Papers

I have published papers in five areas: Numerical Solution of Singularly Perturbed Differential Equations, Knowledge Compilation, PDE based Image Restoration, Regularization in Learning Theory, and Numerical Linear Algebra. I also have written some expository papers in basic mathematics.

Published-papers     Unpublished     Adapted-as-Text-in-Univ-of-Hyderabad-PGDCS

The image on the top right is Hogwarts Library.

• Real linear operators and factorization of real polynomials, Mathematics News Letter 32:1 (2021), 1-6. Journal site. A preprint is here.
  
• On proving a program shortest, Resonance 25: 9 (2020) 1251-1260. DOI: 10.1007/s12045-020-1043-6. paper on the web Also, Preprint
  This paper answers the questions: Can one write a program that determines whether any given program is the shortest program? How does one prove that a given program is the shortest? And then it introduces the notion of Kolmogorove complexity of bit-strings leading to Chaitin's barrier on any axiomatic system.
• The Least squares and line search in extracting eigenpairs in Jacobi–Davidson method, BIT Numerical Mathematics 60 (2020) 1033-1055. DOI: 0.1007/s10543-020-00806-3 Journal site
  
• Construction and Categoricity of the Real Number System Using Decimals, Mathematics News Letter 30 :1 (2019), 1-13. Journal site. A copy of the paper is here.
  
