Om Prakash Singh

Designation: Professor & Head,
                                        &
                    Coordinator, SAP-UGC

Phone: +919415812099

E-mail: opsingh.apm@itbhu.ac.in, singhom@gmail.com, head.apm@iitbhu.ac.in

Research Areas: Distribution Theory, Pseudo- differential Operators, Wavelets, Fractional Calculus, Signal Processing

 

 

Biography:

Dr. O.P. Singh did his M.Sc.(Math) from Banaras Hindu University, A.M. from University Of Pennsylvania (U.S.A.) and Ph.D. from Banaras Hindu University. He was awarded Four Gold Medals including the prestigious CHANCELLOR’S Gold Medal.

His fields of specialization are: Distribution Theory, Pseudo- differential Operators, Wavelets, Non-Linear Analysis.

Additional Information :

(i)  Foreign Assignments :
(a)  Was awarded graduate fellowship by University of Adelaide, Australia in its centenary year 1974
(b) Graduate student at University of Pennsylvania, Philadelphia, USA from Sept. 1975 till Aug. 1977
(c)  Worked at University of British Columbia, Vancouver, Canada from 1977 till April 1980
(d)  Visited Carleton University, Ottawa, Canada, as a Visiting Scientist from July 1989 till Oct. 1989.

(ii)  Reviewer : Math. Reviews
As a reviewer I have solved an open problem posed by the authors concerning their work on certain Hilbert Problem (Published in Can. Math. Bull. 34 (1991), No. 3, pp. 321-328), in my review itself: Singh, O.P., Math. Review, 93g, 44007.

(iii) Member of Learned Bodies :
(a) American Mathematical Society(94-96 & 2000)
(b) Life Member of Jammu Mathematical Soc.
(c) Life Member of Indian Math. Soc.
(d) Life Member of Progress of Math.

 

Teaching Experience : 40 Years

Ph.D. Supervision : 10 produced, 3 enrolled.

 

Publications:

Number of papers: Published- 56 (International Journal 50 + National Journal 6), Articles- 3

List Of Publications:

INTERNATIONAL PUBLICATIONS:

1. O.P. Singh and R.N. Pandey "Generalized Polynomial Set", Bull. Inst. Math. Acad. Sinica 9, 1981, 75-92.

2. O.P Singh and R.N. Pandey "On a generating function for the generalized Polynomial set", Bull. Math. Soc. Sci. Math. R.S. Roumanie (N.S.) 25 No.73, 1981, 171-177.

3. R.S. Pathak and O.P. Singh, "Finite Hankel Transform of Distribution", Pacific J. Math., Vol. 99, No. 2, 1982, pp. 439-458.

4. O.P. Singh and R.S. Pathak, "Analytic Representation of the Distributional Hankel Transform”, International J. Math. & Math. Sci., Vol. 8, No. 2, 1985, pp. 325-344.

5. O.P. Singh, "On distributional Hankel Transform.", Applicable Analysis, Vol.  21, 1986, pp. 245-260.

6. O.P. Singh, "The Distributional Hankel Transform, Its Inversion and Application", Applicable Analysis, Vol. 32, 1989, pp. 87-106.

7. O.P. Singh and J.N. Pandey, "The n-Dimensional Hilbert Transform of Distributions, Its Inversion and Applications", Canadian J. Math., Vol. XLII, No. 2, 1990, pp. 239-258.

8. J.N. Pandey and O.P. Singh, "On the p-norm of Truncated n-Dimensional Hilbert Transform", Bull. Austral. Math. Soc., Vol. 43, 1991, pp. 241-250.

9. O.P. Singh and J.N. Pandey, "The Fourier-Bessel Series Representation of the Pseudo-Differential Operator (-x-1 D)n", Proc. Amer. Math. Soc., Vol. 115, No. 4, 1992, pp. 969-976.

10. O.P. Singh, "Some remarks on Distributional Hankel transforms, Generalized functions and their applications" published by Plenum Publishing Corp., 1993, pp. 235-239.

11. J.N. Pandey and O.P. Singh, "Characterization of function with Fourier transform supported on Orthants (II), Generalized functions and their applications, published Plenum Publishing Corp., 1993, pp. 167-173.

