Department of Mathematics
Research Publications
It is a matter of pride and honour for the department that Acharya Nagarjuna University recognized the department as a research centre in March 2004 to offer M. Phil and Ph.D. in mathematics. The recognition has ignited the creative minds of the post graduate students of mathematics and every year two to three students joined for M. Phil and after its completion registered for Ph.D.
So far 1 Ph.D and 5 M.Phils were awarded, 2 have submitted their M. Phil dissertations, 4 have registered for Ph.D and 4 (2+2) are ready to submit their Ph.D M. Phil dissertation through this research centre. Commendable work is being done in algebra ( rings, lattices ) and graph theory(topological indices, magic labelings).Several papers were published in national and international journals and these research students have presented papers in several national and international conferences and symposia.
| S.No. | Name of the student | Year of Admission | Name of the course | Title of the Dissertation | Name of the guide | Remarks |
|---|---|---|---|---|---|---|
| 1 | K. Lavanya Lakshmi | 2004 | M. Phil | Polars and Annihilators in Seminormal Lattice ordered Autometrized Algebras | Dr. N. Prabhakara Rao | Awarded in 2006 |
| 2 | B.S.K. Chaitanya | 2004 | M. Phil | A group theoretical study of second ordered magneto resistance and second order piezoelectricity in quasicrystals | Dr. P. Hemagiri Rao | Awarded in 2006 |
| 3 | M. Prasanthi | 2004 | M. Phil | Minimal prime ideals in seminormal lattice ordered autometrized algebras | Dr. N. Prabhakara Rao | Awarded in 2006 |
| 4 | P.V. Srinivas | 2005 | M. Phil | On a class of seminormal lattice ordered autometrized algebras | Dr. N. Prabhakara Rao | Awarded in 2007 |
| 5 | M. Siva Mala | 2005 | M. Phil | On a Class of Semi lattice ordered semirings | Dr. N. Prabhakara Rao | Awarded in 2007 |
| 6 | K. Kiran Kumar | 2005 | M. Phil | Implicative Semilattices | Dr. N. Prabhakara Rao | Awarded in 2010 |
| 7 | A. Lakshmi Prasanna | 2006 | M. Phil | On Wiener, PI & Szeged indices of penta chains | Dr. N. Prabhakara Rao | Awarded in 2009 |
| 8 | K. Sunita | 2006 | M. Phil | On Representable Autometrized Algebras | Dr. N. Prabhakara Rao | Awarded in 2010 |
| 9 | M. Srujana | 2008 | M. Phil | A comparative study of topological indices of pentachains | Dr. N. Prabhakara Rao | In Preparation |
| 10 | P. Srinivasa Rao | 2008 | M. Phil | On hyper lattices | Dr. N. Prabhakara Rao | Submitted |
| 11 | K. Lakshmi Lavanya | 2008 | Ph.D | On certain topological indices of phynelynes | Dr. N. Prabhakara Rao | In Preparation |
| 12 | P.V. Srinivas | 2008 | Ph.D | Ideal theory of sum-ordered partial semirings | Dr. N. Prabhakara Rao | Submitted |
| 13 | N. Karunakar | 2008 | Ph.D | Dr. N. Prabhakara Rao | Registered | |
| 14 | M. Siva Mala | 2008 | Ph.D | Dr. N. Prabhakara Rao | Registered |
The staff members of the department who have registered / Completed Ph.D other than the research centre of the department are :
| 15 | J.Bhaskar Babujee | 2000 | Ph.D | On Graph labellings | Dr.N.Prabhakara Rao | Awarded in 2004 |
| 16 | D.Prathap | 2003 | Ph.D | Dr. P.Koteswara Rao | In preparation | |
| 17 | K.V.L.N. Acharyulu | 2003 | Ph.D | Dr. N. Ch. Pattabhiramacharyulu | Awarded in 2011 |
LIST OF RESEARCH PUBLICATIONS (published/accepted)
Dr. N. Prabhakara Rao
1. (with K.L.N. Swamy) Ideals in Autometrized algebras, The Journal of Australian Mathematical Society,Vol. XXIV, Series A, Part 3, pp. 362-374, 1977.
