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Resume with full details of Prof.R.N.Mohan

Application for visiting /otherwise Position in Universities/research institutes in Mathematics

By

Ratnakaram Nava Mohan

 

Mailing Address: 137, Preserve Drive at Crestwood, Royal Palm Beach, Florida-33411, USA

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The information requested below is for the use of the institute only:

 

1. Last Name (Family Name): Ratnakaram

 

2. First Name (Given Name): Nava Mohan

 

3. Title: Professor

 

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The following should be enclosed: I. A brief outline of your current and intended research (enclosed)

II. A list of publications (enclosed)

III. Copies of selected reprints and /or preprints (enclosed)

IV. Any further information which you feel is relevant to this application (enclosed)

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4) Present home address: 9. Term of time required?

137, The Preserve at Crestwood I may be awarded preferably one year term, or

Royal Palm Beach, FL 33411, which ever time that is possible

 

 

 

5) Permanent Home Address:.

 

22-123, Bank Street, Nuzvid-521201, AP, India 10) For visiting Position please specify preference of year:

Or the above American Address itself

Academic Year: Any time possible

 

6) Present institutional affiliation 11) Do you wish to be considered for a two year membership?

Director, (Relinquished on Nov 3, 2008)

Sir CRR International Institute of Mathematics I wish to work for one year or so only and

Eluru-534007, W.G. Dt., AP, India if possible it may also be considered.

 

7) Permanent institutional affiliation: APPLICANT INFORMATION

Relinquished my position as Director

On 11/03/2008 12) Optional

 

8) Which address we use for correspondence Date of Birth: 09/14/1942

Present home address and also email address No medical impediments

13) Is your spouse or companion also applying for institutional position?

 

No, My wife is not applying for any position. But she can work in the library temporarily, if permitted, as she herself a full fledged and well qualified librarian. She is also Green Card holder and legally permitted to work in USA

14) When Available: Almost immedietly

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OFFICE USE ONLY

 

Received: PF Yes No

Acknowledged:

 

 

15) Required

 

To help the selection process, please indicate the discipline as closest to your work

 

[7] Combinatorial configurations and their applications. Computer Science, Logic

 

16) Specific field of (Information needed for the preparation of the Institute’s introductory brochure.)

Uniform Hypergraphs, alienated towards applications

17) Academic Degrees:

Degree awarded	Year Received	Institution and place
Bachelor of Science (B.Sc.)	1964	Andhra University, Visakhapatnam, AP, India
Master of Science (M.Sc.)	1966	University of Saugar, Sagar, MP, India
Doctor of Philosophy (Ph.D.)	1980	Vikram University, Ujjain, MP, India
Doctor of Science (D.Sc.)	1993	Vikram University, Ujjain, MP, India
F.N.A.Sc	2000	National Academy of Sciences , UP, India
Certificate of French	1972	University of Madras, Chennai, India

18). Professional positions and fellowships (former and present-list last three)

S.No.	Name of the position/ dates	Appointed by	Place of Work
1.	Lecturer & Chair 1966-1992 Reader & Chair 1992-2000	Governing Body DAR College, Nuzvid, Krishna Dt. AP, India Pin: 521201	Department of Mathematics DAR College, Nuzvid Krishna Dt., AP, India
2.	Professor & Chair, 2002-2008	Managing Committee Sir CRR College, Eluru-534007, W.G.Dt., AP, India	PG Department of Mathematics Sir CRR College of PG Courses, Eluru-534007, WG Dt., AP, India
3.	Director, 2005-08	Managing Committee Sir CRR International Institute of Mathematics Eluru-534007, W.G.Dt., AP, India	Sir CRR International Institute of Mathematics Eluru-534007, WG Dt., AP, India

18a). Participated in the Summer Institutes held at:

1) SV University, Tirupathi,1968,

2).University of Delhi, Delhi, 1969,

3) Meerut University, Meerut, 1972,

4). Indian Statistical Institute, at Bangalore, 1974,

5). Indian Institute of Technology, New Delhi, 1979,

6). Andhra University, Waltair 1970, and

7). Andhra University, Viasakhapatnam 2004, Refresher course for PG Teachers.

All this academic activity promoted me to go for advanced studies in Mathematics.

18 b) Indian Research Fellowships:

	Name of the Fellowship (Indian)	Awarded by	Place of Work These are top Research institutes in mathematics in India
1.	Teacher Fellow, 1971-72 one year For Advanced study and research	University Grants Commission, New Delhi, India	Ramanujan Institute for Advanced Study in Mathematics, Chennai-600005, India Under the guidance of the then Director: Prof. T.S.Bhanu Murthy,. Member of IAS (1964-66) He is closely associated with IBM Von Neuman Professor, Prof.Harishchandra, who was also a permanent member of IAS. till 1983.
2.	1. Visiting Scholar 1978   2. Visiting Fellow 1983   3. Visiting Professor 1995	Managing council, School of Mathematics Tata Institute of Fundamental Research, Mumbai, India	School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India Associated with Prof.N.M.Singhi
3.	Visiting Professor, 1984	Governing Council, Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad, India	Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad, UP, India Associated with Prof.. B.D.Acharya, SS Shrikhande (Now it is named as the Harishchandra Research Institute in Mathematics)
4.	Visiting Professor, 1985	Governing Council, Indian Statistical Institute, Calcutta, India	School of Mathematics, Indian Statistical Institute, Kolkota, India Associated with Profs. G. M. Saha, BK Sinha, SB Rao
5.	Visiting Fellow	Board of Directors, American Studies Research Center, Hyderabad, India	American Studies Research Center, Hyderabad, AP, India
6.	Visiting Fellow	Board of Directors, Indian Law Institute, New Delhi, India	Indian Law Institute, New Delhi, India.