12. J.N. Pandey and O.P. Singh, "Characterization of Functions with Fourier Transform supported on Orthants", J. Math. Anal. Appl., Vol. 185, No. 2, 1994, pp. 438-463.13.

13. O.P. Singh, "On the Pseudo-Differential Operator (-x-1 D)n, J. Math. Anal.Appl.,  Vol. 191, No. 2, 1995, pp. 450-459.

14. O. P. Singh, "A Class of  Pseudo-Differential Operators Associated  with Hankel  transforms", Analysis and Applications, Allied Publishers  Pvt. Ltd.,2004.

15. V. K. Singh, O. P. Singh, R. K. Pandey, Numerical evaluation of Hankel transforms by using linear Legendre multi-wavelets, Computer Physics Communications 179 (2008) 424-429. (Impact Factor 1.842, as of 2007).

16. R. K. Pandey, O. P. Singh, V. K. Singh, An efficient algorithm for computing zero-order Hankel transforms, Applied Mathematical Sciences. Vol. 2, no 60, (2008) 2991-3000.

17. V. K. Singh, O. P. Singh, R. K. Pandey, Efficient algorithms to compute Hankel transform using wavelets, Computer Physics Communications 179 (11) (2008) 812-818). (Impact Factor 1.842, as of 2007).

18. R. K. Pandey, V. K. Singh, O. P. Singh, An improved method for computing Hankel transform, Journal of the Franklin Institute. (In Press) doi:10.1016/j.jfranklin.2008.07.002 (Impact Factor  .441 as of  2007).

19. V. K. Singh, R. K. Pandey, O. P. Singh, New stable numerical solutions of singular integral equations of Abel type by using normalized Bernstein polynomials, Applied Mathematical - Sciences. Vol. 3 No. 5 (2009)441-455

20. R. K. Pandey, O. P. Singh, V.K. Singh, Efficient algorithms to solve singular integral equations of Abel type, Computer and Mathematics with applications 57 (2009) pp.664-676.(Impact Factor 0.720).

21. R.K. Pandey, O. P. Singh, V. K. Singh, D. Singh, Numerical evaluation of Hankel transforms using Haar wavelets, International Journal of Computer Mathematics(Impact Factor 0.423) . (ACCEPTED)

22. O. P. Singh, R.K.Pandey, V. K. Singh, An analytic algorithm for Lane -Emden equations arising in Astrophysics using MHAM, Computer Physics Communications   (Impact Factor 1.842. as of 2007) DOI: 10.1016/j.cpc.2009.01.012

23. O. P. Singh, V. K. Singh, R.K.Pandey, A New Stable Algorithm for Abel inversion Using Bernstein Polynomials , International Journal of Nonlinear Sciences and Numerical Simulation (Impact Factor 5.099. as of 2007). (Accepted)

24. A. K. Singh, V. K. Singh , O. P. Singh, Bernstein operational matrix of integration,Applied Mathematical Sciences, Vol. 3, 2009, no. 49, 2427-2436.

25. R. K. Pandey, O. P. Singh, V.K. SinghNumerical solution of system of Volterra integral equations using Bernstein polynomials, International Journal of Nonlinear Sciences and Numerical Simulation, 10(7), 891-895, 2009 (Impact  Factor 5.099  )

26. R. K. Pandey, O. P. Singh, V. K. Singh., Numerical evaluation of Hankel transforms using  wavelet series, Numerical Algorithms DOI: 10.1007/S11o75-009-9313-0.

27. O. P. Singh, V. K. SinghR. K. PandeyNew stable numerical inversion of Abel’s integral equation using almost Bernstein operational matrix, Journal of Quantitative Spectroscopy   and Radiative Transfer,111 (2010) 245-252 (Impact Factor 1.972  as of 2007).

28. V. K. Singh,  R. K. Pandey, O. P. Singh, A Stable Algorithm for Hankel transforms using Hybrid  of Block pulse and Legendre polynomialsComputer Physics Communications  181 (2010) 1-10 (Impact Factor 2.2 ).

29. R. K. Pandey, V. K. Singh, O. P. Singh A New Stable Algorithm for Hankel transform using hybrid Block pulse and rationalized Haar functions, Integral Transform & Special  Functions (Accepted –Oct 2009).

30. O. P. Singh, V. K. Singh, R. K. Pandey, On numerical computation of Hankel transforms, Journal of Applied Mathematics and Informatics, (Accepted – Oct 2009). 

