‘s view on untouchability‖.

We have made such a study mainly because the social problem of untouchability in
India is a problem pertaining to the mind set of people so to study or analyze the
problem we have used mathematical models which work like the netweorking of
the brain. It is unfortunate to note that even 60 years after
independence, most of the riots or killings are due to caste clashes. The
study of the views of Periyar who was fighting for social justice and
equality may throw some good suggestions and solutions to
humankind.




* For more refer: Book No. 21
                                         42
 Research books published : 50
10 of the books are on Smarandache Algebra (Book Series) authored by me and
published by American Research Press, United States of America. The books can
be bought online at Amazon.com and other online bookstores. They can be downloaded
from the E-Library of Science of the publishers.

Smarandache Algebra Book Series
  1. Groupoids, pp. 113, $19.95, ISBN : 1-931233-61-6
  2. Semigroups, pp. 93, $19.95, ISBN : 1-931233-59-4
  3. Semirings, Semifields …, pp. 120, $19.95, ISBN: 1 931233-87-6
  4. Loops, pp. 127, $19.95, ISBN : 1-931233-63-2
  5. Rings, pp. 220, $29.95, ISBN : 1-931233-64-0
  6. Near-rings, pp. 199, $ 29.95, ISBN : 1-931233-66-7
  7. Non-associative Rings, pp. 150, $29.95, ISBN : 1-931233-69-1
  8. Bialgebraic Structures, pp. 270, $39.95, ISBN : 1-931233-71-3
  9. Fuzzy Algebra, pp. 453, $49.95, ISBN : 1-931233-74-8
 10. Linear Algebra, pp. 173, $35.95, ISBN : 1-932301-93-3

Other Research Books

11. Love. Life. Lust. Loss: 101 Real Life Stories of Migration and AIDS, pp.276, For
free distribution, ISBN : 1-931233-80-2

12. Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps (with Prof. Florentin),
pp. 212, $23.55, Hexis, USA. ISBN : 1-1-931233-76-4

13. Analysis of Social Aspects of Migrant Labourers Living with HIV/AIDS using
Fuzzy Theory and Neutrosophic Cognitive Maps (With Specific Reference to Rural
Tamilnadu in India) (with Prof. Florentin), pp. 471, $35.00, Hexis, USA. ISBN : 1-931233-83-7

14. Fuzzy Relational Equations and Neutrosophic Relational Equations (with Prof.
Florentin), pp. 301, $49.95, Hexis, USA. ISBN : 1-931233-86-1

15. Basic Neutrosophic Algebraic Structures and their Application to Fuzzy and
Neutrosophic Models (with Prof. Florentin), pp. 149, $ 25.00, Hexis, USA. ISBN : 1-931233-
87-X

16. Women. Work. Worth. Womb: 101 Real Life Stories of Rural Women with AIDS,
pp.304, For free distribution. ISBN : 81-902190-0-6

17. Introduction to Bimatrices (with Prof.Florentin and Ilanthenral), pp. 181, $25.00,
Hexis, USA. ISBN: 1-931233-95-0

18. Fuzzy and Neutrosophic Analysis of Women with HIV/AIDS: With Specific
Reference to Rural Tamil Nadu in India (with Prof. Florentin), pp.316, $35.00, ISBN: 1-931233-
96-9

19. Introduction to Linear Bialgebra (with Prof.Florentin and Ilanthenral), pp. 238,
$30.00, Hexis, USA. ISBN: 1-931233-97-7

                                             43
20. Application of Bimatrices to some Fuzzy and Neutrosophic Models (with Prof.
Florentin and Ilanthenral), pp.273, $30.00, Hexis, USA. ISBN: 1-931233-98-5

21. Fuzzy and Neutrosophic Analysis of Periyar's Views on Untouchability (with Prof.
Florentin and K. Kandasamy), pp. 385, $40.00, Hexis, USA. ISBN: 1-931233-00-4

22. N-Algebraic Structures and S-N-Algebraic Structures (with Prof. Florentin), pp. 209,
$30.00, Hexis, USA. ISBN: 1-931233-05-5

23. Public. Pity. Patients. Peace: Public Opinion on AIDS A Fuzzy Analysis, pp. 240, For free
distribution, ISBN: 81-902190-7-3

24. Introduction to n-adaptive models to analyze Public Opinion on AIDS (with Prof.
Florentin), pp. 235, $35.00, Hexis, USA. ISBN: 1-931233-12-8

25. Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures
(with Florentin Smarandache), pp. 219, $30.00, Hexis, USA. ISBN: 1-931233-15-2

26. Smarandache Neutrosophic Algebraic Structures, pp. 202, $30.00, Hexis, USA.
ISBN: 1-931233-16-0

27. Neutrosophic Rings, (with Florentin Smarandache) pp.154, $25.00, Hexis, USA. ISBN:
1-931233-20-9

28. Fuzzy Interval Matrices, Neutrosophic Interval Matrices and their Applications,
(with Florentin Smarandache) pp.304, $45.00, Hexis, USA. ISBN: 1-59973-003-0

29. Vedic Mathematics ‘Vedic’ or ‘Mathematics’: A Fuzzy and Neutrosophic
Analysis, (with Florentin Smarandache) pp.220, $35.00, Automaton, USA. ISBN: 1-
59973-004-9

30. Elementary Fuzzy Matrix Theory and Fuzzy Models for Social Scientists, (with
Florentin Smarandache and K.Ilanthenral) pp.352, $45.00, Automaton, USA. ISBN: 1-59973-
005-7

31. Special Fuzzy Models for Social Scientists, (with Florentin Smarandache and K.
Ilanthenral) pp. 301, $30.00, Info Learn Quest, Ann Arbor, USA. ISBN: 1-59973-030-8

32. Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists, (with
Florentin Smarandache and K. Amal) pp. 280, $40.00, Info Learn Quest, Ann Arbor, USA.
ISBN: 1-59973-027-8

33. New Classes of Codes for Computer Scientists and Cryptologists, (with Florentin
Smarandache) pp. 206, $40.00, Info Learn Quest, Ann Arbor, USA. ISBN: 1-59973-028-6

34. Set Linear Algebra and Set Fuzzy Linear Algebra, (with Florentin Smarandache and
K. Ilanthenral) pp. 344, $50.00, Info Learn Quest, Ann Arbor, USA. ISBN: 1-59973-029-4

35. Super Linear Algebra, (with Florentin Smarandache) pp. 293, $50.00, Info Learn Quest,
Ann Arbor, USA. ISBN: 1-59973-065-0

36. Methods in Industrial Biotechnology for Chemical Engineers, (with Florentin
Smarandache) pp. 125, $25.00, Info Learn Quest, Ann Arbor, USA. ISBN: 1-59973-034-0

                                            44
37. n-Linear Algebra of Type I and its Applications, (with Florentin Smarandache) pp.
120, $20.00, Info Learn Quest, Ann Arbor, USA. ISBN: 1-59973-074-X.

38. Special Classes of Set Codes and their Application, (with Florentin Smarandache)
pp. 168, $25.00, Info Learn Quest, Ann Arbor, USA. ISBN: 1-59973-079-0

39. n-Linear Algebra of Type II, (with Florentin Smarandache) pp. 229, $35.00, Info Learn
Quest, Ann Arbor, USA. ISBN: 1-59973-031-6

40. Smarandache Special Definite Algebraic Structures, (with Florentin Smarandache)
pp. 139, $25.00, Info Learn Quest, Ann Arbor, USA. ISBN: 1-59973-085-5

41. Superbimatrices and their Generalizations, (with Florentin Smarandache) pp. 408,
30.00, Editura CuArt, Romania. ISBN: 9-73852-088-2

42. Groups as Graphs, (with Florentin Smarandache) pp. 168, 15.00, Editura CuArt,
Romania. ISBN: 1-59973-093-6

43. Reservation for Other Backward Classess in Indian Central Government
Institutions like IITs, IIMs and AIIMs-A Study of the Role of Media using Fuzzy
Super FRM models, (with Florentin Smarandache and K.Kandasamy) pp. 445, 30.00,
Editura CuArt, Romania. ISBN: 1-59973-092-8

44. Special Set Linear Algebra and Special Set Fuzzy Linear Algebra (with Florentin
Smarandache and K. Ilanthenral) pp. 467, 30.00, Editura CuArt, Romania. ISBN: 1-59973-
106-1

45. New Classes of Neutrosophic Linear Algebras (with Florentin Smarandache and
K.Ilanthenral) pp. 467, 25.00, Editura CuArt, Romania. ISBN: 1-59973-116-9

46. Rank Distance Bicodes and their Generalization (with Florentin Smarandache,
N.Suresh Babu and R.S. Selvaraj) pp. 150, 20.00, Svenska fysikarkivet, Stockholm, Sweden.
ISBN: 978-91-85917-12-9

47. Super Special Codes using Super Matrices (with Florentin Smarandache and
K.Ilanthenral) pp. 161, 20.00, Svenska fysikarkivet, Stockholm, Sweden. ISBN: 978-91-85917-
13-6

48. Neutrosophic Bilinear Algebras and their Generalizations (with Florentin
Smarandache) pp. 402, 30.00, Svenska fysikarkivet, Stockholm, Sweden. ISBN: 978-91-
85917-14-3

49. Methods in Environmental Biotechnology for Environmentalists (with Florentin
Smarandache, S.R Kannan and S. Ramathilagam) pp. 142, $25.00, Info Learn Quest, Ann
Arbor, USA. ISBN: 1-59973-094-4

50. Interval Groupoids (with Florentin Smarandache and Moon Kumar Chetry) pp. 240,
$25.00, Info Learn Quest, Ann Arbor, USA. ISBN: 1-59973-125-8




                                            45
Research books in print: 3
 1.   Transsexuals and HIV/AIDS: A Sociological Study with specific reference to
      Tamil Nadu

 2. Fuzzy Analysis of Female Infanticide in the Southern Districts of Tamil Nadu




                                      46
    Research Contributions
   Innovative work in the field of matrix theory and linear algebra which was
    notable for the introduction of several new classes of matrices like bimatrices,
    fuzzy interval matrices, super fuzzy matrices and special n-matrices (large n)
    which find their applications in coding and communication theory, Markov
    processes, and Leontief economic models.
   More recently made fundamental and wide-ranging contributions by applying
    these new classes of matrices to study real-world problems including the
    sociological analysis of HIV/AIDS.
   Best known for work done in the field of bialgebraic structures. The new notion
    of bivector spaces where a bigroup is used finds applications in coding theory
    through bicodes. Best-approximation notion used for the first time to find the
    closest correct codeword. Concept recently generalized to the notion of best bi-
    approximation and n-approximation for use in bicodes and n-codes. This new
    class would be highly beneficial to cryptologists because of its secure features
    which makes it almost impenetrable by hackers.
   Proved that the number of different representations of loops of order 2n (n >=
    3) which are right alternative in which the square of each element is identity is
    equal to the different proper edge colouring of the graph K2n using exactly (2n –
    1) colours.
   Introduced N-algebraic structures that will find applications in fields like finite
    automaton, colouring problems and coding theory.
   Used techniques from basic set theory to build the concept of set-linear algebra
    which is the most generalized form of linear algebra. This can be adopted by
    coding theorists. Has also generalized this to n-set vector spaces and n-set
    linear algebras which can be put to use in web-monitoring and testing because
    of its capacity to work with n set of states simultaneously.
   Worked in the field of ring theory in general and zero divisors in particular and
    defined a new notion called finite zeros and finite zero divisors.
   Defined the notion of S-zero divisors and S-anti-zero-divisors which are zero
    divisors satisfying more properties involving more elements of the ring.
    Emphasized that all zero divisors must be finite barring the matrix zero divisor
    and n-tuple zero divisors. If achieved naturally, this would settle the zero
    divisor conjecture for group rings in the following manner: If G is a torsion-free
    non-abelian group and K is a field of characteristic zero then KG cannot have
    non-trivial finite zero divisors.
   Carried out element-wise study of both associative and non-associative
    algebraic structures. Also obtained zero divisor graphs for groupoids,
    distributive lattices and loop rings.
                                            47
Selected information
about my books

 1.   All my books are available online in the prestigious US Space Research
      organization Los Alamos National Laboratory (LANL) Arxiv
      (www.arxiv.org) which is an Internet archive and resource center for the
      best of contemporary research. In a peak-hour this website gets about
      25,000 hits, and several hundred million hits a month. I am the only
      Indian scientist to have 45 books online in the LANL Arxiv.

 2. My books are available in the libraries of distinguished and renowned
    universities and research institutions in USA, Canada and Europe
    including the Princeton University, USA (where the great scientist Albert
    Einstein worked), the Stanford University, the Harvard University, the
    Virginia Technical University, the University of Pennsylvania, the Penn
    State University, the University of South Alabama, the University of Alaska,
    the Library of Congress, Washington D.C; the York University, Canada; the
    University of Mannheim, Germany; Uppsala University, Sweden.

 3. Books are available for sale through the internet's largest selling
    online shops including Amazon.com. (www.amazon.com) and
    Barnes and Noble.com (www.barnesandnoble.com) and other sites like
    www.antiqbook.com,     www.book.idealo.com,       www.zubalbooks.com,
    www.biblio.com,         www.findarticles.com,          www.ebay.com,
    www.amazon.com,        www.tomfolio.com,         www.123bharath.com,
    www.allbookstores.com,      www.airleaf.com,        www.campusi.com,
    www.bookfinder.com,     www.booknews.com,         www.rbookshop.com.
    Repeatedly among the top 10 best-selling research books on the website
    www.vdsp.net

 4. There are around 17,000 websites on the World Wide Web that refer to me
    (this can be ascertained through a normal Google.com search)

 5. All my books are featured in Planet Math (www.planetmath.org): an online
    encyclopedia of ‗Mathematics for the people, by the people.‘

 6. The books are in Citebase (www.citebase.eprints.org) which is search and
    citation analysis tool for free online research literature and is a project run
    by the University of Southampton, United Kingdom.

 7. The MathForum Internet Mathematics Library (www.mathforum.com)
    features all my books. The MathForum is widely accessed, popular research
    and educational enterprise of the Drexel University, USA.
                                      48
8. Smarandache Algebraic Book Series authored by me are available at the
   www.algebra-online.com which is a comprehensive website hosted from
   Salt Lake City, Utah, USA that provides guidance on algebra textbooks.

9. The books have been reviewed in the American Mathematical Reviews run
   by the American Mathematical Society (www.ams.org) and the Germany
   based     Zentralblatt    Reviews     of    Mathematical     Journals
   (www.emis.de/ZMATH)

10. Free Science, an attempt to make science books more accessible, has put up
    all my books on their website: www.freescience.info Similarly my books are
    also available at the ACM Digital Library run by Google, which is available
    at www.portal.acm.org

11. My applied mathematical research is put to use in the website
    www.aiecon.org which is an Artificial Intelligence Economic Research
    Center run by the National Chengchi University, Taiwan.

12. My research publications are also cited in the Indian Science Abstracts
    www.niscair.res.in

13. British Library Direct (www.direct.bl.uk) that houses the full text of 20,000
    research journals has several of my research articles.

14. SAIL (Search, Alert, Impact, Link) an e-prints service provider is an
    electronic open access service provider for finding scientific or technical
    documents.

15. The 50 books run into a total of 12415 pages.




                                    49
    Book 1




GROUPOIDS AND SMARANDACHE GROUPOIDS
American Research Press, Rehoboth, NM, USA.
Pages: 113, Tables: 133, Published: 2002. Price: US $19.95
ISBN: 1-931233-61-6

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0304490

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book2.pdf

Used as a guidebook and a text in the Tutorgig.com, a tutorial website that caters to
thousands of American students of Mathematics.

                                                                                 (PTO)



                                          50
About the Book


In this book ingenious methods are used in construction of groupoids
using modulo integers. The class of semigroups in contained in the class
of groupoids. Our study in this book is those special groupoids which
contain subsets which are semigroups. All groupoids in general do not
contain subsets in them which are semigroups. Many classes of
groupoids using Zn (n < ) are defined. They find their application in
automaton and semi automaton.




                                  51
Book 2




SMARANDACHE SEMIGROUPS
American Research Press, Rehoboth, NM, USA.
Pages: 93, Published: 2002. Price: US $19.95
ISBN: 1-931233-59-4
(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0304420

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book1.pdf

"I have enjoyed reading your textbook "Smarandache Semigroups and I must tell you
that I am very impressed with the presentation of S-semigroups. I sincerely believe
that a great deal of results can be obtained on these topics."
               - Joyce Allen, Professor of Mathematics, University of Alabama, USA.

Used as a guidebook and a text in the Tutorgig.com, a tutorial website that caters to
thousands of American students of Mathematics.
                                                                              (PTO)

                                          52
About the Book


Semigroups are the generalization of groups. Smarandache semigroups
study the condition when a semigroup contains a group. Group enjoys
several properties and satsfy classical theorems like Lagrange‘s theorem,
Cauchy‘s theorem, Cayley‘s Theorem and Sylow‘s theorem.


      In general a semigroup does not satisfy any of the theorems but
by defining some more conditions and concepts modified theorems are
true for special classes of semigroups which is the main feature of this
book. This book also has suggested many research problems.




                                   53
Book 3




SMARANDACHE SEMIRINGS,
SEMIFIELDS AND SEMIVECTOR SPACES
American Research Press, Rehoboth, NM, USA.
Pages: 120, Figures: 64, Published: 2002. Price: US $19.95
ISBN: 1-931233-61-6

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0305032

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book3.pdf




                                                             (PTO)




                                      54
About the Book


Semirings happens to be the most generalized structure of rings and
fields.    Smarandache    semirings       are   semirings   which    contain
subset(which is proper) that is a semifield.


          Semifields are defined which has led to the definition of
semivector spaces. Research problems are introduced. These structures
are real non negative part of the real line. Distributive lattices alone from
finite semirings. Thus the interlinking of two algebraic structures are
done. Research problems are introduced to make researchers take up
interest in algebra. Here the notion S-zerodivisor, S-unit, S-idempotents
and S-antizero divisors are defined which is an innovation as it will find
lot of applications.




                                     55
Book 4




SMARANDACHE LOOPS
American Research Press, Rehoboth, NM, USA.
Pages: 127, Figures: 18, Tables: 42,
Published: 2002. Price: US $19.95
ISBN: 1-931233-63-2

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0307028

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book4.pdf

                                                            (PTO)




                                      56
About the Book


In this book innovative methods are used to define a new class of loops
using modulo integers Zn for appropriate n. The physical interpretation
of this operation on this class of loop is also given . It is proved the
number of different representations of loops of order Zn. (n  3) which
are right alternative and in which square of each element is identity is
equal to the different proper colouring of the graph K2n using exactly (2n
– 1) colours.




                                   57
Book 5




SMARANDACHE RINGS
American Research Press, Rehoboth, NM, USA.
Pages: 220, Figures: 14, Published: 2002. Price: US $29.95
ISBN: 1-931233-64-0

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0307208

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book5.pdf




                                                             (PTO)




                                      58
About the Book


In this book S-ring of level (1) and (II) are defined. The interrelation
between them are obtain. The innovative feature of this book is special
type of elements called S-zero divisors, S-units and S-idempotents are
introduced. This book has suggested 203 problems to attract researchers
in ring theory.




                                  59
Book 6




4




SMARANDACHE NEAR-RINGS
American Research Press, Rehoboth, NM, USA.
Pages: 200, Figures: 20, Tables: 50
Published: 2002. Price: US $29.95
ISBN: 1-931233-66-7

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0306334

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book6.pdf

                                                            (PTO)




                                      60
About the Book


The study of non-associative structures in algebraic structures has
become a separate entity; for, in the case of groups, their corresponding
non-associative structure i.e. loops is dealt with separately. Similarly
there is vast amount of research on the non-associative structures of
semigroups i.e. groupoids and that of rings i.e. non-associative rings.
However it is unfortunate that we do not have a parallel notions or study
of non-associative near-rings. The only known concept is loop near-rings
where the additive group structures of a near-ring is replaced by a loop.
Though this study was started in 1978, further development and
research is very little. Further, this definition is not in similar lines with
rings. So in chapter eight we have defined non-associative near-rings
and given methods of building non-associative near-rings and seminear-
rings using loops and groupoids which we call as groupoid near-rings,
near loop rings, groupoid seminear-rings and loop seminear-ring. For all
these concepts a Smarandache analogue is defined and several
Smarandache properties are introduced and studied. The ninth chapter
deals with fuzzy concepts in near-rings and gives 5 new unconventional
class of fuzzy near-rings; we also define their Smarandache analogues.
The final chapter gives 145 suggested problems that will be of interest to
researchers. It is worthwhile to mention that in the course of this book
we have introduced over 260 Smarandache notions pertaining to near-
ring theory.




                                     61
Book 7




SMARANDACHE NON-ASSOCIATIVE RINGS
American Research Press, Rehoboth, NM, USA.
Pages: 148, Tables: 40, Problems: 150
Published: 2002. Price: US $29.95
ISBN: 1-931233-69-1

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0306046

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book7.pdf

                                                            (PTO)




                                      62
About the Book


Another generalized class of non-associative algebras are from groupoid
rings. The class of loop rings are strictly contained in the class of
groupoid rings. Several important study in the direction of Smarandache
notions has been done in this book. Groupoid rings are a very new
concept, till date only very few research papers exist in the field of
Groupoid rings. The notion of Smarandache Lie algebras and
Smarandache Jordan algebras are introduced. There are several
informative and exhaustive books on Lie algebras and Jordan algebras.
Further as the study of these two algebras heavily exploits the concepts
of vector spaces and matrix theory we do not venture to approach
Smarandache Lie algebras or Smarandache Jordan algebras in this
direction. But in this book we approach Smarandache Lie algebras and
Smarandache Jordan algebras as a study in par with associative rings for
such a study has not yet been approached by any researcher in this way.
This book is distinct and different from other non-associative ring theory
books as the properties of associative rings are incorporated and studied
even in Lie rings and Jordan rings, an approach which is not traditional.




                                   63
Book 8




BIALGEBRAIC STRUCTURES AND
SMARANDACHE BIALGEBRAIC STRUCTURES
American Research Press, Rehoboth, NM, USA.
Pages: 269, Published: 2003. Price: US $39.95
ISBN: 1-931233-71-3

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0308038
E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book8.pdf

“This well-written book contains a complete study of the following bialgebraic
structures: bigroups, biloops, bigroupoids, bisemigroups, birings, bisemirings,
bivector spaces. Their Smarandache correspondents are also introduced and studied.
About 460 new notions involving these structures, a number of 178
research problems, and an index show the innovative talent of the author
of this book.”
                   Prof. Josef Sandor, review in Zentralblatt MATH, Germany
                                                                                (PTO)
                                        64
About the Book


Bistructures are a very nice tool as this answers a major problem faced
by all algebraic structures – groups, semigroups, loops, groupoids etc.
that is the union of two subgroups, or two subrings, or two
subsemigroups etc. do not form any algebraic structure but all of them
find a nice bialgebraic structure as bigroups, birings, bisemigroups etc.
Except for this bialgebraic structure these would remain only as sets
without any nice algebraic structure on them. Further when these
bialgebraic structures are defined on them they enjoy not only the
inherited qualities of the algebraic structure from which they are taken
but also several distinct algebraic properties that are not present in these
algebraic structures. One such is the reducibility or the irreducibility of a
polynomial, or we can say in some cases a polynomial is such that it
cannot be reducible or irreducible. Likewise, we see in case of groups an
element can be a Cauchy element or a non-Cauchy element or neither …




                                     65
Book 9




SMARANDACHE FUZZY ALGEBRA
American Research Press, Rehoboth, NM, USA.
Pages: 455, Published: 2003. Price: US $49.95
ISBN: 1-931233-74-8

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0309144

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book9.pdf

This book has been receiving critical attention and very high downloads. For instance
in the one month of February 2005, the server of the University of Gallup, New
Mexico, US recorded more than 1500 „hits‟ and downloads to this book.

                                                                               (PTO)


                                         66
About the Book


In this book we introduce new fuzzy algebraic structures like fuzzy bi-
ideal, fuzzy binear ring, fuzzy semiring, fuzzy biloop fuzzy semi
automaton and fuzzy automaton for we see by fuzzification we work in
the unit interval [0 1] which is compatible.




                                    67
Book 10




LINEAR ALGEBRA AND
SMARANDACHE LINEAR ALGEBRA
American Research Press, Rehoboth, NM, USA.
Pages: 175, Problems: 131, Published: 2003. Price: US $35.95
ISBN: 1-931233-75-6

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0308170

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Vasantha-Book10.pdf

                                                               (PTO)




                                      68
About the Book


In this book we analyze the Smarandache linear algebra, and we
introduce several other concepts like the Smarandache semilinear
algebra, Smarandache bilinear algebra and Smarandache anti linear
algebra. We indicate that Smarandache vector spaces of type II will be
used in the study of neutrosophic logic and its applications to Markov
chains and Leontief Economic models — both of these research topics
have intense industrial applications.




                                   69
Book 11




                       LOVE. LIFE. LUST. LOSS:
                       101 Real-Life Stories Of Migration And AIDS
                       Tamil Nadu State AIDS Control Society, India.
                       Pages: 276, Published: 2004. Price: Free
                       ISBN: 1-931233-80-2

A mathematician's sensitivity to sociological issues is amazing. I cannot but
congratulate you for your through scientific approach and an in-depth analysis
of the moving life-narratives of the victims of HIV/AIDS, the captivating and
lucid presentation of the interviews with an emphasis on the patients' emotions
and feelings, sorrows and longings, and aspirations and frustrations. In short,
your book has given voice to the voiceless, face to the faceless and
vision to the visionless and has a set a trend how Mathematics and
Sociology could interact together and offer valuable insights to make
our society a humane one. Your book communicates powerfully the message to
our society that HIV/AIDS is not an incurable disease but more so a livable disease
and underlines the responsibilities of various groups towards the hapless ones of our
social structure and systems.
                  Rev.Dr. Mohan Doss, Rector, Divine Word Seminary, Pune.
                                                                               (PTO)

                                        70
About the Book


In this book we have interviewed 100 migrant labourers who are affected
by HIV/AIDS. Their social, psychological and emotional problems are
analysed using Fuzzy Cognitive Maps, a very sensitive mathematical
model that can give the hidden pattern.




                                  71
Book 12




FUZZY COGNITIVE MAPS AND
NEUTROSOPHIC COGNITIVE MAPS
Xiquan, Phoenix, AZ, USA.
Pages: 213, Published: 2003. Price: US $23.55
ISBN: 1-931233-76-4

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0311063

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/NCMs.pdf

"I am extremely interested in your usage of fuzzy modeling for engineering
problems. This is a pioneer work in our discipline."
    Bulent Tutmez, Mining Engineering, Hacettepe Univ., Turkey

                                                                       (PTO)

                                      72
“Used as an equipment in the Institute for Psychology, Faculty for Human
and Society Sciences, University of Oldenburg, Germany, for the study of
cognitive and general psychology, and knowledge cartography.”

“A reference book used in the project on developing a fuzzy classification
system in an intelligent (computer) vision system.”

“Reviewed in Kybernetika (Cybernetics) published by the Academy of Sciences
of the Czech Republic.”




About the Book
In a world of chaotic alignments, traditional logic with its strict
boundaries of truth and falsity has not imbued itself with the capability
of reflecting the reality. Despite various attempts to reorient logic, there
has remained an essential need for an alternative system that could
infuse into itself a representation of the real world. Out of this need
arose the system of Neutrosophy (the philosophy of neutralities,
introduced by Smarandache), and its connected logic — Neutrosophic
Logic, which is a further generalization of the theory of Fuzzy Logic. In
this book we study the concepts of Fuzzy Cognitive Maps (FCMs) and
their Neutrosophic analogue, the Neutrosophic Cognitive Maps (NCMs).
Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural
networks, and they have powerful and far-reaching consequences as a
mathematical tool for modeling complex systems. Neutrosophic
Cognitive Maps are generalizations of FCMs, and their unique feature is
the ability to handle indeterminacy in relations between two concepts
thereby bringing greater sensitivity into the results.




                                      73
Book 13




ANALYSIS OF SOCIAL ASPECTS OF MIGRANT LABOURERS
LIVING WITH HIV/AIDS USING FUZZY THEORY AND
NEUTROSOPHIC COGNITIVE MAPS : WITH SPECIFIC
REREFENCE TO RURAL TAMILNADU IN INDIA
(With Florentin Smarandache)
Xiquan, Phoenix, USA.
Pages: 468, Published: 2004. Price: $35.00
ISBN: 1-931233-83-7

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0406304

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/NeutrosophyAIDS.pdf

                                                            (PTO)

                                      74
About the Book


HIV/AIDS is everybody's business. Today, it is more an issue of society
than a matter of medicine. . . In this bold attempt that searches for
sociological solutions, gripping real-life stories of sixty migrant
labourers living with HIV/AIDS in rural Tamil Nadu, India have been
documented. Their socio-psychological aspects have been analyzed using
the latest fuzzy mathematical tools like Fuzzy Cognitive Maps,
Bidirectional Associative Memories and Fuzzy Relational Maps. Because
of the need to represent the real-world, Neutrosophy (the philosophy of
neutralities) and its connected structure, Neutrosophic Cognitive Maps
have been employed for their unique ability to handle indeterminacy
between concepts. Presented in a lucid manner, this book is an
important contribution to HIV/AIDS literature.




                                  75
Book 14




FUZZY RELATIONAL EQUATIONS
AND NEUTROSOPHIC RELATIONAL EQUATIONS
(With Florentin Smarandache)
Hexis, Church Rock, USA.
Pages: 301, Published: 2004. Price: $49.95
ISBN: 1-931233-96-1

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0406622

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/NRM.pdf

                                                            (PTO)



                                      76
About the Book


The introduction of Fuzzy Relational Equations (FREs) has made
problems that are unsolvable using algebraic linear equations into
solvable ones. FREs have been applied to problems in medicine,
industry, transportation and all types of social problems where the data
is an unsupervised one. Yet, FREs lack the capacity to tackle problems
where an element of indeterminacy is involved. This book develops the
new concept of Neutrosophic Relational Equations (NREs) that have the
capacity to analyze problems with indeterminacy. Here, earlier models
on FREs are analyzed and new NRE models, with practical applications
are presented.