2. Autometrized Griss Algebras, Math. Seminar Notes, Kobe University, Japan, Vol. 5, pp. 1-21, 1977.
3. Autometrized Griss Algebras II, Math. Seminar Notes, Vol. 5, pp. 151-156, 1977.
4. Generalised Griss Algebras, Math. Seminar Notes, Vol. 5, pp. 261-271, 1977.
5. Brouwerian Semi groups, Mathematical Japanica, Vol 23, No. 1, pp. 49-60, 1978.
6. Seminormal Autometrized Algebras, Math. Seminar Notes, Vol. 6, pp. 91-114, 1978.
7. Representable Griss Algebras Mathematical Japanica, Vol 23, No. 1, pp. 61-69, 1978.
8. Brouwerian Semi groups II, Math. Seminar Notes, Vol. 1, pp. 33-43, 1979.
9. (with J. Baskar Babujee) Complete Bipartite Graphs- Antimagic Property, Proceedings of the National Conference on Mathematical and Computational models, PSG College of Technology, Coambatore, India, 2001.
10. (with J. Baskar Babujee) Edge-Magic Trees, Indian J. Pure appl. Math.33(12), pp. 1837-1840, Dec 2002.
11. (with J. Baskar Babujee) Labellings in Diagraphs, The Mathematics Education, June 2005.
12. (with A. Lakshmi Prasanna) On the Wiener index of Pentachains, Journal of Applied Mathematics Sciences, Vol. 2, No-49, pp. 2443-2457, 2008.
13. (with A. Lakshmi Prasanna) Wiener indices of fused Pentachains, Acta Ciencia Indica, Vol. XXXIVM, No 4, pp. 2065-2084, 2008.
14. (with A. Lakshmi Prasanna) On PI indices of pentachains, Acta Ciencica Indica, Vol. XXXVM, No. 3, pp. 1117-1133, 2009.
15. (with K. Lavanya Lakshmi & A. Lakshmi Prasanna) On the Wiener index of product of path graphs, Proceedings of National Conference on Discrete Mathematics and its Applications, NCDMA 2007, September 27-29, pp. 30-37, 2007.
16. (with K. Lavanya Lakshmi & A. Lakshmi Prasanna) Wiener indices of Pentachains, Proceedings of National Conference on Discrete Mathematics and its Applications, NCDMA 2007, September 27-29, pp. 385-387, 2007.
17. (with K. Lavanya Lakshmi) On the Computation of PI, SZ and S indices of tetragonal systems, Acta Ciencia Indica, Vol. XXXIV M, No. 4, pp. 1753-1766, 2008.
18. (with K. Lavanya Lakshmi) On Wiener, PI indices of multiple Phenylenes, Proceedings of National Conference on Algebra and its Applications with latest trends, VSR & NVR College, Tenali, Sep 11-12, pp. 23-31, 2008.
19. (with K. Lavanya Lakshmi) On PI index of Multiple Phenylenes, International Journal of Combinatorial Graph theory and Applications, Vol. 1, No. 2, pp. 109-116, 2008.
20. (with K. Lavanya Lakshmi) On SZ indices of Multiple Phenylenes, International Journal of Computational Cognition , Vol. 7, No. 3, pp. 44-49, 2009.
21. (with K. Lavanya Lakshmi) On a SVD based Topological Index for Polycenes, accepted for publication in the International Journal of Computational Cognition.
22. (with P. V. Srinivasa Rao) Representable autometrized algebras, Proceedings of National Conference on Discrete Mathematics and Its Applications, pp. 314-317, sep 27-29, 2007.
23. (with P. V. Srinivasa Rao) On a class of seminormal lattice ordered autometrized algebras, Acta Ciencia Indica, Vol. XXXIV M, No.1, pp. 339-344, 2008.
24. (with M. Siva Mala) On a class of semilattice ordered semirings, Acta Ciencia India, Vol XXXIV M, No.1, pp. 345-350, 2008.
Research Publications of students under the guidance of Dr. N. Prabhakara Rao
J. Baskar Babujee
1. (with Dr. N. Prabhakara Rao) Labellings in Diagraphs, The Mathematics Education, June 2005.