31.  R. K. Pandey, V. K. Singh, O. P. Singh, A New Stable Algorithm for Hankel transform  using Chebyshev Wavelets, Communications in Computational Physics(Impact  Factor 2.8  ). (Accepted –Nov 2009).

32.  V. K. Singh, O. P. Singh,  R. K. Pandey,  Almost Bernstein operational matrix method for solving system of  Volterra integral equations of convolution type,  Nonlinear Science Letters A,  Vol.1, No.2 , 201-206, 2010

33. Sunil Kumar, Om P. Singh, Generalized Abel inversion by homotopy  perturbation  method,  Z. Naturforsch  A,, 65a, 677-682, 2010.

34. Sandeep Dixit, Vineet K. Singh, Amit K. Singh, Om P. Singh, Bernstein direct method for solving variational problems, International Mathematical forum, Vol. 5 (48), 2351-2370, 2010.

35. S. Dixit, Om P. Singh and Sunil Kumar, An Analytic Algorithm for solving system of fractional differential Equations, Journal of Modern Methods in Numerical Mathematics, Vol. 1, no. 1 (2010), 12-26.

36. S. Dixit, R. K. Pandey, S. Kumar and Om P. Singh, Solution of the generalized Abel integral equation by using almost Bernstein operational matrix, American Journal of Computational Mathematics, Vol. 1, Issue 4, 226-234, 2011.

37. Sunil Kumar, Om P. Singh and S. Dixit, An analytic algorithm for generalized Abel integral equation, Applied Mathematical Sciences, Vol. 5, no. 5 (2011), 223-232.

38. Sunil Kumar, Om P. Singh and S. Dixit, Generalized Abel Inversion Using Homotopy Perturbation Method, Applied Mathematics, Vol. 2, No. 2, 254-257, 2011.

39. Sunil Kumar, Om P. Singh and S. Dixit, Homotopy Perturbation Method for Solving System of Generalized Abel’s Integral Equations, Applications and Applied Mathematics, Vol. 5, no.10, 2010.

40. S. Dixit, Om P. Singh and S. Kumar, A stable numerical inversion of generalized Abel’s integral equation, Applied Numerical Mathematics (Elsevier), Vol. 62, Issue 5, 567-579, 2012.

41. S. Dixit and Om P. Singh, A stable algorithm for numerical inversion of system of generalized Abel integral equations, Journal of Advanced Research in Scientific Computing, Vol. 3, Issue 4, 25-36, 2011.

42. S. Das, Sunil Kumar and O. P. Singh, Solutions of Nonlinear Second Order Multi-point Boundary Value Problems by Homotopy Perturbation Method, Applications and Applied Mathematics., Vol. 05, Issue 10 (December 2010), pp. 1592-1600.

43. Sunil Kumar, M. P. Tripathi, Om P. Singh, A fractional model of Harry Dym equation and its approximate solution, Ain Sham Engineering Journal, Accepted (2012).

44. Ram K. Pandey, Om P. Singh, Vipul K. Baranwal , An Analytic Algorithm for space-time fractional advection-dispersion equation, Computer Physics Communications (Elsevier), 182 (2011) 1134-1144. [Impact Factor 2.30].

45. Ram K. Pandey, Vipul K. Baranwal, Manoj P. Tripathi, Om P. Singh, Generalized differential transform based analytic algorithm for fractional advection-dispersion equation, Journal of Advanced Research in Scientific Computing, Vol. 4, Issue. 2, 2012, pp. 14-35.

46. Ram K. Pandey, Om P. Singh, Vipul K. Baranwal, Manoj P. Tripathi, Semi-Analytical solution for space-time fractional advection-dispersion equation, Computer Physics Communications (Elsevier) doi:10.1016/j.cpc.2012.05.012. [Impact Factor 2.30].

47. Vipul K. Baranwal, Ram K. Pandey, Manoj P. Tripathi, Om P. Singh, Analytic algorithms for Some Models of Nonlinear Age, Structured Population Dynamics and Epidemiology, Journal of Modern Physics, 2011, 2, 236-247.