                                  77
Book 15




BASIC NEUTROSOPHIC ALGEBRAIC STRUCTURES AND
THEIR APPLICATION TO FUZZY AND NEUTROSOPHIC
MODELS
(With Florentin Smarandache)
Hexis, Church Rock, USA.
Pages: 149, Published: 2004. Price: $25.00
ISBN: 1-931233-87-X

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0412424

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/NAS.pdf

                                                            (PTO)



                                      78
About the Book


The involvement of uncertainty of varying degrees when the total of the
membership degree exceeds one or less than one, then the newer
mathematical paradigm shift, Fuzzy Theory proves appropriate. For the
past two or three decades, Fuzzy Theory has become the potent tool to
study and analyze uncertainty involved in all problems. But, many real-
world problems also abound with the concept of indeterminacy. In this
book, the new powerful tool of neutrosophy that deals with
indeterminacy is utilized. Innovative neutrosophic models are described.
The theory of neutrosophic graphs is introduced and applied to fuzzy
and neutrosophic models.




                                  79
Book 16




          WOMEN. WORK. WORTH. WOMB:
          101 Real-Life Stories Of Rural Women With AIDS
          Tamil Nadu State AIDS Control Society, India.
          Pages: 304, Published: 2005. Price: Free
          ISBN: 81-902190-7-3



                                                   (PTO)




                      80
About the Book


In this book we study the problems faced by HIV/AIDS women patients.
We were shocked to understand from the interviews most of women
have got the disease from their husbands. It is still a pity to know these
women were not only infected by their husbands but abused by their in
laws for being immoral. We use FRM and BAM models to study the
problem.




                                   81
Book 17




INTRODUCTION TO BIMATRICES
(With Florentin Smarandache and K. Ilanthenral)
Hexis, Phoenix, Arizona, USA.
Pages: 181, Published: 2005. Price: $25.00
ISBN: 1-931233-95-0

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0506426

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Bimatrices.pdf


                                                            (PTO)



                                      82
About the Book


Generally, any real world problem is not always solvable, because in that
not only a percentage of uncertainty is present but also a certain
percentage of indeterminacy is present. The presence of uncertainty has
been analyzed using fuzzy logic. In this book, the amount of
indeterminacy is being analyzed using neutrosophic logic. Most of these
models use the concept of matrices. Matrices have certain limitations:
when the models are time-dependent and any two experts' opinions are
being studied simultaneously, one cannot compare both of them at each
stage. The new concept of bimatrices would certainly cater to these
needs. A bimatrix AB = A1  A2, where A1 and A2 are distinct matrices of
arbitrary order. This book introduces the concept of bimatrices and
studies several notions like bieigen values, bieigen vectors, characteristic
bipolynomials, bitransformations, bioperators and bidiagonalization.
Further, we introduce and explore the concepts like fuzzy bimatrices,
neutrosophic bimatrices and fuzzy neutrosophic bimatrices which will
find its application in fuzzy and neutrosophic logic.




                                    83
Book 18




FUZZY AND NEUTROSOPHIC ANALYSIS OF WOMEN WITH
HIV/AIDS
(With Florentin Smarandache)
Hexis, Phoenix, Arizona, USA.
Pages: 316, Published: 2005. Price: $35.00
ISBN: 1-931233-96-9

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0507037

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/WomenAIDS.pdf

                                                            (PTO)



                                      84
About the Book


Rural women form the most neglected area in HIV/AIDS research; this
book sets forth to bridge that gap. The autobiographical contents and
authenticity of the 101 interviews, analyzed with fuzzy and neutrosophic
models change the way normal statistical methods have looked at AIDS.
Our study is not only meant for mathematicians but also for sociologists,
economists, psychologists, human rights activists and women activists
who want to make a difference in the lives of uneducated, rural, poverty-
stricken, HIV-infected women.




                                   85
Book 19




INTRODUCTION TO LINEAR BIALGEBRA
(With Florentin Smarandache and K.Ilanthenral)
Hexis, Phoenix, Arizona, USA.
Pages: 238, Published: 2005. Price: $30.00
ISBN: 1-931233-97-7

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0508260

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Bialgebra.pdf

                                                            (PTO)




                                      86
About the Book


In the modern age of development, it has become essential for any
algebraic structure to enjoy greater acceptance and research significance
only when it has extensive applications to other fields.


       This new algebraic concept Linear Bialgebra is one that will find
applications to several fields like bigraphs, algebraic coding /
communication theory (bicodes, best approximations), Markov bichains,
Markov bioprocess and Leontief Economic bimodels: these are also
brought out in this book.


       Here, the linear bialgebraic structure is given subbistructures and
super-structures    called   the   Smarandache       Neutrosophic      Linear
Bialgebra, which will easily yield itself to the above applications.




                                     87
Book 20




APPLICATIONS OF BIMATRICES TO SOME FUZZY AND
NEUTROSOPHIC MODELS
(With Florentin Smarandache and K.Ilanthenral)
Hexis, Phoenix, Arizona, USA.
Pages: 273, Published: 2005. Price: $30.00
ISBN: 1-931233-98-5

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0509078

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Bimatrices2.pdf

                                                            (PTO)




                                      88
About the Book


This book gives some new types of Fuzzy and Neutrosophic models
which can analyze problems in a revolutionary way. The new notions of
bigraphs, bimatrices and their generalizations are used to build these
models which will be helpful to analyze time dependent problems which
need stage-by-stage comparison of more than two experts. The models
expressed here can be considered as generalizations of Fuzzy Cognitive
Maps and Neutrosophic Cognitive Maps.




                                 89
Book 21




FUZZY AND NEUTROSOPHIC ANALYSIS OF
PERIYAR'S VIEWS ON UNTOUCHABILITY
(With Florentin Smarandache and K.Kandasamy)
Hexis, Phoenix, Arizona, USA.
Pages: 385, Published: 2005. Price: $40.00
ISBN: 1-931233-00-4

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0511559

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Periyar.pdf

                                                            (PTO)




                                      90
About the Book


For the first time, the social problem of untouchability, which is peculiar
to India, is being studied mathematically. We have used Fuzzy Cognitive
Maps and Neutrosophic Cognitive Maps to analyze the views of the
revolutionary Periyar who relentlessly worked for more than five
decades to secure the rights of the oppressed people who were
considered untouchables.


         This thought-provoking book will be of great interest to human
rights     activists,   socio-scientists,   historians,   and   above   all,
mathematicians.




                                       91
Book 22




N-ALGEBRAIC STRUCTURES AND S-N-ALGEBRAIC
STRUCTURES
(With Florentin Smarandache)
Hexis, Phoenix, Arizona, USA.
Pages: 209, Published: 2006. Price: $30.00
ISBN: 1-931233-05-5

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0602591

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/N-AlgebraicStructures.pdf

                                                               (PTO)



                                      92
About the Book


For the first time, we have introduced the concept of N-groups, N-
semigroups, N-loops and N-groupoids. We also define a mixed N-
algebraic structure. The main aim of this book is to attack young
mathematicians to this interesting field. It contains more than 200 new
definitions. These concepts find applications in fields like finite
automaton, colouring problems and coding theory.




                                  93
Book 23




          PUBLIC. PITY. PATIENTS. PEACE
          Public Opinion on AIDS: A Fuzzy Analysis
          101 Real-Life Stories Of Rural Women With AIDS
          Tamil Nadu State AIDS Control Society, India.
          Pages: 240, Published: 2006. Price: Free
          ISBN: 81-902190-0-6




                                                           (PTO)


                        94
About the Book


We have interviewed 100 public people about the social, psychological
and other problems about HIV/AIDS patients and the disease. It was
very difficult in the first place to interview about this subject. They
openly shunned us and ill treated us for they felt stigmatised even to talk
about this disease. We have analysed using newly constructed fuzzy
model to analyse the problem. This book has been used by NGOs‘
working with HIV/AIDS patients.




                                    95
Book 24




INTRODUCTION TO N-ADAPTIVE MODELS TO ANALYZE
PUBLIC OPINION ON AIDS
(With Florentin Smarandache)
Hexis, Phoenix, Arizona, USA.
Pages: 235, Published: 2006. Price: $35.00
ISBN: 1-931233-12-8

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0602403

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/N-AdaptiveFuzzyModels.pdf

                                                               (PTO)




                                      96
About the Book


People living with HIV/AIDS have always been victims of the most
extreme forms of social discrimination. They are stereotyped and
stigmatized, and are seen as people outside the ‗general population‘.
      In this book we use mathematical tools to attempt an
understanding of public awareness and attitude towards people living
with HIV/AIDS.
      Here, for the first time, a new model called the n-adaptive fuzzy
model has been introduced. This model has the capacity to analyse the
same problem in different ways thereby arriving at various solutions that
mirror multiple perspectives.




                                   97
Book 25




NEUTROSOPHIC ALGEBRAIC STRUCTURES AND
NEUTROSOPHIC N-ALGEBRAIC STRUCTURES
(With Florentin Smarandache)
Hexis, Phoenix, Arizona, USA.
Pages: 219, Published: 2006. Price: $30.00
ISBN: 1-931233-15-2

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0603581

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/NeutrosophicN-AlgebraicStructures.pdf

                                                                      (PTO)



                                       98
About the Book


This book for the first time introduces neutrosophic groups,
neutrosophic   semigroups,    neutrosophic    loops   and    neutrosophic
groupoids and their neutrosophic N-structures.


      The special feature of this book is that it tries to analyze when the
general neutrosophic algebraic structures like loops, semigroups and
groupoids satisfy some of the classical theorems for finite groups viz.
Lagrange, Sylow and Cauchy.


      This is mainly carried out to know more about these neutrosophic
algebraic structures and their neutrosophic N-algebraic structures.




                                   99
Book 26




SMARANDACHE NEUTROSOPHIC ALGEBRAIC
STRUCTURES
Hexis, Phoenix, Arizona, USA.
Pages: 202, Published: 2006. Price: $30.00
ISBN: 1-931233-16-0

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0603708

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/SNAS.pdf
                                                            (PTO)




                                      100
About the Book


Smarandache algebraic structures that inter-relates two distinct
algebraic structures and analyzes them relatively can be considered a
paradigm shift in the study of algebraic structures. For instance, the
algebraic structures Smarandache semigroup simultaneously involves
both group and semigroup.
      Recently, Neutrosophic algebraic structures were introduced.
This book ventures to define Smarandache Neutrosophic algebraic
structures.
      Here,    Smarandache     neutrosophic   structures   of   groups,
semigroups, loops and groupoids and their N-ary structures are
introduced and analyzed. There is a lot of scope for interested
researchers to develop these concepts.




                                  101
Book 27




NETUROSOPHIC RINGS
(With Florentin Smarandache)
Hexis, Phoenix, Arizona, USA.
Pages: 154, Published: 2006. Price: $25.00
ISBN: 1-931233-20-9

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0607765

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/NeutrosophicRings.pdf

                                                            (PTO)




                                      102
About the Book


Research on algebraic structure of group rings is one of the leading, most
sought-after topics in ring theory. The new class of neutrosophic rings
defined in this book form a generalization of group rings and semigroup
rings. The study of the classes of neutrosophic group neutrosophic rings
and S-neutrosophic semigroup neutrosophic rings which form a type of
generalization of group rings will throw light on group rings and
semigroup rings which are essential substructures of them. A salient
feature of this book is the many suggested problems on the new classes
of neutrosophic rings, solutions of which will certainly develop some of
the still open problems in group rings. Further, neutrosophic matrix
rings find applications in neutrosophic models like Neutrosophic
Cognitive Maps (NCM), Neutrosophic Relational Maps (NRM),
Neutrosophic Bidirectional Memories (NBM) and so on.




                                   103
Book 28




FUZZY INTERVAL MATRICES, NETUROSOPHIC INTERVAL
MATRICES, AND THEIR APPLICATIONS
(With Florentin Smarandache)
Hexis, Phoenix, Arizona, USA.
Pages: 304, Published: 2006. Price: $45.00
ISBN: 1-59973-003-0

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0609104

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/NIM.pdf
                                                            (PTO)




                                      104
About the Book


This book introduces for the first time the notion of fuzzy interval
matrices, fuzzy interval bimatrices, neutrosophic interval matrices,
neutrosophic interval bi-matrices, neutrosophic interval n-matrices,
fuzzy neturosophic interval matrices and fuzzy neutrosophic interval n-
matrices (where n is greater than, or equal to 2). These new notions find
their applications in FCInM, FRInM, FBAInM, NCInM, NCRInM, and
NRInM models, where n is greater than, or equal to 1. It is important to
mention that these Fuzzy interval n-matrices and interval n-matrices
will find their usage in Leontief economic models and Markov chains
that has lots of industrial applications.




                                     105
Book 29




VEDIC MATHEMATICS ‘VEDIC’ OR ‘MATHEMATICS’:
A FUZZY AND NETUROSOPHIC ANALYSIS
(With Florentin Smarandache)
Automaton, Los Angeles, USA.
Pages: 220, Published: 2006. Price: $35.00
ISBN: 1-59973-004-9

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0611347

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/VedicMath.pdf
                                                            (PTO)




                                      106
About the Book


Here, the authors probe into Vedic Mathematics (that gained renown
during the revivalist Hindutva rule in India and was introduced into the
school syllabus in several states): and explore if it is really ‗Vedic‘ in
origin or ‗Mathematics‘ in content. To gain a better understanding of its
imposition, we interviewed students, teachers, parents, educationalists
and activists. We analyze this problem using models like Fuzzy Cognitive
Maps (FCM), Fuzzy Relational Maps (FRM) and the newly constructed
Fuzzy Dynamical System (and its Neutrosophic analogues). The issue of
imposition of Vedic Mathematics into the school curriculum involves
religious politics, caste supremacy, apart from elementary arithmetic—
so we use fuzzy and neutrosophic techniques to gain acute insight into
how students have been affected because of this politically motivated
syllabus revision.




                                   107
Book 30




ELEMENTARY FUZZY MATRIX THEORY AND FUZZY
MODELS FOR SOCIAL SCIENTISTS
(With Florentin Smarandache and K.Ilanthenral)
Automaton, Los Angeles, USA.
Pages: 352, Published: 2007. Price: $35.00
ISBN(10): 1-59973-005-7

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://www.arxiv.org/pdf/math.GM/0702144

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/FuzzyModels.pdf
                                                            (PTO)




                                      108
About the Book


This book gives the basic notions of fuzzy matrix theory and its
applications to simple fuzzy models. The approach is non-traditional in
order to attract many students to use this methodology in their research.
The traditional approach of mathematicians has conditioned students of
sociology in such a manner that they are averse to using mathematical
tools. Six simple types of fuzzy models that make use of fuzzy matrices
are given. These models are distinct because they are time dependent
and can even be used for statistical data. The Fuzzy Cognitive Maps
models gives the hidden pattern. Fuzzy Relational Maps model not only
gives the hidden pattern but also gives the inter-relations between two
sets of disjoint attributes. The Bidirectional Associative Memories model
analyzes data depending on the time-period, while the Fuzzy Associative
Memories model can give the gradation of importance of each attribute.
Finally, the Fuzzy Relational Equation model is capable of giving a
solution closer to the predicted solution. All the models are illustrated
through elaborate examples of particular social problems.




                                   109
Book 31




SPECIAL FUZZY MATRICES FOR SOCIAL SCIENTISTS
(With Florentin Smarandache and K.Ilanthenral)
Info Learn Quest, Ann Arbor, USA.
Pages: 301, Published: 2007. Price: $30.00
ISBN(10):1-59973-030-8

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0707.4637

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/FuzzyMatrices.pdf
                                                            (PTO)




                                      110
About the Book


This book introduces special classes of fuzzy and neutrosophic matrices.
These special classes of matrices are used in the construction of multi
expert special fuzzy models using FCM, FRM and FRE and their
Neutrosophic analogues (simultaneous or otherwise, according to ones
need). Using the six basic models, we have constructed a multi expert
mutli model called the super special hexagonal fuzzy and neutrosophic
model.


      Given any special input vector, these vector, these models can
give the resultant using special operations. When coupled with computer
programming, these operations can give the solution within a reasonable
time period. Such multi expert multi model systems are not only a boon
to social scientists, but also to anyone who wants to use fuzzy or
Neutrosophic models.




                                  111
Book 32




SUPER FUZZY MATRICES AND SUPER FUZZY MODELS FOR
SOCIAL SCIENTISTS
(With Florentin Smarandache and K.Amal)
Info Learn Quest, Ann Arbor, USA.
Pages: 280, Published: 2008. Price: $40.00
ISBN(10) :1-59973-027-8

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://aps.arxiv.org/abs/0801.2677

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/SuperFuzzyMatrices.pdf
                                                            (PTO)




                                      112
About the Book


The notion of Super Fuzzy Matrices are introduced in this book. The
main motive is to use these Super Fuzzy Matrices to construct Super
Fuzzy Models. We introduce 13 Super fuzzy models that serves as multi
expert models.


      This book will be a boon not only to socio scientists, but also to
researchers, engineers, and teachers who need to work with multi-expert
models.




                                  113
Book 33




NEW CLASSES OF CODES FOR COMPUTER
SCIENTISTS AND CRYPTOLOGISTS
(With Florentin Smarandache)

Info Learn Quest, Ann Arbor, USA.
Pages: 206, Published: 2008. Price: $40.00
ISBN(10):1-59973-028-6

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0801.2681

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/Cryptologists.pdf
                                                            (PTO)



                                      114
About the Book


In this book new classes of n-codes and false n-codes are introduced to
help cryptologists and computer scientists. These codes will find
application in networking and data storage. Further, these new classes of
codes cannot be easily cracked by hackers. We mainly make use of the
new method of pseudo n-best approximation to correct and detect
errors.




                                   115
Book 34




SET LINEAR ALGEBRA AND SET FUZZY LINEAR ALGEBRA
(With Florentin Smarandache and K.Ilanthenral)
Info Learn Quest, Ann Arbor, USA.
Pages: 344, Published: 2008. Price: $50.00
ISBN(10):1-59973-029-4

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0806.2847

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/SetFuzzyLinearAlgebra.pdf
                                                               (PTO)




                                      116
About the Book


Set linear algebras, introduced by the authors in this book, are the most
generalized form of linear algebras. These structures make use of very
few algebraic operations and are easily accessible to non mathematicians
as well. The dominance of computers in everyday life calls for a
paradigm shift in the concepts of Linear algebra. The authors believe
that set linear algebra will cater to that need.




                                     117
Book 35




SUPER LINER ALGEBRA
(With Florentin Smarandache)
Info Learn Quest, Ann Arbor, USA.
Pages: 293, Published: 2008. Price: $50.00
ISBN:1-59973-065-0

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0807.3013

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/SuperLinearAlgebra.pdf
                                                            (PTO)




                                      118
About the Book


Super linear algebras are built using super matrices. These new
structures can be applied to all fields in which linear algebras are used.
Super characteristic values exist only when the related super matrices
are super square diagonal super matrices. Super diagonalization,
analogous to diagonalization is obtained. These new structures can be
applied to Computer Science, Markov chains, and Fuzzy models.




                                   119
Book 36




METHODS IN INDUSTRIAL BIOTECHNOLOGY FOR
CHEMICAL ENGINEERS
(With Florentin Smarandache)
Info Learn Quest, Ann Arbor, USA.
Pages: 125, Published: 2008. Price: $25.00
ISBN:1-59973-034-0

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0807.2018

E-Library of Science: American Research Press
http://gallup.unm.edu/~smarandache/BiotechnologyMethods.pdf
                                                              (PTO)




                                      120
About the Book


In this book, the authors apply some set of fuzzy techniques to chemical
industry problems such as finding the right proportion of raw mix to
control pollution, to study flow rates, and to find out the better quality of
products. Fuzzy control theory, fuzzy neutral networks, fuzzy relational
equations and genetic algorithms are used to find solutions.
Neutrosophic models are used when the indeterminacy factor occurs.




                                     121
Book 37




n-LINEAR ALGEBRA OF TYPE I AND ITS APPLICATIONS
(With Florentin Smarandache)
Info Learn Quest, Ann Arbor, USA.
Pages: 120, Published: 2008. Price: $20.00
ISBN:1-59973-074-X

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0812.1950

E-Library of Science: American Research Press
http://fs.gallup.unm.edu/n-LinearAlgebraType1.pdf
                                                            (PTO)




                                      122
About the Book


n-Linear Algebras of type I, introduced in this book, find applications in
Markov Chains and Leontief Economic models. Innovative scientists and
engineers can adopt this concept in Fuzzy Finite Elements analysis of
Mechanical structures with uncertain parameters.




                                   123
Book 38




SPECIAL CLASSES OF SET CODES AND THEIR
APPLICATIONS
(With Florentin Smarandache)
Info Learn Quest, Ann Arbor, USA.
Pages: 168, Published: 2008. Price: $25.00
ISBN:1-59973-079-0

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0812.5075

E-Library of Science: American Research Press
http://fs.gallup.unm.edu/SetCodes.pdf
                                                            (PTO)




                                       124
About the Book


In this book, the authors for the first time, a few classes of Set Codes, the
most generalized class of algebraic codes. These codes are best-suited for
their applications in cryptography, coding block truncation, image
compression, computer networking and data storage.




                                     125
Book 39




n-LINEAR ALGEBRA OF TYPE II
(With Florentin Smarandache)
Info Learn Quest, Ann Arbor, USA.
Pages: 229, Published: 2008. Price: $35.00
ISBN:1-59973-031-6

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0902.0110

E-Library of Science: American Research Press
http://fs.gallup.unm.edu/n-LinearAlgebraType2.pdf
                                                            (PTO)




                                      126
About the Book


In this book, n-linear algebra of type II is constructed over n-fields. n-
eigen values and n-eigen vectors will find applications in finite element
analysis of civil and mechanical structures with uncertain parameters




                                   127
Book 40




SMARANDACHE SPECIAL DEFINTIE ALGEBRAIC
STRUCTURES
(With Florentin Smarandache)
Info Learn Quest, Ann Arbor, USA.
Pages: 139, Published: 2009. Price: $20.00
ISBN:1-59973-085-5

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0807.2018

E-Library of Science: American Research Press
http://gallup.unm.edu/SmDefAlgStr.pdf
                                                            (PTO)




                                       128
About the Book


In this book, the authors introduce the notion of Smarandache Special
Definite Algebraic Structures.; these new structures are defined as those
strong algebraic structures which have in them a proper subset which is
a weak algebraic structure.




                                   129
Book 41




SUPERBIMATRICES AND THEIR GENERALIZATIONS
(With Florentin Smarandache)
Editura CuArt, Romania.
Pages: 408, Published: 2009. Price: € 35.00
ISBN:9-73852-088-2

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0906.5143

                                                            (PTO)




                                      130
About the Book


In this book, the new notion of superbimatrices are introduced and their
properties are studied. These new structures are best suited in fuzzy
models and coding theory.




                                  131
Book 42




GROUPS AND GRAPHS
(With Florentin Smarandache)
Editura CuArt, Romania.
Pages: 168, Published: 2009. Price: €15.00
ISBN:1-59973-093-6

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0906.5144

                                                            (PTO)




                                      132
About the Book


This book gives an innovative method of representing a group as graph.
Graph representing the properties of the groups are also considered. The
same type of graphs are also constructed for semigroups, groupoids,
loops and rings.




                                  133
Book 43




RESERVATION FOR OTHER BACKWARD CLASSES IN
INDIAN CENTRAL GOVERNMENT INSTITUTIONS LIKE IITS,
IIMS AND AIIMS - A STUDY OF THE ROLE OF MEDIA USING
FUZZY SUPER FRM MODELS
(With Florentin Smarandache and K.Kandasamy)
Editura CuArt, Romania.
Pages: 455, Published: 2009. Price: €30.00
ISBN:1-59973-092-8

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0909.1083

                                                            (PTO)




                                      134
About the Book


The new notion of super column FRM model, super row FRM model and
mixed super FRM model are introduced in this book. These three
models are introduced specially to analyze the role media on 27 percent
reservation for Other Backward Classes (OBC) in educational
institutions run by the central government. The experts were divided
into 19 groups depending on their profession. These groups of experts
gave their opinion and comments on the news items that appeared about
reservations in dailies and weeklies after discussions on them, this forms
the third chapter of this book. This book has four chapters. In chapter
one the authors introduce the notion of the three types of super FRM
models. Chapter two uses these three new super fuzzy models to study
the role of media on 27 percent for OBC in central govt. run institutions
in India. The fourth chapter gives the conclusions based on our study.




                                   135
Book 44




SPECIAL SET LINEAR ALGEBRA AND SPECIAL SET FUZZY
LINEAR ALGEBRA
(With Florentin Smarandache and K. Ilanthenral)
Editura CuArt, Romania.
Pages: 467, Published: 2009. Price: €30.00
ISBN:1-59973-106-1

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/0912.5441

                                                            (PTO)




                                      136
About the Book


This book introduces the notion of special set linear algebra and special
set fuzzy Linear algebra, which is an extension of the notion set linear
algebra and set fuzzy linear algebra. These concepts are best suited in
the application of multi expert models and cryptology. This book has five
chapters. In chapter one the basic concepts about set linear algebra is
given in order to make this book a self contained one. The notion of
special set linear algebra and their fuzzy analogue is introduced in
chapter two. In chapter three the notion of special set semigroup linear
algebra is introduced. The concept of special set n-vector spaces, n
greater than or equal to three is defined and their fuzzy analogue is their
fuzzy analogue is given in chapter four. The probable applications are
also mentioned. The final chapter suggests 66 problems.




                                    137
Book 45




NEW CLASSES OF NEUTROSOPHIC LINEAR ALGEBRAS
(With Florentin Smarandache and K.Ilanthenral)
Editura CuArt, Romania.
Pages: 467, Published: 2010. Price: €25.00
ISBN:1-59973-116-9

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/1003.1905

                                                            (PTO)




                                      138
About the Book


This book is organized into seven chapters. Chapter one is introductory
in content. The notion of neutrosophic set linear algebras and
neutrosophic set linear algebras are introduced and their properties
analysed in chapter two. Chapter three introduces the notion of
neutrosophic semigroup linear algebras and neutrosophic group linear
algebras. A study of their substructures are systematically carried out in
this chapter. The fuzzy analogue of neutrosophic group linear algebras,
neutrosophic semigroup linear algebras and neutrosophic set linear
algebras are introduced in chapter four of this book. Chapter five
introduces the concept of neutrosophic group bivector spaces,
neutrosophic    bigroup    linear   algebras,   neutrosophic   semigroup
(bisemigroup) linear algebras and neutrosophic biset bivector spaces.
The fuzzy analogue of these concepts are given in chapter six. An
interesting feature of this book is it contains nearly 424 examples of
these new notions. The final chapter suggests over 160 problems which
is another interesting feature of this book.




                                    139
Book 46




RANK DISTANCE BICODES AND THEIR GENERALIZATION
(With Florentin Smarandache, N. Suresh Babu and R.S. Selvaraj)
Svenska fysikarkivet, Stockholm, Sweden.
Pages: 150, Published: 2010. Price: €25.00
ISBN:978-91-85917-12-9

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/1004.2881

                                                                 (PTO)




                                      140
About the Book


This book has four chapters. In chapter one we just recall the notion of
RD codes, MRD codes, circulant rank codes and constant rank codes and
describe their properties. In chapter two we introduce few new classes of
codes and study some of their properties. In this chapter we introduce
the notion of fuzzy RD codes and fuzzy RD bicodes. Rank distance m-
codes are introduced in chapter three and the property of m-covering
radius is analysed. Chapter four indicates some applications of these
new classes of codes.




                                   141
Book 47




SUPER SPECIAL CODES USING SUPER MATRICES
(With Florentin Smarandache with K.Ilanthenral)
Svenska fysikarkivet, Stockholm, Sweden.
Pages: 161, Published: 2010. Price: €20.00
ISBN:978-91-85917-13-6


(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/1006.5790

                                                            (PTO)




                                      142
About the Book


The new classes of super special codes are constructed in this book using
the specially constructed super special vector spaces. These codes mainly
use the super matrices. These codes can be realized as a special type of
concatenated codes. This book has four chapters. In chapter one basic
properties of codes and super matrices are given. A new type of super
special vector space is constructed in chapter two of this book. Three
new classes of super special codes namely, super special row code, super
special column code and super special codes are introduced in chapter
three. Applications of these codes are given in the final chapter.




                                    143
Book 48




NEUTROSOPHIC BILINEAR ALGEBRAS AND THEIR
GENERALIZATIONS
(With Florentin Smarandache)
Svenska fysikarkivet, Stockholm, Sweden.
Pages: 420, Published: 2010. Price: €30.00
ISBN:978-91-85917-14-3


(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/1007.0186

                                                            (PTO)




                                      144
About the Book


This book introduces the concept of neutrosophic bilinear algebras and
their generalizations to n-linear algebras, n>2. This book has five
chapters. The first chapter is introductory in nature and gives a few
essential definitions and references for the reader to make use of the
literature in case the reader is not thorough with the basics. The second
chapter deals with different types of neutrosophic bilinear algebras and
bivector spaces and proves several results analogous to linear bialgebra.
In chapter three the authors introduce the notion of n-linear algebras
and prove several theorems related to them. Many of the classical
theorems for neutrosophic algebras are proved with appropriate
modifications. Chapter four indicates the probable applications of these
algebraic structures. The final chapter suggests about 80 innovative
problems for the reader to solve.




                                    145
Book 49




METHODS IN ENVIRONMENTAL BIOTECHNOLOGY FOR
ENVIRONMENTALISTS
(With Florentin Smarandache, S.R. Kannan and S. Ramathilagam)
InfoLearnQuest, Ann Arbor.
Pages: 142, Published: 2010. Price: €25.00
ISBN:1-59973-094-4




                                                                (PTO)




                                  146
About the Book


The study of environmental pollution by chemicals used in agriculture as
pesticide or as fertilizers or pollution caused by industries and chemical
plants which use chemicals have not been analysed systematically.
      This book has five chapters. First chapter is introductory in
nature. Here we just study chemical pollution caused by garment
industries in chapter two of this book using fuzzy associative memories.
      In chapter three we give ways to control pollution by improving
the system performance using hierarchical genetic fuzzy control
algorithm. This study is carried out using the past data reported by
Shimada et al (1995). Health hazards suffered by the agriculture
labourers; caused by the chemicals used as fertilizers and pesticides is
analysed in chapter four using RTD matrices. Chapter five gives a
method of minimization of SOx and NOx using fuzzy control theory in
cement industries to reduce pollution.




                                   147
Book 50




INTERVAL GROUPOIDS
(With Florentin Smarandache and Moon Kumar Chetry)
InfoLearnQuest, Ann Arbor.

