Research experience :
Joined as a CSIR Junior Research Fellow in May 1969 and
submitted the Ph.D. thesis in May 1971 to Andhra University.
Since then continuing research on various problems in Number
Theory and published about 35 research papers in National
and International journals. Also research work is being
carried out in Non-linear Analysis. (Please see enclosure
I for the list of publications).
Also authored several mathematics books published by Telugu
Academy and a co-author of certain books published by Dr.
B.R.Ambedkar Open University, Hyderabad. Further edited
several books at different levels, both in Telugu and English.
(Please see Enclosure II for the list of books).
Apart from the above I have about 20 unpublished research
papers.
Research Guidance Experience :
Supervised the research work of 22 candidates for Ph.D.
and 11 candidates for M.Phil. from Osmania University. (Please
see Enclosure III for details)
Academic Activities :
1. General Secretary, Andhra Pradesh Society for Mathematical
Sciences, 1997-2000
2. Reviewer, Mathematical Reviews (Published by American
Mathematical Society
3. Member, American Mathematical Society since 1990
4. Organized 'Problem - Coordinators Camp' sponsored by
the National Board for Higher Mathematics
(Department of Atomic Energy, Govt. of India) in connection
with the International
Mathematical Olympiad held during 1996 in India.
5. Conducted “VIJAYA VAARADHI” programme on
All India Radio, Hyderabad during 1997. This programme
of 40 episodes (each of half-an-hour duration) was aimed
at coaching the Telugu medium
Intermediate students for EAMCET held in Andhra Pradesh.
6. Given seven video lectures on "Geometry" at
graduate level, for a UGC sponsored project of Mathematical
lessons (recorded at Lucknow University, Lucknow, Uttar
Pradesh)
7. Serving / Served
on academic bodies of
a. Board
of Intermediate Education, Andhra Pradesh;
b. Dr.B.R.Ambedkar Open University,
Hyderabad;
c . Kakatiya University, Warangal;
d. Sri Krishnadevaraya University,
Ananthapur;
e. J.N.T.University, Hyderabad
f. Andhra University, Visakhapatnam.
g. Nagarjuna University, Nagarjunanagar,
Guntur
Research projects :
1. Principal Investigator
for the Project 'Number Theory and its application' funded
by Department of Atomic Energy,
Govt. of India (1995-1998).
2. Principal Investigator for the CSIR Project 'Computations
in Number Theory and Number Theory
in Computing' (1996-1998).
CONFERENCES / SEMINARS
/ SYMPOSIA ATTENDED:
1. International
conference on Number Theory, University of Alberta, Edmonton,
Canada (1983).
2. Ramanujan Centenary International
Conference on Mathematics, Anna University, Madras (1988).
3. National workshop on
Continuum Mechanics, Osmania University, Hyderabad.
4. Attended all the annual Congresses of the Andhra
Pradesh Society for Mathematical Sciences held
at Hyderabad, Guntur, Vizag, Ananthapur, Warangal, Kakinada
and Srikakulam.
5. Delivered an invited talk at the National Conference
on New Trends in Number Theory held at Osmania
University, Hyderabad
Visits Abroad:
Visited University of Alberta, Edmonton, Canada during 1983
for collaborative research, as an Associate Professor.
Also invited to University of Alberta, Edmonton, Canada
during 1989 but could not make the visit for personal reasons.
Administrative Experience
:
1. Chairman, Board of Studies in Mathematics, Osmania
University, 1986 to 1989.
2. Head, Department of Mathematics, Osmania University,
August 1989 to September 1993.
3. Chairman, Board of studies in Computer Science,
Osmania University, July 1998 to Nov. 2000.
4. Principal, University College of Science (Autonomous),
Osmania University, from January 2001 to
May 2005.
5. Honorary Director, Prof. C R Rao Advanced Institute
of Mathematics, Statistics and Computer Sciences,
OU campus from December 2003 to August 2006.
6. Appointed as In charge Dean, Faculty of Sciences,
Osmania University, Hyderabad for the period
7 July, 2006 to 28 December, 2006.
Enclosure - I
LIST OF RESEARCH PAPERS OF
V. SIVA RAMA PRASAD
1. The number
of k-free divisors of an integer, Acta, Arith., XVII (1971)
: 345-354
(with D. Suryanarayana).
2. The number of pairs of generalized integers with
LCM £ x , J. Austral. Math. Soc., XIII (1972) : 411-416
(with D. Suryanarayana).
3. Sum functions of k-ary and semi-k-ary divisors,
J. Austral. Math. Soc., XV (1973) : 148-162 (with D.
Suryanarayana).
4. The number of k-free and k-ary divisors of m which
are prime to n, J. fur die reine ang. Math., 264
(1973) : 56-75 (with D. Suryanarayana).
5. The number of k-ary divisors of a generalized integers,
Portugaliae Mathematica, 33 (1974) : 85-92
(with D. Suryanarayana).