 

18 c) Foreign Fellowships:

S.No	Fellowship Name (Foreign)	Awarded by	Place of Work
1.	Visiting Scientist, February 1989	Japan Society for Promotion of Science, Japan & Indian National Science Academy, New Delhi	Hiroshima University, Okayama University of Sciences, Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan   Collaborated with: Prof. Sanpei Kageyama
2.	Visiting Scientist, 1992-93	Commission of European Communities, Brussels,Belgium	LERMAT,ISMRA, Caen, France Collaborated with: Prof.J.P.Jernot
3.	Visiting Scientist, 1995	Royal Society, London, UK	University of Wales, Aberysythwith, UK University of London, UK Collaborated with: Prof.V.C.Mavron, Prof. Fred Piper, and Prof.Peter Wild
4.	Visiting Professor- Associate Member, 1996-98	The Third World Academy of Sciences, Trieste, Italy	Instituto Mathematica de Pura e Aplicada, IMPA, Rio De Janiero, Brazil Associated with: Prof.J.Palis Promoted by Prof.MGK Menon,New Delhi
5.	Visiting Professor 1968	Polish Academy of Sciences, Warsaw, Poland	Agricultural University of Poznan , & Adam Mickiewicz University of Poznan, Poland Collaborated with: Prof.B Ceranka
6.	Visiting Professor, 1999	University Grants Commission, New Delhi and Invitation from Australia	SITACS, University of Wollongong, Australia Collaborated with Prof. Jennifer Seberry
7.	Visiting Scientist& Associate Member, 2005-06	The Third World Academy Of Sciences, Trieste, Italy	continued   Center for Combinatorics and SS Chen Institute of Mathematics, Nankai University, Associated with Prof. William YC Chen PR China Discussed with Prof. Adreas Dress, Germany, regarding Mathematical Theory of Evolution
8.	Visiting Professor, 2005-06	Exchange of Foreign Scientists/ experts Invitation Program, South Korean Government, South Korea	Institute for Information and Communication, Chonbuk National University, South Korea Collaborated with Prof. Moon Ho Lee

 

18d). Honors and Recognition

Serial no	Recognized by	Name of the recognition
1.	Marquis Who’s Who , USA	Biography present in the Marquis who is who in the world since 1999
2.	Marquis who’s who, USA	Biography present in the Marquis who is who in the Asia
3.	Marquis who’s who, USA	Biography present in the Marquis who is who in America
4.	Government of Andhra Pradesh, Hyderabad, India	The Best Teacher Award 1998, for College Teachers in AP, India
5.	American Studies Research Center, India	Directory of American Studies Specialists
6.	2000 outstanding intellectuals ofg 21 st Century UK	Directory of World Intellectuals published by International Biographical Reserch Center, Cambridge, England.

19) References: (Names of at least three mathematicians who know your work. The applicant must ask that letters of recommendation be sent directly to the school of Mathematics)

 

S.No.	Name	Email & Snail Mail addresses
1.	Prof Sanpei Kageyama, Professor and co-researcher, known since 1978	Hiroshima Institute of Technology, Hiroshima, Japan
2.	Prof.William YC Chen, Professor, Director, known since 2005	Director, CFC, Vice President, Nankai University, Tianjin, PR China
3.	Prof. Moon Ho Lee, Professor, co-researcher, known since 2005	Director, Institute for Information and Communication, Chonbuk National University, Jianju, South Korea.
4.	Prof. Michel Deza, Professor, co-researcher, known since 1997	, Directeur de recherché au CNRS, Laboratoire de Geometrie Appliquee, LIGA-EuJC, Ecole Normale Superieure, 45, rue d'Ulm, F-75230, Paris, Cedex 05 - France
5.	Prof. M.G.K.Menon, Known since 1992	, Former Minister for Science and Technology, Member for Rajya Sabha, Government of India, New Delhi

Date Signature

I. A Brief outline of current and intended Research:

 

My main line of research both the current trends and intended is as follows:

 

Hypergraphs and their Applications

Overview: The broad area of my research will be on “Hypergraphs and their Applications," which includes all types of combinatorial designs and graphs both of which are strongly interlaced. Specific focus will be towards their applications such as in the investigations in cryptography, codes and security systems, networks and communication systems, genetic engineering and gene structures, and even as far as Nanoscience. In particular, uniform hypergraphs play a pivotal role in the understanding and advancements in the structures of combinatorial configurations like the BIB designs, PBIB designs and orthogonal arrays (OA). Certain combinatorial matrices like M_n-matrices and some of their next generation structures are important for carrying out investigations in these directions. In many of the conceivable disciplines numerous unsolvable problems could perhaps be solved by using graph-theoretic or, more generally, uniform hypergraph techniques. For instance, uniform hypergraphs have been efficiently used in enhancing the understanding of the organization in computer network systems. Domination theory in particular plays important role in information and communication systems. The highly fault-tolerant graphs/networks have still remained unexplored. Thus, I wish to explore design of experiments, BIBDs, PBIBDs, OA and combinatorial matrices, coding theory and their applications to cryptography, group testing and biometrics, and security systems, secret sharing schemes, hierarchical schemes and robust designs, graphs, labeled and signed graphs, hypergraphs, and uniform hypergraphs, directed hypergraphs, social networks and probabilistic models and network design with applications to computer science, RAMSEY type theorems and their applications.

 

Main Problems to be investigated:

 

1. In connection with the above aspects, I wish to study the new systems of

M_n-matrices, and M-matrices of Types I, II, and III, and their corresponding combinatorial configurations, namely M_n-graphs, M-graphs of types I, II, III with

application oriented approach. And I propose to use graph transformation techniques over these new graphs.