N. Karunakar
1. (with N. Prabhakara Rao) PI, Sz, M2 and Sh Indices of Fibonacenes, communicated to the International Journal of Computational cognition.
2. "Eccentric-connectivity, GA, Harary, hyper-Wiener and Wiener Polarity indices of Helicenes communicated to the IJAMC.
K. Lavanya Lakshmi
1. On Wiener Index of Multiple Phenylenes, International Journal of Combinatorial Graph Theory and Applications, Vol. 2, No. 1, pp. 13-18, 2009.
2. A Comparative Study of Topological indices of Benzenoid Graphs, The Global Journal of Applied Mathematical Sciences, Vol. 3, No. 1-2, pp. 15-26, 2010.
3. On FR Index of Phenylenes, International Journal of Computational Cognition, Vol. 8, No. 3, pp. 44-46, September 2010.
4. A Highly Corrected topological index for polyacenes, communicated to the International Journal of Computational cognition.
P. V. Srinivasa Rao
1. Ideals of Sum Ordered Semirings, International journal of Computational Cognition, Vol. 7, No. 2, pp. 59-64, 2009.
2. ø-representation of So-rings, International journal of Computational Cognition, Vol. 7, No. 2, pp. 65-70, 2009.
3. Partial semimodules over partial semirings, International Journal of Computational Cognition(IJCC), Vol. 8, No.4, pp. 80-84, Dec 2010.
4. On prime subsemimodules of Partial semimodules, International Journal of Computational Cognition(IJCC), Vol. 9, No. 2, pp. 40-44, June 2011.
5. On Strongly prime partial semirings, Advances in Algebra, Vol. 3, No.1, pp. 91-96, 2010.
6. Euclidean Partial Semirings, communicated to the Jordan Journal of Mathematics and Statistics (JJMS).
M. Siva Mala
1. (With P.V. Srinivasa Rao) Primary subsemimodules of partial semimodules, communicated to the Kyngpook Mathematical Journal.
2. (With P.V. Srinivasa Rao) On a class of P-primary subsemimodules of partial semimodules, communicated to the International Journal of Computational Cognition(IJCC).
K. Suneetha
1. (with N. Prabhakara Rao & P.V. Srinivasa Rao) Representable autometrized algebras, Proceedings of National Conference on Discrete Mathematics and Its Applications, pp. 314-317, Sep-27-29, 2007.
A. Lakshmi Prasanna
1. (with N. Prabhakara Rao) On PI indices of pentachains, Acta Ciencica Indica, Vol. XXXV M, No. 3, pp. 1117-1133, 2009.
P. Srinivasa Rao
1. Direct Products of Hyperlattices, International Journal of Computational Cognition(IJCC), Vol. 8, No.3. pp. 104-107, September 2010.
2. ø- Representation of Hyperlattices, International Journal of Computational Cognition(IJCC), Vol. 9, No. 2, pp.36-39, June 2011.
M. Srujana
1. (With K. Lavanya Lakshmi): A Comparison of certain Topological indices of Penta Chains, accepted to publish in the International Journal of Computational Cognition.
2. Eccentric and Wiener Indices of Nano Pentachains, communicated for publication in International Journal of Applied Mathematics and Computation.
3. Wiener, Hyper Wiener and Reverse Wiener Indices of concatenated Pentagons in Three rows, communicated for publication in International Journal of Computation and Cognition.
RESEARCH PUBLICATIONS OF OTHER STAFF MEMBERS
Dr. P. Vijaya Saradhi
1. (with V. Srinivasan) Irregular Graphs, Graph Theory Notes of New York, Vol. XLI, pp. 33-36, 2001.
2. (with V. Srinivasan) Graph with a given Maximal Domination Number, Bulletin of the Allahabad Mathematical Society, Golden jubilee year volume, Vol. 23, part 1, pp. 169-175, 2008.
Dr. T. Srinivasa Rao
1. (with P. Koteswara Rao) On Pre A*-Algebras, International Journal of Computauional Congnition, Vol. 8, No. 1, pp. 33-36, 2010.
