D degree. 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. Selvaraj may be awarded the Ph. D degree in Mathematics and the thesis may be regarded as Highly commended --Prof. Kirangi, Dept. 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.
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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.
Karl-Heinz Zimmermann, Technical Univ. Engineering, Hamburg, Germany. 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.
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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. 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.
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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 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. 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.
Category: Algebraic Graph Theory
For this the thesis supervisor and the candidate deserve to be congratulated. Without any hesitation, I strongly recommend for the award of the Ph. Raja Durai in Mathematics. 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. Hema Srinivasan, Dept. 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. As the work suggests various benefits like increase in production, reduction in power consumption, consistent quality, reduction in mill stoppages, etc. Reddy, Dept.
Applications of Algebraic Graph Theory
Tanaka, and M. Ozawa, Comments on "Best conventional solutions to the King's problem", Z. Gijswijt, A.
Schrijver, and H. Tanaka, New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming, J. Theory Ser. A — Tanaka, Classification of subsets with minimal width and dual width in Grassmann, bilinear forms and dual polar graphs, J. Ozawa, Solution to the mean king's problem with mutually unbiased bases for arbitrary levels, Phys. A 73 R 4pp. Tanaka, Association schemes of affine type over finite rings, Adv.
Mizukawa and H. Bannai and H. Algebra — Other manuscripts J. Tanaka, On some Gelfand pairs and commutative association schemes, Jpn. Ceccherini-Silberstein, F. Scarabotti, and F. The original version of the appendix appeared in the unofficial proceedings, "Combinatorial Number Theory and Algebraic Combinatorics", November , Yamagata University, Yamagata, Japan, pp. Linear Algebra 34 , Aalipour, Z. Berikkyzy, L. Hogben, F. Kenter, J. Lin and M.
Brimkov, A. Erey, L. Leshock, X. Song and J. Yang and J. Abiad, S.
M Cioaba and M. Berikkyzy, J. Cummings, J.