 

Directed hypergraphs can be used as a tool to solve problems in operational research and computer science. Concepts such as connectivity, paths and cuts in a special class of hypergraph systems usable in data bases and telecommunication and transportation analysis. Hypergraphs, a generalization of graphs have been studied by C. Berge, who proved that these combinatorial structures will form a successful tool to represent and model concepts and structures in various areas of computer science and discrete mathematics.

 

2. In the light of the M-matrices, the century old Hadamard Conjecture will be explored.

 

3. Considering mutually orthogonal Latin squares (MOLS) the orthogonality in Latin squares; and considering the orthogonal property of Hadamard Matrices, the orthogonality in combinatorial matrices will be studied.

 

4. Most interestingly there exists certain coherence amidst Deza graphs, Hypergraphs, and the M_n-graphs, and M-graphs, which is highly tractable and in this direction I wish to further my study. The Deza graphs, which are a generalization of strongly regular graphs, are very interesting in association with graphs generated through combinatorial transformations and some combinatorial matrices, together with certain combinatorial configurations.

 

5. T. Calinski’s C-Matrices, Moon Ho Lee’s jacket matrices and the M-matrices are yet to be further studied in the direction of their inter-relationships and compatibility along with Hadamard matrices.

 

6. Besides, the 5759 parametric relations of BIB designs enlisted by us so far have not been studied with regard to their existence and non-existence. These studies may reveal the possible sufficient conditions for the existence of BIB designs, which have remained as a challenging open problem for decades. Raghavarao, Takeuchi and Collins have enlisted a few parametric relations of these designs. With a new technique this enlistment has been done, which opened new vistas for further research in these lines.

 

References:

1. Belevitch,V. (1968). "Conference Matrices and Hadamard Matrices." Ann. de la Société scientifique de Bruxelles, 82, 13-32,.

2. Berge C.(1963). Théorie des graphes et ses applications. Deuxième édition Dunod. Paris, viii+269 pp.

3. Berge C., (1970). Sur certains hypergraphes généralisant les graphes bipartites. Combinatorial theory and its    applications, I (Proc. Colloq., Balatonfüred, 1969), pp. 119-133. North-Holland, Amsterdam.

 

4. Berge.C., (1973) Graphes et hypergraphes Monographies Universitaires de Mathématiques, No. 37. Dunod,    Paris, 1).

5. Berge,C. (1989)., Hypergraphs: Combinatorics of Finite Sets, North Holland

6. Bondy, J.A. and Murthy, U.S.R. (1979). Graph Theory with Applications. North- Holland, Amstersdam:.

7. Brenner. J. and Cummings, L.(1972)... "The Hadamard Maximum Determinant Problem." Amer. Math. Monthly, 79, 626-630.

8. Brouwer A.E., Cohen A.M and Neumaier A. (1989). "Conference Matrices and Paley Graphs." In: New York: Springer-Verlag, p. 10.

9. Ceranka, B. (1983). Planning of Experiments in C-Designs, Annals of Poznan Agricultural University, Scientific Dissertations, Poznan, Poland.

10. Colbourn C.J. and Dinitz J.H. (1996). (Eds.), Boca Raton, FL: CRC Press, p. 689.

11. Cox; D.R (1958) Planning of Experiments, Wiley International Edition, New York

12. Collins,R.J.(1976), Constructing BIB designs with a computer, Ars Combinatoria, 2, 285-303.

13. Ericson, M., Fernando, S. , Haemers, W.H., Hardy, D. and Hemmerter, J. (1999) Deza Graphs, A generalization of strongly regular graphs, J.Combin.Dez.7, 395-405.

14. Gross, J. L. Yellen, J (207). Graph Theory and Applications, Chapman and Hall CRC Press

15. Hadamard, J.(1893).. Résolution d'une question relative aux déterminants. Bulletin des Sciences Mathématiques, 17:240-246.

16. Harary, F. (1972).Graph Theory, Addison Wesley, London

17. Hughes, D.R., Piper, E.C. (1985). Design Theory, Cambridge University Press, New York.

18. Kaishun Wang and Yan-quan Feng, (2006). Deza digraphs, European J. Combinatorics, 27, 995-1004

19. Marshall Hall Jr. (1986), Combinatorial Designns, Wiley Inter-science Publication Series in Discrete Mathematics, New York.

20. Martin, J.(1977) Computer Data Base Organization, Prentice Hall, Eaglewood Cliffs , NJ.

21. Mathon and Rosa, A. (1996). 2-(v,k,λ)-signs of small order. The CRC Hand Book of Combinatorial Designs (Ed. Colbourn, CJ, and Dinitz, JM)

22. Mohan, R.N. (2001). Some Classes of Mn- M_n-matrices and M_n-graphs and their applications. J. Combin. Inform. System.Sci.26, no.1-4,51-78.

23. Mohan R.N. and Nair M.M. (2005) Enlisting BIB designs small and higher order and their Classification, SCRRIM, TR 2., Jan 14, 2005 Sir CRR International Institute of Mathematics, Eluru-534007, AP, India.

24. Mohan, R.N., Kageyama, S., Moon Ho Lee, Yang, G.. (2008) Certain new M-matrices and their properties and applications. Discuss. Math. Probab. Stat (to appear).

25. Moon Ho Lee (2006). Jacket Matrix Principles and Applications, With applications to Communications and Signal/image Processing, Institute of Information and Communications, Chonbek National University, Jianju, South Korea.