D. Prathap
1. (with J. Baskar Babujee & A. Joshi) Wiener index for cartesian product graphs, Mathematical and Computational Models, pp. 1-8, 2007.
2. (with J. Baskar Babujee) Magic and Bimagic Labeling for Star Graphs, International Review of Pure and Applied Mathematics, Vol. 5, No. 1, pp. 67-76, 2009.
2. (with J. Baskar Babujee) Magic and Bimagic Labeling for Star Graphs, International Review of Pure and Applied Mathematics, Vol. 5, No. 1, pp. 67-76, 2009.
3. On some Antimagic and Bimagic Labeling of Cycles, accepted for publication in.
K.V.L.N. Acharyulu
1) (with N.Ch. Pattabhi Ramacharyulu) On The Stability of An Enemy-Ammensal Species Pair with Limited Resources, International Journal of Applied Mathematical Analysis and Applications, Volume 4, No.2, pp. 149-161, July 2009.
2) (with N.Ch. Pattabhi Ramacharyulu) An Ammensal-Enemy Specie Pair With Limited And Unlimited Resources Respectively-A Numerical Approach, Int. J. Open Problems Compt. Math (IJOPCM), Vol. 3, No. 1, pp.73-91, March 2010.
3) (with N.Ch. Pattabhi Ramacharyulu) In View of The Reversal Time Of Dominance In An Enemy-Ammensal Species Pair With Unlimited And Limited Resources Respectively For Stability By Numerical Technique, International journal of Mathematical Sciences and Engineering Applications(IJMSEA), Vol.4, No. II, pp.109-131, June 2010.
4) (with N.Ch. Pattabhi Ramacharyulu) On The Stability of an Ammensal - Enemy Species Pair With Unlimited Resources, International e Journal of Mathematics and Engineering, Volume-1, Issue-II, pp-140-149, 2010.
5) (with N.Ch. Pattabhi Ramacharyulu) Some Threshold Results for an Ammensal- Enemy Species Pair with Limited Resources, International Journal of Scientific Computing (IJSC), pp.33-36, Jan-June 2010.
6) (with N.Ch. Pattabhi Ramacharyulu) On the Stability of an Ammensal- Harvested Enemy Species Pair with Limited Resources, International Journal of computational Intelligence Research (IJCIR), Vol. 6, No.3, pp.343-358, June 2010.
7) (with N.Ch. Pattabhi Ramacharyulu) Liapunov’s Stability Analysis on the Stability of an Ammensal-Enemy Species Pair with Limited Resources, International Journal of Mathematics and Engineering, Volume-1, Issue-III, pp.240-245, 2010.
8) (with N.Ch. Pattabhi Ramacharyulu) On The Carrying Capacities Of An Ammensal And Enemy Species Pair With Limited Resources At Low Ammensalism - A Numerical Approach, International Journal of Mathematics and Applications, Vol.3,No.1,pp.15-22,Jan-June 2010.
9) (with N.Ch. Pattabhi Ramacharyulu) A Study On The Global Stability Of An Ammensal Species With Unlimited Resources - The Enemy Species With Limited Resources, International Journal Of Mathematics And Engineering,Volume-1,pp.Issue-IV, pp.498-505, 2010.
10) (with N.Ch. Pattabhi Ramacharyulu) On The Stability Of Harvested Ammensal - Enemy Species Pair with Limited Resources, International Journal of Logic Based Intelligent Systems, Vol.4, No.1, pp.1-16, 2010.
11) (with N.Ch. Pattabhi Ramacharyulu) Liapunov’s Function for Global Stability of Harvested Ammensal and Enemy Species Pair with Limited Resources, International Review of pure and applied mathematics, July-Dec.2010. (In press)
12) (with N.Ch. Pattabhi Ramacharyulu) On The Stability Of An Enemy - Ammensal Species Pair with Resources Limited for One Species and Unlimited for the other, International e Journal of Mathematics and Engineering Volume-1, Issue-I, pp.1-14, 2010.
13) (with N.Ch. Pattabhi Ramacharyulu) On The Stability of an Ammensal- Enemy Harvested Species Pair with Limited Resources, Int. J. Open Problems Compt. Math (IJOPCM), Vol. 3, No. 2, pp.241-266, June2010.
