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Publications
Introduction to Numerical Mathematics, A text for the course 6.144/6.120.
1. Dislocations in an infinite isotropic solid containing a cylindrical ltunnel, Journal of the Karnatak University, Vol. V, 1960, 135-142.
2. Dislocation of translation of the material whose cross-section is bounded by two concentric ellipses,.Proceedings of the National Institute of Sciences of India, Vol. 26, A, No. 2, 1960, 129-133.
3. Dislocations in isotropic cylinders of concentric circular cross-section, Journal of the Karnatak University, Vol. VI, 1961, 99-105.
4. Dislocations of the materials whose cross-section is bounded by two concentric ellipses, Proceedings of theNational Institute of Sciences of India, Vol. 28, A, No. 2, 1962, 287-293.
5. Dislocations in isotropic cylinders of eccentric circular cross-sections, Quarterly Journal of Mechanics and Applied Mathematics, Vol. l6, Part 2, 1963,129-136.
6. Plane strain dislocations in orthotropy, Proceedings of the National Institute of Sciences of India, Vol. 29, A, No. 6, 1963, 670-675.
7. A note on a paper by Milne-Thomson, Proceedings of the Cambridge Philosophical Society, 61, 1965, 300-301.
8. Diagonally dominant infinite matrices in linear equations, Utilitas Mathematica, Vol. 1, 1972, 235-248.
9. Linear equations in infinite matrices, Journal of Linear Algebra and its Applications, Vol. 7, 1973, No. l, 553-562 (with R. Wong).
10.Viscous flow in pipes whose cross-sections are doubly connected regions, Applied Scientific Research, Vol. 27, 1973, 355-365.
11.A sufficient condition for the vanishing of determinants, Procedings of the American Mathematical Society, Vol. 43, No. 1, 1974, 63-66 (with K. H. Chew).
12.Iterations for diagonally dominant matrices, Bulletin of the Canadian Mathematical Society, Vol. 19 (3), 1976, 375-377 (with K. H. Chew).
13.On the conformal mapping of a circular disc with a curvilinear polygonal hole,Proceedingsof the Indian Academy of Sciences, Vol. 85, A, No. 6, 1977, 406-414 (with K. H. Chew).
14.Asymptotic expansion of multiple Fourier Transforms, SIAM Journal of Mathematical Analysis, Vol. 10, No. 6, Nov. 1979, 1095-1104 (with R. Wong).
15.On some aspects of infinite matrices, Proceedings of the Conference on Matrix Algebra, MATSCIENCE, India, 1 1977 (24 pages).
16. Error bounds for the truncation of infinite linear differential systems, Journal of the Institute of Mathematics and its Applications, Vol. 25, 1980, 37-51 (with K. H. Chew and 98. J. Williams).
17. Asymptotic expansion of the Lebesgue constants associated with polynomial interpolation, Mathematics of Computation, Vol. 39, 1982, 195-200 (with R. Wong).
18. On solutions of Poisson's equation for doubly connected regions, Pusat Pengajan Sains Matematik, University Sains Malaysia, Tech. Rep., 2/82, (with K. H. Chew).
19. Bounds for solutions of linear systems, Pusat Pengajan Sains Mathmatik, University Sains Malaysia, Tech. Rep. 1/83 (with K.H. Chew).
20.Longitudinal disperson of tracer particles in a channel bounded by porous media using a slip condition, International Journal of Mathematics and Mathematical Sciences, Vol. 7, 4, 1984, 755-764 (with N. Rudraiah and others).
21.Numerov's method for nonlinear two point boundary value problems, International Journal of Computer Mathematics, Vol. 17, 1985, 167-176 (with M. M. Chawla).
22 (a) Modelling of the human heart inside the pericardium, (with C. S. Man and S. W. Rabkin),Proceedings of the CANCAM Conference, 1985, E59-E60.
(b) IMA Preprint Series #265, Sept. 1986, Institute of Mathematics and its Applications, University of Minnesota.
23. Closed form for unsteady convective diffusion in a fluid saturated sparsely packed porous medium with the convective acceleration, International Communications in Heat and Mass Transfer, Vol. l4, 1987, 137-145 (with N. Rudraiah).
24. A finite difference method for a class of two point b.v.p.s over a semi-infinite range, Journal of Computational and Applied Mathematics,15, 1986, 251-256 (with M. M. Chawla).
25. Eigenvalues for infinitematrices, Journal of Linear Algebra and its Applications,1987 Vol. 96, 35-63 (with N. Rudraiah and J. J. Williams).