Pages: 240, Published: 2010. Price: $25.00
ISBN:1-59973-125-8

(Also available for download as an ebook)

Los Alamos National Laboratory and Cornell University USA
http://arxiv.org/abs/1009.1288

                                                            (PTO)




                                      148
About the Book


This book introduces several new classes of groupoid, like polynomial
groupoids, matrix groupoids, interval groupoids,polynomial interval
groupoids, matrix interval groupoids and their neutrosophic analogues.
Interval groupoid happens to be the first non-associative structure
constructed using intervals built using Zn or Z or Q or R or Z+ \cup {0}
or Q+ \cup {0} and so on. This book has five chapters. Chapter one is
introductory in nature. In chapter two new classes of groupoids and
interval   groupoids   are   defined   and   described.   The   analogous
neutrosophic study is carried out in chapter three. The applications of
this new structure is given in chapter four. The final chapter suggests
more than 200 problems. This book has given 77 new definitions, 426
examples of these new notions and over 150 theorems.




                                   149
List of Ph.D. Students
Completed under my Guidance: 13

      Satya Veer Singh   ON A NEW CLASS OF LOOPS AND       AUG
1.
       (90PMA00R1)       LOOP RINGS                        1994

      Suresh Babu N.                                       FEB
2.                       STUDIES ON RANK DISTANCE CODES
       (91PMA01RE)                                         1995

       Meiyappan D                                         JUN
3.                       STUDIES ON FUZZY SUBGROUPS
       (94PMA03R0)                                         1998

                         MATHEMATICAL APPROACH TO THE
          Indra V                                          JUN
4.                       PASSENGER TRANSPORTATION
        (MA94P005)                                         1998
                         PROBLEM USING FUZZY THEORY

                         CONSTRUCTION OF CONCATENATION
         Sujatha R       AND ERASURE TECHNIQUES FOR        AUG
5.
        (MA96P001)       THE CLASS OF MRD CODES AND        1999
                         THEIR APPLICATIONS


        Kannan S R       MATHEMATICAL APPROACH TO THE
                                                           OCT
6.                       CHEMICAL INDUSTRY PROBLEMS
        (MA97P004)                                         2001
                         USING FUZZY THEORY

                         MATHEMATICAL APPROACH TO THE
      Ramathilagam S                                      NOV
7.                       CEMENT INDUSTRY PROBLEMS
         (MA98P04)                                        2002
                         USING FUZZY THEORY

                         ON LINEAR CODES WITH RANK
       Rajadurai R S                                      MAY
8.                       METRIC: CONSTRUCTIONS,
         (MA00P06)                                        2004
                         PROPERTIES AND APPLICATIONS

      Moon K. Chetry     STUDY OF SPECIAL ELEMENTS IN     JULY
9.
        (MA01D007)       GROUP RINGS AND LOOP RINGS       2005

       Selvaraj R S      METRIC PROPERTIES OF RANK        MARCH
10.
        (MA00P02)        DISTANCE CODES                    2006




                              150
        Johnson T     SOME NEW FUZZY DATA ANALYSIS     FEB
11.
        (MA03D017)    MODELS AND THEIR APPLICATIONS    2006


      Paramasivam K   COLORING OF ZERO DIVISOR GRAPH
                                                       JUNE
12.                   OF SOME SPECIAL ALGEBRAIC
        (MA03D001)                                     2008
                      STRUCTURES

                      ROLE OF BI-CODES IN
       Rajkumar.R     COMMUNICATION THEORY             AUG
13.
        (MA04D014)                                     2009
                      (Submitted his thesis)




                            151
Extracts from Ph.D. Reports

                                          13
Student Name             :       Mr. Raj Kumar
Thesis Title             :       STUDIES ON CODES AND GRAPHS WITH
                                 ROSEBLOOM-TSFASMAN METRIC

The thesis titled ―Studies on codes and graphs with Rosenbloom-Tsfasman Metric‖
submitted by Mr.R.Rajkumar makes a significant contribution to the theory of error
correcting codes and distance graphs. The thesis mainly focuses on the role played by
the RT metric—introduced by Rosenbloom and Tsfasman in diverse areas, namely
coding theory, graph theory and interconnection networks. The RT metric is known for
its usefulness in case of interference in several consecutive channels in coding theory
literature. And there has been a considerable amount of study going on in this direction
in recent years. The work presented by Mr. Rajkumar proceeds in making a good
contribution to the advancement of knowledge in this field.
         Overall, the thesis is well-structured, easy to read, and the results are correct
and clearly stated. In summary, this thesis is a significant contribution to coding and
graph theory that opens up possible applications to interconnection networks. The
candidate exhibits skill and made substantial advancement of knowledge in this field.
Hence without hesitation I strongly commend the thesis for the award of the Ph.D.
degree.

-- Dr.R.S.Selvaraj, Assoc. Prof, NIT Warangal, Andhra Pradesh, India.

The thesis is dedicated to the theoretical properties and applications of the
Rosenbloom and Tsfasman metric in several very important areas algebraic coding
theory, metric graph theory and interconnection networks. A number of novel concepts
are introduced and explored. For example, a new class of circulant RT distance codes
and the notion of fuzzy RT distance codes are defined and investigated.
        In my opinion, this is the very best doctoral thesis among the many theses
that I have evaluated. The results obtained in the thesis have been published in eight
high-quality journal articles and have been presented at seven conferences. This
work belongs to the intersection of several research directions. All of these directions
are very important and the results obtained in the thesis are excellent. They clearly
demonstrate that R. Rajkumar has acheived high level of expertise in all of these
branches and is well qualified for productive work in these areas. The text in the
present form is well-written and constitutes enjoyable and enlightening reading. This
is why the thesis in its present form is highly commended for the award of the PhD
degree.

--Prof. Andrei Kelarev, Dept. of Computing and Maths., Univ. of Tasmania,
Tasmania, Australia.

                                           152
                                         12


Student Name            :       Mr. K. Paramasivam
Thesis Title            :       COLORING OF ZERO DIVISOR GRAPH OF
                                SOME SPECIAL ALGEBRAIC STRUCTURES



The researcher has tried to discuss the zero divisor graphs of some special class of
loopring using Z2 and Z and their chromatic numbers are determined in chapter 4.
Fifth chapter deals with the concept of generalized k-strongly edge magic labeling. For
this, necessary and sufficient conditions have been applied to get the desired results.
On the whole the thesis provides sufficient evidence of the candidate‘s capacity for
originality and capability of carrying out research work independently. The thesis is
satisfactory in point of language and presentation of the subject matter. In my view,
the thesis can be approved for the award of Ph.D. degree in mathematics in the
present form.

--Prof. Bijendra Singh, S.S. in Mathematics, Vikram University, Ujjain,
India.




The thesis contains a detailed exposition of the research work undertaken by the
candidate. It is devoted to the important notion of a zero-divisor graph, which falls
neatly into the intersection of graph theory and universal algebra. The thesis begins
with a thorough and comprehensive overview of the required preliminaries and
previous results obtained by scientists who have contributed to this research direction.
Subsequent chapters contain new facts and techniques discovered by the candidates.
Complete proofs are given to new theorems obtained by the author of the thesis. The
Thesis contains many new interesting results and is strongly recommended for the
award of Ph.D. degree.

--Prof. Andrei Kelarev, Dept. of Computing and Maths., Univ. of Tasmania,
Tasmania, Australia.




                                          153
                                         11


Student Name            :       Mr. T. Johnson
Thesis Title            :       SOME NEW FUZZY DATA ANALYSIS MODELS
                                AND THEIR APPLICATIONS

This thesis is a considerable work covering ideas of the Data analysis models using
fuzzy techniques. The author has taken ideas from the existing fuzzy models and
generalized to some interesting new fuzzy models. . . The theis provides appropriate
illustrations emphasizing on the social and real world problems as a whole. The
formulation of the thesis is correct and well planned. I recommend the thesis for the
award of the degree of doctor of philsosophy.

Dr Kuncham Syam Prasad, Dept. of Maths, Manipal Institute of
Technology, Manipal Academy of Higher Education, Manipal, India


The thesis is devoted to novel applications of important concepts of fuzzy set theory
and is focusing on data processing. The kind of data considered in the thesis is
particularly difficult to analyze using previous traditional methods. It is remarkable
that the choice of fuzzy set theory has turned out more meaningful and appropriate
for tackling broad classes of problems including social and psychological problems.
The classes considered are very broad and can be also applied in engineering and to
handle scientific questions. The thesis introduces several new models, all of these are
novel and esstenial contributions seriously advancing this direction.
        In my opinion the thesis is very well written and should be commened for the
award of the Ph.D degree.
--Prof. Andrei Kelarev, Dept. of Computing and Maths., Univ. of
Tasmania, Tasmania, Australia.




                                         154
                                        10


Student Name           :       Mr. R.S.Selvaraj
Thesis Title           :       METRIC PROPERTIES OF
                               RANK DISTANCE CODES


The thesis is self content and well presented. It contains many new ideas and orginal
results. The coding theory is becoming more and more important in communication.
This way he as developed the thesis shows that the author reveals a complete mastery
over the subject and the author is familiar with contemporary research on RD codes.
Hence, I strongly feel that the one must congratulate the supervisor and the student
for this valuable work.
I have great pleasure in recommending that R.S.Selvaraj may be awarded the Ph.D
degree in Mathematics and the thesis may be regarded as Highly commended
--Prof. Kirangi, Dept. of Math., Univ. of Mysore, Mysore, India.



This thesis provides several new results on rank distance codes. The work presented
by Selvaraj proceeds in good tradition with previous work conducted by Dr(Mrs)
Vasantha and her collaborators. The thesis is well-written, well-structured, and the
results are clearly stated. The candidate exhibits skill to solve substantial
mathematical problems (in particular, Chapter 2, 4 and 5). Based on this thesis, the
candidate deserves to receive the Ph.D in Mathematics.
-- Prof. Karl-Heinz Zimmermann, Technical Univ. of Hamburg-
Harburg, Dept. of Comp. Elec. Engineering, Hamburg, Germany.




                                        155
                                            9


Student Name             :       Mr. Moon Kumar Chetry
Thesis Title             :       STUDY OF SPECIAL ELEMENTS IN
                                 GROUP RINGS AND LOOP RINGS


It is rare to see a thesis, which carries out study in both associative and non associative
rings. He uses number theoretic techniques in solving the problems. The concepts are
very clearly illustrated by examples, which happens to be a positive point, as these
examples not only help in understanding the theorems but also makes one concretely
understand the definition and results. This is well presented and has several chapters.
          Enumeration of the zero divisors of this form is in fact a new method used in
case of loop rings.
--Prof. Kirangi, Dept. of Math., Univ. of Mysore, Mysore, India.


I must first congratulate the supervisor and the candidate for one of good thesis in
algebra. They have introduced new definitions, proved many results in detail and
suggested many interesting research problems in their thesis.
Most of the theorems are interesting and well presented.
To summarize
    1. The thesis is self content, theorems are proved with all details. Further it
        contains many examples and counter examples, which clarifies the theory.
    2. Contains many new ideas and opened the new channel of S-rings.
    3. The author is familiar with contemporary research on related topics.
    4. The thesis makes a valuable contribution to the field of Algebra.
I have great pleasure in recommending that Moon Kumar Chetry may be awarded
the Ph.D degree.

--Florentine Smarandache, Dept. of Maths., University of New Mexico,
Gallup Campus, USA




                                           156
                                        8


Student Name           :       Mr. R. S. Raja Durai
Thesis Title           :       ON LINEAR CODES WITH RANK METRIC:
                               CONSTRUCTIONS, PROPERTIES AND
                               APPLICATIONS


One just can't think of the world without information. Today it is mainly digital,
but it is prone to error. Any new method which detects and corrects errors,
maintains secrecy is appreciated. This thesis is on those lines. The Introduction
and preliminaries are well presented and it makes the thesis self-contained. The
Chapter II introduces combined error-erasure decoding technique for the first time
to the class of [n,k,d] and MRD codes. Most of the results are worth mentioning
and in particular are theorem 2.4.11 (p.52) and example 2.2.1 (pp. 31-35) really
deserve to be appreciated. Good contribution to the field. The chapter V deserves to
be appreciated as it presents some of the possible applications and further scope
for research. The author has mastered the works of many eminent scholars. Most
of the examples add clarity of the theme. For this the thesis supervisor and the
candidate deserve to be congratulated. Without any hesitation, I strongly
recommend for the award of the Ph.D. degree to R.S. Raja Durai in Mathematics.
--Prof. Kirangi, Dept. of Math., Univ. of Mysore, Mysore, India.


A well-written thesis […] The last section on applications is a persuasive
summary of the importance of some of the results in the thesis. In sum, the
number and the significance of the results appear to be suitable for the award of
Ph.D. -– Prof. Hema Srinivasan, Dept. of Mathematics, University of
Missouri, Colombia, MO 65211, USA.




                                        157
                                         7


Student Name           :       Ms. S. Ramathilagam
Thesis Title           :       MATHEMATICAL APPROACH TO THE
                               CEMENT INDUSTRY PROBLEMS USING
                               FUZZY THEORY


Keeping in mind the problems faced by the Cement Industry in the country and
recalling the previous works done by various authors, S. Ramathilagam made good
attempt to solve some of the problems faced by the Cement Industry by using new
techniques and in fact these were tested. [...] Over all the candidate made
substantial survey and collected enough data related to the work and analyzed the
data by using new techniques to suggest the cement industry to mitigate its
hardships in running the industry more effectively. As the work suggests various
benefits like increase in production, reduction in power consumption, consistent
quality, reduction in mill stoppages, etc. this can be considered as one of the most
useful works either directly or indirectly to the cement industry. -- Prof. G. L.
Reddy, Dept. of Maths. and Computer Science, Univ. of Hyderabad, AP,
India.


She has researched the earlier models and have incorporated them in her work
using Fuzzy matrices. The thesis gives a nice introduction to Fuzzy Theory in the
beginning which would be useful to an outsider. From the rest of the thesis it is
clear that Ms. Ramathilagam has obtained an expert knowledge in Fuzzy logic
and techniques from Fuzzy theory. Techniques from Fuzzy logic have already
become the norm dealing with many difficult or imprecise problems of the
industry. Ms. Ramathilagam's research appears to be a very good addition to our
existing knowledge in that field. Much of the results in the thesis has been
presented in professional conferences as well as published or submitted for
publishing in journals. The amount of work is certainly quite substantial. -- Prof.
Hema Srinivasan, Dept. of Maths., Univ. of Missouri, Colombia, USA.




                                        158
                                       6

Student Name          :       Mr. S. R. Kannan
Thesis Title          :       MATHEMATICAL APPROACH TO THE
                              CHEMICAL INDUSTRY PROBLEMS USING
                              FUZZY THEORY


The thesis is well written. The candidate has taken up the problems which are very
relevant to the present day situation. -- Prof. P.Dheena, Dept. of Maths,
Annamalai Univ. TN, India.


The thesis contains significant new results devoted to the development of new
valuable practical mathematics algorithms using the novel methods of fuzzy
theory and neural networks. The results have been published in several good
publications, and the overall amount of work is significant by all international
standards. I am sure that the methods developed by the applicant will find
applications also in other branches of industry. The is very well written, and I
strongly recommend awarding the degree without making any changes to the
text of the thesis. -- Prof. Andrei Kelarev, Dept. of Maths., Univ. of
Tasmania, Tasmania, Australia.




                                       159
                                        5


Student Name           :       Ms. R. Sujatha
Thesis Title           :       CONSTRUCTION OF CONCATENATION AND
                               ERASURE TECHNIQUES FOR THE CLASS OF
                               MRD CODES AND THEIR APPLICATIONS


I have gone through the thesis with great interest. The thesis is well-written and
the exposition is good. I recommend the thesis for the award of the Ph.D. degree. --
Prof. Loganathan, Dept. of Maths., RIASM, Univ. of Madras, India.


The study of Rank Distance codes (RD codes) is a newer branch of algebraic
coding. RD codes have been invented by E.M.Gabidulin. He has studied so called
MRD codes, a subclass of RD codes which attain the Singleton bound. Another
major contribution of RD codes has been given by N.Suresh Babu, a former
student of IIT, Madras. The thesis of R. Sujatha is a major contribution to RD
codes... The results may have some practical relevance in the future. In
particular, the guessing technique for MRD codes provides a very nice example of
the strength of RD codes... These codes may be useful in byte-organized
memories. This sort of construction is very original. -- Prof. Karl-Heinz
Zimmermann, Technical Univ. of Hamburg-Harburg, Dept. of Comp.
Elec. Engineering, Hamburg, Germany.




                                        160
                                        4


Student Name           :      Ms. Indra Venkatbabu
Thesis Title           :      MATHEMATICAL APPROACH TO THE
                              PASSENGER TRANSPORTATION PROBLEM
                              USING FUZZY THEORY


Indra's thesis contributes decisively to the study of the passenger transportation
problem using Fuzzy Theory... On the other hand, good analysis is made to present
the transportation problem solely for the operator's benefit in such a way that
perfect balance was obtained both from the operator's as well as from the
passenger's point of view... The entire study of the transportation problem was
presented lucidly and satisfactorily. -- Prof. G. Lakshma Reddy, Dept. of
Comp. Sci and Math., Univ. of Hyderabad, Hyderabad, India.


This is a very good thesis at a very high degree difficulty particularly because it
combines mathematical modeling and analysis with empirical work, which can
be found rather solemnly in a Ph.D. thesis. The work is undoubtedly of such a
quality that it makes significant contributions to the advancement of knowledge
and I recommend it by all means to accept this thesis for the award of the Ph.D.
degree. The combination of computer programming, empirical work (working on
a real problem as well as acquiring real data) and mathematical modeling also
normally requires much more work than in either purely mathematical or purely
empirical research work. I have also checked the programs in the world wide web
and I am impressed by the work... -- Prof. Dr. Dr. h.c.H-J. Zimmermann,
(Author: Fuzzy Sets and Systems), RWTH, Aachen, Germany.




                                       161
                                         3



Student Name           :       Mr. D. Meiyappan
Thesis Title           :       STUDIES ON FUZZY SUBGROUPS


The author and the student deserve to be congratulated for their detailed study of
the concept and beautiful presentation of the results... the thesis makes an valuable
contribution to the theory of fuzzy subgroups.-- Prof. Kirangi, Dept. of Math.,
Univ. of Mysore, Mysore, India.


Fuzzy sets and groups is an interesting and important topic of current research in
algebra. It is a topic that is perhaps at a relatively early age of development and
this makes it especially suitable for a thesis. I highly commend Professor
Vasantha for her ingenuity in guiding her students in this interesting and fruitful
direction. In summary this is a very well written thesis which contains a number
of interesting results on an important topic.-- Prof. Hema Srinivasan, Dept.
of Math., Univ. of Missouri-Columbia, USA.




                                        162
                                        2


Student Name           :       Mr. N. Suresh Babu
Thesis Title           :       STUDIES OF RANK DISTANCE CODES


This thesis gives a detailed analysis of error correcting codes in rank metric which
is a very efficient metric in the sense that it can be utilized for error correcting
codes defined over any higher dimensional Galois field wherein usual Hamming
metric is inappropriate. In conclusion, I would like to say that this thesis is an
excellent piece of work in coding theory. -- Prof. M. Vijayalakshmi, Dept. of
Math., RIASM, Univ. of Madras, India.


This thesis makes a significant contribution to the theory of error correcting
codes. Indeed the thesis contains several very important results: a) the non-
existence theorem of perfect rank distance codes over GF(2N) which is certainly
one of the triumphs of the theory...--Prof. Karl-Heinz Zimmermann,
Technical Univ. of Hamburg-Harburg, Dept. of Comp. Elec.
Engineering, Hamburg, Germany.




                                        163
                                         1

Student Name           :       Mr. Satya Veer Singh
Thesis Title           :       ON A NEW CLASS OF LOOPS AND LOOP
                               RINGS


The result seems to be new and interesting... Finally I may say that this is a
reasonably good thesis. -- Prof. R.K.Sharma, Dept. of Math., IIT Kharagpur,
WB, India.


This thesis studies a special type of loops and motivates the reader by providing an
application...-- Prof. M. Satyanarayana, Dept. of Math., Univ. of California,
USA.




                                        164
Post-Graduate Research Projects
Awarded under my Guidance: 76
72 + 4(working)

                            BOOLEAN ALGEBRA AND ITS
       Venkateswaran K S
1.                          APPLICATION TO SWITCHING            1990
           (MA88453)        CIRCUITS

      Sivaramakrishnan S    SEMISIMPLICITY PROBLEM FOR
2.                                                              1990
           (MA88449)        GROUP RINGS

           Revati V S       COVERING RADIUS OF A CODE AND
3.                                                              1992
           (MA90441)        ITS ORTHOGONAL CODE

            Aruna S         ON SOME SPECIAL ELEMENTS OF
4.                                                              1992
           (MA90433)        THE GROUP RING Z2D6

                            ORTHOGONAL IDEALS IN THE LOOP
           Anburaj S
5.                          RING Z2L AND ITS APPLICATION TO     1993
           (MA91431)        CODES

          Sridhar M S
6.                          S-LATTICES                          1993
           (MA91453)

                            ORTHOGONAL IDEALS IN THE
        Govindarajan A
7.                          LATTICES AND ITS APPLICATION TO     1994
           (MA92437)        CODES

                            ON THE IDEALS OF THE GROUP
      Saravana Nambirajan
8.                          RING Z2S3 AND ITS APPLICATIONS TO   1994
           (MA92439)        LINEAR CODES

                            CONSTRUCTION OF FINITE NON-
           Sheela S
9.                          ASSOCIATIVE RINGS USING             1996
           (MA94550)        INTEGERS

        Murugeshwari R
10.                         n-MODULAR LATTICES                  1996
           (MA94539)

        Venkiteswaran S     BALANSOR IN LATTICES AND
11.                                                             1997
           (MA95556)        BALANCED LATTICES


                                165
           Uma S         ESTIMATION OF EXPERT WEIGHTS USING
12.                                                            1997
         (MA95555)       FUZZY COGNITIVE MAPS

        Anitha Devi      POWER ASSOCIATIVE LOOPS WHICH ARE
13.                                                            1998
         (MA96532)       JORDAN LOOPS AND ITS LOOP RINGS

       Meena Kumari
14.                      ON BIRINGS AND BIVECTOR SPACES        1999
         (MA97537)

         Kavitha B       ON SOME CLASSICAL THEOREMS IN
15.                                                            1999
         (MA97536)       BIGROUPS

       Raja Durai R S    ON HYPERLOOPS AND ITS
16.                                                            1999
         (MA97541)       GENERALIZATIONS

        Ram Kishore
17.                      SYMPTOM DISEASE MODEL IN CHILDREN     1999
         (MA97542)

      Akhilandeswari A
18.                      BOOLEAN FUZZY MEASURES                2000
         (MA98531)

          Anitha V       APPLICATION OF BAM MODEL TO STUDY
19.                                                            2000
         (MA98532)       FEMALE INFANTICIDE

         Kamala R        PERSONALITY MEDICINE MODEL USING
20.                                                            2000
         (MA98539)       FUZZY ASSOCIATIVE MEMORIES

        Mary Samuel      PSEUDO COMMUTATIVITY IN LOOPS AND
21.                                                            2000
         (MA98545)       GROUPOIDS

                         A NEW CLASS OF FUZZY RELATIONAL
         Praseetha
22.                      EQUATION AND ITS APPLICATION TO       2000
         (MA98550)       TRANSPORT PROBLEM

                         STUDY OF BASIS IN SEMIVECTOR SPACES
        Promodh P
23.                      AND CONSTRUCTION OF SEMIVECTOR        2000
         (MA98552)       SPACES USING LATTICES

                         CONSTRUCTION OF EMPLOYEE EMPLOYER
      Yasmin Sultana
24.                      RELATIONSHIPS MODEL USING FUZZY       2000
         (MA98562)       RELATIONAL MAPS

          Balu M S       APPLICATIONS OF FUZZY THEORY TO
25.                                                            2001
         (MA99608)       INDIAN POLITICS


                                166
          Baskar A
26.                         WEAKLY SEMISUPER BOOLEAN ALGEBRA      2001
          (MA99609)

           Chitra K
27.                         GROUP SEMI-RINGS                      2001
          (MA99611)

         Sukumar D          A NEW TYPE OF COSUBRING RELATION IN
28.                                                               2001
          (MA99639)         RINGS

       Dennis Williams      ON A NEW CLASS OF PSEUD0-FIELDS
29.                                                               2001
          (MA99614)         USING Zn

                            A MATHEMATICAL APPROACH TO THE
         Devi Yamini
30.                         CHILD LABOUR PROBLEM USING FUZZY      2001
          (MA99615)         DATABASES

         Komathi P V        APPLICATION OF FUZZY THEORY TO THE
31.                                                               2001
          (MA99617)         OLD AGED PEOPLES PROBLEMS

                            RULE BASED CONTROL SYSTEM TO STUDY
          Madhan N
32.                         THE PERFORMANCE ASPECTS OF SCHOOL     2001
          (MA99621)         STUDENTS

       Regin Thangaraj      DEMISUBRINGS AND DEMI-IDEALS IN
33.                                                               2001
          (MA99630)         RINGS

        Subhashree S        APPLICATION OF FUZZY LOGIC TO
34.                                                               2001
          (MA99636)         UNEMPLOYMENT PROBLEM

           Minor A          STUDIES OF PROBLEMS IN TEXTILE
35.                                                               2002
      (M.Tech. 2000-2002)   INDUSTRIES USING FUZZY THEORY

          Johnson T         NEW SPECTRAL THEOREM FOR VECTOR
36.                                                               2003
         (MA01C011)         SPACES OVER FINITE FIELDS

       Madan Kumar N        GENERALIZED r-CHINESE GROUPS AND
37.                                                               2003
         (MA01C019)         NORMAL CHINESE GROUPS

         Pradhab M
38.                         A STUDY ON SEMIDIVISION RINGS         2003
         (MA01C024)

         Natarajan C
39.                         FINITE PSEUDO INNER PRODUCT SPACES    2004
         (MA02C009)


                                   167
      Thiruvengadam N       APPLICATON OF PSEUDO BEST
40.                                                              2004
         (MA02C026)         APPROXIMATION TO ALGEBRAIC CODES

       Bhumika Bhatia       LATTICES POLYNOMIALS AND ITS
41.      (MA03C005)                                              2005
                            APPLICATION TO SWITCHING CIRCUITS

        Brahanayaki S
42.                         NCM TO STUDY INDUSTRIL PROBLEMS      2005
         (MA03C006)

                            USE OF BAM TO STUDY STRESS AND
       Raghavendran R
43.                         STRAIN RELATION AMONG PARENTS AND 2005
         (MA03C019)         CHILDREN

        Ravikumar S
44.                         ON NEAR RINGS                        2005
         (MA03C022)

         Selvarani M
45.                         BI-AUTOMATON                         2005
         (MA03C025)

      Kishore Kumar V
46.                         A STUDY ON SMARANDACHE SEMIGROUPS    2006
         (MA04C009)

                            USE OF NEW FRBM MODEL TO STUDY THE
       Karuppasamy T        SOCIO ECONOMIC PROBLEMS OF
47.                                                              2006
      (M.Tech. 2003-2006)   GARMENT INDUSTRY WORKERS OF
                            TIRUPUR

        Maharaj Singh       SMARANDACHE GROUPOIDS AND THEIR
48.                                                              2007
         (MA05C009)         APPLICATIONS

          Payel Paul
49.                         LOOPS AND SMARANDACHE LOOPS          2007
         (MA05C014)

         Sukhen Das         GROUPOIDS RINGS AND THEIR
50.                                                              2007
         (MA05C029)         PROPERTIES

         Khethavat
51.      Anjaneyulu         SPECIAL ELEMENTS IN BIGROUPS         2008
         (MA06C011)

           Ramya I
52.                         SMARANDACHE SEMIVECTOR SPACES        2008
         (MA06C022)

53.      Naga Raju J        S-SPECIAL ELEMENTS IN GROUPS         2008


                                   168
          (MA06C009)

         Payel Kundu        SPECIAL ELEMENTS IN SMARANDACHE
54.                                                            2008
          (MA06C019)        RINGS

           Arka Sen
55.                         SUBSTRUCTURES IN SMARANDACHE RINGS 2008
          (MA06C004)

             Vijay
56.                         S-SEMIRINGS AND THEIR PROPERTIES   2008
          (MA06C031)

          Dinesh T P
57.                         S-NEARRINGS                        2008
          (MA06C031)

          Debjit Ash        ALGEBRAIC BINARY CODES AND THEIR
58.                                                            2009
          (MA07C004)        PROPERTIES

        Goutam Haldar
59.                         FUZZY SETS AND FUZZY RELATIONS     2009
          (MA07C006)

         Venkata Siva
60.       Krishna G         GROUP RINGS                        2009
          (MA07C007)

       Liton Mayumdar
61.                         BCH CODES AND THEIR PROPERTIES     2009
          (MA07C010)

        Palash Ranjan
                            A STUDY OF RSA CRYPTOSYSTEM AND
62.          Das                                               2009
                            OTHER PUBLIC KEY CRYPTOGRAPHY
          (MA07C015)

        Prabhu Kalyan
63.        Behera           LATTICES AND THEIR PROPERTIES      2009
          (MA07C016)

          Raghu Ram
                            BLACK SCHOLES OPTION PRICING
64.        Kolluru                                             2009
                            FORMULA
          (MA07C019)

      Srinivas Gudukuntla
65.                         FUZZY SUBGROUPS                    2009
          (MA07C024)

      Syamsundar Dhara
66.                         HAMMING CODES                      2009
          (MA07C026)

                                   169
         Venkatesh K
67.                        FUZZY SUBRINGS                      2009
         (MA07C029)

68.    Soni (MA07C022)     BIMATRICES AND BICODES              2009

       C.N.Celine Priya
69.                        STUDY ON LINEAR CODES AND MRD CODES 2010
         (MA08C003)

       B.Sudhakar Goud     FUZZY PRIMARY IDEALS AND FUZZY
70.                                                            2010
         (MA08C002)        SEMIPRIMARY IDEALS OF RINGS

          K.Ramulu         THE NONEXISTENCE OF PLANES OF ORDER
71.                                                            2010
         (MA08C006)        SIX

       S.Sowndrarajan
72.                        LATTICE OF SUBSTRUCTURES            2010
         (MA08C027)




Currently working under me : 4

        Arun Kumar
1.        Paswan          CODING THEORY                       2011
        (MA09C003)

         Pradip Jana
2.                        ALGEBRAIC STRUCTURES                2011
         (MA09C026)

       Banothu Mangu
3.                        CODING THEORY                       2011
         (MA09C008)

       Suvendu Kumar
4.                        ALGEBRAIC STRUCTURES                2011
      Naskar (MA04C029)




                                  170
Individual Research Publications: 211

 1. W.B.Vasantha Kandasamy, On zero-divisors in reduced group rings over
    ordered groups, Proc. Japan Acad., 60 no.9 (1984) 333-334.
    ISSN: 0386-2194

 2. W.B.Vasantha Kandasamy, On semi-idempotents in group rings, Proc.
    Japan Acad., 61 no.4 (1985) 107-108. ISSN: 0386-2194

 3. W.B.Vasantha Kandasamy, A note on the modular group ring of a finite
    p-group, Kyungpook Math. J., 26 no.2 (1986) 163-166. ISSN: 1225-6951

 4. W.B.Vasantha Kandasamy, Zero square group rings, Bull. Cal. Math.
    Soc., 80 (1988) 105-106. ISSN: 0008-0659

 5. W.B.Vasantha Kandasamy, Semi-idempotents in semigroup rings, J.
    Guizhou Inst. of Tech., 18 no.4 (1989) 73-74. ISSN: 1000-2685

 6. W.B.Vasantha Kandasamy, Semigroup rings which are zero square rings,
    News Bull. Cal. Math. Soc., 12 no.4 (1989) 8-10.