6. The number of k-ary, (k+1)-free divisors of an
integer, J. fur die reine ang. Math., 276 (1975) : 15-35
(with D. Suryanarayana).
7. The number of k-free divisors of an integer II,
Annals, Univ. Sci. Budapest, Rolando Eotvos Wohinate,
20 (1977) : 5-19 (with D. Suryanarayana).
8. Some analogues of a Lehmer Problems on the totient
functions, Rockey Mountains J. Math., 15 (1985)
: 609-620 (with M.V. Subbarao).
9. Regular convolutions and a related Lehmer problem,
Nieuw Archief Voor Wiskunde, 3 (1985) : 1-18.
MR 87g : 11018 (with M.V. Subbarao).
10. On composite n satisfying a problem of Lehmer,
Indian J. pure appl. Math., 16 (1985) : 1244-1248.
MR 87g : 11017 (with M. Rangamma).
11. On composite n for which ?(n)?n?1, Nieuw
Archief Voor Wiskunde, 5 (1987) : 77-81. MR 88k :
11108 (with M. Rangamma).
12. On functions arising from generalized Euler functions,
Indian J. pure appl. Math., 18 (1987) : 941-946.
MR 88k : 11013 (with M. Rangamma and Philippina Fonseca).
13. The solutions of a class of arithmetic equations,
Math. Student, 56 (1988) : 149-157 (with Philippina
Fonseca).
14. On the Schnirelmann density of M-free integers,
The Fibonacci Quarterly, 27 (1989) : 366- 368
(MVS Bhramarambica).
15. On the forms of n for which ?(n)?n?1, Indian J.
pure & appl. Math., 20 (1989) : 871-873 (with M.
Rangamma).
16. On the Schnirelmann density of (k,r)-integers,
Indian J. Math., 32 (1990) : 33-39 (with MVS Bhramarambica).
17. On primitive abundant numbers, Indian J. pure
appl. Math., 21 (1990) : 40-44 (with D. Ram Reddy).
18. On Unitary abundant numbers, Math. Student, 52
(1984) : 141-144 (with D. Ram Reddy).
19. On the iterates of arithmetic functions
in a class, Indian J. pure appl. Math., 23 (1992) : 7-14,
(with
Philippina Fonseca).
20. Congruence properties of a class of arithmetic
functions, Indian J. pure appl. Math., 24 (1993) :
87-90 ( with M. Rangamma and D. Radhika).
21. On the densities of (M1 , M2 , M3 , ... )-free
integers, J. Indian Math., Soc., 60 (1994) : 221- 223.
22. A generalization of Mobius inversion formula,
Indian J. pure appl. Math., (1994).
23. Pentagonal numbers in the Associated Pell Sequence
and Diophantine Equations x2(3x?1)2 =
8y2 ± 4, The Fibonacci Quarterly, 39.4 (August, 2001)
: 299-303, (with B. Srinivasa Rao)
24. Pentagonal numbers in Pell sequence and Diophantine
equations 2x2 = y2(3y?1)2 ± 2, The Fibonacci
Quarterly, 40.3 (June-July 2002) : 233-241, (with B. Srinivasa
Rao).
25. On a fixed point theorem of Fisher and its generalization
(To appear) (with T. Phaneendra).
26. Fixed point theorems for a pair of self maps (To
appear) (with T. Phaneendra).
27. Triangular numbers in the Associated Pell sequence
and Diophantine equations x2(x+1)2= 8y2
± 4, Indian J. pure appl. Math., 33(11) : 1643-1648,
November 2002, (with B. Srinivasa Rao).
28. Contractive modulus and Common fixed points (with
T. Phaneendra) (Communicated)
29. Orbits relative to a self-map and a fixed point
theorem (with T. Phaneendra) (Communicated)
30. Weakly Commuting self-maps and common fixed points
(with T. Phaneendra) (Communicated)
31. Inequalities related to Unitary analogue of Lehmer
problem, J. Inequalities in Pure and Applied
Mathematics ( with Uma Dixit ), accepted for publication.
32. On r-totatives of an integer ( with G Kamala and
L Madhusudan ) ( communicated )
33. Fixed point theorems on -complete topological
spaces (with V. Naga Raju and D. Srinivasa Chary)
(communicated)
Enclosure - II
List of Books by V. Siva Rama Prasad
(i) Author/Co-Author of
1. PROBABILITY (Intermediate),
Telugu Academy.
2. TRIGONOMETRY (Intermediate), Telugu Academy.
3. Monograph on DIFFERENTIAL GEOMETRY, Telugu Academy.
4. Monograph on MATRICES, Telugu Academy.
5. Monograph on ELEMENTARY NUMBER THEORY, Telugu Academy.
6. Text book MEASURE AND INTEGRATION, Dr. B.R. Ambedkar
Open University (M.Sc. level).
7. Text book COMPLEX ANALYSIS, Dr. B.R. Ambedkar Open University
(M.Sc. level).
8. Study material REAL ANALYSIS - CDE, Osmania University
(M.Sc. level).