48.  Vipul K. Baranwal, Ram K. Pandey, Manoj P. Tripathi, and Om P. Singh, Analytic solution of fractional order heat and wave like equations using generalized n-dimensional differential transform method, Zeitschrift für Naturforschung A 66a, 581- 590 (2011). [Impact Factor 0.9].

49. Vipul K. Baranwal, Ram K. Pandey, Manoj P. Tripathi, Om P. Singh, An analytic algorithm for time fractional nonlinear reaction - diffusion equation based on a new iterative method, Communication in Nonlinear Science Numerical Simulation (Elsevier), 17 (2012) 3906-3921. [Impact Factor 2.70].

50. Manoj P. Tripathi, Vipul K. Baranwal, Ram K. Pandey, Om P. Singh,  A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions, Communications in Nonlinear Science and Numerical Simulation (Elsevier), Accepted (2012). [Impact Factor 2.70].

NATIONAL PUBLICATIONS:

1. O.P. Singh and J.N. Pandey, "The n-dimensional Hilbert transform of distributions", Prog. Of Math. Vol. 24(1&2) 1990, pp. 95-105.

2. O.P .Singh, "The n-Dimensional Distributional Hankel Transform of Complex Order", Vikram Math. J.,Vol. 21, 2001, pp.78-88.

3. O.P. Singh, "A Distributional Cauchy Problem", Vikram Math. J., Vol. 22,2002,. pp. 13-22 .

4. O.P. Singh, " The Fourier-Hermite  Series  Representation of  The Psuedo-Differential Operator  (-x-1 D)n,  Varahmihir  J. Math. Sci., Vol. 3,No.2, 2003, 233-245.

5. O. P. Singh, " Orthogonal  Expansions  of  Certain  Pseudo-Differential  Operator", International  J. Math.  Sci., Vol.3 No.1, June 2004,pp. 131-144.

6. O.P. Singh, "Partial Differential equations for Classical Polynomials" J. Sci. Res. (BHU), Vol. 34(2), 1984, pp. 85-90.

Conference/Seminars/Symposia/Workshops attended  : 

He has given invited talks at national and international level. Few of them are as follows :


(i)         Title : The Fourier-Bessel Series Representation of the Pseudo-Differential Operator
                       
            Author/Speaker  :   Dr. O.P. Singh
            Place                  :   Carleton University, Canada
            Occasion           :    Analysis Seminar
            Month/Year       :    Oct. 31, 1989

(ii)        Title :  The Hilbert Transform of Schwartz Distribution, Its Inversion and Application.
Author/Speaker  :   Dr. O.P. Singh
            Occasion  :   International Symposium on Generalized Functions and Their Application.
                                          More than hundred mathematicians from ten countries participated.
            Place                  :   Department of Mathematics, B.H.U., Varanasi
            Month/Year       :    Dec. 23-26, 1991

(iii)       Title : Some Remarks on Distributional Hankel Transform.
Author/Speaker  :   Dr. O.P. Singh
            Occasion            :   Annual Indian Math. Soc. Conference
            Place                  :   B.H.U., Varanasi
            Month/Year       :    Feb. 1991

(iv)       Title :  Historical Development of Limits and Continuity (Popular lecture)
Author/Speaker  :    Dr. O.P. Singh
            Occasion            :    Annual Conference of Jammu Math. Soc.
            Place                  :    Jammu University, Jammu
            Month/Year       :     Feb. 1994

(v)        Title :  On the p-norm of the truncated Hilbert transform
Author/Speaker  :    Dr. O.P. Singh
            Occasion       :    Joint Annual Conference on Jammu Math. Soc. with Lucknow University
            Place                  :    Lucknow University
            Month/Year       :     Dec. 1998

(vi)       Title :  Fourier-Hermite series representations of certain P.D.O.
Author/Speaker  :    Dr. O.P. Singh
            Occasion       :    International Conference on Geometry, Analysis and Application
            Place                  :    B.H.U.
                Month/Year       :    August 21 to 24, 2000


Conferences Organized : 2

i) National Conference on 'Mathematical Modeling and Computer Simulation' during March 25-27, 2011 at the Department of Applied Mathematics,Institute of Technology, Banaras Hindu University, Varanasi.
ii) National Conference on 'Mathematical Modeling and Computer Simulation' during March 23-25, 2012 at the Department of Applied Mathematics,Institute of Technology, Banaras Hindu University, Varanasi.

 





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