26. Paley, R. E. A. C. (1933).On orthogonal matrices. Journal of Mathematics and Physics, 12, 311–320.

27. Raghavarao D. (1971) Constructions and Combinatorial Problems in Design of Experiments, John Wiley, New York

28. Raghavarao,D. and Laxmi V. Padgett (2005). Block Designs: Analysis, Combinatorics And Applications, Series in Applied Mathematics, Volume 17, World Scientific Publishing Company.

29. Sylvester, J.J (1867). Hadamard Matrices. Thoughts on inverse orthogonal matrices, simultaneous sign successions, and tessellated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers. Philosophical Magazine, 34:461-475.

30. Takeuchi, K (1962). A Table of difference sets generating Balanced Incomplete Block Designs, Rev. Inst. Internet. Statist., Vol.30, 361-366.

31. W.D. Wallis (1988) Combinatorial Designs, Marcel Dekker

32. W.D. Walls, H.Shen, W.Wei, L.Zhu (1990) Combinatorial Designs And Applications, Lecture Notes in pure and Applied Mathematics, International Conference in April 1988 at Tunxi (now Hunangshan), China. CRC Publisher ,126 Zhongguo ke xue yuan Hefei fen yuan CRC Press.

33. Walter T. Federer (1955) Experimental Designs, Theory and Applications Oxford & IBH Publications, New Delhi

II a. Research Guidence:

 

Guided Mr.M.Madhusoodhanan Nair for the award of Ph.D.degree, from the JNTU, Hyderabad on the topic entitled, Resolvable and Affine Resolvable BIB Designs and Application. He had been awarded in July, 2006

 

II b. Research Projects:

 

After completing my degree I have worked out on two research projects, both of them

were being sponsored by University Grants Commission, New Delhi, India.

 

1. Constructions of Designs, 2. Resolvability in BIB Designs

 

II c. I have organized three national level seminars during my tenure.

 

1.: National level seminar: “Designs, Graphs and their applications” at Department of

Mathematics DAR College, Nizvid-521201, AP, India, during January 28-30, 1985.

 

2. National level seminar on “ Designs, graphs and codes and their applications,” at PG Department of Mathematics, Sir CRR College of PG Courses, Eluru-534007, WG Dt. AP India Jan 25-28, 2007.

 

3. National level workshop on “ Uniform Hyper Graphs and their applications at Sir CRR

International Institute of Mathematics, Sir CRR College Precincts, Eluru-534007, WG Dt., AP, India during Jan 30-Feb 5, 2008.

 

II d. Delivered lectures at:

 

1. Hiroshima University, Hiroshima; Okayama University of Sciences, Okayama; Research Institute for Mathematical Sciences, Kyoto University, Japan, .(Invited lectures 1989);

2. The School of Mines, Paris, France (In International Conference);

3. Adam Mickiewicz University of Poznan, Poland (Invited Lecture)

4. University of Southern Maine, Portland, (In International Conference, Lecture in the plenary session); Florida Atlantic University, Florida International University, Southern Illinois University, Carbondale.(Invited lectures)

5. University of Wales and University of London, UK, (Invited lectures)

6. University of Wollongong, Australia, (Invited lectures)

7. Indian Statistical Institute, Calcutta, (Invited lectures)

8.  

9. Chonbuk National University, Jianju, South Korea in the International workshop on Multimedia, Signal processing and Transmission, during October 16, 2005 and February 13, 2006 South Korea. Plenary session lectures twice on two occasions.

10. In our national conferences held at DAR College, Nuzvid, one lecture and at Sir CRR International Institute of Mathematics, Eluru two lectures in the two conferences one in each occasion.

11. National Conference held at University of Rajasthan, Jaipur, India

12. Tata Institute of Fundamental Research, Mumbai, India (Invited Lecture)

II d. A List of Publications

[1] R.N.Mohan (1980). A note on the construction of certain BIB Designs. Discrete Mathematics, 19,209-211.

 

[2] R.N.Mohan (1981) A Note: Certain Arrangement with Prime. The Mathematical Education, Vol XV 1, Siwan, Bihar, India

 

[3] R.N.Mohan and Kageyama, Sanpei (1982). On the Characterization of Affine

-Resolvable BIB Designs. Utilitas Mathematica 22, pp 17-23

 

[4] R.N.Mohan and Kageyama Sanpei (1981). A method of construction of Group divisible designs. Utilitas Mathematica, Vol 24, pp. 311-318

 

[5] R.N.Mohan (1983) On the Dual of a Partially Balanced Incomplete Block Design. Indian Journal of Pure And Applied Mathematics 14, pp, 13-17.

 

[6] Kageyama Sanpei and R.N.Mohan (1984) On the Construction of Group Divisible Partially Balanced Incomplete Block Designs. Bull. Of the Faculty of School Education, Hiroshima University, Part II, Vol 7, pp. 57-60.

 

[7] Kageyama, Sanpei and R.N.Mohan (1984) Dualising w.r.t s-tuple. Proc.of Japan Academy, Vol 60 A (7) pp. 226-271

 

[8] Kageyama Sanpei and R.N.Mohan (1984). Three methods of Construction of PBIB Designs. Comm. Stat. Th. Methods. 13, (25) pp. 3185- 3189

 

[9] R.N.Mohan and Kageyama, Sanpei (1984). Two Constructions of Group Divisible Designs, J. of Comb. Inf.and Syst. Sciences (JCISS) vol 9 (2) pp 81-86

 

[10] Kageyama Sanpei and R.N.Mohan (1985). On -Resolvable BIB Designs. Discrete Mathematics 45,pp 113-122.