26. Fluid movement in a channel of varying gap with permeable walls covered with porous media, International Journal of Engineering and Science, Vol. 24, No. 4, 1986, 479-492 (with S. Nagaraj, R. Veerabhadriah, N. Rudraiah).
27. On the existence of solutions of a class of singular nonlinear two point boundary value problems Journal of Computational and Applied Mathematics, 19,1987, 379-388.
28. Modelling of the heart and pericardium at end-diastole, Journal of Biomechanics, 22, 1989, 201-209 (with C. S. Man and S. W. Rabkin).
29. Numerov's method for nonlinear two point boundar value problems II, International Journal of Computer Mathematics, 26, 1989, 219-227 (with M. M. Chawla and R. Subramanian).
30. An iterative method with truncation for infinite linear systems, Journal of Computational and Applied Mathematics, 24, 1988, 109-207 (with J. J. Williams).
31. Error bounds for a uniform asymptotic expansion of Legendrefunction P,Quarterly of Applied Mathematics (Vol. XLVI, Sept. 1988, 483-488) (with R,. Wong).
32. Effect of slip and magnetic field on composite systems, Fluid Dynamics Research, 4, 1988, 255-270 (with N. Rudraiah and D. Pal).
33. A recursive partitioning algorithm for inverting tridiagonal matrices, International Journal of Computer Mathematics 1990, 35, 153-158 (with M. M. Chawla and K. Passi).
34.On some higher order derivatives of solutions ofy" + p(x)y = 0, Utilitas Mathematica, 41,1992 3-10 (with I. Leung) .
35. Symmetric finite difference method for computing eigenvalues of Sturm-Liouville problems (with M. M. Chawla), Computers and Mathematics with Applications.
36. A fast parallel algorithm for the solution of tridiagonal linear systems, International Journal of Computer Mathematics 45,1992, 113-121 (with M. M. Chawla).
37. On Poisson's equation for doubly connected regions , Canadian Applied Mathematics Quarterly, Vol.1, No. 4, Fall 1993 (with C. Ji).
38. Upper and lower bounds for inverse elements of finite and infinite tri-diagonal matrices,Linear Algebra and its Applications 247:297-316, 1996(with C. Ji).
39. Bounds for the width of instability intervals in the Mathieu equation, accepted for publication in the Proceedings of the International Conference on Applications of Operator Theory, Birkhauser series "Operator Theory: Advances and Applications", Vol.87, 348-357, 1996(withQ. Ye) .
40. An efficient fourth order finite difference method for general nonlinear two-point boundary value problems, Neural, Parallel and Scientific Computations, Vol. 4, No. 3, September 1996.
41. Delay time bounds for RC ladder networks, IEEE Transactions on Circuits and Systems, I: Fundamental Theory and Applications, Vol.43, No.7,613-614, July 1996 (with C. A. Marinov).
42. On two-sided bounds related to weakly diagonally dominant M-matrices with application to digital circuit dynamics, accepted for publication in Siam J. Matrix Analysis and Applications, Vol.17, No.2, 298-312, April 1996 (with J. J. Williams, Q. Ye and C. Marinov).
43. A finite element method for double integrals with application to a Dirchlet problem arising in fluid dynamics, Communications in Numerical Methods in Engineering, Vol. 13, 627-634, 1997 (with N. Yan and C. Ji).
44. Flow past and through a porous medium in a doubly connected region, Applied Mathematics Letters, Vol. 11, No. 2, pp. 49-54, 1998 (with M. Luca and S. Kocabiyik)
45.On the nonsingularity of matrices with certain sign patterns, Linear Algebra and its Applications 273:29-43, 1998 (with C. Ji).
46. An analysis of groundwater flow in an infinite region with a sinusoidal top, J. Numerical Functional Analysis and Optimization, Vo.21, No.1-2, 263-271, 2000(with J.J.Williams, Q.Ye, C.Ji)
47. Inequalities for the minimal eigenvalue of the Laplacian in an annulus, Mathematical Inequalities & Applications, Vo. 1, No. 4, 559-563. 1998 (with A. G. Ramm).
48. On the double points of a Mathieu equation, J.of Computational and Applied Mathematics, 109, 111-125, 1999 (with J. Xue).
49. A Mathematical model for the dynamics of HIV-1 during the typical course of infection, Nonlinear Analysis 47, 1773-1783, 2001 (with A.B.Gumel, B.M.Sahai).
50. Numerical modelling of the perturbation of HIV-1 during combination anti-retroviral therapy, Computers in Biology and Medicine 31, 287-301, 2001 (with A.B.Gumel, T.D.Lowen, B.M.Sahai, P.Yu, M.L.Garba).
