Government Engineering College, Bhojpur ( Science,Technology and Technical Education Department, Govt. Of Bihar )

Dr. Kalika Prasad (Faculty)

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Dr. Kalika Prasad

Assistant Professor,
Applied Science& Humanities

9971591806   |   [email protected]

Website | Blog



Qualifications
PhD in Pure Mathematics (Number Theory & Algebra) (CSIR-NET, JRF, SRF, HP-SET, GATE)
Subject Expertise
Number Theory, Abstract Algebra, Linear Algebra, Matrix Theory, Integer Sequences, Probability Theory and Statistics
Area Of Research
Number sequences, Matrix theory, Fibonacci like numbers, Mersenne numbers, Special matrices
Professional Experience
Junior Research Fellow (2019-2021)
Senior Research Fellow (2021-2024)
List Of Publications
◆ K. Prasad, H. Mahato: Cryptography using generalized Fibonacci matrices with Affine-Hill cipher, Journal of Discrete Mathematical Sciences and Cryptography, Vol. 25(8):2341-2352, 2022. DOI: 10.1080/09720529.2020.1838744
◆ K. Prasad, H. Mahato, M. Kumari: On the generalized k-Horadam like sequences, Algebra, Analysis and Associated Topics, Trends in Mathematics, Springer, Ch-2:11-26, 2022. DOI: 10.1007/978-3-031-19082-7 2
◆ K. Prasad, H. Mahato: On Some New Identities of Lucas Numbers and Generalized Fibonacci Trace Sequences, Palestine Journal of Mathematics, Vol. 12(2), 2023
◆ K. Prasad, H. Mahato, M. Kumari: On the norms of r-Circulant matrices involving balancing and Lucas-balancing numbers. TWMS J. App. & Eng. Math. (Accepted: Sept 27, 2022, To appear in 2024).
◆ K. Prasad, R. Mohanty, M. Kumari, H. Mahato: Some new families of generalized k-Leonardo and Gaussian Leonardo numbers, Communications in Combinatorics and Optimization, DOI: 10.22049/CCO.2023.28236.1485
◆ K. Prasad, H. Mahato, M. Kumari, R. Mohanty: On the generalized Leonardo Pisano Octonions, National Academy Science Letters, Springer. DOI: 10.1007/s40009-023-01291-2
◆ K. Prasad, H. Mahato, M. Kumari: Some properties of r-Circulant Matrices with k-Balancing and k-Lucas Balancing Numbers, Boletın de la Sociedad Matematica Mexicana, Springer, Vol. 29 (2), #Article 44, 2023. DOI: 10.1007/s40590-023-00510-6
◆ K. Prasad, H. Mahato: On the generalized Fibonacci like sequences and matrices, Annales Mathematicae et Informaticae DOI: 10.33039/ami.2023.05.001
◆ K. Prasad, M. Kumari, C. Kızılates: Some Properties and Identities of Hyperbolic Generalized k-Horadam Quaternions and Octonions, Communications in Combinatorics and Optimization, 2023. DOI: 10.22049/CCO.2023.28272.1495
◆ K. Prasad, M. Kumari, J. Tanti: Generalized k-balancing and k-Lucas balancing numbers and associated polynomials, Kyungpook Mathematical Journal, 2023. (Accepted: August 08, 2023).
◆ M. Kumari, J. Tanti, K. Prasad: On some new families of k-Mersenne and generalized k-Gaussian Mersenne numbers and their polynomials, Contributions to Discrete Mathematics, Vol. 18 (2), 2023. (Accepted: Feb 2022, Appear in 2023)
◆M. Kumari, K. Prasad, H. Mahato: On the k-Mersenne and k-Mersenne-Lucas Octonions. TWMS J. App. & Eng. Math. (Accepted: Dec 14, 2022, Appear in 2024)
◆ M. Uysal, M. Kumari, B. Kuloglu, K. Prasad, E. Ozkan: On the Hyperbolic ¨ k-Mersenne and k-Mersenne-Lucas Octonions. Kragujevac Journal of Mathematics, Vol. 49(5):765–779, 2025. (Online published: Feb 14, 2023).
◆ M. Kumari, K. Prasad, J. Tant: A Note On Linear Codes With Generalized Fibonacci Matrices, Jnanabha, Vol. 52(2):77-81, 2022. DOI: 10.58250/jnanabha.2022.52209
◆ M. Kumari, K. Prasad, B. Kuloglu, E. Ozkan: The k-Fibonacci group and periods of k-step Fibonacci sequences., WSEAS Transactions on Mathematics, Vol. 21(#Art 95):838-843, 2022. DOI: 10.37394/23206.2022.21.95
◆ M. Kumari, K. Prasad, J. Tanti, E. Ozkan: On the r-circulant matrices with Mersenne and Fermat numbers, International Journal of Nonlinear Analysis and Applications, Vol. 14 (5), 121–131, 2023. DOI: 10.22075/IJNAA.2023.27875.3742
◆ M. Kumari, K. Prasad, J. Tanti: On the generalization of Mersenne and Gaussian Mersenne polynomials, The Journal of Analysis, 2023. DOI: 10.1007/s41478-023-00666-4
◆ M. Kumari, K. Prasad, E. Ozkan, J. Tanti: On the Norms and Eigenvalues of r-circulant matrices with k-Mersenne and k-Mersenne-Lucas numbers, Mathematical Notes, Vol. 114 (4), 522–535, 2023. DOI: 10.1134/S0001434623090225