 

[11] Kageyama Sanpei and R.N.Mohan (1985) On the Constructions of GDPBIB designs, Sankhya, 47, B-2, pp. 292- 293.

 

[12] Kageyama, Sanpei and R.N.Mohan (1985). New Constructions of BIB Designs Biom.J.27 (3) pp. 345-348.

 

[13] Kageyama, Sanpei and R.N.Mohan (1985). Constructions of -Resolvable PBIB Designs, Cal. Stat. Assoc. Bull. Vol 34, pp 222-224.

 

[14] R.N.Mohan and Kageyama, Sanpei (1986). On the Reduction of Associate Classes of Certain Generalized type. J.of. Comb. Inf. and System Sciences (JCISS), Vol II, no 2-4 pp 92-98

 

[15] R.N.Mohan and Kageyama Sanpei (1987) A note on Pair wise Balanced Designs, Indian Journal of Pure and Applied Mathematics, 18 (10) pp. 874-875.

[16] R.N.Mohan and Kageyama, Sanpei (1988). A Kronicker Product Design and its Reducible Associate Class. J. Probability and Mathematical Statistics, vol 9, pp. 45-49.

 

[17] R.N.Mohan and Kageyama, Sanpei (1989). Two Constructions of -Resolvable PBIB Designs. Utilitas Mathematica. 36, PP to 1993 worked on D.Sc., Thesis and Awarded the degree in November 1993. And from 1993 working on the monograph on the topic entitled, “ Resolvability and Affine Resolvability,”

 

[18] R.N.Mohan (1993). The sum of the P^th powers of the first n natural numbers. Mathematical Education vol. 10-2 John Wiley, New Delhi.

 

[19]. R.N.Mohan and Kageyama Sanpei ((1997). A new Series of -Resolvable and almost -Resolvable PBIB Designs. Utilitas Mathematica 51, pp. 21-26.

 

[20] R.N.Mohan and A.H.Ahmed (1998) A Construction for Authentication/Secrecy Codes based on Latin Square Theory. Far East Journal of Applied Mathematics, Allahabad India. Vol. 2. No. 2. PP. 163-168

 

[21] R.N.Mohan (1999) A new series of Affine -Resolvable (d+1)-Associate Class PBIB Designs. Ind. J. Pure and Ap.Maths, New Delhi, Vol. 30,1,pp.89-98.

 

[22] R.N.Mohan and V.C. Mavron (2000) Almost -Resolvable and Almost Affine

-Resolvable Designs. JCISS Vol.25 pp267-275

 

[23] A.H.Ahmed and R.N.Mohan and R.Bhanu Teja (2001). On Certain Ciphering Systems on Mn- Matrices. Varahmihir J. of Math. Sc., Vol. 1 no 2, 125-134.
 .

[24] R.N.Mohan, B.Ceranka and Sanpei Kageyama (2001). Some observations on the constructions of Chemical Balance Weighing Designs. Discussiones Mathematicae - Probability and Statistics. Poland, 21, 99-110.

 

[25] R. N. Mohan. (2001) Some classes of Mn-Matrices and Mn-Graphs and their applications J.Comb.Infor. System Sci.,26, no. 1-4, 51-78.

 

[26] R.N.Mohan, M.M.Nair & R.Bhanu Teja (2002). Secret Sharing Schemes and M_n-Matrices. Varahmihir Journal of Mathematical Sciences (VJMS) 2, 1, 105-120

 

[27] Sanpei Kageyama, R.N.Mohan and M.M.Nair. (2003). On the impact of Characterization of Symmetric Balanced Incomplete Block designs on their complements. Bulletin of Hiroshima University, Japan.Part II, no. 52,7-13.

 

[28] R.N.Mohan and M.M.Nair. (2003). On the characterization of BIB designs when λ =1. Far East J. of Appl. Math. 13, no.2, 127-143.

 

[29] R.N.Mohan, Sanpei Kageyama and M.M.Nair, (2004). On the Characterization of Symmetric Balanced Incomplete Block designs. Discussiones Mathematicae, P & S, 24, 41-58.

 

[30] R.N.Mohan, Moon Ho Lee and Subhas Shree Pokrel (2005) On Orthogonality of Latin Squares J.Comb.Infor. System Sci.,30, no. 1-4, 151-179

 

[31] Mohan, R.N. On t-partite graphs. (2005) J.Comb.Infor. System Sci.,26, no. 1-4, 51-78.

 

[32] Kageyama,S. R.N.Mohan, M.M.Nair (2005) Classification of affine μ-resolvable BIB designs.Bull Grad. Schoo;. Educ. Hiroshima Univ.Part II. No.34, 31-38..

 

[33]. R.N.Mohan S.Kageyama and M.M.Nair (2006) A method of construction of a quasi affine A- resolvable PBIB design with Latin squares Varahmihir J. of Math. Sci. (VJMS) 6, 1, 355-362.

 

[34] Moon Ho Lee and R.N.Mohan (2006) Certain Hadamard Polynomials Varahmihir J. of Math. Sci. (VJMS)Dedicated to Prof SP Singh. 6, 1, 99-104.

 

[35] R. N. Mohan, and Jennifer Seberry (2005) Anti-Jamming Codes. International J. Math. Sci. India 4, 2, Dec 2005.

 

[36] R.N.Mohan, Sanpei Kageyama, Moon Ho Lee, Gao Yang (2008). Certain new M-matrices and their properties and applications Discussiones Mathematicae, P &S, 28, 2 183-207..

 

[37] Quang Khai Trinh,Pingzhi Fan, Ernst M Gabidulin and R.N.Mohan (2007) On the Existence of Multilevel Hadamard Matrices with Odd Order. Proceedings of IWSDA’07 123-127

 

Papers and problems awaiting further study, preparation and exploration.