 7. W.B.Vasantha Kandasamy, On pre J-group semirings, Pure Math.
    Manuscript, 8 (1989) 95-100.

 8. W.B.Vasantha Kandasamy, On group rings which are p-rings, Ganita, 40
    no.1 (1989) 1-2. ISSN: 0046-5402

 9. W.B.Vasantha Kandasamy, Near loop rings of Moufang loops, Extracta
    Mathematica, Universidad De Extremadura, 5 no.3 (1990) 121-123.
    ISSN: 0213-8743

10. W.B.Vasantha Kandasamy, Semigroup rings of ordered semigroups
    which are reduced rings, J. Math. Res. Expo., 10 no.4 (1990) 493-494.
    ISSN: 1000-341X




                                  171
11. W.B.Vasantha Kandasamy, Regularly periodic elements of a ring, J.
    Bihar Math. Soc., 13 (1990) 12-17. ISSN: 0972-8716

12. W.B.Vasantha Kandasamy, Semigroup rings which are p-rings, Bull. Cal.
    Math. Soc., 82 (1990) 191-192. ISSN: 0008-0659

13. W.B.Vasantha Kandasamy, On quasi-group rings, Scientist of Phys. Sci.,
    2 no.2 (1990) 137-138. ISSN: 0970-9150

14. W.B.Vasantha Kandasamy, Idempotents in the group ring of a cyclic
    group, Vikram University Math. J., 10 (1990) 59-73.

15. W.B.Vasantha Kandasamy, A note on the modular group ring of the
    symmetric group Sn, J. Nat. Phys. Sci., 4 (1990) 121-124.

16. W.B.Vasantha Kandasamy, Zero square group semirings, Buletinul
    (Institute of Bucharest Scientific Bulletin), 52 (1990) 7-9.
    ISSN: 1220-3041

17. W.B.Vasantha Kandasamy, On E-rings, J.Guizhou Inst.Tech., 20 no.1
    (1991) 42-44. ISSN:1000-2685

18. W.B.Vasantha Kandasamy, A note on pre-J-group rings, Qatar Univ. Sci.
    J., 11 (1991) 27-31. ISSN: 1023-8948

19. W.B.Vasantha Kandasamy, Zero divisors in loop algebras of power
    associative and diassociative loops, Ceske Vyoske Uceni Technicke v
    Praze Acta Polytechnica, 16 (1991) 21-26. ISSN: 0554-9205

20. W.B.Vasantha Kandasamy, On strongly subcommutative near-rings,
    Saitama Math. J., 9 (1991)7-8. ISSN: 0289-0739



21. W.B.Vasantha Kandasamy, Inner zero square rings, News Bull. Cal.
    Math. Soc., 14 (1991) 9-10.




                                  172
22. W.B.Vasantha Kandasamy, A note on semigroup rings which are Boolean
    rings, Scientist of Phys. Sci., 3 no.1 (1991) 67-68.
    ISSN: 0970-9150

23. W.B.Vasantha Kandasamy, A note on units and semi-idempotent
    elements in commutative group rings, Ganita, 42 no.1 (1991) 33-34.
    ISSN: 0046-5402

24. W.B.Vasantha Kandasamy, Superboolean algebras, J. Northeast Normal
    Univ., 4 (1991) 9-11. ISSN: 1001-6201

25. W.B.Vasantha Kandasamy, Semi-idempotents in the group ring of a
    cyclic group over the field of rationals, Kyungpook Math. J., 31 no.2
    (1991) 243-251. ISSN: 1225-6951

26. W.B.Vasantha Kandasamy, A note on the mod p-envelope of a cyclic
    group, Math. Student, Indian Mathematical Society, 59 (1991) 84-86.
    ISSN: 0025-5742

27. W.B.Vasantha Kandasamy, Idempotents in quasi-reflexive group rings,
    Scientist of Phys. Sci., 3 no.2 (1991) 136-137. ISSN: 0970-9150

28. W.B.Vasantha Kandasamy, On semigroup rings which are Marot rings,
    Revista Intergracion Temas De Mathematics, 9 no.1 (1991) 59-62.
    ISSN: 0151-4105

29. W.B.Vasantha Kandasamy, Idempotents in group seminear-rings, IPB-
    Bulletin Stiinfic, 53 (1991) 13-17. ISSN: 1220-305x

30. W.B.Vasantha Kandasamy, On the ring Z2S3, Math. Student, Indian
    Mathematical Society, 61 (1992) 246-248. ISSN: 0025-5742

31. W.B.Vasantha Kandasamy, On subsemi-ideal rings, Chinese Quart. J.
    Math., 7 no.1 (1992) 107-108. ISSN: 1002-0462

32. W.B.Vasantha Kandasamy, On chain semirings, J. of Bangladesh Acad.
    Sci., 16 no.2 (1992) 257-258. ISSN: 0378-8121



                                  173
33. W.B.Vasantha Kandasamy, A note on semi-idempotents in group rings,
    Scientist Phys. Sci., 4 no.1 (1992) 77-78. ISSN: 0970-9150

34. W.B.Vasantha Kandasamy, On near loop rings which are Marot near
    loop rings, Zeszyty Naukowe Politechniki Rzeszowskiej Matematyka i
    Fizyka, Z.14 NR.101 (1992) 55-58. ISSN: 0209-2670

35. W.B.Vasantha Kandasamy, Semigroup rings that are pre-Boolean rings,
    J. Fuzhou Univ., 20 no.1 (1992) 6-8. ISSN: 1000-2243

36. W.B.Vasantha Kandasamy, Filial semigroups and semigroup rings,
    Libertas Mathematica, 12 (1992) 35-37. ISSN 0278-5307

37. W.B.Vasantha Kandasamy, Semirings in rings, J. Inst. Math. Comp. Sci.,
    5 no.3 (1992) 379-380.

38. W.B.Vasantha Kandasamy, Loops over near-rings, J. Shanghai Univ. Sci.
    Tech., 15 no.1 (1992) 41-43. ISSN: 0258-7041

39. W.B.Vasantha Kandasamy, On null semigroups, Math. Education, 24
    no.3 (1992) 186-187. ISSN: 0047-6269

40. W.B.Vasantha Kandasamy, n-ideal rings, J. Southeast Univ., 8 no.2
    (1992) 109-111.

41. W.B.Vasantha Kandasamy, On normal elements in loop rings, Ultra
    Scientist of Phys. Sci., 4 no.2 (1992) 210-212. ISSN: 0970-9150

42. W.B.Vasantha Kandasamy, On perfect less by r-numbers, Pure Appl.
    Math. J., 8 (1992) 107. ISSN: 0019-5588



43. W.B.Vasantha Kandasamy, A note on group near-rings which are p-near-
    rings, Acta ciencia Indica, 28 no.2 (1992) 175-176.
    ISSN: 0970-0455




                                  174
44. W.B.Vasantha Kandasamy, Zero divisors in group seminear-rings, Riazi
    J. of Karachi Math. Asso., 14 (1992) 25-28. ISSN: 0255-7568

45. W.B.Vasantha Kandasamy, On generalized semi-ideals of a group ring, J.
    Qufu Shifan Daxue Xuebao, Normal University, 18 no.4 (1992) 25-27.
    ISSN: 1001-5337

46. W.B.Vasantha Kandasamy, On inner commutative groups, Math.
    Student, Indian Mathematical society, 61 (1992) 249-252.
    ISSN 0025-5742

47. W.B.Vasantha Kandasamy, Idempotents in rational loop algebras, Ganit,
    J. Bangladesh Math. Soc., 12 no.1 (1992) 53-56. ISSN 0936-7195

48. W.B.Vasantha Kandasamy, Semivector spaces over semifields, Zeszyty
    Naukowe Politichniki, Rze. Folia. Scie. Univ. Tech. Res., Matematyka i
    Fizyka, Z.17 Nr 118 (1993) 43-51. ISSN: 0209-2670

49. W.B.Vasantha Kandasamy, S-weakly regular group rings, Archivum
    Mathematicum, 29 (1993) 39-41. ISSN: 0044-8753

50. W.B.Vasantha Kandasamy, Strongly modular subsemigroups in finite
    semigroups, Analele universitatii Din galati Matematica, 16 no.11 (1993)
    49-54. ISSN: 1221-4531

51. W.B.Vasantha Kandasamy, On strongly subcommutative group ring,
    Revista ciencias Matematicas, 14 no.1 (1993) 92-93. ISSN: 0256-5374

52. W.B.Vasantha Kandasamy, On loop semirings, Toimetised proceedings
    Estonian Acad. Sci., 42 no.4 (1993) 347-349. ISSN: 0373-6431



53. W.B.Vasantha Kandasamy, Modularity and supermodularity of
    subsemigroups in finite semigroups, Proc. Pak. Acad. Sci., 30 no.1 (1993)
    45-47. ISSN: 0377-2969




                                    175
54. W.B.Vasantha Kandasamy, Loop Boolean algebras, Zeszyty Naukowe
    Politichniki, Rze. Folia. Scie. Univ. Tech. Res., Matematyka i Fizyka,
    Z.17 Nr 121 (1993) 95-98. ISSN: 0072-0372

55. W.B.Vasantha Kandasamy, Semi group rings which are chinese rings, J.
    of Math. Res. Exposition, 13 No.3 (1993) 375-376. ISSN: 1000-341x

56. W.B.Vasantha Kandasamy, Units in loop rings, Ultra Scientist Phys. Sci.,
    5 no.1 (1993) 86-88. ISSN:0970-9150

57. W.B.Vasantha Kandasamy, On subgroups satisfying quasi strongly
    modular identity, Pure Math. Manuscript, 10 (1993) 141-145.

58. W.B.Vasantha Kandasamy, On quasi supermodular lattices, Ultra
    Scientist Phys. Sci., 5 no.2 (1993) 218-219. ISSN: 0970-9150

59. W.B.Vasantha Kandasamy, Integral loop semi-near-rings, Zeszyty
    Naukowe Politichniki, Rze. Folia. Scie. Univ. Tech. Res., Matematyka i
    Fizyka, Z.17 Nr 121 (1993) 99-103. ISSN: 0072-0372

60. W.B.Vasantha Kandasamy, Group rings which are a direct sum of
    subrings, Revista Investigacion operacinal, Journal of the Universidad
    de la Habana, 14 no.1 (1993) 85-87.

61. W.B.Vasantha Kandasamy, Orthogonal ideals in lattices and its
    application to codes, Proc. National Seminar on algebra and its
    applications, Bharatidasan Univ., 17th-18th April 1993, 69-72.

62. W.B.Vasantha Kandasamy, A new type of product on lattices near-ring
    semilattices, Vikram University Math. J., 13 (1993) 23-27.

63. W.B.Vasantha Kandasamy, Strong right S-rings, J. of Fuzhou Univ, 21
    no.4 (1993) 6-8. ISSN: 1000-2243

64. W.B.Vasantha Kandasamy, On strictly right chain group rings, Hunan
    Annele math., 14 no.2 (1994) 47-49.




                                   176
65. W.B.Vasantha Kandasamy, I*- Semigroups, Math. Education, 28 (1994)
    30-31. ISSN: 0047-6269

66. W.B.Vasantha Kandasamy, On a problem of the group ring Z2S3, Ultra
    Scientist Phys. Sci., 6 no.1 (1994) 147. ISSN: 0970-9150

67. W.B.Vasantha Kandasamy, J-semigroups and J-semigroup rings, Math.
    Education, 28(1994) 84-86. ISSN: 0047-6269

68. W.B.Vasantha Kandasamy, On a new type of group rings and its new
    divisors, Ultra Scientist Phys. Sci., 6 no.1 (1994) 136-137.
    ISSN: 0970-9150

69. W.B.Vasantha Kandasamy, On multi differentiation of decimal and
    fractional calculus, Math. Education, 28 no.4 (1994) 220-224.
    ISSN: 0047-6269

70. W.B.Vasantha Kandasamy, Coloring of group rings, J. Inst. Math. Comp.
    Sci.,7 no.1 (1994) 35-37.

71. W.B.Vasantha Kandasamy, Lie ideals of Z2S3, Technical university of
    Cluj Napoca, Acta Technica Napocensis, 37 no.1 (1994) 113-116.
    ISSN: 1221-5872

72. W.B.Vasantha Kandasamy, On a new type of product rings, Ultra
    Scientist of Phys. Sci., 6 no.2, (1994) 270-271. ISSN: 0970-9150

73. W.B.Vasantha Kandasamy, n-ideal near-rings, J. Math. Res. Exposition,
    14 no.2 (1994) 167-168. ISSN: 1000-341X

74. W.B.Vasantha Kandasamy, On decimal and fractional Calculus, Ultra
    Scientist of Phys. Sci., 6 no.2 (1994) 283-285. ISSN: 0970-9150

75. W.B.Vasantha Kandasamy, On SPI semigroups, Proc. Pak. Acad. Sci., 31
    no.1 (1994) 49-50. ISSN: 0377-2969




                                  177
76. W.B.Vasantha Kandasamy, On pseudo commutative elements in a ring,
    Ganita Sandesh, Rajasthan Ganita Parishad, 8 no.1 (1994) 19-21.
    ISSN: 0970-9169

77. W.B.Vasantha Kandasamy, f-semigroup rings, Math. Education, 28 no.3
    (1994) 162-164. ISSN: 0047-6269

78. W.B.Vasantha Kandasamy, On weakly Boolean grouprings, Libertas
    Mathematica, Amer. Romanian Acad. Arts Sci., 14 (1994) 111-113.
    ISSN: 0278-5307

79. W.B.Vasantha Kandasamy, Supermodular subgroups in finite groups,
    Rostock. Math. Kolloq, 47 (1994) 27-30. ISSN: 0138-3248

80. W.B.Vasantha Kandasamy, On strong ideal and subrings of a ring, J.
    Inst. Math Comp. Sci., 7 no.3 (1994) 197-199.

81. W.B.Vasantha Kandasamy, On strictly right loop rings, J. of Harbin Inst.
    of Sci. and Tech., 18 no.3 (1994) 116-118. ISSN: 1005-9113

82. W.B.Vasantha Kandasamy, On the ring (R x G x S), J. of Xoinjiang
    University, 11 no.1 (1994) 33-34. ISSN: 1000-2839

83. W.B.Vasantha Kandasamy, Semi idempotents in loop algebras, J. Inst.
    Math. Comp. Sci., 7 no.3 (1994) 241-244.



84. W.B.Vasantha Kandasamy, Weakly regular group rings, Acta ciencia
    Indica, 20 (1994) 57-58. ISSN: 0970-0455

85. W.B.Vasantha Kandasamy, Zero divisors in semiloop near-rings, Zeszyty
    Naukowe Politichniki, Rze. Folia. Scie. Univ. Tech. Res., Matematyka i
    Fizyka, Z.15 Nr 127 (1994) 79-84. ISSN: 1232-7867

86. W.B.Vasantha Kandasamy, A note on the modular semigroup ring of a
    finite idempotent semigroup, J. Natural Phys. Sci., 8 (1994) 91-94.




                                   178
87. W.B.Vasantha Kandasamy, Group Boolean algebras, J. Math. Res.
    Exposition, 14 no.4 (1994) 522-524. ISSN: 1000-341X

88. W.B.Vasantha Kandasamy, A note on semigroup rings which are pre-p-
    rings, Kyungpook Math. J., 34 no.2 (1994) 223-225. ISSN: 1225-6951

89. W.B.Vasantha Kandasamy, On rings satisfying at = bs = (ab)t, Proc. Pak.
    Acad., 31 no.4 (1994) 289-292. ISSN: 0377-2969

90. W.B.Vasantha Kandasamy, Regularly periodic elements of a group rings,
    Ultra Scientist J. Phys. Sci., 8 (1994) 47-50. ISSN: 0970-9150

91. W.B.Vasantha Kandasamy, On the mod p-envelope of Sn, Math.
    Education, 29 no.3 (1995) 171-173. ISSN: 0047-6269

92. W.B.Vasantha Kandasamy, Right multiplication ideals in rings, Opuscula
    Mathematica, 15 (1995) 115-117. ISSN: 1232-9274

93. W.B.Vasantha Kandasamy, Complex fuzzy sets and systems, Ultra
    Scientist Phys. Sci., 7 no.1 (1995) 110-111. ISSN: 0970-9150

94. W.B.Vasantha Kandasamy, A note on the modular loop ring of a finite
    loop, Opuscula Mathematica, 15 (1995) 109-112.

95. W.B.Vasantha Kandasamy, On semigroup rings in which (xy)n = xy, J.
    Bihar Math. Soc., 16 (1995) 47-50. ISSN: 0972-8716

96. W.B.Vasantha Kandasamy, Essential subgroups of a group, J. Math. Res.
    Exposition, 15 no.3 (1995) 350-352. ISSN: 1000-341x

97. W.B.Vasantha Kandasamy, On quasi-commutative rings, Carbib J.
    Math. Comp. Sci., 5 (1995) 22-24. ISSN 1017-6764

98. W.B.Vasantha Kandasamy, On fuzzy semifields and fuzzy semivector
    spaces, Ultra Scientist Phys. Sci., 7 no.1 (1995) 115-116. ISSN: 0970-9150




                                    179
 99. W.B.Vasantha Kandasamy, The units of semigroup seminear-rings,
     Opuscula Mathematica, 15 (1995) 113-114. ISSN: 1232-9274

100. W.B.Vasantha Kandasamy, Zero divisors in loop-loop near-rings, J.inst.
     Math. Comp. Sci., 8 no.2 (1995) 139-143.

101. W.B.Vasantha Kandasamy, On fuzzy reflexive non-associative matrices,
     J. Phys. Sci., 7 no.2 (1995) 230-232.

102. W.B.Vasantha Kandasamy, On group semigroup rings, Octogon Math.
     Mag., 3 no.2 (1995) 44-46. ISSN: 1222-5657

103. W.B.Vasantha Kandasamy, Orthogonal sets in group rings, J. Inst. Math.
     Comp. Sci., 8 no.2 (1995) 87-89.

104. W.B.Vasantha Kandasamy, Obedient ideals in a finite ring, J. inst. Math.
     Comp. Sci., 8 no.3 (1995) 217-219.

105. W.B.Vasantha Kandasamy, On lin-group rings, Zeszyty Naukowe
     Politichniki, Rze. Folia. Scie. Univ., Matematyka i Fizyka, Z.18 Nr.129
     (1995) 23-26.

106. W.B.Vasantha Kandasamy, Fuzzy subloops of some special loops, Proc.
     fuzzy Math. workshop, 26th Iranian Math. Conf., Shahib Bahonar Univ.
     of Kerman, 28th - 31st Mar., 1995, Iran.

107. W.B.Vasantha Kandasamy, On semigroup superboolean Algebras,
     Analele Stiintifice Ale Universtatii Al. I. Cuza Iasi., 4 (1995) 33-36.
     ISSN: 1217-8950

108. W.B.Vasantha Kandasamy, Group rings which satisfy super ore
     condition, Vikram University Math. J., 15 (1995) 67-69.

109. W.B.Vasantha Kandasamy, On loop rings which are marot loop rings,
     Ultra Scientist J. Phys. Sci., 7 no.2 (1995) 224-226. ISSN: 0970-9150




                                    180
110. W.B.Vasantha Kandasamy, Complex Polynomial near-rings, Analele
     Stiintifice Ale Universtatii Al. I. Cuza Iasi., 4 (1995) 29-31.
     ISSN: 1217-8950

111. W.B.Vasantha Kandasamy, On looprings which are marot loop rings,
     Ultra Scientist Phys. Sci., 8 no.1 (1996) 126-128. ISSN: 0970-9150

112. W.B.Vasantha Kandasamy, I*-ring, Chinese Quart. J. Maths., 11 no.2
     (1996) 11-12. ISSN: 1002-0462

113. W.B.Vasantha Kandasamy, On N-harmonious subgroups of a group,
     Acta ciencia indica, 22 (1996) 457-458. ISSN: 0970-0455

114. W.B.Vasantha Kandasamy, Loops over real quaternions, Vikram
     University Math. J., School of Studies in Math., Vikram University, MP,
     India, 16 (1996) 1-6.

115. W.B.Vasantha Kandasamy, On fuzzy reflexive non-associative matrices,
     Ultra Scientist Phys. Sci., 8 no.1 (1996) 110-112. ISSN: 0970-9150

116. W.B.Vasantha Kandasamy, Division of lattice intervals and new lattices,
     Octogon Math. Mag., 4 no.1 (1996) 45-50. ISSN: 1222-5657

117. W.B.Vasantha Kandasamy, On ordered groupoids and its groupoid rings,
     J. of Math. Comp. Sci., 9 no.2 (1996) 145-147.

118. W.B.Vasantha Kandasamy, Idempotents in loop semi-near-rings, Ganit,
     J. Bangladesh Math. Soc., 16 (1996) 35-39. ISSN 0936-7195

119. W.B.Vasantha Kandasamy, Finite rings which has isomorphic quotient
     rings, formed by non-maximal ideals, Math. Education, 30 no.2 (1996)
     125-126. ISSN: 0047-6269

120. W.B.Vasantha Kandasamy, On semipotent linear operators and matrices,
     Ultra Scientist Phys. Sci., 8 (1996) 254-256. ISSN: 0970-9150




                                    181
121. W.B.Vasantha Kandasamy, A note on group rings which are F-rings,
     Acta ciencia indica, 22 no.3 (1996) 251-252. ISSN: 0970-0455

122. W.B.Vasantha Kandasamy, On pseudo niven numbers, Math. Education,
     30 no.4 (1996) 191-192. ISSN: 0047-6269

123. W.B.Vasantha Kandasamy, Multi-Fuzzy differentiation in Fuzzy
     polynomial rings, J. Inst. Math. Comp. Sci., 9 no.2 (1996) 171-173.

124. W.B.Vasantha Kandasamy, Polynomial Tri-operational rings, Bul. Inst.
     Polit. Iasi, XLII (1996) 1-3. ISSN: 1011-2855

125. W.B.Vasantha Kandasamy, On the matrix equation Xn + Ym = Zp, Ultra
     Scientist Phys. Sci., 8 no.2 (1996) 265-266. ISSN: 0970-9150

126. W.B.Vasantha Kandasamy, The matrix equation X12 + … + Xn2 =
     MX1X2Xn, J. of Inst. Math. Comp. Sci., 9 (1996) 283-284.

127. W.B.Vasantha Kandasamy, On ideally strong group rings, Math.
     Education, 30 no.2 (1996) 71-72. ISSN: 0047-6269

128. W.B.Vasantha Kandasamy, Idempotents and semi-idempotents in near-
     rings, J. of Sichuan Univ., 33 no.3 (1996) 330-332.ISSN: 0490-6756

129. W.B.Vasantha Kandasamy, Loop algebras          of   Moufang   loops,
     Mathematical forum, 11 (1997) 21-25.

130. W.B.Vasantha Kandasamy, Gaussian Polynomial rings, Octogon Math.
     Mag., 5 no.2 (1997) 58-59. ISSN: 1222-5657

131. W.B.Vasantha Kandasamy, On a natural trinary operation in the modulo
     integers Zn, J. of Inst. Math. Comp. Sci., 10 no.1 (1997) 59-61.

132. W.B.Vasantha Kandasamy, Permutable Matrices, Ultra Scientist Phys.
     Sci., 9 no.1 (1997) 137-138. ISSN: 0970-9150



                                  182
133. W.B.Vasantha Kandasamy, On semi nilpotent elements of a ring, Punjab
     Univ. J. Math., 30 (1997) 143-147. ISSN: 1016-2526

134. W.B.Vasantha Kandasamy, On fuzzy complex near-rings, Math.
     Education, 31 no.2 (1997) 90-91. ISSN: 0047-6269

135. W.B.Vasantha Kandasamy, On tripotent elements of a ring, J. Inst.
     Math. Comp. Sci., 10 no.1 (1997) 73-74.

136. W.B.Vasantha Kandasamy, On SS-ring, Math. Education, 32 no.2 (1998)
     68-69. ISSN: 0047-6269

137. W.B.Vasantha Kandasamy, On a quasi subset theoretic relation in a ring,
     Acta ciencia indica, 24 no.1 (1998) 9-10. ISSN: 0970-0455

138. W.B.Vasantha Kandasamy, Strongly Modular Lattices, Ultra Scientist
     Phys. Sci., 10 no.1 (1998) 106-113. ISSN: 0970-9150

139. W.B.Vasantha Kandasamy, Inner Associative rings, J. Math. Res.
     Exposition, 18 no.2 (1998) 217-218. ISSN: 1000-341x

140. W.B.Vasantha Kandasamy, Group-loop-rings, Acta ciencia Indica, 24
     no.1 (1998) 13-14. ISSN: 0970-0455

141. W.B.Vasantha Kandasamy, On plane sphere intersecting problem, Ultra
     Scientist Phys. Sci., 10 no.1 (1998) 137-138. ISSN: 0970-9150

142. W.B.Vasantha Kandasamy, On tight matrix pairs, Octogon Math. Mag.,
     6 no.1 (1998) 51-53. ISSN: 1222-5657

143. W.B.Vasantha Kandasamy, On quasi loops, Octogon Math. Mag., 6 no.1
     (1998) 63-64. ISSN: 1222-5657

144. W.B.Vasantha Kandasamy, On fuzzy near matrix rings, Math. Education,
     32 no.3 (1998) 169-171. ISSN: 0047-6269




                                    183
145. W.B.Vasantha Kandasamy, A note of f-group rings without non-zero
     nilpotents, Acta ciencia indica, 24 no.1 (1998) 15-17. ISSN: 0970-0455

146. W.B.Vasantha Kandasamy, On a new class of Jordan loops and their loop
     rings, J. Bihar Math. Soc., 19 (1999) 71-75. ISSN: 0972-8716

147. W.B.Vasantha Kandasamy, Matrices over the Boolean algebra [0, 1],
     Math. Education, 33 no.1 (1999) 9-10. ISSN: 0047-6269

148. W.B.Vasantha Kandasamy, Mathematical approach to the industrial
     problem of maximizing the industries profit and the workers incentive,
     Ultra Scientist Phys. Sci., 11 no.1 (1999) 23-29. ISSN: 0970-9150

149. W.B.Vasantha Kandasamy, On E-semigroup rings, Caribbean J. Math.
     Computing Sci., The Univ. West Indies, 9 (1999) 52-54. ISSN: 1017-6764

150. W.B.Vasantha Kandasamy, On non-associative semi-rings, Acta ciencia
     indica, 25 no.4 (1999) 359-360. ISSN: 0970-0455

151. W.B.Vasantha Kandasamy, The game Pallamkuzhi-its mathematical
     aspects, Appl. Sci. Periodical, 1 (1999) 74-76. ISSN: 0972-5504

152. W.B.Vasantha Kandasamy, r-semi-identity matrices, J. Inst. Math.
     Comp. Sci., 12 (1999) 157-159.

153. W.B.Vasantha Kandasamy, Bi-vector spaces, Ultra Scientist Phys. Sci., 11
     no.2 (1999) 186-190. ISSN: 0970-9150

154. W.B.Vasantha Kandasamy, Quasi vector spaces, Octogon Math. Mag., 7
     no.2 (1999) 76-78. ISSN: 1222-5657

155. W.B.Vasantha Kandasamy, Group rings which have trivial subrings,
     Math. Education, 33 no.3 (1999) 180-181. ISSN: 0047-6269

156. W.B.Vasantha Kandasamy, On fuzzy semirings, Acta ciencia indica, 25
     no.4 (1999) 361-362. ISSN: 0970-0455



                                    184
157. W.B.Vasantha Kandasamy, On group rings which are gamma n rings and
     errata, Math. Education, 33 no.2 (1999) 72-73 and 34 no.1 (2000) 61.
     ISSN: 0047-6269

158. W.B.Vasantha Kandasamy, Loop algebras of an operator loop over Z,
     Acta ciencia Indica, 24 no.2 (2000) 129-131. ISSN: 0970-0455

159. W.B.Vasantha Kandasamy, Some applications of the decimal derivative,
     Math. Education, 34 no.2 (2000) 128-129. ISSN: 0047-6269

160. W.B.Vasantha Kandasamy, On pseudo identities in fuzzy matrices,
     Octogon Math. Mag., 8 no.1 (2000) 98-100. ISSN: 1222-5657

161. W.B.Vasantha Kandasamy, On an infinite group and the lattice of its
     subgroups, Octogon Math. Mag., 8 no.1 (2000) 115-118.
     ISSN: 1222-5657

162. W.B.Vasantha Kandasamy, On finite quaternion rings and skew fields,
     Acta ciencia indica, 24 no.2 (2000) 133-135. ISSN: 0970-0455

163. W.B.Vasantha Kandasamy, Pallamkuzhi - (Kattattam), Math. Education,
     34 no.3 (2000) 143-144. ISSN: 0047-6269

164. W.B.Vasantha Kandasamy, On non associative fuzzy semirings, Ultra
     Scientist Phys. Sci., 12 no.3 (2000) 417-418. ISSN: 0970-9150

165. W.B.Vasantha Kandasamy, On the equation x2 + 1 = 0, J. Inst. Math.
     Comp. Sci., 13 no.3 (2000) 311-313.

166. W.B.Vasantha Kandasamy, On the partial differentiation of decimal and
     fractional calculus, J. Inst. Math. Comp. Sci.,13 no.3 (2000) 287-290.