• A new variant of Arnoldi method for approximation of eigenpairs(with M. Ravibabu) Journal of Computational and Applied Mathematics 344 (2018) 424-437. (You can access the article for a limited time Here)
• Incompleteness Phenomena in Arithmetic, Mathematics News Letter 29 :1 (2018), 14-18. Preprint
  This paper contains a simple proof of Diagonalization Lemma. Theis result is then used to derive Negation incompleteness, Omega incompleteness, and there exists-incompleteness of Peano's Arithmetic.
• From a ball game to incompleteness, Resonance 22 No. 12 (2017) 1205-1211. via Springer Nature SharedIt Also, Preprint
  In this paper, we consider an infinite ball game invented by R. M. Smullyan. After showing that the ball game ends, we show how it leads to the omega-incompleteness of Arithmetic.
• On Refined Ritz vectors and polynomial characterization (with M. Ravibabu) Computers and Mathematics with Applications 67 (2014) 1057-1064.
• A survey on computing prime implicants and implicates in classical and on-classical logics (with M. K. Raut) Comput. Sys. Sc. and Engg., 2 ( 2014) 1-11.
• Comparing Cardinalities of Sets, Mathematics News Letter 24 No. 2 (2013) 1-6. Preprint
  This paper contains a simple proof of Cantor-Schroder-Bernstein Theorem and also a simple proof of uncountability of real numbers using the completeness principle.
• An adaptive anisotropic diffusion scheme for image restoration and selective smoothing, (with V. B. Surya Prasath) International Journal of Image and Graphics, 12 (2012) 18 pages.
• A Simple Proof of Godel's Incompleteness Theorems, Mathematics News letter 22 No. 3 (2012) 1-3. Preprint
• Pi at School, Mathematics News Letter 21 No. 1 (2011) 1-5. Preprint
• Well-posed inhomogeneous nonlinear diffusion scheme for digital image denoising, (with V. B. Surya Prasath) Journal of Applied Mathematics, 2010 (2010) 14 pages
• Multichannel image restoration using combined channel information and robust M-estimator approach, (with V. B. Surya Prasath) International Journal of Tomography and Statistics, 15 (2010) 9-22.
• Multispectral image denoising by well-posed anisotropic diffusion scheme with channel coupling, (with V. B. Surya Prasath) International Journal of Remote Sensing, 31 (2010) 2091-2099.
• A hybrid convex variational model for image restoration, (with V. B. Surya Prasath) Applied Mathematics and Computation, 215 (2010) 3655-3664.
• An estimate of the misclassification error with hinge and square loss, (with J. K. Sahoo), International Journal of Computational and Applied Mathematics, 5:1 (2010) 89-102.
• An error analysis of Lavrentiev regularization in learning theory, (with J. K. Sahoo), Asian-European J. of Mathematics, 2 (2009) 129-140.
• Ringing artifact reduction in blind image deblurring and denoising problems by regularization methods, (with V. B. Surya Prasath), Seventh International Conference on Advances in Pattern Recognition (ICAPR-09), Kolkata, India, Proc. of IEEE Computer Society, Feb (2009) 333-336.
• Controlled inverse diffusion models for image restoration and enhancement, (with V. B. Surya Prasath), First International Conference on Emerging Trends in Engineering and Tech- nology (ICETET-08), Nagpur, India. Proc. of IEEE Computer Society, July (2008) 90-94.
• Controlled inverse diffusion models for image restoration and enhancement, (with V. B. Surya Prasath), First International Conference on Emerging Trends in Engineering and Technology (ICETET-08), Nagpur, India. Proc. of IEEE Computer Society, pp. 90-94, Jul 2008.
• Edge detectors based anisotropic diffusion for enhancement of digital images, (with V. B. Surya Prasath), Sixth Indian Conference on Computer Vision, Graphics and Image Processing (ICVGIP-08), Bhubaneswar, India, Proc. of IEEE Computer Society, pp. 33-38, Dec 2008. (Best Paper Award)
• Robust M-Estimators in Early Computer Vision Problems, (with V. B. Surya Prasath) International Conference in Statistics and Optimization, Kasmir, India, 2008. (Best Paper Award)
• The role of edge indicator function in Perona-Mallik diffusion equation, International Conference on Recent Trends in Computational PDE, Mumbai, India, 2008.
• An algorithm for computing prime implicates in first order logic (with M.K.Raut), International Journal of Information and Communication Technology, 1 (2007) 4-13.
• Mapcode computability, In: Proceedings of CIT2005 held at Bhubaneswar, 8:4.2 (2005) 125-130. Preprint
• An algorithm for computing prime implicants in first order logic (with M.K.Raut), In: Proceedings of CIT2005 held at Bhubaneswar, 8:5.1 (2005), 147-151 (Awarded best paper in the conference.)
• Convergence of two regularization methods for singularly perturbed PDE, Special Issue of J. Orissa Mathematical Society on Numerical methods,23-24 (2004-05) 232-242.
• Prime implicants of first order formulas via transversal clauses (with Manoj K Raut), Int. J. Computer Mathematics 81:2 (2004) 157-167.
• Prime implicants of first order formulas (with Manoj K. Raut), Int. J. Computer Science and Applications 1:1 (2004) 1-11.
• Cantor's little theorem, Resonance: Journal of Science Education, 9 :8 (2004), 8-17. Preprint
• Showalter's regularization of an elliptic PDE (with S.Sheela), J. Applied Mathematics and Computation 158 (2004) 19-28.
• Lavrentiev regularization of an elliptic PDE (with S.Sheela), J. Applied Mathematics and Computation 18 (2004) 189-205.
• A unit resolution approach to knowledge compilataion (with Manoj K Raut), WSEAS Transactions on Computers 4:2 (2003) 945-950.
• Lardy's regularization of a singularly perturbed elliptic PDE (with S.Sheela), J. Computational and Applied Mathematics 151 (2003) 25-37.
• Adequacy of calculational logic (with M.K.Raut), J. Orissa Mathematical Society 21-22 (2002-03), 53-68.
• Spectral Regularization of a Singularly Perturbed Elliptic Partial Differential Equation, Chapter 11 in Differential Equations and Dynamical Systems, Ed. D.~Bahuguna, Narosa Pub. House, 2004. (Procc. Int Conf on Diffl Eqns \& Dynam Syst, held at IIT Kanpur, December 2002)
• Triangles with given distances from a centre (withA.K.Maloo, A.K.Lal), Int. J. Mathematics Education in Science and Technology 33 (2002) 615-620.
• Convergence of Tikhonov regularization for unbounded operators, The Mathematics Education XXXVI (2002) 50-51.
• Tikhonov regularization of an elliptic PDE (with S.Sheela), Mathematics and Computers in Simulation 57 (2001) 1-4.
• Computing prime implicants via transversal clauses, Int. J. Computer Mathematics 70 (1999) 417-427.
• Oscillation and dominance, J. Orissa Mathematical Society 16 (1997) 27-30.
• A matrix method of computation of prime implicates of propositional formula in CNF (with A.K.Shiny, A.K.Pujari), In: Innovative Applications in Computing (Proc. Int. Computing Congress Series, ed. E. Balagurusamy, B. Sushila, Tata Mc Graw Hill), 1993, pp.32-38.
• A numerical method for singularly perturbed systems of linear two-point boundary-value problems using partial decoupling, J. Computational and Applied Mathematics 40 (1992) 55-62.
• Comments on partial decoupling and Euler's one-step schemes, Mathematics and Computers in Simulation 33 (1991) 197-203.
• Partial decoupling of slow and fast variables (with M.K.Kadalbajoo), J. Mathematical Analysis and Applications 155 (1991) 46-54.
• A modified version of Newton's iteration (with M.K.Kadalbajoo), Int. J. Computer Mathematics 33 (1990) 107-113.
• A numerical method for solving singularly perturbed systems of nonlinear two-point boundary-value problems (with M.K.Kadalbajoo), Int. J. Computer Mathematics 30 (1989) 117-127.
• An estimate of boundary layer thickness for linear singularly perturbed two-point boundary-value problems (with M.K.Kadalbajoo), J. Optimization Theory and Applications 63 (1989) 143-151.
• Boundary value technique to solve linear state regulator problems (with M.K. Kadalbajoo), J. Optimization Theory and Applications 63 (1989) 91-107.
• A boundary value technique for solving singularly perturbed fixed end-point optimal control problems (with M.K.Kadalbajoo), Optimal Control Applications and Methods 9 (1988) 443-448.
• A cutting point technique for solving nonlinear state regulator problems (with M.K. Kadalbajoo), IMA J. Mathematical Control and Information 4 (1987) 183-194.

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