 

[38] Monographs: Three monographs are under active preparation:

 

I. Resolvability and Affine Resolvability in Designs

II. A Study of Certain Combinatorial Matrices

III. On Mn-Matrices and their Applications.

[39] R.N.Mohan and PT Kulkarni. Some new M-Networks, Submitted to IEEE Transactions on Computers.

 

[40] Moon Ho Lee,R.N.Mohan, Huojia Euler Hadamard Polynomial, Submitted to IEEE Electronics Letters

 

[41] Moon Ho Lee,R.N.Mohan, Huojia Euler Hadamard DCT Polynomial, Submitted to IEEE Information Theory.

 

[42] R.N.Mohan, Certain M-matrices and their applications to be Submitted to

 

[43] V.M.Sidelnikov, Moon Ho Lee, and R.N.Mohan. Group on Linear Fractional Transformations. To be Submitted to

 

[44] P.Fan, Moon Ho Lee , R.N.Mohan , and Jia Huo. Constructions of some new binary sequences with low auto correlation. (to be finalized)

 

[45]. R.N.Mohan, Moon Ho Lee, and Jia Hou. Construction of a new orthogonal code.

(to be finalized)

 

[46] Moon Ho Lee, R. N. Mohan and Jia Hou. Euler KLT polynomial based on Hadamard Matrix. submitting

 

[47] R.N.Mohan et all. Some Network Systems: Combinatorial Configurations to be finalized.

 

[48]. An M-matrix of Type III and its properties and applications

 

[49] A class of fault-tolerant M-networks on an M-matrix of Type III.

 

[50] R.N.Mohan and M.M.Nair, On the construction of certain SBIB designs which gain independent existence.

 

[51] R.N.Mohan and M.M.Nair, On the constructions of some affine -resolvable PBIB designs

 

Papers in Finalization:

 

 [52] B. Ceranka and R.N.Mohan . Analysis of Variance of Affine -Resolvable BIB Designs. Working also on the designs with s-duals.

 

[53] R.N.Mohan and T.Calinski . On Certain Matrices having Orthogonal Numbers or Pseudo Hadamard Matrices.

 

[54] R.N.Mohan . On the construction of Symmetric PBIB Designs with Dual Property.

 

[55] R.N.Mohan On the reduction of associate classes for certain Kronecker product designs.

 

[56] R.N.Mohan (1997). Some Observations of Certain Matrix of Combinatorial Interest.

 

[57] R.N.Mohan (1997) An Application of a family of Graphs to certain Network Systems.

 

[58] R.N.Mohan and Madhusoodhanan Nair (2001) On defining sets of certain series of designs.

 

[59] R.N.Mohan and Madhusoodhanan Nair. Some construction of Resolvable designs

 

[60] R.N.Mohan and M.M Nair. Certain mathematical expressions on some BIB designs.

 

[61] R.N.Mohan and M.M.Nair, On certain correspondence between SBIB designs and Affine μ-resolvable designs (regarding their characterizations)

 

[62] R.N.Mohan and M.M.Nair, on the construction of certain designs which gain independent existence

 

 [63] B.Ceranka and R.N.Mohan (2001) Analysis of Variance of Affine -Resolvable BIB Designs..

 

[64] R.N.Mohan and T.Calinski (1998). On Certain Matrices having Orthogonal Numbers or Pseudo Hadamard Matrices.

 

[65] R.N.Mohan (1998) On the construction of Symmetric PBIB Designs with Dual Property.

 

[66] R.N.Mohan On the reduction of associate classes for certain Kronecker product designs.

 

[67] R.N.Mohan and Madhusoodanan Nair. Certain mathematical expressions on some BIB designs.

 

[68] R.N.Mohan (1997). Some special matrices associated with Combinatorial concepts.

 

[69] R.N.Mohan (1997) On a family of graphs usable as network systems.

 

[70] R.N.Mohan and Madhusoodhanan Nair (2001) On defining sets of some special designs.

 

[71] R.N.Mohan and Madhusoodhanan Nair. Some construction of alpha resolvable designs.

 

[72] R.N.Mohan and A. Arnold. Multipartite Graphs in Genomics

 

[73] R.N.Mohan and Madhusoodhanan Nair Some properties of Mn-Graphs

 

[74] R.N.Mohan and Madhusoodanan Nair. Some Sub Arrangements with Mn-matrices.

 

Technical Reports: Hiroshima University Japan

 

[75] R.N.Mohan and Sanpei Kageyama (1981) Some new -resolvable BIB designs.

Tech.Report No. 39, Statistical Research Group, Hiroshima University, Hiroshima, Japan.

 

[76] Sanpei Kageyama and R.N.Mohan (1983) Three methods of constructing PBIB designs. Tech.Report No. 29, Statistical Research Group, Hiroshima University, Hiroshima, Japan.

 

[77] R.N.Mohan and Sanpei Kageyama (1983) Kronecker Product design and new regular GD designs. Tech.Report No. 90, Statistical Research Group, Hiroshima University, Hiroshima, Japan.

 

[78] R.N.Mohan and Sanpei Kageyama (1983). Some properties of affine -resolvable BIB designs. Tech.Report No.94, Statistical Research Group, Hiroshima University, Hiroshima, Japan.

 

[79] Sanpei Kageyama and R.N.Mohan (1983) Constructions of -resolvable PBIB designs. Tech.Report No. 97 Statistical Research Group, Hiroshima University, Hiroshima, Japan.

 

[80] Sanpei Kageyama and R.N.Mohan (1983) Dualizing w.r.t.s-tuple. Tech.Report No. 98, Statistical Research Group, Hiroshima University, Hiroshima, Japan.