167. W.B.Vasantha Kandasamy, On demi modules over rings, J. of Wuhan
     automotive polytechnic Univ., 22 no.6 (2000) 123-125.
     ISSN: 1007-144X




                                   185
168. W.B.Vasantha Kandasamy, A note on f-group near-rings without non
     zero nilpotent, Acta ciencia indica, 26 no.4 (2000) 335-338.
     ISSN: 0970-0455

169. W.B.Vasantha Kandasamy, On dimension for Boolean polynomial, Acta
     ciencia indica, 26 no.4 (2000) 339-342. ISSN: 0970-0455

170. W.B.Vasantha Kandasamy, Tight rings and group rings, Acta ciencia
     indica, 27 no.1 (2001), 87-88. ISSN: 0253-732X

171. W.B.Vasantha Kandasamy, On n-pseudo normal subgroups of a group,
     Acta ciencia indica, 27 no.1 (2001) 89-90. ISSN: 0253-732X

172. W.B.Vasantha Kandasamy, On locally semi unitary rings, Octogon Math.
     Mag., 9 no.1 (2001) 260-262. ISSN: 1222-5657

173. W.B.Vasantha Kandasamy, On the game pallamkuzhi with a single
     player, Math. Education, 35 no.3 (2001) 127-128. ISSN: 0047-6269

174. W.B.Vasantha Kandasamy, CN rings, Octogon Math. Mag., 9 no.1 (2001)
     343-345. ISSN: 1222-5657

175. W.B.Vasantha Kandasamy, On the triple {1, n2 - 2p, n2 +2n – (2p-1)},
     J. Inst. Math. Comp. Sci., 14 no.2 (2001) 149-150.

176. W.B.Vasantha Kandasamy, On quasi semi group rings, Math. Education,
     35 no.4 (2001) 192-195. ISSN: 0047-6269

177. W.B.Vasantha Kandasamy, On a new class of semi vector spaces,
     Varahmihir J. Math. Sci., Sandipani Acad., 1 no.1 (2001) 23-31.
     ISSN: 0972-7329

178. W.B.Vasantha Kandasamy, New class of finite groupoids using Zn,
     Varahmihir J. Math. Sci., Sandipani Acad., 1 no.2 (2001) 135-143.
     ISSN: 0972-7329




                                  186
179. W.B.Vasantha Kandasamy, Bi-loops, Ultra Scientist Phys. Sci., 14 (2002)
     127-130. ISSN: 0970-9150

180. W.B.Vasantha Kandasamy, Smarandache semirings and semi fields,
     Smarandache notions journal, 13 (2002) 88-91. ISSN: 1084-2810

181. W.B.Vasantha Kandasamy, On semi idempotent matrices, Ultra Scientist
     Phys Sci., 14 (2002) 294-296. ISSN: 0970-9150

182. W.B.Vasantha Kandasamy, Smarandache cosets, Smarandache notions
     journal, 13 (2002) 245-251. ISSN: 1084-2810

183. W.B.Vasantha Kandasamy, Smarandache loops, Smarandache notions
     journal, 13 (2002) 252-258. ISSN: 1084-2810

184. W.B.Vasantha Kandasamy, Normal near rings, Acta ciencia Indica, 28
     (2002) 47-48. ISSN: 0253-732X

185. W.B.Vasantha Kandasamy, Group rings which have SV-groups, Acta
     ciencia Indica, 28 (2002) 49-50. ISSN: 0253-732X

186. W.B.Vasantha Kandasamy, A new identity in loops, Octogon Math.
     Mag., 10 (2002) 739-741. ISSN: 1222-5657

187. W.B.Vasantha Kandasamy, The concept of super idempotents and zero
     divisors, Octogon Math. Mag., 10 (2002) 823-825. ISSN: 1222-5657

188. W.B.Vasantha Kandasamy, Quasi ideals in group rings, Acta ciencia
     Indica, 28 no.3 (2002) 295-296. ISSN: 0253-732X

189. W.B.Vasantha Kandasamy, On sub-rings satisfying a special identity SI-
     rings, Acta ciencia Indica, 28 no.3 (2002) 297-298. ISSN: 0253-732X

190. W.B.Vasantha Kandasamy, Link relation in rings, Acta ciencia Indica, 28
     no.3 (2002) 299-302. ISSN: 0253-732X




                                    187
191. W.B.Vasantha Kandasamy, On Loop near-rings, Ultra Scientist Phys.
     Sci., 14 no.3 (2002) 557-560. ISSN: 0970-9150

192. W.B.Vasantha Kandasamy, Smarandache Groupoids, Smarandache
     Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/Groupoids.pdf

193. W.B.Vasantha Kandasamy, Smarandache Pseudo-Ideals, Smarandache
     Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/pseudo-ideals.pdf

194. W.B.Vasantha Kandasamy, Units and Smarandache Units, Smarandache
     Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/Units.pdf

195. W.B.Vasantha Kandasamy, Smarandache Idempotents, Smarandache
     Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/Idempotents.pdf

196. W.B.Vasantha Kandasamy, Smarandache Automaton, Smarandache
     Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/Automaton.pdf

197. W.B.Vasantha Kandasamy, Smarandache Zero Divisors, Smarandache
     Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/ZeroDivisor.pdf

198. W.B.Vasantha Kandasamy, Smarandache Galois Fields, Smarandache
     Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/GaloisFields.pdf

199. W.B.Vasantha Kandasamy, Smarandache Non-associative        Rings,
     Smarandache Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/NA-Rings.pdf




                                 188
200. W.B.Vasantha Kandasamy, Smarandache Near-rings , Smarandache
     Notions Journal, (2002).
     http://www.gallup.unm.edu/~smarandache/NearRings.pdf

201. W.B.Vasantha Kandasamy, Smarandache Groupoids and its Applications,
     Vikram Univ. Mathematical Journal, 19 (2001) 60-72.

202. W.B.Vasantha Kandasamy, On Group Semisuperboolean Algebras, Buletinul
     Institutului Politechnic Din Iasi, XLVI (2000), 1-5. ISSN: 1011-2855

203. W.B.Vasantha Kandasamy, Finite Zeros and Finite Zero Divisors,
     Varahmihir Journal of Mathematical Sciences, 2 no. 2 (2002), 295-302.
     ISSN: 0972-7329

204. W.B.Vasantha Kandasamy, On Normally Inner Commutative Groups,
     Varahmihir Journal of Mathematical Sciences, 4 no. 1 (2004), 85-87.
     ISSN: 0972-7329

205. W.B.Vasantha Kandasamy, Bi-rings, Jour. Inst. of Math. and Com. Sci, 17
     no. 2 (2004) 101-103.

206. W.B.Vasantha Kandasamy, On Fuzzy Calculus over Fuzzy Polynomial Rings,
     Vikram Univ. Mathematical Journal, Vikram University, MP. India, 22
     (2002) 1-5.

207. W.B.Vasantha Kandasamy, Bisemigroups and its Applications, J. Bihar
     Math. Soc., 23 (2003) 35-44. ISSN: 0972-8716

208. W.B.Vasantha Kandasamy, Smarandache group near-rings               and
     Smarandache semi-near rings, Ultra Sci., 17 (2005) 119-126.
     ISSN: 0970-9150

209. W.B.Vasantha Kandasamy, Smarandache Seminear-rings, Ultra Sci., 17
     (2005) 127-132. ISSN: 0970-9150



210. W.B.Vasantha Kandasamy, On Smarandache ideals in near-rings, Jour. Of
     Inst. Of Math and Comp. Sci. , (Math ser), 18, (2005) no.2, 119-120.



                                    189
211. W.B.Vasantha Kandasamy, Bistructures and S-Bistructures, Jour. of Inst. of
     Math and Comp. Sci. , (Math ser), 18, (2005) no.1, 95-97.




                                     190
Combined Research Publications: 106



 1. Vasantha Kandasamy, W.B., and Suresh Babu, N., On orthogonal ideals
    in group rings, J. Nat. Phys. Sci., 5-8 (1991-4) 139-142.

 2. Vasantha Kandasamy, W.B., and Anburaj, S.A., Orthogonal ideals in the
    loop ring Z2L and application to codes, Proc. of the National Seminar
    on Algebra, Bharatidasan Univ., 58-62 (1993).

 3. Vasantha Kandasamy, W.B., and Sridhar, M.S., A new definition of
    lattices, Proc. of the National Seminar on Algebra, Bharatidasan Univ.,
    63-68 (1993).

 4. Vasantha Kandasamy, W.B., and Suresh Babu, N., On some linear codes
    using semigroup rings, Proc. of the National Seminar on Algebra,
    Bharatidasan Univ., 73-77 (1993).

 5. Vasantha Kandasamy, W.B., and Suresh Babu, N., Relation between the
    covering radius and minimum distance of in-decomposable binary
    cyclic codes over 2-groups, Mathematics Today, 12 (1994) 53-56.

 6. Vasantha Kandasamy, W.B., and Meiyappan, D., Note on lower and
    upper approximations in a fuzzy group, Ganita Sandesh, Rajasthan
    Ganita Parishad, 11 (1997) 85-90. ISSN: 0970-9169

 7. Vasantha Kandasamy, W.B., and Meiyappan, D., Fuzzy symmetric
    subgroups and conjugate fuzzy subgroups of a group, J. of Fuzzy Maths,
    Int. Fuzzy Mat. Inst., 6 (1998) 905-913. ISSN: 1066-8950

 8. Vasantha Kandasamy, W.B., and Meiyappan, D., Bigroup and fuzzy
    bigroup, Boletim da Sociedade Paranaese de Matematica, 18 (1998)
    59-65. ISSN: 0037-8712


                                  191
 9. Vasantha Kandasamy, W.B., and Meiyappan, D., Fuzzy continuous map
    on groups, Progress of Mat., Banaras Hindu Univ., 32 (1998) 39-51.

10. Vasantha Kandasamy, W.B., and Indra, V., Maximizing the passengers
    comfort in the madras transport corporation using fuzzy programming,
    Progress of Mat., Banaras Hindu Univ., 32 (1998) 91-134.

11. Vasantha Kandasamy, W.B., and Sujatha, R., Effective erasure codes for
    reliable computer communication protocols using codes over arbitrary
    integer rings, Progress of Mat., Banaras Hindu Univ., 32 (1998) 187-
    207.

12. Vasantha Kandasamy, W.B., and Suresh Babu, N., On covering radius of
    rank distance codes, Ganita Sandesh, 13 (1999) 43-48. ISSN: 0970-
    9169

13. Vasantha Kandasamy, W.B., and Uma, S., Fuzzy cognitive map of Socio-
    economic model, Appl. Sci. Periodical, 1 (1999) 129-136. ISSN:0972-
    5504

14. Vasantha Kandasamy, W.B., and Ram Kishore, M., Symptom - disease
    model in children using FCM, Ultra Sci. Phy. Sci., 11 (1999) 318-324.
    ISSN: 0970-9150

15. Vasantha Kandasamy, W.B., and Sujatha, R., A note on erasure
    decoding of maximum rank distance codes, Proc. of Symposium on
    Algebra, Univ. of Madras, 108-119, (1999).

16. Vasantha Kandasamy, W.B., and Raja Durai, R.S., Hyperloops and
    hypergroupoids, Ultra Sci. Phy. Sci., 12 (2000) 337-347. ISSN:0970-
    9150

17. Vasantha Kandasamy, W.B., and Uma, S., Combined fuzzy cognitive
    map of socio-economic model, Appl. Sci. Periodical, 2 (2000) 25-27.
    ISSN: 0972-5504

18. Vasantha Kandasamy, W.B., and Yasmin Sultana, Knowledge
    processing using fuzzy relational maps, Ultra Sci. Phy. Sci., 12 (2000)
    242-245. ISSN: 0970-9150

                                  192
19. Vasantha Kandasamy, W.B., and Indra, V., Applications of fuzzy
    cognitive maps to determine the maximum utility of a route, J. of Fuzzy
    Maths, Int. fuzzy Mat. Inst., 8 (2000) 65-77.

20. Vasantha Kandasamy, W.B., and Praseetha, R., New fuzzy relation
    equations to estimate the peak hours of the day for transport systems, J.
    of Bihar Mat. Soc., 20 (2000) 1-14. ISSN: 0972-8716

21. Vasantha Kandasamy, W.B., Neelakantan, N.R., and Kannan, S.R.,
    Replacement of algebraic linear equations by fuzzy relation equations in
    chemical engineering, Recent trends in Mathematical Sciences, Proc. of
    International Conference on Recent Advances in Mathematical Sciences
    held at IIT Kharagpur on Dec. 20-22, 2001, published by Narosa
    Publishing House, 161-168, 2001. ISBN: 81-7319-405X

22. Vasantha Kandasamy, W.B., and Selvaraj, R.S., Fuzzy RD codes with
    rank metric and distance properties, Recent trends in Mathematical
    Sciences, Proc. of International Conference on Recent Advances in
    Mathematical Sciences held at IIT Kharagpur on Dec. 20-22, 2001,
    published by Narosa, 341-348, 2001. ISBN: 81-7319-405X

23. Vasantha Kandasamy, W.B., and Sujatha, R., A new class of codes to
    detect and correct byte errors, Applicable Mathematics its perspectives
    and challenges, Proc. of International Conference on Recent Advances
    in Mathematical Sciences held at IIT Kharagpur on Dec. 20-22, 2001,
    published by Narosa Publishing House, 277-284, 2001.
    ISBN: 81-7319-405X

24. Vasantha Kandasamy, W.B., and Minor, A., Estimation of production
    and loss or gain to industries using matrices, Proc. of the National Conf.
    on Challenges of the 21st century in Mathematics and its allied topics,
    Feb. 3-4 (2001), Univ. of Mysore, 211-218, 2001.

25. Vasantha Kandasamy, W.B., and Raja Durai, R.S., An error erasure
    decoding algorithm to the M – [NXD, K] tensor codes with rank metric,
    Proc. of the National Conf. on Challenges of the 21st century in
    Mathematics and its allied topics, Feb. 3-4 (2001), Univ. of Mysore,
    219-223, 2001.




                                    193
26. Vasantha Kandasamy, W.B., and Selvaraj, R.S., Divisible MRD codes,
    Proc. of the National Conf. on Challenges of the 21st century in
    Mathematics and its allied topics, Feb. 3-4 (2001), Univ. of Mysore,
    242-246, 2001.

27. Vasantha Kandasamy, W.B., Kannan, S.R., and Neelakantan, N.R., Use
    of fuzzy set theory to obtain temperature set point of kerosene in
    Kalundborg refinery, Proc. of Nat. Conf. on Challenges of 21st century
    in Maths. and its allied topics, Feb. 3-4, Univ. of Mysore, 268-276,
    2001.

28. Vasantha Kandasamy, W.B., Ramathilagam, S., and Neelakantan, N.R.,
    Fuzzy optimisation techniques in kiln process, Proc. of the National
    Conf. on Challenges of the 21st century in Mathematics and its allied
    topics, Feb. 3-4 (2001), Univ. of Mysore, 277-287, 2001.

29. Vasantha Kandasamy, W.B., and Anita, S., Studies on female infanticide
    problem using neural networks BAM-model, Ultra Sci. Phy. Sci., 13
    (2001) 174-183. ISSN: 0970-9150

30. Vasantha Kandasamy, W.B., and Promodh, P., Parent children model
    using FCM to study dropouts in primary education, Ultra Sci. Phy. Sci.,
    13, (2001) 362-367. ISSN: 0970-9150

31. Vasantha Kandasamy, W.B., and Kannan S.R., and Neelakantan, N.R.,
    Use of fuzzy theory to control waste gas pollution in environment by
    chemical plants, Dimensions of pollution (an collection), 1, (2002) 771-
    785. ISBN: 81-7525-284-7

32. Vasantha Kandasamy, W.B., Mary John, M., and Kanagamuthu, T.,
    Study of social interaction and woman empowerment relative to
    HIV/AIDS, Maths Tiger, 1(4) (2002) 4-7. ISBN: 0972-5873

33. Vasantha Kandasamy, W.B., and Singh, S.V., Loops and their
    application to proper edge colouring of the graph K 2n, Algebra and its
    Applications, Narosa Publishing House, (2001) 273-284. ISBN: 81-
    7319-419-X



                                   194
34. Vasantha Kandasamy, W.B., and Mary John, M., Fuzzy analysis to study
    the pollution and the disease caused by hazardous waste from textile
    industries, Ultra Sci. Phy. Sci., 14 (2002) 248-251. ISSN: 0970-9150

35. Vasantha Kandasamy, W.B., and Yasmin Sultana, Knowledge
    processing with fuzzy relational maps, Ultra Sci. Phy. Sci., 12 (2000)
    242-245. ISSN: 0970-9150

36. Vasantha Kandasamy, W.B., and Balu, M.S., Use of weighted multi-
    expert neural network system to study the Indian politics, Varahmihir
    J. Math. Sci., Sandipani Academy, 2 (2002) 44-53. ISSN: 0972-7329

37. Vasantha Kandasamy, W.B., and Yasmin Sultana, FRM to analyse the
    employee employer relationship model, J. Bihar Math. Soc., 21 (2001)
    25-34. ISSN: 0972-8716

38. Vasantha Kandasamy, W.B., and Raja Durai, R.S., T-direct codes: An
    Application to T-user BAC, Proc. of the 2002 IEEE Info. Theory
    workshop held at Banglore on 20-25 Oct. 2002, 214, 2002.

39. Vasantha Kandasamy, W.B., and Selvaraj, R.S., Multi-covering radius
    with rank metric, Proc. of the 2002 IEEE information theory workshop
    held at Banglore on 20-25 Oct. 2002, 215, 2002.

40. Vasantha Kandasamy, W.B., Pathinathan, P., and Narayan Murthy, S.,
    Child labour problem using Bi-directional associative memories (BAM)
    model, Proc. of the 9th National Conf. of the Vijnana Parishad of India
    on Applied and Industrial Mathematics held at Netaji Subhas Inst. of
    Tech. on Feb. 22-24, 2002.

41. Vasantha Kandasamy, W.B., Neelakantan, N.R., and Ramathilgam,S.,
    Maximize the production of cement industries by the maximum
    satisfaction of employees using fuzzy matrix, Ultra Sci. Phy. Sci., 15 no.1
    (2003) 45-56. ISSN: 0970-9150




                                    195
42. Vasantha Kandasamy, W.B., Neelakantan, N.R., and Ramathilagam, S.,
    Minimization of Pollution by CKD in cement industries using Fuzzy
    Theory, Dimensions of Pollution, ed. A. H. Ansari, Vol. 2, (2003) 12-43.
    ISBN: 81-901874-05

43. Vasantha Kandasamy, W.B., and Raja Durai, R.S., Some results in T-
    direct codes, Proceedings of the Third Asian European Workshop on
    Information Theory, Japan, (2003) 43-44.

44. Vasantha Kandasamy, W.B., and Suresh Babu, N., Circulant Rank
    Codes in Communication Channels, Varahmihir J. of Math. Sci., 3 no. 1
    (2003) 167-173. ISSN: 0972-7329

45. Vasantha Kandasamy, W.B., and Devi Yamini, Use of Fuzzy Databases
    to study the Child Labour Problem, Journal of the Bihar Mathematical
    Society, 22 (2002) 51-56. ISSN: 0972-8716

46. Vasantha Kandasamy, W.B., and Komathi, P.V., An Analysis of Old Age
    People's Problem using Fuzzy Theory, Journal of the Bihar
    Mathematical Society, 9-16. ISSN: 0972-8716

47. Vasantha Kandasamy, W.B., and Ilavenil, K.P.S.K., Reshuffled Identity
    in Matrices, Ultra Science, 14 no. 3 (2002) 553-556. ISSN: 0970-9150

48. Vasantha Kandasamy, W.B., Pathinathan, P., and Narayana Murthy, S.,
    Child Labour Problem using Bi-directional Associative Memories
    (BAM) Model, Mathematics and Information Theory: Recent topics
    and applications, ed. V. K. Kapoor, Anamaya Publishers, New Delhi
    (2004), 62-71. ISBN: 81-88342-15-7

49. Vasantha Kandasamy, W.B., and Raja Durai, R.S., Maximum Rank
    Distance Codes with Complementary Duals, Mathematics and
    Information Theory: Recent topics and applications, ed. V. K. Kapoor,
    Anamaya Publishers, New Delhi (2004), 86-90. ISBN: 81-88342-15-7




                                   196
50. Vasantha Kandasamy, W.B., Kannan, S.R., and N. R. Neelakantan,
    Operability Study of Decision Tables in a Chemical Plant using
    Hierarchical Genetic Fuzzy Control Algorithms, Vikram University
    Mathematical Journal, 19 (1999) 48-59.

51. Vasantha Kandasamy, W.B., Neelakantan N.R., and Ramathilagam, S.,
    Use of Fuzzy Neural Networks to Study the Proper Proportions of Raw
    Material Mix in Cement Plants, Varahmihir J. of Math. Sciences. 2
    (2002) no. 2, 231-246. ISSN: 0972-7329

52. Vasantha Kandasamy, W.B., and Raja Durai, R.S., T-Direct Cyclic
    Codes--A Necessary and Sufficient Condition, Proceedings of the
    National Seminar on Discrete Mathematics and its Applications,
    organized by the Department of Mathematics, St.Thomas College and
    Kerala Mathematical Association, January 9 to 11, 2003, (2003), 83-87.

53. Vasantha Kandasamy, W.B., and Johnson, T., New Spectral Theorem
    for Vector Spaces over Finite Fields Zp, Varahmihir Journal of
    Mathematical Sciences 3 (2003) no. 2, 355-364. ISSN: 0972-7329

54. Vasantha Kandasamy, W.B., and Meiyappan, D., Fuzzy Subhalf-
    groupoids and its Fuzzy Extension Chains, Ultra Science, 16(1)M
    (2004) no. 2, 97-102. ISSN: 0970-9150

55. Vasantha Kandasamy, W.B., and Satya Veer Singh, Quasi Regularity in
    Loop Rings, Ultra Science, 16(1)M, (2004) 43-48. ISSN: 0970-9150

56. Vasantha Kandasamy, W.B., and Paramasivam, K., The chromatic
    number of a commutative groupoid, Ultra Science, 16(2)M, (2004) 111-
    118. ISSN: 0970-9150

57. Vasantha Kandasamy, W.B., and Victor Devadoss, Some New Fuzzy
    Techniques, Jour. of Inst. of Math. and Comp. Sci., 17 (2004) no. 2,
    157-160.




                                  197
58. Vasantha Kandasamy, W.B., Neelakantan, N.R., and Ramathilagam, S.,
    Control of the Grinding Circuit in Cement Industry using Fuzzy Expert
    Systems, in Combinatorial and Computational Mathematics, ed.
    S.Nanda and G.P.Raja Sekhar, Narosa Publishing House, 2004, 221-
    235. ISBN: 81-7319-598-6

59. Vasantha Kandasamy, W.B., Pathinathan, T. and Mary John, M., The
    Impact of Missionary Intervention on Education and Rehabilitation of
    Deprived Children--A Fuzzy Analysis, Proceedings of the National
    Seminar on Graph Theory and Fuzzy Mathematics held on August 28-
    30, 2003, at the Department of Mathematics, Catholicate College,
    Pathanamthitta & Kerala Math. Assoc., India, (2004), 151-162.

60. Vasantha Kandasamy, W.B., and Paramasivam, K., The chromatic
    number of commutative semirings, Proceedings of the National
    Seminar on Graph Theory and Fuzzy Mathematics held on August 28-
    30, 2003, at the Department of Mathematics, Catholicate College,
    Pathanamthitta & Kerala Math. Assoc. (2004), 129-136.

61. Vasantha Kandasamy, W.B., and Praveen Prakash, Technical education
    in Tamil Nadu--A Fuzzy Approach, Proceedings of the National
    Seminar on Graph Theory and Fuzzy Mathematics held on August 28-
    30, 2003, at the Department of Mathematics, Catholicate College,
    Pathanamthitta & Kerala Math. Assoc. (2004), 163-175.

62. Vasantha Kandasamy, W.B., Narayana Moorthy, S., and Mary John, M.,
    The effect of globalization on silk-weavers who are bonded labourers
    using Fuzzy Relational Equations, Proceedings of the National Seminar
    on Graph Theory and Fuzzy Mathematics held on August 28-30, 2003,
    at the Department of Mathematics, Catholicate College,
    Pathanamthitta & Kerala Math. Assoc. (2004), 177-186.

63. Vasantha Kandasamy, W.B., and Abdul Hakeem Raja, Migrant
    Labourers as a High Risk Group to HIV/AIDS, Proceedings of the
    National Seminar on Graph Theory and Fuzzy Mathematics held on
    August 28-30, 2003, at the Department of Mathematics, Catholicate
    College, Pathanamthitta & Kerala Math. Assoc. (2004), 137-149.




                                 198
64. Vasantha Kandasamy, W.B., Elumalai, P. and Mary John, M., Study of
    the employment of Child Labourers in Teashops and Hotels using Fuzzy
    Associative Memories, Proceedings of the National Seminar on Graph
    Theory and Fuzzy Mathematics held on August 28-30, 2003, at the
    Department of Mathematics, Catholicate College, Pathanamthitta &
    Kerala Math. Assoc. (2004), 187-195.

65. Vasantha Kandasamy, W.B., and Madan. N., Performance aspects of
    School Students using rule based Control System, Acta ciencia Indica,
    30(1)M, (2004), 215-219. ISSN: 0253-732-X

66. Vasantha Kandasamy, W.B., and Dennis Williams, Non associative
    Finite Pseudo Fields, Acta ciencia Indica, 30(1)M, (2004), 221-225.
    ISSN: 0253-732-X

67. Vasantha Kandasamy, W.B., and Paramasivam, K., The Chromatic
    Number of some new classes of commutative semirings using Zn, Ultra
    Science, 16(2)M, (2004), 301-306. ISSN: 0970-9150

68. Vasantha Kandasamy, W.B., and Paramasivam. K., On the Chromatic
    Number  (KL) of the commutative loop rings using new class of loops
    Ln(m), Trends in Theory of Rings and Modules, Anamaya Publishers,
    (2005), 162-171.

69. Vasantha Kandasamy, W.B., and Selvaraj. R.S., Multicovering Radius of
    Codes for Rank metric, Proceedings of Workshop on Concepts in
    Information Theory held on October 06-08, 2004 at Viareggio, Italy,
    96-98.

70. Vasantha Kandasamy, W.B., and Moon Kumar Chetry, Smarandache
    Zero-Divisors in group rings,
    http://www.gallup.unm.edu/~Smarandache/S-zero-divisors.pdf

71. Vasantha Kandasamy, W.B., and Moon Kumar Chetry, On the Number
    of Smarandache Zero-Divisors and Smarandache Weak Zero-divisors in
    loop rings of the loops Ln(m), Scientia Magna, 1, no.2 (2005) 96-99
    http://www.gallup.unm.edu/~Smarandache/Sm-zero-divisors.pdf




                                 199
72. Vasantha Kandasamy, W.B., and Moon Kumar Chetry, Smarandache
    idempotents in Loop Rings ZtLn(m) of the Loops Ln(m), Scientia
    Magna, 1 no.2 (2005), 188-195
    http://www.gallup.unm.edu/~Smarandache/WBVK-Chetry.pdf

73. Vasantha Kandasamy, W.B., and Victor Devadoss, A., Identification of
    the Maximum age group in which the agricultural labourers suffer
    health hazards due to chemical pollution using fuzzy matrix, Dimension
    of Pollution, 3, (2005) 1-55. ISSN: 81-901878-1-3

74. Vasantha Kandasamy, W.B., and Singh, S.V., Some Similarities and
    Dissimilarities in loop and group algebras, J. Of Bihar Math Soc., 23,
    (2003) 129-134. ISSN: 9072-8716

75. Vasantha Kandasamy, W.B., and Thiruvengadam, N., Application of
    pseudo best approximation in coding theory, Ultra Sci. Phy. Sci., 17,
    (2005) 139-144. ISSN: 0970-9150

76. Vasantha Kandasamy, W.B and Moon Kumar Chetry, Smarandache
    idempotents in finite ring Zn and in the group ring ZnG, Scientia
    Magna, 1, (2005) 179-187. ISSN: 1556-6706

77. Vasantha Kandasamy, W.B., and Johnson, T., Multi FAM model and its
    applications to analyse habits and its consequence in HIV/AIDS
    patients, Ultra Sci. Phy. Sci., 17, (2005) 241-246. ISSN: 0970-9150

78. Vasantha Kandasamy, W.B., and Ilanthenral, K., System of linear
    biequations, Jour. of Inst. of Math. and Comp. Sci., 18 (2005), 165-179.

79. Vasantha Kandasamy, W.B., and Natrajan, C., Pseudo adjoint of a
    pseudo inner product space, Jour. of Inst. of Math. and Comp. Sci., 18
    (2005), 132-139.

80. Vasantha Kandasamy, W.B., Pathinathan, T., and Mary John, Migration
    of parents and their children dropping out of schools – a fuzzy
    approach, Ultra Sci. Phy. Sci., 17, (2005) 449-460. ISSN: 0970-9150




                                   200
81. Vasantha Kandasamy, W.B., and Showriraju, Y.I., Semiprime biring,
    Jour. of Inst. of Math. and Comp. Sci., 18 (2005), 151-153.

82. Vasantha Kandasamy, W.B and Ilanthenral, K., Bitransformation of
    bivector spaces, Ultra Science, 17, (2005) 497-502. ISSN: 0970-9150

83. Vasantha Kandasamy, W.B and Natrajan, C., Some properties of pseudo
    inner product spaces, Jamal Academic Research Jour., (2005) 54-57.
    ISSN: 0973-0303

84. Vasantha Kandasamy, W.B., Nirmala, K., and Nallasamy, R., Cancer
    among rural men due to use of Tobacco – A FCM analysis, Jour. of Inst.
    of Math. and Comp. Sci., 19 (2006) no. 1, 1-6.

