Extracts from Ph.D. Reports

13. Mr. Raj Kumar : 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.

12. Mr. K. Paramasivam: COLORING OF ZERO-DIVISOR GRAPH OF SOME SPECIAL ALGEBRAIC STRUCTURES

The researcher has tried to discuss the zerodivisor 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 edgemagic 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.

11. Mr. T. Johnson: 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.

10. Mr. R.S.Selvaraj: 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.

9. Mr. Moon Kumar Chetry: STUDY OF SPECIAL ELEMENTS IN GROUP RINGS AND LOOP RINGS

I must congratulate the supervisor and the candidate for one of the good theses in Algebra. They have introduced new definitions, proved many results in detail and suggested interesting research problems in their thesis. The thesis not only studies the special elements of both associative rings and non-associative rings, it also introduces several new Smarandache special elements and using these new Smarandache algebraic structures have been introduced. To summarize, the thesis is self-contained, theorems are proved with all details. Further, it contains many examples and counter examples, which clarifies the theory. Contains many new ideas and opened the channel of S-rings. The author is familiar with contemporary research on related topics. The thesis makes a valuable contribution to the field of Algebra. --Prof. Kirangi, Dept. of Math., Univ. of Mysore, Mysore, India.

In this thesis, Moon Kumar Chetry introduces and studies about Smarandache special elements in rings. It is rare to see a thesis, which carries out stufy 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 definitions and results. This thesis is well presented... Prof.Dr.Florentin Smarandache, Department of Mathematics, University of New Mexico, Gallup, USA.

8. Mr. R. S. Rajadurai: 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.

7. Ms. S. Ramathilagam: 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 infact these were tested. [...] Over all the candidate made substantial survey and colleced 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 Hyderabed, 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 teh 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 substanial. -- Prof. Hema Srinivasan, Dept. of Maths., Univ. of Missouri, Colombia, USA.

6. Mr. S. R. Kannan: 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.

5. Ms. R. Sujatha: 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, Techical Univ. of Hamburg-Harburg, Dept. of Comp. Elec. Engineering, Hamburg, Germany.

4. Ms. Indra Venkatbabu: 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, emperical 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 emperical 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.

3. Mr. D. Meiyappan: 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 contributiin 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 deverlopment 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.

2. Mr. N. Suresh Babu: STUDIES OF RANK DISTANCE CODES

This thesis gives a detailed analysis of error correcting codes in rank metric which is a very effiecient 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. Hence, this thesis is commended for the award of the Ph.D. degree. -- 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 truimphs of the theory...--Prof. Karl-Heinz Zimmermann, Techical Univ. of Hamburg-Harburg, Dept. of Comp. Elec. Engineering, Hamburg, Germany.

1. Mr. Satya Veer Singh : 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.

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