14) (with N.Ch. Pattabhi Ramacharyulu) An Ammensal Species With Limited Resources And Enemy Species With Unlimited Resources - Global Stability Analysis, International e Journal of Mathematics and Engineering, Volume-1, Issue-III, pp.241-256, 2010.
15) (with N.Ch. Pattabhi Ramacharyulu) An Enemy- Ammensal Species Pair With Limited Resources –A Numerical Study, Int. J. Open Problems Compt. Math (IJOPCM), Vol. 3, No. 3, pp.339-356, September 2010.
16) (with M. Lakshmi Sailaja & N.Ch Pattabhi Ramacharyulu)A Cover Protected Ammensal with Constant Harvesting Rate and Enemy Species Pair with Limited Resources, International e Journal of Mathematics and Engineering , Volume-1,Issue-IV, pp.577-591,2010.
17) (with M. Lakshmi Sailaja, N.Rama Gopal and P.Rama Mohan), Ecological Ammensal Model With Reserve for One Species and Harvesting both The Species at Variable Rates, International Journal of Advances in Soft Computing and Its Applications, Vol.3, No.3, 2010.
18) (with M.Lakshmi Sailaja & N.Ch Pattabhi Ramacharyulu),A Mathematical Model of Ecological Ammensalism for Three Interacting Species with Harvesting at Variable rates, International Journal of Mathematics and Engineering, Volume-1, Issue-IV, pp.639-662, 2010.
19) Global Stability Analysis on Ecological Immigrated Ammensalism, International Journal of Advanced Engineering Technology, Volume II, Issue I, January-March, pp.203-208, 2011.
20) (with N.Ch Pattabhi Ramacharyulu) An Immigrated Enemy- Ammensal Model with Mortality Rate for Ammensal species, Journal of Engineering Research and Studies, Volume II, Issue I, January-March, pp.139-146, 2011. 21) (with N.Ch. Pattabhi Ramacharyulu)On An Ammensal-Enemy Ecological Model with Variable Ammensal Coefficient, International Journal of Computational Cognition, Vol.9, No.2, pp.9-14, 2011.
22) (with N.Ch. Pattabhi Ramacharyulu) ,A Migrated Ammensal and an Immigrated Enemy and model With limited resources International Journal of Advanced Engineering Technology, Volume II, Issue I, January-March, pp.176-184, 2011.
23) (with N.Ch Pattabhi Ramacharyulu) A Three Species Ecological Ammensalism with Mortality Rate for Prey, Journal of Engineering Research and Studies, Volume II, Issue I, January-March, pp.71-75, 2011.
24) (with N.Ch. Pattabhi Ramacharyulu) A Numerical Approach on an Enemy - Ammensal Species Pair with Unlimited Resources, International Journal of Mathematics and Applications, Vol.4, No.1, Jan-June 2011.
25) (with N.Ch. Pattabhi Ramacharyulu) Global Stability Analysis on an Ammensal- Enemy Species Harvested Pair with Limited Resources, Journal of Analysis and computation, 2011.(Accepted)
26) A Two Species Monad Ammensalism -Global Stability Analysis, International Journal Of Mathematics And Engineering, Volume II, Issue I,pp.866 - 872,2011.
27) (with N.Ch. Pattabhi Ramacharyulu), Some Threshold Results of An Ammensal-Enemy Ecological Model With Variable Ammensal Coefficient, Global Journal of Mathematical Sciences: Theory and Practical (GJMS), 2011.(In press)
28) (with N.Ch Pattabhi Ramacharyulu) A Complex Case in Three Species Ammensal Ecosystem, International Journal of Advanced Engineering Technology, Volume II, Issue I, January-March, pp163-168, 2011.
29) An Enemy And Time Delayed Ammensal Species Pair- Liapunov’s Stability Analysis International Journal Of Mathematics And Engineering, Volume II, Issue I, pp. 809 - 813, 2011.