 

[81] R.N.Mohan and Sanpei Kageyama (1988) Two constructions of -resolvable PBIB designs. Tech.Report No. 227, Statistical Research Group, Hiroshima University, Hiroshima, Japan.

 

Technical Reports: Indian Statistical Institute, Culcatta

 

[82] R.N.Mohan and Sanpei Kageyama (1982) A method of construction of group divisible designs. Tech.Report No. 28/82, Stat/Math. Division, Indian Statistical Institute, Calcutta.

 

[83] Sanpei Kageyama and R.N.Mohan (1982) New construction of BIB designs. Tech.Report No. 30/82, Stat/Math. Division, Indian Statistical Institute, Calcutta.

 

[84]Sanpei Kageyama and R.N.Mohan (1982) On the construction of group divisible partially balanced incomplete block designs. Tech.Report No. 31/82, Stat/Math. Division, Indian Statistical Institute, Calcutta.

 

Technical Reports: Instituto Matematica Pura e Aplicada, Rio de Janaiero, Brazil

 

[85]R.N.Mohan (1996) A generalized formula for the sum of the pth powers of the first n-natural numbers. Informes de Matematica (IMPA-Preprint), Series A-130 Maio/96 Instituto de Matematica Pura e Aplicada, Rio De Janeiro, Brazil

 

[86] R.N.Mohan and Sanpei Kageyama (1996) A new series of -resolvable and quasi -resolvable PBIB designs. Informes de Matematica (IMPA-Preprint), Series -B, 102-Maio/96 Instituto de Matematica Pura e Aplicada, Rio De Janeiro, Brazil

 

[87] R.N.Mohan V.C.Mavron and Sanpei Kageyama (1996) Quasi -resolvable and quasi-affine -resolvable designs. Informes de Matematica (IMPA-Preprint), Series -B, 105,Junho/96 Instituto de Matematica Pura e Aplicada, Rio De Janeiro, Brazil

 

[88] R.N.Mohan (1996) On an M_n - Matrix. Informes de Matematica (IMPA-Preprint). Series B-104, Junho/96. Instituto de Matematica Pura E Aplicada, Rio de Janeiro, Brazil.

 

[89] R.N.Mohan (1996) A new series of -resolvable (d+1)-associate class GD PBIB designs Informes de Matematica (IMPA-Preprint), Series -B, 103-Junho/96 Instituto de Matematica Pura e Aplicada, Rio De Janeiro, Brazil

 

[90] R.N.Mohan and A.H.Ahmed (1997) On the General Formula for Matrices of Combinatorial Interest. Informes de Matematica (IMPA-preprint), Series B-113, August/97 Instituto de Matematica Pura e Aplicada , Rio de Janeiro, Brazil.

 

 

 

[92] R.N.Mohan and A.H.Ahmed (1997) A construction for Authentication/secrecy codes based on Latin square theory. Informes de Matematica (IMPA-Preprint), Series -B, 114,Agosto/97 Instituto de Matematica Pura e Aplicada, Rio De Janeiro, Brazil

 

[93] R.N.Mohan (1997). On Orthogonality of Latin Squares. Informes de Matematica (IMPA-Preprint), Series -B, 117-Setembro/97 Instituto de Matematica Pura e Aplicada, Rio De Janeiro, Brazil

 

[94] R.N.Mohan (1997). On Certain t-partite Graphs. Informes de Matematica (IMPA-Preprint), Series -B, 116,Setembro/97 Instituto de Matematica Pura e Aplicada, Rio De Janeiro, Brazil

 

Technical Reports : Sir CRR International Institute of Mathematics, Eluru-534007, W.G.Dt., AP, India

 

SCRRIIM Technical Reports

 

Sir CRR International Institute of Mathematics, Eluru is publishing its own Technical Reports, of the work done by the research scholars of the Institute, and the researchers and communication to Research Institute the world over and also receiving such Technical Reports and Research Communications from all over the world.

 

TR1. RN Mohan , S.Kageyama, and MM Nair. On a characterization of symmetric balanced incomplete block designs, Jan 2003.

 

TR1A. RN Mohan, MM Nair, R Bhanu Teja Secret sharing schemes: M_N -Matrices, Jan 2003.

 

TR 2 RN Mohan and MM Nair, Enlisting BIB Designs small and higher order and their classification, Jan 2005.

 

TR3 RN Mohan and MM Nair. On µ-resolvable balanced incomplete block designs. Feb 2005.

 

TR4.RN Mohan, S.Kageyama, and MM Nair. A method of construction of a quasi affine α-resolvable PBIB design with latin squares. May 2005.

 

TR 5. RN Mohan , S.Kageyama, and MM Nair. Classification of affine µ-resolvable balanced incomplete block designs. Aug 2005.

 

TR 6. RN Mohan and MM Nair On a characterization of symmetric balanced incomplete block designs on their complements, Nov 2005.

 

TR 7. RN Mohan and MM Nair Some properties of Complement designs of the BIB Design when λ=1. Feb 2006.

 

TR 8. RN Mohan and MM Nair On a characterization of BIB Design when λ=1. May 2006.

 

TR 9. RN Mohan, Moon Ho Lee and Subhash Shree Pokhrel. On orthogonality of Latin Squares, June 2006.

 

TR10 RN Mohan On Orthogonalities in Matrices, June 2006.

 

TR 11 RN Mohan, Moon Ho Lee and Subhash Shree Pokhrel. Certain t-partite graphs. Sep 2006.

 

TR 12 RN Mohan , On Hadamard Conjecture , Oct 2006.