◆ M. Kumari, K. Prasad, H. Mahato: On the norms of Toeplitz and Hankel matrices with balancing and Lucas-balancing numbers. Advanced Mathematical Techniques in Computational and Intelligent Systems (Edited book chapter), Ch-12, 2023.
◆ M. Kumari, K. Prasad, R. Frontczak: On the k-Fibonacci and k-Lucas Spinors, Notes on Number Theory and Discrete Mathematics, Vol. 29(2):322–335, 2023. DOI: 10.7546/nntdm.2023.29.2.322-335
◆ R. Frontczak, M. Kumari, K. Prasad: New integrals involving a function associated with Euler-Maclaurin summation formula, Contributions to Mathematics, Vol. 7:11-14, 2023. DOI: 10.47443/cm.2022.060
◆ R. Frontczak, K. Prasad: Balancing polynomials, Fibonacci numbers and some new series for π, Mediterranean Journal of Mathematics, Vol.: 20, Article no.: 207, 2023. DOI: 10.1007/s00009-023-02413-2
Conference Attended (National/International)
📌 International E-Conference of Young Researchers in Algebra and Number Theory-2023 by the Faculty of Sciences Dhar El Mahraz, Fez, Morocco on January 12-13, 2023 (Online)
📌 International Conference on Nonlinear Analysis and Applications by the Department of Mathematics, Assam Don Bosco University, Assam, India. during Nov. 22-23, 2022, (Offline) (Entitled: ‘The k-Binomial and Catalan Transforms of the k-Leonardo Sequence’)
📌 International Conference on Mathematical Analysis & Applications, 2022 (ICOMAA 2022) by the Department of Mathematics, University of Kalyani, India during June 28-29, 2022, (Online) (Entitled: ‘Extended k-Horadam like sequences & Binet’s Formula’)
📌International Conference on Mathematical Science and Its Recent Advancements (ICMSRA-2022) by Rathinam College of Arts and Science, Coimbatore on May 5-7, 2022, (Online). (Entitled: ‘Generalization of Fibonacci Trace Sequences and Associated Matrix’)
📌International Conference on Advance Trends in Computational Mathematics, Statistics and Operations Research by The NorthCap University, Gurugram, India during April 2-3, 2022. (Entitled: ‘On the role of generalized Lucas matrices in reducing key construction complexity in cryptography’)
📌International Conference on ’Analysis and Discrete Mathematics & 49th Annual Conference of OMS’ at P.G. Dept. of Mathematics, Utkal University, Bhubaneswar, India held on March 26-27, 2022, (Offline). (Entitled: ‘On the properties of generalized Lucas matrices’)
📌International Conference On ‘New Trends In Differential Equations And Applied Mathematics (ICNTDEAM - 2021)’ by Sri Vidya Mandir Arts and Science College, Krishnagiri on April 12-13, 2021. (Entitled: ‘Generalization Of Fibonacci Matrix and Its Application In Cryptography’)
📌3rd International Conference on Advanced Mathematical Analysis and its Application (ICAMMA-2020) at Berhampur University, Odisha Feb 04-05, 2020. (Entitled: ‘On The Key Space with Higher Dimensional Multinacci Matrices’)
📌Delivered Hands-on-session on workshop ’LaTeX Learning: A Hands on Training’ in Collaboration with NIT Andhra Pradesh, IEEE PES & PELS Student Branch Chapter on December 27-30, 2020.
📌Delivered invited talk on ’CYBER SURAKSHA: How to Be Secure in This Digital Era’ at Government Polytechnic, Nawada, Department of Science & Technology(DST), Govt. of Bihar, on August 30, 2020.
📌Delivered Invited talk on ’CYBER SECURITY: WHY & HOW?’ at Government Polytechnic, Gaya, Department of Science & Technology(DST), Govt. of Bihar, June 27, 2020
Membership
Life Member of ’Cryptology Research Society of India’: L/1035
Awards and Honors
📌2019: Certificate by ’AIU’, Govt. of India, for NATIONAL Level Cultural Youth fest
📌2019: Medal & Certificate by ’AIU’, Govt. of India, for EAST ZONE Cultural Youth fest.
📌2017: Certificate by ’AIU’, Govt. of India, for NATIONAL Level Cultural Youth fest
📌2017: Medal & Certificate by ’AIU’, Govt. of India, for WEST ZONE Cultural Youth fest
📌2016: Medal & Certificate by ’AIU’, Govt. of India, for WEST ZONE Cultural Youth fest
📌2016: Best out of Waste Award (Trophy for First Position, CURAJ)
📌2012-2017: INSPIRE SCHOLAR for 5yrs, by DST, Govt. of India
📌2009: High School Regional Topper Award (Rs 10,000 one time, Govt. of Bihar)
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