85. Vasantha Kandasamy, W.B., Elumalai, Victor Devadoss and Mary John,
    Application of CETD matrix techniques to study the social and
    psychological problems faced by rag pickers, Vikram Mathematical
    Journal, 25 (2005) 1-8.
86. Vasantha Kandasamy, W.B and Nagarajan, E.K.R., Some new classes of
    Smarandache seminear ring and their properties, Vikram
    Mathematical Journal, 26 (2006) 25-29.
87. Vasantha Kandasamy, W.B and Rajkumar, R., Use of Best
    Biapproximation in algebraic bicoding theory, Varahmihir Jourrnal of
    Mathematical Sci., 6 (2006) 509-516. ISSN: 0972-7329
88. Vasantha Kandasamy, W.B and Karuppusamy, T., Environmental
    pollution by dyeing industries: A FAM analysis, Ultra Science., 18(3)
    (2006) 541-546. ISSN: 0970-9150
89. Vasantha Kandasamy, W.B and Showri Raju, Y.I., A subbistructure over
    birings, Varahmihir Journal of Mathematical Sciences, 5 (2005) 505-
    513. ISSN: 0972-7329
90. Vasantha Kandasamy, W.B and Johnson, T., Analyzing the raw data
    using fuzzy trapezoidal model, Varahmihir Journal of Mathematical
    Sciences, 5 (2005) 343-350. ISSN: 0972-7329
91. Vasantha Kandasamy, W.B., Khoshnevisan, M. and Ilanthenral, K.,
    Smarandache representations and its applications, Scientia Magna, 1
    (2006) 59-74. ISSN: 1556-6706




                                   201
 92. Vasantha Kandasamy, W.B., Elumalai, P., and Mary John, Use of CETD
     matrix techniques to analyse the vulnerable age group among runaway
     children who become rag pickers, Proceedings on Industrial
     Mathematics, Dept. of Maths, Islamiah College, Vaniyambadi, (2005)
     97-104.

 93.
       Vasantha Kandasamy, W.B., and Johnson, T., Fuzzy non-homogeneous
       data analysis model, Proceedings on Industrial Mathematics, Dept. of
       Maths, Islamiah College, Vaniyambadi, (2005) 104-110.

 94. Vasantha Kandasamy, W.B., and Karuppasamy, T., A fuzzy analysis of
     the labourers standards in the Tirupur garment industries, Proceedings
     on Industrial Mathematics, Dept. of Maths, Islamiah College,
     Vaniyambadi, (2005) 111-118.

 95. Vasantha Kandasamy, W.B., Narayanamoorthy, S., and Mary John, Use
     of overlap block FCMs to study bonded labourer problem, Proceedings
     on Industrial Mathematics, Dept. of Maths, Islamiah College,
     Vaniyambadi, (2005) 119-126.

 96. Vasantha Kandasamy, W.B., Pathinathan, T., and Mary John, School
     Environment: A cause for increase in school dropouts – Fuzzy Analysis,
     Proceedings on Industrial Mathematics, Dept. of Maths, Islamiah
     College, Vaniyambadi, (2005) 127-136.

 97. Vasantha Kandasamy, W.B., Praveen Prakash, A. and Thirusangu, K.,
     Study of the Problems of Persons with Disability (PWD) using FRMs,
     International Journal of Mathematical Combinatorics, (2009) 1-8.

 98. Vasantha Kandasamy, W.B., Elumali, P., and Mary John, Analysis of
     health hazards faced by rag pickers on Chennai city using Fuzzy
     Relational Maps, Mathematical Modeling, Ane Books India, (2007)
     289-295.

 99. Vasantha Kandasamy, W.B., Narayanamoorthy, S., and Mary John,
     Study of problems faced by bonded labourers near Kodainal forests
     using FCMs, Mathematical Modeling, Ane Books India, (2007) 297-
     304.
100. Vasantha Kandasamy, W.B., Pathinathan, T., and Mary John, Study of
     problems faced by school dropouts using applied fuzzy analysis,
     Mathematical Modeling, Ane Books India, (2007) 305-312.


                                    202
101. Vasantha Kandasamy, W.B., and Rajkumar, R., Distance Graphs on
     Constant Weight Metric Spaces with Rosenbloom-Tsfasman Metric,
     Ultra Scientist, 22 (2010) 195-204.

102. Vasantha Kandasamy, W.B., and Rajkumar, R., Some metrical problems
     on symmetric groups with Rosenbloom- Tsfasman metric, Ultra
     Scientist, 22 (2010) 291-294.

103. Vasantha Kandasamy, W.B., and Rajkumar, R., A Class of Cayley Graph
     Interconnection Networks based on Rosenbloom-Tsfasman Metric,
     Proceedings of the 2009 International Conference on Computer and
     Network Technology (ICCNT 2009), World Scientific, (2009) 66-72.
104. Vasantha Kandasamy, W.B. and Praveen Prakash, A., Fuzzy Analysis of
     the Reservation for OBC students in Technical Institutions, Proceedings
     of the National Conference on Recent Development in the Applications
     of Mathematics towards Bio-Sciences and Management Sciences,
     Sacred Heart College, Vellore, (2006), 107-117.
105. Vasantha Kandasamy, W.B., Thirusangu, K. and Subhramaniyan, T.,
     Subsemigroups of Bisemigroups and their applications to N-
     automatons, Proceedings of the National Conference on Recent
     Development in the Applications of Mathematics towards Bio-Sciences
     and Management Sciences, Sacred Heart College, Vellore, (2006), 155-
     164.
106. Vasantha Kandasamy, W.B., and Rajkumar, R., On the minimum
     distance of circulant RT distance codes, Ultra Scientist, 21 (2009) 725-
     730.




                                     203
Papers presented in Conferences: 351
Students who worked under my guidance have presented along with me, 351
research papers in various conferences.

Conferences, both national and international, have been the major forum for
presenting our research results; primarily because of the spontaneous feedback
and encouragement.

Sometimes, we have created unparalleled benchmarks in presentations.

For instance in the International Conference on Recent Advances in
Mathematical Sciences held at the IIT Kharaghpur during 20-22 December
2000, 13 of the research scholars enrolled under my guidance presented their
results.

In the National Symposium on Mathematical Methods and its Applications
(2004), held at the IIT Madras, 25 students of mine (from various universities
and colleges) came together and each of them presented a research paper.

The abstracts for each and every research paper is available on my
website http://mat.iitm.ac.in/wbv/public_html/home.htm and
http://www.vasantha.in




                                     204
List of Papers Presented in Conferences: 351

        Name of the         Date and        Title of the         Name of the
S.No.
        Conference           Venue          Research Paper       Authors

   1.      All India      7-10 Dec. 1978,   On the Zero          W.B.Vasantha
          Seminar in         R.I.A.M.       Divisor Conjecture
           Algebra        Univ.of Madras    in Group rings

   2.     All India         20-24 Nov.    On Super modular       W.B.Vasantha
        Symposium in       1979, R.I.A.M. lattices
          Algebra         Univ. of Madras

   3.    Tamil Nadu        17thNov. 1990, Super Boolean          W.B.Vasantha
         Academy of         A.C.College   algebras
          sciences            Campus,
          Meetings        Univ. of Madras

   4.    56th Annual       27-30 Dec.       Quasi-Regular        W.B.Vasantha and
        Conference,           1990,         elements in loop     S.V.Singh
           Indian         South Gujarat     algebra
        Mathematical          Univ.
           Society            Surat

   5.      Diamond         3-5 May 1991,    Semi Simplicity of   W.B.Vasantha and
        Jubilee Session      Allahabad      Loop Rings of        S.V.Singh
        of the National                     Finite Loops
          Academy of
            Sciences

   6.    China-Japan      20-25 Oct.1991    Semi-Idempotents     W.B.Vasantha and
         International       Guangxi        in the Group Ring    Cheng Fuchang
        Symposium on      Teachers Univ.,   of a Cyclic Group
         Ring Theory          China         Over the Field of
                                            Rationals

   7.    61st Annual      19-21 Dec. 1991, Relation between   W.B.Vasantha and
         Session, The         Meerut       J(FL) and W(FL) in S.V.Singh
           National                        Loop Algebras
         Academy of
           sciences

   8.        -do-              -do-         Covering Radius of   W.B.Vasantha and
                                            Cyclic Code and      N.Suresh Babu
                                            that of its
                                            Orthogonal Code




                                        205
 9.     One Day         22ndDec.1991,     A new approach to     W.B.Vasantha
      Symposium on       IIT Madras       ring theory
       Advances in
       Mathematics

10.    57th Annual        27-30 Dec.       Orthogonal ideals    W.B.Vasantha and
      Conference,            1991,        in group rings        N.Suresh Babu
         Indian         Aligarh Muslim
      Mathematical           Univ.,
         Society.           Aligarh

11.        -do-              -do-         Study of some         W.B.Vasantha and
                                          special elements in   S.V.Singh
                                          loop Algebras

12.    International    3-5 Nov. 1992,    Strongly Modular      W.B.Vasantha
      conference on     Aligarh Muslim    Lattices
      algebra and its        Univ.,
        applications        Aligarh

13.        -do-              -do-         Modularity and        W.B.Vasantha and
                                          quasi-modularity      S.V.Singh
                                          in loops and
                                          subloops

14.        -do-              -do-         Orthogonal codes      W.B.Vasantha and
                                          in semigroup rings    N.Suresh Babu

15.     One Day         22nd Dec. 1992,   S-Lattices            W.B.Vasantha and
      Symposium on        IIT Madras                            S.Sridhar
      Mathematical
       Methods and
       Applications

16.        -do-              -do-         Orthogonal ideals     W.B.Vasantha and
                                          as codes in semi      N.Suresh Babu
                                          group rings

17.        -do-              -do-         A new identity in     W.B.Vasantha
                                          lattices

18.    58th annual        22-25 Mar.      Idempotents in        W.B.Vasantha
       conference,      1993, Banaras     loop algebras
         Indian          Hindu Univ.,
      Mathematical         Varanasi
         Society




                                      206
19.        -do-              -do-         A note on the         W.B.Vasantha
                                          modular semi
                                          group ring of a
                                          finite idempotent
                                          semigroup

20.        -do-              -do-         On SI radical in      W.B.Vasantha and
                                          group rings           S.V.Singh

21.      National       17-18 Apr.1993,   On some Linear        W.B.Vasantha and
       Seminar on       Bharathidasan     codes using           N.Suresh Babu
      Algebra and its     University,     semigroup rings
       applications         Tiruchi

22.        -do-              -do-         Orthogonal ideals     W.B.Vasantha
                                          in lattices and its
                                          applications to
                                          codes

23.        -do-              -do-         A new definition      W.B.Vasantha and
                                          for lattices          M.S.Sridhar

24.        -do-              -do-         Orthogonal ideals     W.B.Vasantha and
                                          in the loop ring      S.A.Anburaj
                                          Z2L and
                                          applications to
                                          codes

25.   Mathematical      22nd Dec. 1993,   On rank distance      W.B.Vasantha and
      Methods and         IIT Madras      codes and their       N.Suresh Babu
      Applications                        covering radius

26.        -do-              -do-         Semi idempotents      W.B.Vasantha
                                          in loop Algebras

27.        -do-              -do-         On inner              W.B.Vasantha and
                                          commutative           A.Govindarajan
                                          groups

28.        -do-              -do-         On the two sided      W.B.Vasantha and
                                          ideals of the group   N.Saravana
                                          ring Z2S3             Nambirajan

29.      Annual         17-19 May 1994, On circulant rank       W.B.Vasantha and
      Conference of       University of codes                   N.Suresh Babu
       Ramanujan          Trivandrum
         Society

30.   Mathematical      23rd Dec. 1994,   Study of the new      W.B.Vasantha and
      methods and        IIT Madras       class of loops        S.V.Singh
      applications


                                      207
31.        -do-              -do-          Strong Modularity     W.B.Vasantha
                                           of subloops in
                                           loops

32.        -do-              -do-          On Perfect Rank       W.B.Vasantha and
                                           Codes                 N. Suresh Babu

33.        -do-              -do-          On Semipotent         W.B.Vasantha and
                                           Elements of a Ring    D.Meiyappan

34.   60th Annual         27-30 Dec.       On Chinese Groups     W.B.Vasantha
      Conference,           1994,
        Indian           University of
      Mathematical          Poona
        Society

35.        -do-              -do-          Commutator and        W.B.Vasantha and
                                           Associator of a new   S.V.Singh
                                           class of loops

36.        -do-              -do-          Single Error          W.B.Vasantha and
                                           Correcting Rank       N.Suresh Babu
                                           Distance Code :A
                                           Characterization

37.   Algebra and its    1-3 Feb. 1995, Representations          W.B.Vasantha and
       Applications     Univ. of Madras and Isotopes of a        S.V.Singh
                                        New Class of loops

38.   Proceedings of      28-31 Mar.       Fuzzy Subloops of  W.B.Vasantha
        the Fuzzy           1995,          some Special Loops
       Mathematics         Keman,
        Workshop             Iran

39.   Mathematical      22nd Dec. 1995,    Semirings Which       W.B.Vasantha
      Methods And        IIT, Madras       Are Marot
      applications                         Semirings

40.        -do-              -do-          Fuzzy sets Theory     W.B.Vasantha and
                                           Application –to       V.Indra
                                           Transportation
                                           Problem of
                                           Passengers
                                           travelling in a bus

41.        -do-              -do-          Performance           W.B.Vasantha
                                           Aspects of
                                           Concatenated RD-
                                           codes




                                         208
42.       -do-          -do-        Associative and       W.B.Vasantha
                                    Non-associative
                                    Semirings using
                                    Boolean Algebras

43.       -do-          -do-        The Best              W.B.Vasantha and
                                    Alternative for an    V.Indra
                                    urban mass
                                    Transportation
                                    Project using
                                    Triangular Fuzzy
                                    Numbers

44.       -do-          -do-        Construction and      W.B.Vasantha and
                                    study of New          S.Karthikeyan
                                    Classes of Infinite
                                    Groupoids

45.       -do-          -do-        Fuzzy cosets of       W.B.Vasantha and
                                    Fuzzy subsets,        D.Meiyappan
                                    Fuzzy subgroups
                                    and their
                                    generalizations

46.       -do-          -do-        Prime Matrices and W.B.Vasantha and
                                    Prime Operators     P.L.Narasimhan
                                    Their Fuzzification

47.       -do-          -do-        Boolean Parity        W.B.Vasantha,
                                    Check Codes           R.Sujatha and
                                                          P.L.Narasimhan

48.   62nd Annual    22-25 Dec.     On Balanced           W.B.Vasantha and
      Conference,       1996,       Lattices              S.Venkateswaran
        Indian       IIT Kanpur
      Mathematical
        Society

49.       -do-          -do-        On Boolean-Vector     W.B.Vasantha
                                    like structures

50.       -do-          -do-        On CO-rings           W.B.Vasantha and
                                                          S.Uma

51.       -do-          -do-        On semi-super         W.B.Vasantha and
                                    Boolean algebras      N. Suresh Babu

52.       -do-          -do-        On a subring link     W.B.Vasantha and
                                    relation in rings     S.V.Singh




                                  209
53.        -do-               -do-        Note on lower and     W.B.Vasantha and
                                          upper                 D. Meiyappan
                                          approximations in
                                          a fuzzy group

54.   9th MINI-EURO      17-19 Sep. 1997, Estimation of         W.B.Vasantha,
       conference on         Budva-       parameters in         V.Indra and
        Fuzzy Sets in      Yugoslavia     transportation        S.Mandalam
         Traffic and                      problems by
          Transport                       triangular fuzzy
           Systems                        numbers over
                                          internet using Java
                                          programming

55.    International      13-16 Nov.      Groupoids in the      W.B.Vasantha
      Conference on      1997, Aligarh    construction of
      Algebra and it's   Muslim Univ.,    finite Machines
       Applications         Aligarh
                              UP

56.        -do-               -do-        Circulant Rank        W.B.Vasantha and
                                          Codes in              N. Suresh Babu
                                          Communication
                                          Channels

57.        -do-               -do-        Transportation        W.B.Vasantha and
                                          Problem -- An         V. Indra
                                          Algebraic
                                          Approach via
                                          Matrices

58.        -do-               -do-        Fuzzy Symmetric       W.B.Vasantha and
                                          Groups and its        D.Meiyappan
                                          Applications in
                                          Chemistry

59.        -do-               -do-        Loops and its         W.B.Vasantha and
                                          Applications to       S.V.Singh
                                          Proper Edge
                                          Colouring of the
                                          Graph K2n

60.   Conference on        23-24 Dec.     Finite Groupoids      W.B.Vasantha
      Mathematics        1997, Lucknow    using integers
                             Univ.

61.        -do-               -do-        On Loop Algebras      W.B.Vasantha and
                                                                S.V.Singh




                                       210
62.   Mathematical   22nd Dec. 1997,   Semigroup rings       W.B.Vasantha
      Methods And     IIT, Madras.     which are E-Rings
      Applications

63.       -do-            -do-         Fuzzy groupoid        W.B.Vasantha and
                                       and its fuzzy         D.Meiyappan
                                       extension chains

64.       -do-            -do-         On rank distance      W.B.Vasantha and
                                       codes over            R.Sujatha
                                       arbitrary integer
                                       rings

65.       -do-            -do-         Some special          W.B.Vasantha and
                                       elements of loop      A.Anitha Devi
                                       algebras of power
                                       associative loops

66.       -do-            -do-         Determination of      W.B.Vasantha and
                                       the best parameter V.Indra
                                       in data analysis of a
                                       transportation
                                       problem

67.       -do-            -do-         A semi-lattice        W.B.Vasantha
                                       theory approach to
                                       the design of fault
                                       tolerant systems

68.   63rd Annual      27-30 Dec.      Unique product        W.B.Vasantha and
      Conference,    1997, N.A.C.S.    and two unique        A.Anitha Devi
        Indian          College,       product loops and
      Mathematical    Ahmednagar       their loop algebras
        Society

69.       -do-            -do-         On quasi non          W.B.Vasantha and
                                       associative           N.Suresh Babu
                                       semivector spaces

70.       -do-            -do-         Bigroup and Fuzzy     W.B.Vasantha and
                                       Bigroup               D.Meiyappan

71.       -do-            -do-         Isotopes of Loops     W.B.Vasantha and
                                                             S.V.Singh

72.       -do-            -do-         Zero divisors in      W.B.Vasantha
                                       integral loop
                                       algebras

73.       -do-            -do-         Hyperrings (Zn,q)     W.B.Vasantha and
                                                             V.Vaithiyanathan


                                   211
74.        -do-               -do-         Equational classes    W.B.Vasantha
                                           on Modular lattices

75.        -do-               -do-         Applications of       W.B.Vasantha and
                                           Fuzzy set Theory to   V.Indra
                                           passenger
                                           Transportation
                                           Problem

76.        -do-               -do-         On influential        W.B.Vasantha and
                                           subgroups and         R.Sujatha
                                           normal subgroups
                                           of a group

77.     International    2-5 Mar. 1998,    Maximizing the     W.B.Vasantha and
       Conference on     Banaras Hindu     Passengers comfort V.Indra
           Recent          University      in Madras
       Developments         Varanasi       Metropolitan
      in Mathematical                      Transport
        Analysis with                      Corporation using
       Applications to                     Fuzzy
          Industrial                       Programming
          Problems

78.        -do-               -do-         Fuzzy Continuous      W.B.Vasantha and
                                           Map on Groups         D.Meiyappan

79.        -do-               -do-         Effective Erasure     W.B.Vasantha and
                                           Codes for reliable    R.Sujatha
                                           computer
                                           communication
                                           protocols using
                                           codes over
                                           arbitrary integers
                                           rings

80.     8th World        12-17 July 1998, Estimation of          W.B.Vasantha,
      Conference on         Antwerp-      parameters &           V.Indra and
        Transport            Belgium      interval of            S.Mandalam
        Research                          confidence in
                                          transportation
                                          problems by
                                          triangular fuzzy
                                          numbers over
                                          internet using Java
                                          programming

81.    International     8-10 Dec. 1998,   A new class of        W.B.Vasantha and
      Symposium on       Aligarh Muslim    codes with higher     R.Sujatha
       Optimization        University,     error correcting
       and Statistics        Aligarh       capability

                                       212
82.       -do-           -do-        Fuzzy approach to    W.B.Vasantha and
                                     the dynamic          S.R.Kannan
                                     optimization
                                     problems in
                                     chemical
                                     engineering

83.       -do-           -do-        Fuzzy modeling in    W.B.Vasantha and
                                     process synthesis    S.R.Kannan
                                     from multi-period
                                     heat integrated
                                     distillation
                                     sequences

84.    64thAnnual      19-22 Dec.    A new Identity for   W.B.Vasantha
      Conference,    1998, Gurukal   lattices and its
         Indian       Kangri Univ.   properties
      Mathematical      Hardwar
         Society

85.       -do-           -do-        Semimodules over     W.B.Vasantha and
                                     semirings            N. Suresh Babu

86.       -do-           -do-        Group Matrices       W.B.Vasantha and
                                                          S.R.Kannan

87.       -do-           -do-        Hamiltonian group    W.B.Vasantha and
                                     rings                V.Vaithiyanathan


88.       -do-           -do-        Construction of      W.B.Vasantha and
                                     finite groupoids     A.Govindaraj
                                     using integers

89.       -do-           -do-        Mathematical         W.B.Vasantha
                                     approach to socio-
                                     economic problem
                                     using Fuzzy
                                     Cognitive Map

90.       -do-           -do-        Study of socio-      W.B.Vasantha and
                                     economic problem     S.Uma
                                     using combined
                                     Fuzzy Cognitive
                                     Map

91.       -do-           -do-        Supermodularity of   W.B.Vasantha and
                                     subloops in loop     S.V.Singh




                                 213
 92.       -do-            -do-         Estimation of          W.B.Vasantha and
                                        passengers             V Indra
                                        preference using
                                        Fuzzy Cognitive
                                        Map

 93.       -do-            -do-         Concatenated           W.B.Vasantha and
                                        codes with rank        R.Sujatha
                                        metric

 94.   Mathematical   22nd Dec. 1998,   CN-Rings               W.B.Vasantha
       Methods and     IIT, Madras
       Applications

 95.       -do-            -do-         Mathematical           W.B.Vasantha
                                        Approach to the
                                        Feedback Controls
                                        in Jobshops using
                                        Fuzzy Theory

 96.       -do-            -do-         Some Classical         W.B.Vasantha and
                                        Results on             B.Kavitha
                                        Bigroups

 97.       -do-            -do-         On Birings             W.B.Vasantha and
                                                               B.Meenakumari

 98.       -do-            -do-         Flexibility analysis   W.B.Vasantha,
                                        of chemical plants     N.R.Neelankantan
                                        using fuzzy theory     and S.R.Kannan

 99.       -do-            -do-         Hypergroupoids         W.B.Vasantha and
                                        and its                R.S.Raja Durai
                                        Generalizations

100.       -do-            -do-         Hidden pattern on W.B.Vasantha and
                                        diseases in children M. Ram Kishore
                                        using FCMs

101.       -do-            -do-         Concatenation of       W.B.Vasantha and
                                        integer rank           R.Sujatha
                                        distance codes and
                                        it's applications

102.    86th Indian   3-7 Jan. 1999,    Hyper groupoids        W.B.Vasantha
          Science      Anna Univ.       and Hyper-Loops
         Congress        Chennai        using modulo
                                        integers Zn




                                    214
103.        -do-               -do-        Determination of       W.B.Vasantha,
                                           existence of           N.R.Neelakantan
                                           polymers with          and S.R.Kannan
                                           given melting
                                           points using fuzzy
                                           theory

104.     Ramanujan        24-26 Feb. 1999 Fuzzy                   W.B.Vasantha
       Symposium on        Univ. Madras   representation of
       Algebra and it's                   the inter relation
        applications                      between Indian
                                          politics and
                                          economy

105.        -do-               -do-        Fuzzy approach to      W.B.Vasantha,
                                           the structural         N.R.Neelakantan
                                           flexibility for heat   and S.R.Kannan
                                           integrated
                                           distillation
                                           columns

106.        -do-               -do-        A equilibrium          W.B.Vasantha and
                                           model for supply       S.Ramthilagam
                                           and demand in
                                           industries with
                                           fuzzy preferences

107.        -do-               -do-        On erasure             W.B.Vasantha and
                                           decoding of            R.Sujatha
                                           maximum rank
                                           distance codes

108.     65th Annual       20-23 Dec.      New class of codes     W.B.Vasantha,
         Conference,          1999         to correct and         R.Ramani,
        Indian Math.      Univ. of Pune,   detect                 R.S.Selvaraj and
           Society            Pune         unidirectional and     R.Sujatha
                                           bi-directional error

109.        -do-               -do-        Application of         W.B.Vasantha and
                                           Fuzzy Cognitive        P.Promodth
                                           Maps to study drop
                                           outs in primary
                                           education

110.     87th Indian      3-7 Jan. 2000,   New fuzzy Relation     W.B.Vasantha and
           Science        Univ. of Pune,   Equations to           R.Praseetha
          Congress             Pune        estimate the peak
                                           hours of the day




                                        215
111.        -do-             -do-        Applications of the   W.B.Vasantha and
                                         BAM model to the      V. Anita
                                         problem of female
                                         infanticide

112.        -do-             -do-        Personality-       W.B.Vasantha and
                                         Medicine model for R.Kamala
                                         Homeopathic
                                         medicine using
                                         fuzzy associative
                                         memories

113.        -do-             -do-        FRM to analyze the    W.B.Vasantha and
                                         employer-             Yasmin Sultana
                                         employee
                                         relationship model

114.        -do-             -do-        On pseudo             W.B.Vasantha and
                                         commutative           Mary Samuel
                                         elements

115.        -do-             -do-        Study of dropouts     W.B.Vasantha and
                                         in primary            P.Pramodth
                                         education using
                                         Fuzzy Cognitive
                                         Map

116.      National      1-3 Mar. 2000,   Applications of       W.B.Vasantha and
       Conference on     Univ. Madras    BAM to obtain         S.Ramathilagam
       Optimization                      optimal solutions
       Techniques in                     in industrial
         Industrial                      problems
       Mathematics

117.        -do-             -do-        Use of optimization W.B.Vasantha and
                                         techniques in the   S.R.Kannan
                                         chemical plant
                                         industries

118.     5th Annual     5-7 June 2000, FCMs and signal         W.B.Vasantha,
        Conference of   Univ. of Madras flow graphs to         N.R.Neelakantan,
       the Ramanujan                    study the loss and     S.Ramathilagam
        Mathematical                    gain in cement
           Society                      factories




                                      216
119.       -do-             -do-        A new class of        W.B.Vasantha and
                                        fuzzy RD codes to     R.S.Selvaraj
                                        determine
                                        symmetric,
                                        asymmetric and
                                        unidirectional
                                        errors

120.       -do-             -do-        Application of        W.B.Vasantha,
                                        fuzzy theory to       N.R.Neelakantan
                                        study the             and S.R.Kannan
                                        production
                                        demand aspects in
                                        chemical plants

121.       -do-             -do-        On divisible RD       W.B.Vasantha and
                                        codes                 R.Sujatha

122.       -do-             -do-        Hybrid ARQ            W.B.Vasantha and
                                        scheme using MRD      R.Mohan Raj
                                        codes

123.       -do-             -do-        A new error           W.B.Vasantha and
                                        erasure decoding      R.S.Rajadurai
                                        algorithm for the
                                        class of MRD codes

124.       -do-             -do-        Application of        W.B.Vasantha and
                                        fuzzy evidence        S.Devakumar
                                        theory to study the
                                        cause of heart
                                        disease

125.   International     20-22 Dec.     Construction and     W.B.Vasantha and
       Conference on        2000,       study of a new class Shaibu
          Recent       IIT Kharaghpur   of semivector
        Advances in                     spaces
       Mathematical
         Sciences

126.       -do-             -do-        A new type of co-     W.B.Vasantha and
                                        subring relation in   D.Sukumar
                                        rings

127.       -do-             -do-        On a new class of     W.B.Vasantha and
                                        non-associative       Dennis Williams
                                        pseudo fields using
                                        Zn




                                    217
128.   -do-   -do-     A mathematical         W.B.Vasantha
                       approach to child      and S.Devi Yamini
                       labour problem
                       using fuzzy
                       databases

129.   -do-   -do-     Fuzzy multi-index      W.B.Vasantha,
                       transportation         N.R.Neelakantan ,
                       problems for           S.Ramathilagam
                       export of coal,
                       cement and clinker
                       in cement

130.   -do-   -do-     Rule based control     W.B.Vasantha and
                       system to study the    N.Madan
                       performance
                       aspect of school
                       students

131.   -do-   -do-     Use of fuzzy sets to   W.B.Vasantha and
                       study the problems     P.V.Komathi
                       of old age people

132.   -do-   -do-     Applications of        W.B.Vasantha and
                       fuzzy theory to        M.S.Balu
                       Indian politics

133.   -do-   -do-     On a new class of      W.B.Vasantha and
                       Q-ary codes using      R.S.Rajadurai
                       circulant matrices

134.   -do-   -do-     A new class of         W.B.Vasantha and
                       codes to detect and    R.Sujatha
                       correct byte errors

135.   -do-   -do-     Fuzzy RD codes         W.B.Vasantha and
                       with rank metric       R.S.Selvaraj
                       and distance
                       properties

136.   -do-   -do-     Use of fuzzy           W.B.Vasantha,
                       evidence theory to     S.Devakumar and
                       study symptom          N.Uma Sankari
                       disease model




                     218
137.        -do-               -do-         Replacement of          W.B.Vasantha,
                                            algebraic linear        N.R.Neelakantan
                                            equations by fuzzy      and S.R.Kannan
                                            relational
                                            equations in
                                            chemical
                                            engineering

138.     88th Indian      3-7, Jan. 2001,   Estimation of           W.B.Vasantha,
           Science         Agricultural     overall profit to the   N.R.Neelakantan ,
          Congress             Univ.        industries and the      S.Ramathilagam
                            New Delhi       maximum
                                            satisfaction to the
                                            employer using
                                            special fuzzy
                                            matrix

139.        -do-               -do-         Application of          W.B.Vasantha,
                                            fuzzy theory to         S.R.Kannan and
                                            reduce the waste        N.R.Neelakantan
                                            flow gas in oil
                                            refinery

140.   Seminar on the     16th Feb. 2001,   Communication           W.B.Vasantha
        Mathematical      Loyola College,   theory
       String that Cuts      Chennai
         Across All...

