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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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