30) (with N.Ch. Pattabhi Ramacharyulu),An Ammensal-prey with three Species Ecosystem, International Journal of Computational Cognition ,Vol.9, No.2, pp.30-39,2011.(In press)
31) (with N.Ch Pattabhi Ramacharyulu) An Immigrated Ecological Ammensalism with Limited Resources, International Journal of Advanced Science and Technology (IJAST), Vol. 27, pp.79-85, February, 2011.
32) (with N.Ch Pattabhi Ramacharyulu) ,Stability Case in a Mathematical Model of Time Delayed Ammensal and an Enemy Ecological Species with Limited Resources,Journal of Engineering Research and Studies (JERS) Volume II, Issue II,PP.28-33, April-June, 2011.
33) (with N.Ch Pattabhi Ramacharyulu) ,An Ecological Ammensalism with Replenishment Rate for Both the Species -A Recursive and Numerical Study, International Journal of Advanced Engineering Technology (IJAET), Volume II, Issue II, April-June,pp.20-26, 2011.
34) (with N.Ch Pattabhi Ramacharyulu), Special Cases in a Mathematical Model of an Ecological Ammensalism with Unlimited Resources -A Numerical Study, International journal of Applied Mathematics (IJAM))(In press).
35) (with N.Ch Pattabhi Ramacharyulu),Mortal Ammensal and an Enemy Ecological Model with Immigration for Ammensal Species at a Constant Rate, International Journal of Bio-Science and Bio-Technology (IJBSBT) (In press).
36) (with N.Ch Pattabhi Ramacharyulu),Liapnov’s Stability Analysis On The Stability Of An Ammensal-Enemy Species Pair With Limited Resources”- International e Journal Of Mathematics And Engineering, Volume-1, Issue-III, pp.240-245, 2010.
37) (with N.Ch Pattabhi Ramacharyulu),An Immigrated Ecological Ammensalism with Limited Resources”- International Journal of Advanced Science and Technology (IJAST) Vol. 27, pp.87-92, 2011.
38) (with N.Ch Pattabhi Ramacharyulu),A Study on Global Stability of the Harvested Enemy and An Ammensal Species Pair with Limited Resources”- International Journal of Mathematics Research (IJMSR) (In press).
39) (with N.Ch Pattabhi Ramacharyulu),An Ecological Mathematical Model of an Immigrated Ammensal and a Migrated Enemy Model with Mortality Rate for Ammensal Species-An Analytical Investigation, Int. J. Pure Appl. Sci. Technol., 4(2), pp. 71-84,2011.
40) (with N.Ch Pattabhi Ramacharyulu),A Monad Ammensalism With Reserve For Ammensal Species And Harvesting For The Both The Species At Variable Rates”- International e Journal Of Mathematics And Engineering (IeJMAE)
41) (with N.Ch Pattabhi Ramacharyulu), A Two Species Ecological Ammensalism with Decay for Ammensal Species and Replenishment Rate for Both the Species -A Recursive and Numerical Approach”- International Journal of Advanced Engineering Technology (IJAET), Volume II, Issue III, pp. 143-147, July-2011.
42) (with N.Ch Pattabhi Ramacharyulu), A Numerical Study on an Ammensal - Enemy Species Pair with Unlimited Resources and Mortality Rate for Enemy Species”- International Journal of Advanced Science and Technology (IJAST), Vol. 30, pp.13-24,May, 2011.
43) Global Stability Analysis Of A Mortal Ammensal And An Enemy Ecological Model With Immigration For Both The Species”- International journal of Applied Mathematics,(In press).
44) (with N.Ch Pattabhi Ramacharyulu),An Ecological Ammensalism with Multifarious restraints- A Numerical Study” International Journal of Bio-Science and Bio-Technology (IJBSBT), Vol. 3, No. 2, pp.1-12,June, 2011.
M. Srujana
1. (With K. Lavanya Lakshmi): A Comparison of certain Topological indices of Penta Chains, accepted to publish in the International Journal of Computational Cognition.
2. Eccentric and Wiener Indices of Nano Pentachains, communicated for publication in International Journal of Applied Mathematics and Computation.
3. Wiener, Hyper Wiener and Reverse Wiener Indices of concatenated Pentagons in Three rows, communicated For publication in International Journal of Computation and Cognition.