141.   National Conf.       23-25 Mar.   On quantum codes           W.B.Vasantha and
       on the Role of         2001,      obtained from RD           R.S.Raja Durai
       Maths in New       Jadavpur Univ. codes
        Millennium           Calcutta
       Theories and
        Applications

142.        -do-               -do-         Tilings of rank-        W.B.Vasantha and
                                            metric spaces           R.S.Selvaraj

143.        -do-               -do-         Hypersemigroups         W.B.Vasantha and
                                                                    S.Shaibu

144.        -do-               -do-         Error and erasure       W.B.Vasantha and
                                            techniques for          R.Sujatha
                                            circulant codes

145.        -do-               -do-         Study of electro        W.B.Vasantha and
                                            physiologic models      S.Devakumar
                                            of heart cells and
                                            cell networks using
                                            fuzzy theory


                                        219
146.        -do-               -do-        Extension            W.B.Vasantha and
                                           semifield and        A.Arockiasamy
                                           Galois Semigroup

147.        -do-               -do-        Performance          W.B.Vasantha and
                                           aspects of           A. Minor
                                           employee &
                                           satisfaction of
                                           employer using
                                           fuzzy theory

148.        -do-               -do-        Loop semiring        W.B.Vasantha and
                                           where semirings      K. Senthilkumar
                                           are lattice

149.        -do-               -do-        Use of fuzzy         W.B.Vasantha,
                                           associative          N.R.Neelakantan
                                           memories (FAM)       and
                                           to predict the       S.Ramathilagam
                                           cement quality

150.        -do-               -do-        Fuzzy linear         W.B.Vasantha,
                                           programming          N.R.Neelakantan
                                           model for the        and S.R.Kannan
                                           productions
                                           schedule of
                                           chemical plants

151.     National           19-22 Dec.     Use of Fuzzy         W.B.Vasantha,
       Conference of          2000         Network to study     N.R.Neelakantan
        the Indian         Aurangabad,     material Mix in      and
       Mathematical        Maharashtra     Cement Plant         S.Ramathilagam
          Society

152.        -do-               -do-        Fuzzy Control to     W.B.Vasantha,
                                           study Crude          N.R.Neelakantan
                                           Fractionators        and S.R.Kannan

153.       National       3-4 Feb. 2001, Divisible MRD          W.B.Vasantha and
        Conference on     Dept. of Maths, Codes                 R.S.Selvaraj
        Challenges of     Univ. of Mysore
       the 21st Century
       in Mathematics
         and its allied
            topics

154.        -do-               -do-        Fuzzy Logic          W.B.Vasantha and
                                           Control Systems to   S.Devakumar
                                           Study Symptom
                                           Disease Model


                                         220
155.       -do-             -do-         Use of Fuzzy set      W.B.Vasantha,
                                         theory to obtain      N.R.Neelakantan
                                         Temperature Set       and S.R.Kannan
                                         Point of Kerosene
                                         in Kalundborg
                                         Refinery

156.       -do-             -do-         Demi-Modules          W.B.Vasantha and
                                                               K.S.Kumar

157.       -do-             -do-         An Error Erasure      W.B.Vasantha and
                                         Decoding              R.S.Raja Durai
                                         Algorithm to the [n
                                         A , k] tensor codes
                                         with rank metric

158.       -do-             -do-         Fuzzy Optimization W.B.Vasantha,
                                         Techniques in Kiln N.R.Neelakantan &
                                         Process            S.Ramathilagam

159.       -do-             -do-         Estimation of         W.B.Vasantha and
                                         production and        A.Minor
                                         Loss and Gain to
                                         Industries using
                                         Matrices

160.   Symposium on    22nd Dec. 2000,   Linear                W.B.Vasantha and
       Mathematical      IIT Madras      Transformation for    A. Arockiasamy
        Methods and                      Semi-vector spaces
        Applications

161.       -do-             -do-         Groupoid Rings        W.B.Vasantha and
                                                               S.Balaguru

162.       -do-             -do-         On Weakly Semi        W.B.Vasantha and
                                         Super Boolean         A.Baskar
                                         Algebras

163.       -do-             -do-         Idempotents in        W.B.Vasantha and
                                         Group Semirings       K.Chitra

164.       -do-             -do-         Fuzzy Techniques      W.B.Vasantha and
                                         to Study the          S.Devakumar
                                         Electrocardiogram
                                         Diagnosis

165.       -do-             -do-         A New Fuzzy           W.B.Vasantha and
                                         Multidimensional      Henry Jerome
                                         System to Study
                                         Complicated
                                         problems


                                    221
166.   -do-   -do-     Quality of Working     W.B.Vasantha and
                       Life in Industries -   A.Minor
                       A Fuzzy Analysis

167.   -do-   -do-     Properties of          W.B.Vasantha and
                       Group Semirings        R.Mohanraj
                       when Semirings
                       are finite
                       distributive
                       Lattices

168.   -do-   -do-     Risk Assessment        W.B.Vasantha and
                       and Accident           V.Mugundan
                       Analysis in
                       Industries using
                       Fuzzy Possibility
                       Programming

169.   -do-   -do-     Development of         W.B.Vasantha,
                       Long Range             N.R.Neelakantan
                       Planning for           and S.R.Kannan
                       Chemical Plant
                       using Fuzzy
                       Programming

170.   -do-   -do-     Minimization of        W.B.Vasantha,
                       Manufacturing          N.R.Neelakantan
                       Cost using Fuzzy       and
                       Control in Cement      S.Ramathilagam
                       Plant

171.   -do-   -do-     On the Covering        W.B.Vasantha and
                       Radius of Q-Ary        R.S.Raja Durai
                       Circulant MRD
                       Codes

172.   -do-   -do-     Fuzzy Group Rings W.B.Vasantha and
                       and Fuzzy Subrings Regin Thangaraj
                       of Group rings

173.   -do-   -do-     On a New Error         W.B.Vasantha and
                       Correcting             R.S.Selvaraj
                       Decoding
                       Technique for
                       Circulation Codes

174.   -do-   -do-     Multivalent Fuzzy      W.B.Vasantha and
                       Cognitive Maps to      S.Subhaashree
                       study the
                       Unemployment
                       Problems

                     222
175.       -do-          -do-         Fuzzy Theory to        W.B.Vasantha and
                                      study the relation     N.Uma Sankari
                                      between publicity
                                      and marketing

176.   International   12-14 Aug.     Operability study      W.B.Vasantha,
       Conference on      2001,       of decision tables     N.R.Neelakantan
         Industrial    IIT Madras     in a Chemical Plant    and S.R.Kannan
       Mathematics                    using Hierarchical
                                      Genetic Fuzzy
                                      Control Algorithms

177.       -do-          -do-         Work related &         W.B.Vasantha and
                                      compensation           V.Mugundan
                                      assessment to
                                      workers in
                                      industries

178.       -do-          -do-         Application of         W.B.Vasantha,
                                      Fuzzy Control          N.R.Neelakantan
                                      Theory to minimize     and
                                      the pollution due to   S.Ramathilagam
                                      waste dust emitted
                                      by the cement
                                      industries

179.       -do-          -do-         Frameproof rank        W.B.Vasantha and
                                      distance codes for     R.S.Selvaraj
                                      copyright
                                      protection of
                                      digital data

180.       -do-          -do-         Use of Modified        W.B.Vasantha and
                                      Fuzzy Baye's           S.Devakumar
                                      method in medical
                                      expert systems

181.       -do-          -do-         Study of               W.B.Vasantha and
                                      occupational           A.Minor
                                      hazards in Textile
                                      industries using
                                      Fuzzy Cognitive
                                      Map

182.       -do-          -do-         A multicast hybrid     W.B.Vasantha and
                                      ARQ scheme using       R.S.Rajadurai
                                      MDS codes with
                                      rank metric




                                    223
183.       Third       1-5 Dec.2001,     Study of              W.B.Vasantha
       International   M.G.R. Medical    Interrelational
       Conference on       Univ.,        Feelings between
        AIDS India        Madras         AIDS Patients and
                                         Public Using Fuzzy
                                         Theory

184.     National      22nd Dec. 2001,   Study of pollution    W.B.Vasantha,
       Symposium on     IIT Madras,      by textile            N.R.Neelakantan
       Mathematical                      industries using      and A.Minor
        Methods and                      Bidirectional
        Application                      Associative
                                         Memories

185.       -do-             -do-         Symmetric group       W.B.Vasantha and
                                         semirings             A.Arockiasamy

186.       -do-             -do-         Trinary Matrices of   W.B.Vasantha and
                                         Fuzzy Cognitive       T.Pathinathan
                                         Maps and their
                                         Fuzzy Directed
                                         Graphs

187.       -do-             -do-         Jordan Loops and      W.B.Vasantha and
                                         Jordan groupoids      V.Vaithiyanathan

188.       -do-             -do-         A new type of         W.B.Vasantha and
                                         relation of rings     M.Mary John

189.       -do-             -do-         Fuzzy Analysis of    W.B.Vasantha and
                                         unemployment         Ernest Piriyakumar
                                         problem respect to
                                         the technical
                                         closure of units and
                                         implementation of
                                         machine

190.       -do-             -do-         On Fuzzy Graph        W.B.Vasantha and
                                         Pairs                 T.Pathinathan

191.       -do-             -do-         Seminilpotent         W.B.Vasantha and
                                         elements of a         T.Kanagamuthu
                                         group ring

192.       -do-             -do-         Near semilattices &   W.B.Vasantha and
                                         quasi near            P.Ganesan
                                         semilattices




                                     224
193.    UGC sponsored     1-2 Feb. 2002,   A Study of Hacking    W.B.Vasantha and
           National          Sri G.V.G.    of E-mail by          E.L.Piriyakumar
          Seminar on        Visalakshi     students using
            Recent          College for    Fuzzy Cognitive
        Developments          Women,       Maps
       in Mathematical     Udumalaipet,
         Applications            TN

194.       Joint 9th       22-24 Feb.      Fuzzy Model to        W.B.Vasantha and
        National Conf.        2002,        study the             K. Amal
          of Vijnana      Netaji Subhash   Hazardous and
          Parishad of        Inst. of      Large Scale social
       India on Appl. &    Technology      problems due to
        Industrial Mat.      Dwarka,       the rapid increase
         & 5th Annual       New Delhi      of Technical
        Conf. of Indian                    Institutions in
          Soc. of Info                     India
        Theory & Appl.

195.        -do-               -do-        Study of Women        W.B.Vasantha and
                                           Empowerment           Sebastian Jeyaraj
                                           relative to
                                           community
                                           mobilization using
                                           FAM Model

196.        -do-               -do-        Fuzzy Cognitive       W.B.Vasantha and
                                           Map Model to          K. Nirmala
                                           study the
                                           depression and the
                                           wish for death in
                                           the terminally ill
                                           patients

197.        -do-               -do-        Child Labour          W.B.Vasantha and
                                           problem using the     T.Pathinathan
                                           BAM-model

198.        -do-               -do-        Maximum Rank          W.B.Vasantha and
                                           distance codes with   R.S.Rajadurai
                                           complementary
                                           duals




                                       225
199.     UGC-CSIR        15-16 March      Failed Technical    W.B.Vasantha and
          National          2002,         Education           E.L.Piriyakumar
       Symposium on        Dept. of       Planning -- A Study
         Statistical      Statistics,     of the adverse
        Methods and       Annamalai       effects in Tamil
        Applications        Univ.         Nadu using Fuzzy
                                          Associative
                                          Memories

200.        -do-             -do-         Social and             W.B.Vasantha and
                                          Psychological          S.Rajasekharan
                                          aspects of HIV-
                                          infected children --
                                          A fuzzy theory
                                          approach

201.        -do-             -do-         Minimization of        W.B.Vasantha ,
                                          SOx using fuzzy        S.Ramathilagam
                                          control theory in      and
                                          cement industry        N.R.Neelakantan

202.        -do-             -do-         A New Fuzzy            W.B.Vasantha and
                                          Cluster Analysis       Moon K. Chetry
                                          applied to FAMs

203.        -do-             -do-         Internet Addiction W.B.Vasantha and
                                          and its effects on  M.Mary John
                                          student behaviour -
                                          - A fuzzy analysis

204.        -do-             -do-         Estimation of          W.B.Vasantha
                                          unknown flow           S.R.Kannan and
                                          rates of splinter      N.R.Neelakantan
                                          mixer using new
                                          fuzzy relational
                                          neural network
                                          method

205.     17th Annual     June 10-13,      Study of Health        W.B.Vasantha and
        Conference of   2002, Dept. of    Hazards associated     M.S.Balu
       the Ramanujan     Appl. Math.,     with handling of
        Mathematical    Banaras Hindu     solid wastes using
           Society          Univ.,        neural networks
                          Varanasi

206.        -do-             -do-         Study of Bonded        W.B.Vasantha and
                                          Labour problem         E.L.Piriyakumar
                                          using fuzzy
                                          relational
                                          equations


                                        226
207.        -do-              -do-          Can Information       W.B.Vasantha and
                                            on HIV/AIDS to        T. Kanagamuthu
                                            school children be
                                            given in a non-
                                            school
                                            environment: A
                                            Fuzzy Analysis

208.        -do-              -do-          Analysis of           W.B.Vasantha and
                                            education             Moon Kumar
                                            deprivation in        Chetry
                                            India using Multi-
                                            FAMS

209.        -do-              -do-          On the                W.B.Vasantha and
                                            construction of       R.S. Rajadurai
                                            circulant tensor
                                            codes

210.      National       Aug. 30-Sept. 1,   T-direct codes:       W.B.Vasantha and
         Seminar on           2002,         simplifies            R.S.Rajadurai
       Algebra and its   Dept. of Maths.,   maximum
         Applications     Andhra Univ.,     likelihood of
        sponsored by     Vishakapatnam,     decoding problem
       the UGC, CSIR,          AP
       DST and Indian
          National
          Academy

211.        -do-              -do-          An algorithm for      W.B.Vasantha and
                                            reducibility of       T.Johnson
                                            polynomials in
                                            Zp[x]

212.        -do-              -do-          Study of the inter-   W.B.Vasantha
                                            relation between
                                            HIV/AIDS patients
                                            and their socio-
                                            economic
                                            conditions using
                                            Fuzzy Theory

213.        -do-              -do-          Loop semirings        W.B.Vasantha and
                                                                  T.Pathinathan




                                       227
214.        -do-             -do-          Health hazards        W.B.Vasantha and
                                           associated with       A. Victor Devdoss
                                           wastes from
                                           chemical industry
                                           using Fuzzy
                                           relational
                                           equations

215.        -do-             -do-          MRD-Fire codes        W.B.Vasantha and
                                                                 N.Madan Kumar

216.        -do-             -do-          Groupoid              W.B.Vasantha and
                                           semirings             Moon Kumar
                                                                 Chetry

217.   Proceedings of     20-25 Oct.       T-direct codes: An    W.B.Vasantha and
         2002 IEEE          2002,          application to BAC    R. S. Rajadurai
        Information     IISc Bang lore,
           Theory
         Workshop
       (Sponsored by
         the IEEE)

218.        -do-             -do-          Multi-covering        W.B.Vasantha and
                                           radii of codes with   R. S. Selvaraj
                                           rank-metric

219.    International     22-24 Dec.       New Spectral       W.B.Vasantha and
        conference on       2002,          Theorem for Vector T.Johnson
         analysis and   Dept. of Maths.,   spaces over finite
           discrete           IIT          fields Zp
          structures     Kharaghpur,
       (ICADS - 2002)

220.        -do-             -do-          Generalized r-        W.B.Vasantha and
                                           Chinese groups        N.Madan Kumar
                                           and normal
                                           Chinese groups

221.        -do-             -do-          Semidivision rings    W.B.Vasantha and
                                                                 M. Pradhab

222.        -do-             -do-          On Groupoid Rings     W.B.Vasantha and
                                                                 Moon Kumar
                                                                 Chetry

223.        -do-             -do-          Super idempotents     W.B.Vasantha and
                                           and Zero divisors     Debdas Mishra
                                           in Group rings




                                      228
224.       -do-             -do-        Awareness of           W.B.Vasantha and
                                        HIV/AIDS in rural      P. Ganesan
                                        areas -- a fuzzy
                                        approach

225.       -do-             -do-        On multi covering      W.B.Vasantha and
                                        radii of rank metric   R. S. Selvaraj
                                        codes

226.       -do-             -do-        On the                 W.B.Vasantha and
                                        construction of        R. S. Rajadurai
                                        circulant [ndn,k]
                                        tensor codes with
                                        an erasure
                                        technique

227.       -do-             -do-        Maximum rank           W.B.Vasantha and
                                        distance codes with    R. S. Rajadurai
                                        complementary
                                        duals -- an
                                        application to F-
                                        adder channel

228.       -do-             -do-        Control of             W.B.Vasantha and
                                        Grinding circuit in    N.R.Neelakantan
                                        cement industries      and
                                        using Fuzzy Expert     S.Ramathilagam
                                        Systems

229.     National      21st Dec. 2002, Study of children       W.B.Vasantha and
       Symposium on    Dept. of Maths., as victims of cyber-   K.Amal
       Mathematical      IIT Madras     crime using FAM-
        Methods and                     model
        Applications

230.       -do-             -do-        Loop semirings         W.B.Vasantha and
                                        which are Marot        J.Jon Arockiaraj
                                        semirings

231.       -do-             -do-        On loop rings of a     W.B.Vasantha and
                                        special class of       A.Virgin Raj
                                        loops

232.       -do-             -do-        Study of               W.B.Vasantha and
                                        depression in          K. Nirmala
                                        Cancer patients
                                        using FCM model




                                     229
233.   -do-   -do-     Bhopal Gas          W.B.Vasantha and
                       Tragedy &           Victor Devdoss
                       Aftermath : A study
                       using Fuzzy Models

234.   -do-   -do-     A Fuzzy Analysis of     W.B.Vasantha and
                       Suicide by Farmers      Henry Jerome

235.   -do-   -do-     High Risk Groups        W.B.Vasantha and
                       of AIDS carriers        N.R.Neelakantan
                       are street children :
                       A Fuzzy Approach

236.   -do-   -do-     The danger of           W.B.Vasantha and
                       genetically             E. L. Piriyakumar
                       engineered crops:
                       A fuzzy approach

237.   -do-   -do-     Study of a new          W.B.Vasantha and
                       identity in lattices    D.Rajan

238.   -do-   -do-     Dropouts in             W.B.Vasantha and
                       primary education       P.Pathinathan
                       using Fuzzy
                       Relational Maps
                       (FRM)

239.   -do-   -do-     A new class of non-     W.B.Vasantha and
                       associative partial     S. Johnson
                       rings                   Savarimuthu

240.   -do-   -do-     On Quasi Loop           W. B. Vasantha
                       rings                   M.Mary John and
                                               Rosemary

241.   -do-   -do-     Normal elements         W. B. Vasantha and
                       in groupoids            Z. Joyce

242.   -do-   -do-     Smarandache             W.B.Vasantha and
                       Groupoids               J.Sujatha

243.   -do-   -do-     Orthogonal ideals       W.B.Vasantha and
                       and filters in          T.Henson
                       lattices

244.   -do-   -do-     On non-associative      W.B.Vasantha and
                       semirings               N.Kannappa

245.   -do-   -do-     A new type of inner     W.B.Vasantha and
                       commutativity in        M.P.Gnanavel
                       groups


                     230
246.       -do-              -do-        On Quasi semi-        W.B.Vasantha and
                                         commutative rings     M.Mary John

247.       -do-              -do-        SG-rings              W.B.Vasantha and
                                                               Stephen Dinagar

248.       -do-              -do-        Semiright             W.B.Vasantha and
                                         commutativity in      L.Henry
                                         loops

249.       -do-              -do-        Coded semivector      W.B.Vasantha and
                                         spaces                V.Vaithiyanathan

250.       -do-              -do-        Generalized semi-     W.B.Vasantha and
                                         ideals of groupoid    S.Narayanamoorthy
                                         rings

251.       -do-              -do-        A Study of n-like     W.B.Vasantha and
                                         group rings           S.Elumalai

252.       -do-              -do-        Semigroup             W.B.Vasantha and
                                         semirings             Fr.A.Arockiasamy

253.       -do-              -do-        Loop rings of         W.B.Vasantha and
                                         Jordan loops          J.M.Parimala
                                                               Kanthi

254.      NBHM          9–11 Jan. 2003, T-direct codes - A     W. B.Vasantha and
         sponsored        St.Thomas     necessary and          R. S. Rajadurai
          National         College,     sufficient condition
       Symposium on      Kozhenchery
        Mathematics         Kerala

255.   Conference on       3-5 March    Reservation in         W.B.Vasantha and
       Recent Trends         2003,      India : A Fuzzy        E.L.Piriyakumar
       in Algebra and   Dept. of Maths. Analysis
          Analysis      Aligarh Muslim
                           Univ., UP

256.       -do-              -do-        Semi-automaton        W.B.Vasantha and
                                         and automaton         Moon Kumar
                                         using                 Chetry
                                         Smarandache
                                         groupoids

257.       -do-              -do-        Quasi strongly        W.B.Vasantha and
                                         modular lattices      D.Rajan
                                         and its properties

258.       -do-              -do-        Types of              W.B.Vasantha and
                                         commutativity in      Z.Joyce
                                         rings

                                      231
259.        -do-              -do-        Commutative        W.B.Vasantha and
                                          group rings KG and S.Paramasivam
                                          their chromatic
                                          number (KG)

260.        -do-              -do-        Quasi center in      W.B.Vasantha and
                                          semirings            N.Kannappan

261.        -do-              -do-        S-Biloops            W.B.Vasantha and
                                                               Y.I.Showriraju

262.        -do-              -do-        Serial and weakly    W.B.Vasantha and
                                          serial groups        M.P.Gnanavel

263.    International    7-8 May 2003, On Smarandache          W.B.Vasantha
       Symposium on      Dept. of Maths., Rings and their
       Theory of Rings   Aligarh Muslim properties
        and Modules      University, UP

264.        -do-              -do-        Smarandache          W.B.Vasantha and
                                          Groupoid Rings       Moon Kumar
                                          and its properties   Chetry

265.        -do-              -do-        On the chromatic     W.B.Vasantha and
                                          number (KL) of      K.Paramasivam
                                          the commutative
                                          loop rings using
                                          the new class of
                                          loops Ln(m)

266.        -do-              -do-        Semi-modules over    W.B.Vasantha and
                                          semirings            M.Pradhab

267.        -do-              -do-        Bimodules over       W.B.Vasantha and
                                          birings              Y.Showri Raju

268.    Third Asian-      25-28 June      Some results on T-   W.B.Vasantha and
         European            2003,        Direct Codes         R.S.Rajadurai
        Workshop on      The Society of
        Information       Information
           Theory        Theory and its
                         Applications,
                          Kamogawa,
                             Japan




                                      232
269.      National       28-30 Aug.     The Impact of         W.B.Vasantha,
        Seminar on         2003,        Missionary            T.Pathinathan and
       Graph Theory    Department of    Intervention on the   M.Mary John
         and Fuzzy      Mathematics,    Education and
       Mathematics       Catholicate    Rehabilitation of
                          College,      Deprived Children
                       Pathanamthitta   -- A Fuzzy Analysis
                       & Kerala Math.
                        Assoc., India

270.       -do-             -do-        Chromatic number      W.B.Vasantha and
                                        of commutative        K.Paramasivam
                                        semirings

271.       -do-             -do-        Technical             W.B.Vasantha and
                                        education in Tamil    Praveen Prakash
                                        Nadu -- A Fuzzy
                                        Approach

272.       -do-             -do-        The Effect of         W.B.Vasantha,
                                        Globalization on      Narayana Moorthy
                                        Silk Weavers who      and Mary John
                                        are Bonded
                                        Labourers using
                                        Fuzzy Relational
                                        Equations

273.       -do-             -do-        Use of Fuzzy          W.B.Vasantha,
                                        Associative           S.Elumalai and
                                        Memories (FAM)        Mary John
                                        Model to study the
                                        employment of
                                        child labourers in
                                        Teashops and
                                        Hotels

274.       -do-             -do-        Migrant labourers     W.B.Vasantha and
                                        as a high-risk        Abdul Hakeem Raja
                                        group to
                                        HIV/AIDS --- A
                                        BAM Model

275.     National      21st Dec. 2003, Smarandache            W.B.Vasantha, J.
       Symposium on    Dept. of Maths., Notions in Groups     Sujatha and
       Mathematical      IIT Madras                           M.Mary John
        Methods and
        Applications

276.       -do-             -do-        S-semirings and its   W.B.Vasantha and
                                        properties            A. Arockiamary


                                    233
277.   -do-   -do-     Special Elements in W.B.Vasantha and
                       S-semirings         T. Henson

278.   -do-   -do-     S-semifields and S-   W.B.Vasantha and
                       semivector spaces     S. Johnson
                                             Savarimuthu

279.   -do-   -do-     S-substructures in    W.B.Vasantha and
                       loops                 J. Jon Arockiaraj

280.   -do-   -do-     Fuzzy relational      W.B.Vasantha
                       maps to study the     R. Nallaswamy and
                       types of cancers      K. Nirmala
                       and causes

281.   -do-   -do-     Chromatic Number      W.B.Vasantha and
                       of a groupoid         K. Paramasivam

282.   -do-   -do-     The plight of rag-    W.B.Vasantha
                       pickers in Madras     P.Elumalai and
                       city using Fuzzy      M. Mary John
                       Cognitive Maps

283.   -do-   -do-     Study of brick-       W.B.Vasantha
                       makers as bonded      S. Narayanamurthy
                       labourers using       and M. Mary John
                       weighted multi-
                       expert neural
                       networks

284.   -do-   -do-     Use of fuzzy          W.B.Vasantha and
                       analysis to study     A. Praveen Prakash
                       the parent student
                       inter-relationship
                       model in case of
                       engineering
                       students

285.   -do-   -do-     Some classical        W.B.Vasantha and
                       theorems in           M. Mary John
                       S-semigroups

286.   -do-   -do-     On some special       W.B.Vasantha and
                       elements of           Moon Kumar
                       groupoid rings        Chetry

287.   -do-   -do-     S-commutative         W.B.Vasantha and
                       loops and its         M. Parimala Kanthi
                       properties




                     234
288.        -do-              -do-          A note on t-direct     W.B.Vasantha and
                                            cyclic codes and its   R. S. Raja Durai
                                            applications

289.        -do-              -do-          On Bisemigroups        W.B.Vasantha and
                                            and its                Y. I. Showriraju
                                            Applications

290.        -do-              -do-          S-rings and their      W.B.Vasantha and
                                            properties             T.Subramaniyam

291.        -do-              -do-          S-elements in Non-     W.B.Vasantha and
                                            associative rings      Virgin Raj

292.        -do-              -do-          Analysis of School     W.B.Vasantha, T.
                                            Dropouts among         Pathinathan and
                                            female children        M.Mary John
                                            using Fuzzy
                                            Associative
                                            Memories

293.        -do-              -do-          Bidirectional          W.B.Vasantha and
                                            Associative            Victor Devadoss
                                            Memories to study
                                            chemical hazards
                                            faced by farmers

294.        -do-              -do-          Study of HIV/AIDS      W.B.Vasantha and
                                            patients using RTD     T. Johnson
                                            matrices

295.   UGC Sponsored     4- 5 Sep. 2004,    Prevalence of          W.B.Vasantha,
        Seminar on        A.V.V. M. Sri     Tobacco Related        K. Nirmala and R.
         Decision            Puspam         Cancers Among          Nallasamy
          Making         College, Poondi,   Rural Men using
        Techniques           Tanjore        FCM

296.   UGC Sponsored     8- 9 Sep. 2004,    On Some                W.B.Vasantha,
         Seminar on      Department of      Properties of          T. Ramaraj and
        Mathematical      Mathematics,      Smarandache            N. Kannappa
         Methods in           Jamal         Near-rings
       Social Sciences    Mohammed
                         College, Tiruchi

297.        -do-              -do-          Analysis of Social     W.B.Vasantha, K.
                                            and Economic           Nirmala and R.
                                            Problems related       Nallasamy
                                            with Cervical
                                            Cancer Patients
                                            using BAM Model


                                       235
298.       -do-             -do-         Estimation of max.   W.B.Vasantha and
                                         age group of         Victor Devadoss
                                         Agricultural
                                         Labourers with
                                         Pollution Related
                                         Cardio Vascular
                                         Problem using
                                         Fuzzy Matrices

299.       -do-             -do-         Linked Fuzzy         W.B.Vasantha,
                                         Relational Maps to   T.Pathinathan and
                                         Study the Relation   M.Mary John
                                         between Migration
                                         and School
                                         Dropouts in Tamil
                                         Nadu

300.       -do-             -do-         Smarandache Free     W.B.Vasantha and
                                         Groupoids and its    Moon K. Chetry
                                         Application to
                                         Automaton

301.       -do-             -do-         Analysis of the      W.B.Vasantha, S.
                                         Socio-economic       Narayanamoorthy
                                         Problems faced by    and M.Mary John
                                         Bonded Labourers
                                         using Fuzzy Neural
                                         Network Systems

302.       -do-             -do-         Socio-Economic       W.B.Vasantha,
                                         Problems faced by    P.Elumalai and
                                         Rag-pickers using    M.Mary John
                                         Overlap Block
                                         Fuzzy Cognitive
                                         Maps

303.       -do-             -do-         Allocation of Funds W.B.Vasantha and
                                         to Benefit          T.Johnson
                                         HIV/AIDS Patients
                                         using
                                         Transportation
                                         Model

304.     National      8-9 Oct. 2004,    Study of Problems    W.B.Vasantha,
       Conference on    Birla Inst. of   faced by School      T.Pathinathan and
       Mathematical    Tech. and Sci.    Dropouts Using       M.Mary John
       Modelling and    BITS, Pilani,    Applied Fuzzy
         Analysis        Rajasthan       Analysis




                                     236
305.        -do-              -do-         Study of Problems    W.B.Vasantha,
                                           faced by Bonded      S.Narayanamoorthy
                                           Labourers near       and M.Mary John
                                           Kodaikanal forests
                                           using Fuzzy
                                           Cognitive Maps

306.        -do-              -do-         Analysis of Health   W.B.Vasantha,
                                           Hazards faced by     P.Elumalai and
                                           Rag-pickers of       M.Mary John
                                           Chennai city using
                                           Fuzzy Relational
                                           Maps

307.     National          25-27 Nov.      Mathematical         W.B.Vasantha
        Seminar on            2004,        analysis of social
       Mathematical      Dept. of Math.,   and psychological
         Methods          Sacred Heart     problems faced by
                             College,      HIV/AIDS Patients
                           Tiruppattur

