Publications

Prof. Manish Kumar

Associate Professor
Department of Mathematics

Pseudo-Differential Operators, Wavelet Analysis and its Applications, Distribution Theory, Digital Image Processing, Cryptography and Information Security

Birla Institute of Technology & Science, Pilani
Hyderabad Campus
Jawahar Nagar, Kapra Mandal
Dist.-Medchal-500 078
Telangana, India

manishkumar@hyderabad.bits-pilani.ac.in

+91 40 66303622

Book(s)/Chapter publication(s):

Book Title: Mathematics and Computing

Chapter Title: Cybersecurity: A Survey of Vulnerability Analysis and Attack Graphs

Authors: Rachid Ait Maalem Lahcen, Ram Mohapatra, and Manish Kumar

Book Title: Differential and Integral Inequalities

Chapter Title: Application of Davies–Petersen Lemma

Authors: Manish Kumar and R.N. Mohapatra

Editors: Andrica, Dorin, Rassias, and Michael Th (Eds.)

Book Series: Studies in Computational Intelligence

Book Title: Multimedia Security Using Chaotic Maps: Principles and Methodologies

Chapter Title: A Survey on Chaos-Based Image Encryption Techniques

Authors: Manish Kumar, Amogh Saxena, and Sai Satvik Vuppala

Editors: Hosny, Khalid M. (Ed.)

Book Series: Springer Proceedings in Mathematics & Statistics

Book title: Optimization, Variational Analysis and Applications

Chapter Title: A secure RGB image encryption algorithm in optimized virtual planet domain

Authors: Manish Kumar

Editors: Laha, Vivek, Marechal, Pierre, and Mishra, S. K. (Eds.)

Book Series: Springer Proceedings in Mathematics & Statistics

Book Title: Mathematical Analysis and Computing

Chapter Title: Asymptotic series of a general symbol of pseudo-differential operators involving linear canonical transform

Authors: Manish Kumar and Tusharakanta Pradhan

Editors: Mohapatra, R.N., Yugesh, S., Kalpana, G., Kalaivani, C. (Eds.)

Book Series: Springer Optimization and Its Applications
Book Title: Harmonic Analysis and Applications

Chapter Title: Degree of convergence of some operators associated with Hardy Littlewood series for functions of class Lip(a,p), p>1

Authors: Manish Kumar, Benjamin A. Landon, R. N. Mohapatra, and Tusharakanta Pradhan

Editors: Michael Th. Rassias (Ed.)

Book Series: Advances in Computers

Book title: Perspective of DNA Computing in Computer Science

Chapter Title: Secure data communication using DNA computing adaptable to wireless sensor network

Authors: Sathish Gunasekaran and Manish Kumar

Editors: Suyel Namasudra

Publisher: Elsevier

Research article publications:

(1) A. Prasad and M. Kumar, Continuity of pseudo-differential operator hm,a involving Hankel translation and Hankel convolution on some Gevrey spaces, Integral Transforms & Special Functions, Vol. 21, Issue no. 6, pp. 465–477, 2010 (Taylor & Francis).

(2) R.S. Pathak, A. Prasad, and M. Kumar, n-Dimensional Sobolev type spaces involving Hankel transform, Applied Mathematics and Computation, Vol. 218, Issue No. 3, pp. 899–905, 2011 (Elsevier).

(3) A. Prasad and M. Kumar, Product of two generalized pseudo-differential operators involving fractional Fourier transform, Journal of Pseudo-Differential Operators and Applications, Vol. 2, Issue no. 3, 355–365, 2011 (Springer).

(4) A. Prasad, M. Kumar, and Devdeep Roy Choudhury, C olor image encoding using fractional Fourier transformation associated with wavelet transformation, Optics Communications, Vol. 285, pp. 1005–1009, 2012 (Elsevier).

(5) R.S. Pathak, A. Prasad, and M. Kumar, An n-Dimensional pseudo-differential operator involving the Hankel transformation, Proc. Indian Acad. Sci. Math. Sci., Vol. 122, Issue no. 1, pp. 99–120, 2012 (Springer).

(6) R.S. Pathak, A. Prasad, and M. Kumar, Fractional Fourier transform of tempered distributions and generalized pseudo-differential operator, Journal of Pseudo-Differential Operators and Applications, Vol. 3, No. 2, pp. 239–254, 2012 (Springer).

(7) Manish Kumar, Image encryption using TSRMSC associated with DWT, AIP Conf. Proc., Vol. 1558, pp. 865–868, 2013 (American Institute of Physics).

(8) Akhilesh Prasad, Manoj Kumar Singh, and Manish Kumar, The continuous fractional wave packet transform, AIP Conf. Proc., Vol. 1558, pp. 856–859, 2013 (American Institute of Physics).

(9) Manish Kumar, Preface of the "First Symposium on pure and applied mathematics (2013)" AIP Conf. Proc., Vol. 1558, pp. 855, 2013 (American Institute of Physics).