51.A new mathematical model for assessing therapeutic strategies for HIV infection, J.of Theoretical Medicine, Vol.4(2), 147-155 (with A.B.Gumel, Xue-Wu Zhang, M.L.Garba, B.M.Sahai).
52.Mathematical modeling of ice on transmission lines, accepted for publication, Proceedings of the International Conference on Industrial Mathematics, IIT, Bombay, India (with S.H.Lui, R.Thulasiram).
53. Flow of fluid through a pipe whose cross-section is bonded by eccentric circles, sent for publish (with Y. Wu)
54. Eigenvalues of the Laplacian on an elliptic domain, accepted for publication in Computers and Mathematics with Applications(with Y.Wu)
55. Mathematical Modeling of Ice Melting on Transmission Lines, J Math Model Algor 2007 6 273-286(with S. Yu. Sadov, D. Firsov, S.H.Lui, R. Thulasirm)
56. On a spectral decomposition of a finite difference operator, sent for publication (with S.H.Lui).
57. On the eigenvalue problem -y"+ f(x) y = λy on a semi infinite interval, Mathematical and Computer Modelling Vol 46. No. 3-4, August 2007 (Available online at Science Direct) (with Issic Kui Chiu Leung).
58. Spectral decomposition of a finite-diference operator, International Journal of Computer Mathematics Vol. 82, No. 10 Oct. 2005, 1275-1286 (with S.H.Lui).
59. Modelling the effect of CSII on the control of glucose concentration in type 1 diabetes, Applied Mathematics and Computation, Vol.187,Issue 2,2007, 1476-1483 (with Nilam, Murray E. Alexander, Ruchi Mathur, Seyed M. Moghadas).
60. Chapter 22, Type 1 diabeets-Complications, Pathogenesis and Alternative Treatments Ed.Chiu-Pin Liu, INTECH 2011, withNilam and S. Moghadas.
61. Shape of a drum, a constructive approach, Latest Trends on Systems, Vol.II, 14th WSEAS Interntional Confernce, Greece, 2010 (with Y.Wu)
62. Shape of a drum, a constructive approach, Transactions on Mathematics, WSEA, 2011 with (Yan.Wu, Yang Zhang)
63. On series solutions of y” – f(x) y = 0 and applications, Advances in difference equations, 2013,201:47 with Yang Zhang
64. A review of infinite matrices and their applications, Linear Algebra and its Applications430 (2009) 976-998 (with K.C.Sivakumar)
WORK IN PROGRESS
- AZT inhibits clonal expansion of T cells (with collaborators)
- On zeros of a Taylor Series
- A Monograph on “Finite and Infiinte Matrices and Applications”
- A Graduate Text on “Mathematical Modelling of Some Major Human Diseases (with collaborators
- Developing a protoype piggyback device for continuous infusion of insulin (industrial collaboration), based on a temporary US Patent filing by U of M. 2013
- Industrial problems:
- Simultaneous flow of oil and gas in pipes
- Modeling Gravity and Buoyancy in a mechanical device
- Shape of a drum for doubly connected regions
OTHER:
1. Uniqueness Theorems in Linear Elasticity by R. J. Knops and L. E. Payne, Canadian Mathematical Bulletin, Vol. 3, 1975 (Book Rev.)
2. Recent Developments in Operator Theory and Applications, Operator Theory: Advances and Applications, Vol. 87, (Editors: P. N. Shivakumar, I. Gohberg and P. Lancaster).
3. Proceedings of International Conference on Porous Media in Science, Engineering and Industry, Hawaii, 1997, (Editors: P. N. Shivakumar and K. Vafai).
4. Special Issue of the Symposium on Fast Algorithms for Control, Signals and Image Processing, International Linear Algebra Society, 1998 (Editors: D. P. O'Leary, H. Park, A. H. Sayed and P. N. Shivakumar).
5. Associate Editor, Journal on Porous Media, published by Marcel Dekker, 1997.
6. Proceedings of the International Conference on Operator Theory and its Applications to Scientific and Industrial Problems, October 7-11, 1998, Winnipeg.(Editors: A. G. Ramm, A. V. Strauss and P. N. Shivakumar).Fields Institute Series
7. Lead Guest Editor, Advances in Matrices, Finite and Infinite, with Applications, Journal of Applied Mathematics, 2013
8. Lead Guest Editor, Advances in Matrices, Finite and Infinite,with Applications, Journal of Applied Mathematics, 2014
9. Invitation by BIRS 2013 to be a Participant in the Workshop:Laplacians and eat Kernels, March 22-27
10. Filing of a Temporary Patent in U.S.A.by University of Manitoba Technology Office for continuous therapy for Diabetes, 2013
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