308. Interdisciplinary    17-18 Dec.       Use of FRMs to    W.B.Vasantha
        Seminar on           2004,         analyse the socio
     Social Problems     Post Graduate     economic problems
                         and Research,     of HIV/AIDS
                         Dept. of Social   affected women
                         Work, Sacred      Patients
                         Heart College,
                          Tiruppattur

309.     National        22nd Dec. 2004, On Bisemirings         W.B.Vasantha,
       Symposium on      Dept. of Maths.,                       V.W.J. Anand and
       Mathematical        IIT Madras                           A.Victor Devadoss
        Methods and
        Applications

310.        -do-              -do-         Smarandache          W.B.Vasantha and
                                           Jordan Algebras      C.Christopher

311.        -do-              -do-         S-biquasigroups      W.B.Vasantha and
                                           and its properties   Y.I.Showriraju

312.        -do-              -do-         Smarandache          W.B.Vasantha and
                                           substructures in     J.Jon Arokiaraj
                                           groupoid rings

313.        -do-              -do-         Smarandache          W.B.Vasantha,
                                           double cosets in a   J.Sujatha and
                                           S-semigroup          M.Mary John



                                       237
314.   -do-   -do-     Pollution related     W.B.Vasantha,
                       cancers--A FAM        R.Nallasamy and
                       Analysis              K.Nirmala

315.   -do-   -do-     Analysis of drop-     W.B.Vasantha,
                       outs from private     Pathinathan and
                       schools using fuzzy   M.Mary John
                       morphisms

316.   -do-   -do-     Study of S-zero       W.B.Vasantha and
                       divisors and          T.Subramaniyan
                       S-idempotents in
                       rings

317.   -do-   -do-     Some new classes      W.B.Vasantha and
                       of commutative        K.Paramasivam
                       groupoids and
                       their chromatic
                       number

318.   -do-   -do-     Special elements in   W.B.Vasantha,
                       S-rings               P.Ganesan and
                                             M.Mary John

319.   -do-   -do-     Bisemivector          W.B.Vasantha and
                       spaces and its        S.Johnson
                       properties

320.   -do-   -do-     Study of the          W.B.Vasantha and
                       problems faced by     Praveen Prakash
                       new engineering
                       colleges using a
                       FCM model

321.   -do-   -do-     A note on super       W.B.Vasantha,
                       edge-magic graphs     K.Paramasivam and
                                             R.Balakrishnan

322.   -do-   -do-     Estimation of the     W.B.Vasantha and
                       maximum age-          A.Victor Devdoss
                       group of the
                       agricultural
                       labourers having
                       health problems
                       due to chemical
                       pollution using
                       matrices




                     238
323.        -do-              -do-        Analysis of the raw   W.B.Vasantha and
                                          data related to       T.Johnson
                                          symptoms of
                                          HIV/AIDS patients
                                          using fuzzy
                                          relational
                                          operators

324.        -do-              -do-        Analysis of social    W.B.Vasantha,
                                          and psychological     S.Narayanamoorthy
                                          problems of           and M.Mary John
                                          bonded labourers
                                          using overlap
                                          FCMS

325.        -do-              -do-        Crime and Media       W.B.Vasantha,
                                          Analysis using        J.Maria Roy Felix
                                          FRM                   and A.Victor
                                                                Devadoss

326.        -do-              -do-        Group B-algebras      W.B.Vasantha and
                                          and Group L-          E.K.R. Nagarajan
                                          algebras

327.        -do-              -do-        Social and            W.B.Vasantha,
                                          psychological         P.Elumalai and
                                          problems faced by     M.Mary John
                                          rag pickers of
                                          Chennai city using
                                          BAM model

328.        -do-              -do-        S-quasi regular       W.B.Vasantha and
                                          elements of a non-    Moon Kumar
                                          associative ring      Chetry

329.       National        24-26 Feb.    On a new class of      W.B.Vasantha and
          Seminar on         2005,       codes                  R.Rajkumar
        Recent Trends    Union Christian
       in Cryptography      College,
         with Coding     Alwaye, Kerala
            Theory         and Kerala
                          Mathematical
                           Association

330.   Proceedings of      19-20 Nov.     Use of CETD           W.B.Vasantha,
       the State Level   2005, Islamiah   matrix techniques     P.Elumalai and
         Seminar on         College,      to analyse the        M.Mary John
          Industrial      Vaniyambadi     vulnerable age
        Mathematics                       group among run
                                          away children who
                                          become rag pickers

                                      239
331.       -do-              -do-       Fuzzy non             W.B.Vasantha and
                                        homogeneous data      T.Johnson
                                        analysis model

332.       -do-              -do-       A fuzzy analysis of   W.B.Vasantha and
                                        the labour            T.Karuppusamy
                                        standards in the
                                        Tirupur garment
                                        industries

333.       -do-              -do-       Use of overlap        W.B.Vasantha,
                                        block FCMs to         S.Narayanamoorthy
                                        study bonded          and M.Mary John
                                        labourer problem

334.       -do-              -do-       School                W.B.Vasantha,
                                        Environment – A       Pathinathan and
                                        cause for increase    M.Mary John
                                        in school dropouts
                                        – Fuzzy analysis

335.    71st Annual     26-29 Dec.      Use of best           W.B.Vasantha and
       Conference of   2005, Dept. of   biapproximztion in    R.Rajkumar
          Indian       Maths, Indian    algebraic bicoding
       Mathematical     Institute of    theory
          Society       Technology,
                         Roorkee

336.       -do-              -do-       Study of social and   W.B.Vasantha,
                                        Psychological         P.Elumalai and
                                        problems faced by     M.Mary John
                                        rag pickers – using
                                        CETD matrix
                                        techniques

337.       -do-              -do-       Analysis of socio W.B.Vasantha,
                                        economic problems S.Narayanamoorthy
                                        faced by bonded   and M.Mary John
                                        labourers using
                                        AFCM Techniques

338.       -do-              -do-       Environmental       W.B.Vasantha and
                                        pollution by dyeing T.Karuppusamy
                                        industries – A FAM
                                        analysis

339. 25th Colloquium   Otto van         On colouring          W.B.Vasantha and
     on                Guericke         Boolean Algebra       K.Paramasivam
     Combinatorics     University,      and Boolean
                       Germany          Semigroup


                                     240
340. International      10-14 June         On k-super edge-     W.B.Vasantha and
     Conference on      2007,              magic graphs         K.Paramasivam
     Recent             Kalasinglam
     Developments in    Univ., India
     Combinatorics
     and Graph
     Theory

341. 14th               6-8 Jan 2007,      A Characterization   W.B.Vasantha and
     International      Indian Institute   of super edge-       K.Paramasivam
     Conference in      of Technology      magic graphs
     Computational      Madras
     Mathematical
     and Statistical
     Methods of the
     FIM

342. National           6 Oct 2007,        The Problem faced    W.B. Vasantha, K.
     Conference on      Rajiv Gandhi       by People with       Thirusangu and
     Emerging           College of         Disabilities-A       A.Praveen Prakash
     Trends in          Engineering &      Fuzzy Analysis
     Automaton          Technology,
                        Pondicherry

343. National           29-30 Sept         Fuzzy Analysis of    W.B. Vasantha and
     Conference on      2006, Sacred       the Reservations     A.Praveen Prakash
     Recent             Heart College,     for OBC students
     Development in     Tirupattur,        in Technical
     the Applications   Tamil Nadu         institutions
     of Mathematics
     towards Bio-
     Sciences and
     Management
     Sciences

344. -do-               -do-               Subsemigroups of     W.B. Vasantha,
                                           Bisemigroups and     K.Thirusangu and
                                           their applications   T.Subhramaniyam
                                           to N-automatons

345. International      24-26 July         A class of Cayley    W.B.Vasantha and
     Conference on      2009, Chennai,     graph                R.Rajkumar
     Computers and      India              interconnection
     Network                               networks based on
     Technology                            Rosenbloom-
                                           Tsfasman metric

346. International      24-25 July         Fuzzy codes with    W.B.Vasantha and
     Conference on      2009, Jamal        RT Metric and       R.Rajkumar
     Mathematical       Mohamed            Distance Properties


                                         241
     Methods and       College, Trichy
     Computation

347. -do-              -do-                Automorphism         W.B.Vasantha and
                                           group of distance    R.Rajkumar
                                           graphs of metric
                                           spaces with RT
                                           metric

348. 24th Annual       30-31 Dec           Some metrical        W.B.Vasantha and
     National          2008, Banaras       problems with RT     R.Rajkumar
     Conference of     Hindu               metric
     the               University,
     Mathematical      Varanasi
     Society

349. International     15-17 Dec 2008,     Distance properties W.B.Vasantha and
     Conference on     Sri                 of Fuzzy RT         R.Rajkumar
     Operations        Venkateswara        Distance Codes
     Research for a    University,
     Growing Nation    Tirupati, India

350. National          10-12 Dec           Distance graphs of   W.B.Vasantha and
     seminar on        2008,               metric spaces with   R.Rajkumar
     Algebra,          University of       RT metric
     Analysis and      Kerala, Kerala,
     Discrete          India
     Mathematics

351. 2nd National      26-28 Sep           Circulant Codes      W.B.Vasantha and
     Conference        2008, Deen          with RT metric       R.Rajkumar
     Mathematical      Dayal
     Techniques:       Upathyaya
     Emerging          College, New
     Paradigms for     Delhi, India
     Electronics and
     IT Industries




                                         242
Editor, Board Member of Journals




                           1. Editor,
                              Smarandache Notions
                              Journal,
                              American Research Press,
                              USA.




2. Editorial Advisor
   Ultra Scientist of
   Physical Sciences,
   Bhopal (MP), India.




                         243
                                   3. Associate Editor,
                                      Varahmihir Journal of
                                      Mathematical Sciences,
                                      Ujjain (MP), India




4. Editorial Board Member,
   Applied Science Periodical,
   Bihar, India.




                                 244
                                    5. Editorial Board Member,
                                       The Mathematics
                                       Education,
                                       Bihar, India.




6. Editorial Board Member,
   Vikram Mathematical Journal,
   School of Mathematics,
   Vikram University, India.




                              245
                                   7. Editorial Board Member,
                                      ANJAC Journal of
                                      Sciences,
                                      Ayya Nadar Janaki Ammal
                                      College, Sivakasi, Tamil
                                      Nadu, India.




8. Associate Editor
   International Journal
   of Applied Mathematics
   and Statistics,
   Centre for Environment,
   Social and Economic
   Research (CESER)
   India.




                             246
9. Associate Editor,
Scientia Magna,
Northwest University,
Xi’an, Shaanxi, P.R.China




                                  10. Editor,
                                  International Journal of
                                  Mathematical
                                  Combinatorics,
                                  The Madis of Chinese
                                  Academy of Sciences,
                                  China




                            247
     Kalpana Chawla Award given to
Dr.W.B.Vasantha Kandasamy by the Tamil
  Nadu Chief Minister Dr. Kalaignar on
   15th August 2006, Independence Day

PRESS RELEASE AND NEWS CLIPPINGS
                  248
  Press Release No.276                                     Date 09-08-2006


 KALPANA CHAWLA AWARD TO DR.VASANTHA KANDASAMY

            WHO FOUGHT FOR SOCIAL JUSTICE IN IIT


Every year, the Tamil Nadu Government has been giving an award for
Courage and Daring Enterprise in the name of renowned space scientist
Kalpana Chawla to a daring woman from Tamil Nadu.

      The Chief Minister Kalaignar has announced that this year's Kalpana
Chawla award will be given to Dr.W.B.Vasantha Kandasamy.

       Dr.Vasantha Kandasamy is an extraordinary scientist and researcher
in the field of mathematics. She has worked from 1987 for 17 years as a
lecturer in the mathematics department of I.I.T. She has also guided several
students to get the doctoral degree in Mathematics. Majority of the 14
mathematical books that she has authored have been published in America.
She has written 2 books about AIDS awareness. It is worth mentioning that
out of the 480 faculty members in IIT Madras, she is the only person who
stressed that teachers must be recruited on the basis of social justice and
carried on a struggle with the Institution.

        The Chief Minister Kalaignar has announced that Dr.Vasantha
Kandasamy has been bestowed the Kalpana Chawla award in appreciation
for her exemplary intellectual contribution to mathematics and her mental
strength to daringly fight with determination for the establishment of social
justice. The Kalpana Chawla award given to Dr.Vasantha Kandasamy
carries a cash prize of Rs.5 lakhs and a medal. This award shall be presented
on the coming Independence Day.



Released by the Director, Department of Information and Public
Relations, Chennai – 9.


                                     249
Excerpts (and Translations) from News Items
about Kalpana Chawla Award given to me

―Speaking to this newspaper on Wednesday, the Mathematics expert said that she
wants to start a Mathematics Institute for the oppressed and downtrodden sections
of society. ―Maths does not belong to only a particular section of the society, but
also to other sections, particularly the oppressed and downtrodden,‖ she said.
         Dr.Vasantha has authored three books on AIDS, published by the Tamil
Nadu AIDS Control Society. She has also helped numerous persons affected by
AIDS.
         Dr.Vasantha has authored a book on Periyar, titled ―Fuzzy and
Neutrosophic Analysis of Periyar‘s Views on Untouchability.‖ All her books are
available on her website ―www.vasantha.net‖ for free download, which she says will
help students read them free of cost, instead of buying them.‖

       Deccan Chronicle, Chennai, Thursday, 10 August 2006




                                        250
It is well known that in Chief Minister Kalaignar‘s rule, right from the day of
assuming power, all the electoral promises are being fulfilled at the speed of
rockets. One can release a separate press release about the various fulfilled
promises including the renowned schemes that have been implemented: One kilo
of rice for two rupees, announcement that people of all castes can become priests,
cancellation of farmer‘s debts, two eggs per week in the nutritious noon-meal
scheme, two acres of land for poor farmers and so on.
         More than that, he has placed ensured social-justice by making the people
of the oppressed sections of society occupy key posts. Several Dalit and Backward
Class IAS and IPS officers have been given important portfolios. The new Advocate
General, Government Pleader belong to the backward sections of society. Likewise,
even the member of the Public Service Commission is a Most Backward Caste.
         More than all this, Honourable Dr.Kalaignar recently
announced that the Kalpana Chawla Award (of 5 lakh rupees cash-prize
and a medal) was to be given to backward caste Assistant Professor Dr.
Mrs. Vasantha Kandasamy who has been the victim of injustice in the
Chennai IIT for long years—any amount of praise of the Chief Minister
and his Government will be worthy for this deed. Professor Vasantha
Kandasamy is a fighter who has written more than 150 research papers
in International journals, and has been the Ph.D guide of numerous
students, and written several books, and she has got acclaim the world
over.

       Dravidar Kazhagam President Dr.K. Veeramani’s Press Release
in the Viduthalai, 13 August 2006, Vol. 71, No.74




                                       251
 ―There are more than 480 faculty members in Madras I.I.T. The number of faculty
members belonging to downtrodden section is miserably low. Dauntlessly and
relentlessly but single handedly she has been agitating for the cause of social justice
in the institutions of national importance like I.I.T.
         Marxist Periyarist Communist Party congratulates Prof.Vasantha
Kandasamy on this memorable occasion.‖

        Periyar Era, September 2006, Vol.12, No.12




                                         252
―I would not have been consoled if I had been given this award in recognition of my
mathematical contributions. I would not have become so happy. In this country,
nobody recognizes a person who is a ‗fighter‘. They will merely move away from
them. But Kalaignar has pushed aside all that, and has given this award to me by
breaking the convention. When I think of that I whole heartedly praise that
honourable man. […]
        Her father W. Balasubramaniam served as the headmaster of the
Thondaimandala Thulluva Vellala Higher Secondary School in north Madras. She
has 4 brothers and 5 sisters, 2 of them are not alive now. The rest of them made
inter-caste marriages. Her husband Dr.Kandasamy has obtained five M.A. degrees
in Tamil, History, Political Science, Saiva Siddhanta and Defence Studies. He has
also obtained an M.Ed, M.Phil and Ph.D. Further, he has even got a D.Litt degree.
[…]
        It seems Vasantha madam has not gone to any temple, nor have they
followed rituals like ear-piercing and tonsuring. She says that I still have the hair I
was born with. […]
        Though she has risen to this greatness, she says, ―Students and faculty from
the backward classes who are talented do not get the rightful share in employment
in educational institutions, so they are pushed back. I have been fighting for the
past 18 years in the IIT demanding that they should get the 27% reservation for
Backward classes.

        Devi, 23.08.2006, Vol.28, No.19




                                         253
―Sanskrit was her second language in college.
       When we asked her about the Kalpana Chawla Award, she happily says, ―I
am glad that I have been accepted as a fighter. It makes me more mentally strong
to know that I have been recognized for my courage in an unconventional manner.‖

       Kungumam, 20.08.2006, Vol. 29, No.35




                                      254
“Have any of your students who obtained Ph.D. under your guidance received a
honour at the national level?

In the year 1997, a Dalit student named Kannan had come from Virudhunagar for
pursuing his Ph.D. in Mathematics. After a major struggle, he could get a seat in
IIT. Three years later, that Dalit student Kannan was called as an invitee to a
scientific conference that took place in New Delhi. That was a major conference:
the Indian National Science Congress and it took place at the national capital. That
year, 38 people submitted their research papers.

The Dalit student Kannan‘s research paper was selected for the first prize for the
Best Paper Award. The other 37 people who participated were Professors from
reputed educational institutions—this is the most notable point! Majority of the
students who obtained Ph.D. under my guidance are first generation learners.

“Are all the books that you have written related to your mathematical field?”

Majority of the books are mathematical. That too, they are books that make use of
mathematics to benefit the other walks of life. Mathematics can be used to control
satellites, it can also be used to tell to the world the feelings of the people affected
by AIDS.

“Please tell us about the books on AIDS that have been authored by you?”

With the support of the Tamil Nadu State AIDS Control Society, I have authored
two research books in English on AIDS. The book Love.Life.Lust.Loss dealt with
the life-stories of the migrant workers who were affected by AIDS. In this book the
emotions of 101 migrant labourers who are living with AIDS has been captured.
Another book is about women who are affected by AIDS. It is titled Women. Work.
Worth. Womb. Even in this book the feelings of these women has been recorded in
a mathematical way. Feelings cannot be recorded in mere numbers. When they
came to know that they had been affected by the disease… When they were taking
treatment for the disease… When they were ostracized by the society… To know
their feelings at such various points of time, this book will be helpful. Out of
numerous questions, we asked only the necessary questions to the patients and we
listed out their reactions to our questions: silence, anger, frustration—this will help
the medical research into AIDS. This method of mathematics is called Fuzzy
theory.



                                          255
“You would have done a lot of fieldwork for these two books. What are the facets
that you could uncover because of your research?”

Majority of the migrant workers who are infected by AIDS are men. That too, a vast
majority of these migrant workers are drivers and those involved in heavy, manual
labour. Many men are over-confident about their masculinity. They had the faith
that no matter what they did, no matter how many illicit affairs they had, nothing
would harm them. When we interviewed these AIDS patients we could observe that
they had such feelings. Likewise, majority of them don‘t have great concern about
their families. They have the arrogance that they are the bread-winners of the
family. They are irresponsible towards their families; they keep bad company and
consequently develop several bad habits; poverty—these are the major reasons that
lead them to acquire AIDS. Majority of those who were affected belong to the 31-34
age group. That is, they would have had illicit sexual relations in the age of 21-24.
That is the reason why they are now disease-ridden. As far as women are
concerned 90% of them have been infected with this disease by their husbands.

“How to understand fuzzy theory easily? To what other research topics are you
using Fuzzy theory?”

One can say that fuzzy theory is a generalization of the probability theory that you
learnt in ninth or tenth standards.
        If you toss a coin it can either be ‗head‘ or ‗tail‘ in probability. But in rare
cases, the coin might roll and go on and stand without falling either way. That is
fuzzy logic.
        My books related to mathematics, can be freely downloaded from the site
www.vasantha.net

        Dinamani Kathir, 20.08.2006, Vol.73, No.240




                                          256
Vasantha Kandasamy! An Assistant Professor of Mathematics at the IIT madras.
She has written 26 research books, published 632 research papers, she has guided
15 students for the Ph.D. degree, and 51 students for post-graduate research
projects. To such an extraordinary mathematician, there‘s another feather in her
cap: she has been awarded the Kalpana Chawla Award by the Tamil Nadu
Government. In what manner does Dr.Vasantha deserve it?
        Dr.Priyakumar is an Associate Professor in the Tharangampadi Bishop
Manickam Luther College. He obtained his doctoral degree under the guidance of
Dr.Vasantha Kandasamy. ―I was born in an ordinary agricultural family. IIT is a
new world that shocks rural and Dalit students. The situation prevailing there will
take these students to develop inferiority complex and will affect them
psychologically. Dr.Vasantha Kandasamy provides self-confidence to such people.
She has written more than 10 books on the modern concept of Fuzzy theory. She is
a world-renowned mathematician, but she has not been given due recognition in
India. When there were expectations that she will receive the Bhatnagar award,
which is India‘s biggest scientific honour, it was given to an unqualified person at
the last minute. It was a major shock. Though she has been affected by mental
tension, she has been bravely working for the weaker sections of society. It is
absolutely right that she has been given the Kalpana Chawla award,‖ says
Priyakumar.
        ―I studied ‗Coding Theory‘ for my Ph.D. degree. There are very few teachers
like Dr.Vasantha madam who teaches everything very patiently. She has a daring
personality, but at the same time she has a mind that is as calm as the deep seas.
Once, Dr.Vasantha Kandasamy carried out research for the Indian Space Research
Organization (ISRO). At first the help from ISRO was on a small scale, later they
had the intention of giving a major grant, so they sent their experts to IIT. But IIT
refused the support from ISRO questioning the connection between Mathematics
and Space Research. Though she is completely qualified to become a Professor,
they still retain her as an Assistant Professor. We have not given her the due
recognition. She fights with an exemplary courage for all the attacks that are made
upon her. Several more awards await her,‖ says Dr.Selvaraj who is a lecturer in the
SSN Engineering College and Dr.Rajadurai, a lecturer in the Vellore Institute of
Technology who spoke to us next are students of Dr.Vasantha Kandasamy.
        ―Vasantha Kandasamy works in full vigour to ensure that everybody gets all
the rights, and that equality must prevail. Though she is a world-renowned
mathematician, she is very humble. Her only wealth is her great intellect. Her
daring and her tireless struggle are worthy of praise. If another person had been in
her position, they would have gone to foreign universities to increase the weight of
their purses. She has ignored offers abroad and continues to work here, because of
her attachment to poor and rural students. The IIT administration should honour

                                        257
her. She struggles continuously without being affected by anything. This award will
further sharpen her struggle and enthuse her,‖ says Rajadurai.

       Kalki, 10.09.2006, Vol.65, No.6




                                        258
―The struggle for social justice waged in the IIT Madras by Dr.Vasantha
Kandasamy are moving. Not only those who know her, but even those who do not
know her, would have known about her struggle.
        Vasantha Kandasamy raised questions with plenty of evidence—even the
last fool would have come to know how many Dalits or BC community people
worked as Professors in the IIT Madras. This is the question she asked 15 years
back when she joined IIT Madras as an Assistant Professor unable to bear it. It was
not a question she asked, it was a fire she set ablaze. The Institute did not have any
reply to her questions.
        Though she has been insulted and disregarded by the IIT administration,
she continues to work for the oppressed sections of society. If she wants she can
leave abroad next month to a rich, foreign country. She firmly says, ―But why
should I run abroad leaving my country, and people like me, because of fear due to
them, or for the sake of money? If I do like that in a manner which gives happiness
to the enemies of the majority of people in this country, how will the struggle of
Periyar and Ambedkar and others be strengthened? That is why I keep waging a
struggle at my level.‖ Several leaders in Tamil Nadu strongly support her struggle
for social justice and reservation in the IITs.
        In these circumstances, the Tamil Nadu government bestowed the Kalpana
Chawla award to her in recognition of her tireless struggle for social justice, to
appreciate her mathematical talent that has surprised the world, and to praise her
for preparing backward class students to become experts in research.
        As far as Vasantha Kandasamy is concerned, it can be said that this award
is not just a recognition for her work, but a medicine for her long-standing
wounds.‖

        Penne Nee, September 2006, Vol.5, No.8




                                         259
Vasantha Kandasamy could not bear to see this injustice take place in front of her
eyes. She resolved to fight for social justice. So, she had to suffer several sorrows.
―In 1990, when everybody got promotion, even I became an Assistant Professor.
After that 16 years have passed, but I remain in the same post. In the interim
period, I was given the post of Associate Professor. Because of a case that I filed
against the IIT Madras, they don‘t address me as an Associate Professor even for
namesake,‖ says Dr.Vasantha. She has been insulted during official meetings. At
times people have barged into her office room and shown lewd gestures, or talked
vulgarly and ran off. The grill-gates that are normally used for fear of theft have
been put up in her room to protect her. Today, it remains as an inerasable symbol
in her quest for social justice.
         But Vasantha adds with passion, ―No matter how many obstacles come,
nothing can stop my journey to establish social justice.‖ In the midst of all this
torture she has authored 632 research papers, 26 books. According to the
American Mathematical Reviews which publishes compiled lists of research
articles in Mathematics, Dr.Vasantha has the highest number of papers.
         What does she say about getting the Kalpana Chawla award? ―In general,
no government will recognize a fighter. But Kalaignar‘s government has recognized
me. To have given me the award is an unconventional act. I express my gratitude. I
would not have become so happy even if I had received the award for mathematical
research. I am proud that my struggle has been rewarded. I will fight even more
daringly,‖ says Dr.Vasantha in a resolute voice.
         Though she was promoted to the post of Associate Professor, she is given
only the salary of an Assistant Professor, stays not in a quarters for the faculty, but
only in the D-type staff quarters.‖

     Dinakaran, 13 August 2006, Tamil Nadu’s largest selling daily
newspaper with a circulation of 10 million copies.




                                         260
―What connection can be there between a professor and an award for courage and
daring enterprise?‖ so we met Vasantha madam.
         ―I am a very strict teacher, discipline is very important to me. But the
amount of strictness I show when I deal with students, the same amount of
enthusiasm I will show in fighting for their problems. I have fought and got
admission for several meritorious students who keep yearning to join IIT. They
have gone to several foreign countries: America, Germany, Japan, France and they
are well-settled. Can a teacher ask for greater happiness?‖ says Dr.Vasantha who
has undertaken another major struggle: teachers must be appointed in IITs on the
basis of social justice.
         It is 17 years since Dr.Vasantha joined IIT Madras. Her struggle for rights
in the IIT Madras is also 17 years old.
         ―Yes, when I joined IIT, all the cuckoos in the campus were going to be shot
dead because the director found it a disturbance. At that time itself, I fought
against it and prevented it. That was the day when all this started! After that the
problems for social welfare started coming to me, I thought that it was my duty to
fight,‖ says Dr.Vasantha.

       Aval Vikatan, 1 September 2006, Vol.8, No.24




                                        261
―There are six IITs in India. One of them is the IIT Madras. The Central
Government sets apart a sum of Rs.1000 crores for these Institutions. The Chennai
IIT is situated in the heart of the city in an area of 300 acres. It was the then Chief
Minister Kamaraj who ensured that this IIT came to Chennai through his great
efforts. With what lofty intentions he brought this Institute to Chennai, all those
intentions have been smashed. This institute functions under the Ministry of
Human Resources Development of the Central Government, but nobody can
question it.‖
         Two years after I joined IIT, in 1990, all the lecturers in the Indian Institute
of Technology were promoted to the post of Assistant Professor by a government
order. At that time, even I became an Assistant Professor. That is the first and last
promotion that I have received in the IITs. Even in this promotion, none of the
increments that I had earned earlier were joined to my salary.
         I submitted an interesting mathematical project to the Indian Space
Research Organization about satellite communication and coding theory. I had
asked for a grant of Rs.7.77 lakhs. After a lot of delay, the IIT allotted only 1 lakh
from the said amount for me to continue my research. They did not give an
extension, or remainder of the amount granted to me by ISRO. Next, I submitted a
proposal to a team of space scientists about mathematically formulating a
technique that will enable us to have a system of coding theory on par with NASA.
But the then Director prevented me from discussing it before the committee.
         Not only was I subjected to this harassment, but several more. All IIT
faculty members are given telephone connections to their residences and office by
the IIT administration itself. But the telephone instruments placed in my residence
and office were removed and taken away by the institute. Till today, I have not
been given a phone. But wantonly they have published two fake numbers under my
name in the Chennai City Telephone Directory and the IIT Phonebook. Likewise,
the employees of IIT are allotted quarters on the basis of their seniority. But
discrimination against me has taken place even in this.
         The reservation policy must be implemented. They have boycotted me and
not given me any promotion for the past 18 years for the sole reason that I voiced
my support to the demand that Backward and Dalit students and faculty must be
admitted to the IIT. That boycott continues even today. But still, I am not afraid. I
do not lose faith. I keep fighting continuously. This is not a struggle that takes place
for a promotion, or for my individual benefit or for my salary hike. I don‘t need any
of that. A particular caste alone experiences the privileges of IIT, as if they have
taken it on a complete lease. They enjoy 100% reservation. This is my struggle for
social justice against that. I am fighting as an individual woman ever since the day I
joined the Institute.


                                          262
         I will not say that I have attained complete victory in my struggle. But I will
say that I have achieved victory to some level. I have taken up the cause for justice
in my hands. If we demand justice itself, we will only get into difficulties. I keep
suffering. But I will struggle to the end. I will fight till the day of my retirement. My
fighting spirit will never stop.
         But no matter how many hindrances I face, I can bear it all. They gave us
many problems. I bore everything. Even now they continue to harass me. These
difficulties will not do anything to me. The difficulties that they give me are my
stepping stones. I will not fear anything,‖ as she says this we can understand her
fighting spirit. Because of such troubles, sorrows and threats, I am unable to send
my girl children to college, and I am making them study through correspondence.
         ―I have written more than 70 letters about the injustice that is meted out to
me addressed right from then President Shankar Dayal Sharma and then Prime
Minister P.V.Narasimha Rao to current President A.P.J. Abdul Kalam. But no reply
has come about leave alone the solution. Today, the demand for 27% reservation in
Institutions of higher learning has become strong. The Central Government must
reserve this 27% of seats to the Backward classes. This is the need of the hour and
it is inevitable,‖ says this woman fighter who struggles for social justice.

        Devi, 30.08.2006, Vol.28, No.20




                                          263

				
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