(10) Manish Kumar, D.C. Mishra, and R.K. Sharma, A first approach on an RGB image encryption, Optics and Lasers in Engineering, Vol. 52, pp. 27–34, 2014 (Elsevier).

(11) D.C. Mishra, R.K. Sharma, Manish Kumar, and Kuldeep Kumar, Security of color image data designed by public-key cryptosystem associated with 2D- DWT, Fractals, Vol. 22, pp. 1450011–1450026, 2014 (World Scientific).

(12) Akhilesh Prasad and Manish Kumar, Boundedness of pseudo-differential operator associated with fractional Fourier transform, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, Vol. 84, Issue No. 4, pp. 549–554, 2014 (Springer).

(13) R.S. Pathak and Manish Kumar, Wavelet packets in Sobolev space , Applicable Analysis, Vol. 94, Issue no. 5, pp. 1068–1084, 2015 (Taylor & Francis).

(14) Manish Kumar, Pradeep Powduri, and Avinash Reddy, An RGB image encryption using diffusion process associated with chaotic map, Journal of Information Security and Applications, Vol. 21, pp. 20–30, 2015 (Elsevier).

(15) Manish Kumar and Kashyap L. S. J. Josyula, An interlaced secure algorithm for RGB image encryption in wavelet packet domain, International Journal of Wavelets, Multiresolution and Information Processing, Vol. 14, pp. 1650008-1–1650008-14, 2016 (World Scientific).

(16) Manish Kumar, Akhlad Iqbal, and Pranjal Kumar, A new RGB image encryption algorithm based on DNA encoding and elliptic curve Diffie-Hellman cryptography, Signal Processing, Vol. 125, pp. 187–202, 2016 (Elsevier).

(17) Manish Kumar, R. N. Mohapatra, Sajal Agarwal, G. Sathish, and S. N. Raw, A new RGB image encryption using generalized Vigen´ere-type table over symmetric group associated with virtual planet domain, Multimedia Tools and Applications, Vol. 78, pp. 10227–10263, 2019 (Springer).

(18) Manish Kumar, Sathish G, Michael Alphonse, Rachid Ait Maalem Lahcen, A new RGB image encryption using generalized heat equation associated with generalized Vigen`ere-type table over symmetric group, Multimedia Tools and Applications, Vol. 78, pp. 28025–28061, 2019 (Springer).

(19) Rachid Ait Maalem Lahcen, Bruce Caulkins, Ram Mohapatra, and Manish Kumar, Review and insight on the behavioral aspects of cybersecurity, Cybersecurity, Vol. 3, Issue No. 10, 2020 (Springer).

(20) Manish Kumar, A new class of pseudo-differential operators involving linear canonical transform, International Journal of Applied and Computational Mathematics, Vol. 6, issue 6, Article No. 165, 2020 (Springer).

(21) Manish Kumar and Prateek Gupta, A new medical image encryption algorithm based on the 1D logistic map associated with pseudo-random numbers, Multimedia Tools and Applications, Vol. 80, pp. 18941–18967, 2021 (Springer).

(22) Manish Kumar and Tusharakanta Pradhan, A framework of linear canonical transform on pseudo-differential operators and its application, Mathematical Methods in the Applied Sciences, pages 11425–11443, Vol. 44, Issue No. 14, 2021 (John Wiley & Sons Ltd.).

(23) Manish Kumar and Tusharakanta Pradhan, A new couple of Sobolev-type spaces and some applications, International Journal of Applied and Computational Mathematics, 7, Article No. 102, 2021 (Springer).

(24) H. M. Srivastava, Manish Kumar, and Tusharakanta Pradhan, A framework of linear canonical Hankel transform pairs in distribution spaces and their applications, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 115, Article No. 171, 2021 (Springer).

(25) Tusharakanta Pradhan, Manish Kumar, and Ram N Mohapatra, Pseudo-differential operators of infinite order on the space W_M^Ω(C) associated with a linear canonical transform, Panamerican Mathematical Journal, Vol. 31, Issue No. 4, pp. 41–60, 2021.

(26) Manish Kumar and Tusharakanta Pradhan, Quadratic-phase Fourier transform of tempered distributions and pseudo-differential operators, Integral Transforms & Special Functions, Vol. 33, Issue no. 6, pp. 449–465, 2022 (Taylor & Francis).

(27) Manish Kumar and Tusharakanta Pradhan, A pair of fractional Hankel-Clifford transform on Sobolev-type spaces: Theory, Examples, and Applications, Advances in Operator Theory, 7, Article No. 61, 2022 (Springer).

(28) Manish Kumar and Tusharakanta Pradhan,

An n-dimensional pseudo-differential operator involving linear canonical transform and some applications in quantum mechanics

, Filomat Vol. 37, No. 13, pp. 4155–4170, 2023.

(29) Manish Kumar and Divye Kalra, Efficient and lightweight data encryption scheme for embedded systems using 3D-LFS chaotic map and NFSR, e-Prime - Advances in Electrical Engineering, Electronics and Energy

Vol. 5, September 2023, 100273, Elsevier.

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