Om Prakash Singh

Designation: Professor
&
Coordinator, SAP-UGC

Phone: +919415812099

E-mail: opsingh.apm@itbhu.ac.in

Research Areas: Distribution Theory, Pseudo- differential Operators, Wavelets

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 Medalfor his out standing performance in the M.Sc. Examination.

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.

(iv) I was a resource person for Refresher Courses for Mathematics at Jammu University, Jammu, Couple of times.

Teaching Experience : Undergraduate: 35 yrs, Post Graduate: 30yrs

Research Experience : Doctoral: 5 yrs, Postdoctoral: 26 yrs

Ph.D. Supervision : 4 produced, 3 enrolled.

Publications:

Number of papers: Published- 28 (International Journal 19 + National Journal 9), 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. Singh, Numerical 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. Singh, R. K. Pandey, New 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 polynomials, Computer 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 (Accepted)

34. Sandeep Dixit, Vineet K. Singh, Amit K. Singh, Om P. Singh, Bernstein direct method for solving variational problems, International Mathematical forum, (Accepted).

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