9. Study material MEASURE AND INTEGRATION - CDE, Osmania
University (M.Sc. level).
10. Study material NUMBER THEORY- CDE, Osmania University
(M.Sc.)
11. Study material COMLPEX ANALYSIS, CDE, Osmania University
(M.Sc.)
12. Study material ANALYTICAL GEOMETRY AND REAL ANALYSIS
(B.Sc.)
13. Study material LINEAR ALGEBRA (B.Sc.)
(ii) Editor for books given
below :
1. THREE DIMENSIONAL GEOMETRY – UG level
2. SEQUENCES, SERIES, NUMBER THEORY - UG level
3. DIFFERENTIAL EQUATIONS - UG level
4. LINEAR ALGEBRA - UG level
5. FOURIER SERIES AND LAPLACE TRANSFORMATION.
6. MATHEMATICAL ANALYSIS - PG level.
7. QUESTION BANK for EAMCET Students.
8. FUNDAMENTAL MATHEMATICAL FORMULAE.
9. MATHEMATICAL DICTIONARY.
10. CO-ORDINATE GEOMETRY AND CALCULUS Intermediate first
year (Telugu and English versions).
11. CO-ORDINATE GEOMETRY AND CALCULUS Intermediate Second
year (Telugu and English versions).
12. Study material of ANALYTIC NUMBER THEORY - CDE, Osmania
University (M.Sc. level).
13. Study material of THEORY OF ORDINARY DIFFERENTIAL EQUATIONS
- CDE, Osmania University
(M.Sc. level).
14. Study material of REAL ANALYSIS - CDE, Osmania University
(M.Sc. level).
15. Study material of COMPLEX ANALYSIS, CDE, Osmania University,
Hyderabad
16. Study material of BA (Mathematics) Papers I & II,
CDE, Osmania University
17. Study material NUMBER THEORY- CDE, Osmania University
(M.Sc.)
18. Study material COMLPEX ANALYSIS, CDE, Osmania University
(M.Sc.)
19. Study material ANALYTICAL GEOMETRY AND REAL ANALYSIS
(B.Sc.)
20. Study material LINEAR ALGEBRA (B.Sc.)
Enclosure - III
List of Research Students under Dr.
V. Siva Rama Prasad
(a) Supervised the research work of the following candidates
for their Ph.D. degree from Osmania University, Hyderabad,
India.
S.No. |
Name |
Year of
Award |
Title
of the thesis |
1. |
Dr. M.A. Rasheed |
1983 |
On Certain unified arithmetic
convolutions. |
2. |
Dr. M. Rangamma |
1985 |
On a problem of Lehmer
Concerning Euler's function. |
3. |
Dr. Philippina
Fonseca |
1987 |
On the iterations of
Generalized Euler functions. |
4. |
Dr. M.V.S. Bhramarambica |
1987 |
On the densities of
certain sets of integers. |
5. |
Dr. D. Ram Reddy |
1989 |
On Unitary abundant
numbers. |
6. |
Dr. B. Krishna Gandhi |
1990 |
On certain isomorphisms
between groups of arithmetic functions. |
7. |
Dr. G. Kamala |
1991 |
On two classes of arithmetic
functions. |
8. |
Dr. C. Goverdhan |
1991 |
On Carmichael Conjecture. |
9. |
Dr. K. Vasudeva Rao |
1991 |
On the classes of arithmetic
functions satisfying certain identities. |
10. |
Dr. D. Radhika |
1992 |
On congruence properties
of certain classes of arithmetic functions. |
11. |
Dr. M. Ganeshwar Rao |
1993 |
On certain results
in Number Theory and their generalizations. |
12. |
Dr. G. Vanisree |
1994 |
On odd perfect numbers. |
13. |
Dr. G. Om Prakasham |
1996 |
On quasiperfect numbers. |
14. |
Dr. Alka Mashalkar |
1997 |
On sums involving certain
divisor functions. |
15. |
Dr. B. Srinivasa Rao |
1998 |
Special types of integers
in certain second order recursive sequences. |
16. |
Dr. T. Phaneendra |
1998 |
Certain fixed point
theorems for selfmaps of metric spaces. |
17. |
Dr.(Mrs.) S. Dharaja Devi |
1999 |
Common fixed points for pairs of
commuting and compatible self-maps of metric spaces. |
18. |
Dr. V. Srinivas |
2000 |
Common fixed point theorems for two or more selfmaps
of metric spaces.
|
19. |
Dr. Uma Dixit |
2001 |
On certain analogues of Lehmer problem
and some special sets of non-deficient numbers. |
20. |
Dr. Ms. P. V. S. Lakshmi |
2004 |
On asymptotic and schnirelmann densities
of certain sets of positive integers. |
21. |
Mr. V. Naga Raju |
2006
|
Fixed point theorems
for
-complete topological spaces |
22. |
Mr. L. Madhusudan |
2006 |
On r-totaties of an integer
|
b) Supervised the research
work of the following candidates for their M.Phil. degrees
from Osmania University.