 

TR 13 RN Mohan, Moon Ho Lee and Ram Paudal. A new M-matrix of type III, its properties and applications. Nov 2006.

 

TR 14 RN Mohan , S.Kageyama, , Moon Ho Lee and Gao Yang Certain new M-matrices and their properties and applications. Dec 2006.

 

TR 15. P Fan, RN Mohan and Xiaohu Tang. Sequences Design through BIB Designs. Feb 2007

 

TR 16 P Fan, RN Mohan and Moon Hoo Lee, Jai Hou. Construction of a new orthogonal code. May 2007.

 

TR 17. P Fan, RN Mohan A Binary Sequence with Low cross correlation: Construction of new Sequences, Aug 2007.

 

TR 18. RN Mohan, Moon Hoo Lee, PT Kulkarni A new Fault- Tolerant M-Networks and its Analysis, Oct 2007.

 

TR 19. P Fan, RN Mohan and Yuan Weina. A new Problem: Taking a initial set of BIB Design can we construct a sequence. Dec 2007.

 

TR 20. RN Mohan , P Fan and Quang Khai Trinh, Ernst M Gabidulin. On the existence of multilevel Hadamard matrices with odd order.

 

TR 21. SCRRIIM. Compendium of lectures delivered at the National Workshop on the

topic entitled“ Uniform Hyper Graphs and their Applications,” that was held during Jan

30- Feb 5, 2008 at Sir CRR International Institute of Mathematics, Eluru with the

Collaboration of CR Rao Advanced Institute of Mathematics, Statistics, and Computer

Science, jointly sponsored by Department of Science and Technology, New Delhi and

Council of Science and Industrial Research, New Delhi.

 

III. Copies of selected preprints / Reprints

Some of my papers can be viewed in arxive and the list is given below:

Arxiv Reprints:

 

95. [pdf]

Title: On fractionally linear functions over a finite field

Authors: V.M.Siddlenikov, R.N.Mohan, Moon Ho Lee

Subjects: Discrete Mathematics (cs.DM)

 

96. [pdf]

Title: On Orthogonalities in Matrices

Authors: R.N.Mohan

Subjects: Discrete Mathematics (cs.DM)

 

97. [pdf]

Title: Certain t-partite graphs

Authors: R.N.Mohan, Moon Ho Lee, Subhash Pokrel

Subjects: Discrete Mathematics (cs.DM)

 

98. [pdf]

Title: A New Fault-Tolerant M-network and its Analysis

Authors: R.N.Mohan, P.T.Kulkarni

Subjects: Information Theory (cs.IT)

 

99. [pdf]

Title: On Hadamard Conjecture

Authors: R.N.Mohan

Subjects: Discrete Mathematics (cs.DM)

 

100. [pdf]

Title: A new M-matrix of Type III, its properties and applications

Authors: R.N.Mohan, Moon Ho Lee, Ram Paudal

Comments: 12 pages, one figure

Subjects: Discrete Mathematics (cs.DM)

 

101. [pdf]

Title: On Orthogonality of Latin Squares

Authors: R.N.Mohan, Moon Ho Lee, Subash Pokreal

Comments: 29 pages

Subjects: Discrete Mathematics (cs.DM)

102. [pdf]

Title: Certain new M-matrices and their properties and applications

Authors: R.N.Mohan, Sanpei Kageyama, Moon Ho Lee, Gao Yang

Comments: 21 pages,3 figures

Subjects: Discrete Mathematics (cs.DM)

IV. Any further information, which you feel is relevant to this application

1.) As a Teacher: I have teaching experience over four decades and I taught at all levels from Pre-University level, under graduate level, post graduate level and I have guided one scholar who had earned his degree under my guidance.

 

I have taught various Subjects in Mathematics: Real Analysis, Numerical Analysis, Mechanics, Modern Algebra (Groups, Rings, Fields, Vector Spaces, Linear. Transformation, Ideals, Modules), Three Dimensional Geometry, Sequences and Series, Differential Equations, Special Functions, Combinatorics, Graph Theory, Complex Analysis, Rings and Modules and so on both at UG and PG levels.

 

I use modern techniques in teaching using computers, Mathematica and other means also.

 

Primarily in teaching I developed the creativity and originality by promoting the independent thinking in the students while teaching the subject. Problem solving sessions are so important for this purpose. Secondly I inspire the students to have independent study of certain mathematical concepts and the seminars will help the student so much. This way I am so successful teacher for decades.

I was selected as a Best Teacher 1998, by the Government of Andhra Pradesh, India

I have much experience in research guidance: Guided Mr.M.Madhusoodhanan Nair for the award of

Ph.D.degree, from the JNTU, Hyderabad on the topic entitled, Resolvable and Affine Resolvable BIB Designs and Application. He has been awarded in July, 2006. If these research concepts have been implanted in the young minds then many enthralling results will emerge out. So I wish to train up students at their prime of their education itself towards research oriented thinking.

I hope if an opportunity is given I will show what exactly I can achieve.

2.) As a researcher: As far as research is concerned, it is more than two and a half decades of research experience and every opportunity that I have got I have fully utilized it and worked so hard and achieved the best possible results. But still many problems remained unsolved, which need some concentration and committed work for an year at least.

 

Through out my research career, I faced many hardships, scanty facilities, scope for the innovation is limited. And in these circumstances I am constrained every nerve of mine and worked incessantly and tackled some century old open problems, which are on the way. Now I have to finish all that work at the earliest possible time. I am searching better palce where I can continue my research to complete the task ahead.

 

Ardently hope that someone will understand my quest and provide me needed scope to work further.

 

R.N.Mohan