Research Publications

Some of my accepted/published research papers. Enjoy reading...

(Dedicated collaborators are welcome.)

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List of my publications

Preprint: 

P1. K. Prasad,  M. Kumari,  R. Mohanta, H. Mahato: The sequence of higher-order Mersenne numbers and associated binomial transforms. arXiv preprint, 2023. Article link: https://arxiv.org/pdf/2307.08073

2026

1. M. Kumari, K. Prasad*, H. Mahato, PMC Catarino: On The Generalized Leonardo Quaternions and Associated Spinors. Kragujevac Journal of Mathematics, Vol. 50(3), 425–438, 2026. DOI: 10.46793/KgJMat2603.425K  (Accepted, Jan. 2024)

2025

2. K. Prasad, M. Kumari, The telephone polynomials: an Appell-type orthogonal polynomials connecting Hermite-Laguerre polynomials, Nuclear Physics Section B, Elsevier (October 2025).

3. K. Prasad, Indubala,  M. Kumari: Higher order balancing numbers: new sequences, recurrence relations, generating functions and identities, Bulletin of the Karaganda University. Mathematics Series (Accepted, Aug. 2025).  HAL open science Preprint link: https://hal.science/hal-04815114 

4. K. Prasad, M. Kumari: The generalized k-Leonardo numbers: a non-homogeneous generalization of the Fibonacci numbers, Palestine Journal of Mathematics, Vol 14(3), 637–650, Nov. 2025. Link: https://pjm.ppu.edu/sites/default/files/papers/PJM_14%283%29_2025_637_to_650.pdf.pdf

5. K. Prasad, M. Kumari, H. Mahato: The k-Binomial and Catalan Transforms of the k-Leonardo Numbers, TWMS J. App. Eng. Math., Vol. 15 (11),  2652-2663, Nov. 2025. Link: https://dergipark.org.tr/en/pub/twmsjaem/issue/95450/1814754

6. M. Kumari, K. Prasad*, R. Mohanty, H. Mahato: On New Sequences of p-Binomial and Catalan Transforms of the k-Mersenne Numbers and Associated Generating Functions, Universal Journal of Mathematics and Applications, 8 (2), 71-80, 2025. DOI: 10.32323/ujma.1641001 ( May 2025)

7. K. Prasad, M. Kumari, H. Mahato: Algebra of generalized (k,n)-Fibonacci Toeplitz and Hankel Matrices, Boletim da Sociedade Paranaense de Matematica, 43, Mar. 2025. DOI: 10.5269/bspm.68455

8. M. Kumari, K. Prasad*, J.Tanti: Generalization of Gaussian Mersenne numbers and their new families. Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science, Vol. 5(67), No. 1, 2025. DOI: 10.31926/but.mif.2025.5.67.1.11 (Jan. 2025)

9. [Book Chapter] K. Prasad, M. Kumari: Sedenion algebra of the k-Mersenne and k-Mersenne-Lucas numbers, Algebra and its Applications, Springer Proceeding, Int. Conference on Algebra and its Applications–2023, Fez, Morocco" Ch-19, 211–223, Jan 2025. DOI: 10.1007/978-981-97-6798-4 19 

10. 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), 2025, pp. 765–779. DOI: 10.46793/KgJMat2505.765U 

2024

11. K. Prasad, M. Kumari*, J.Tanti: On norms, spread, characteristic polynomial and determinant of Hankel and Toeplitz matrices with Mersenne sequence, Communications in Combinatorics and Optimization, Dec. 2024 (appear in 2025). DOI: 10.22049/cco.2024.30037.2287

12. K. Prasad, M. Kumari: Some new properties of Frank matrices with entries Mersenne numbers, National Academy Science Letters, Springer, 2024 (appear in 2025). DOI: 10.1007/s43538-024-00348-0

13. K. Prasad, M. Kumari: The Leonardo polynomials and their algebraic properties, Proceedings of the Indian National Science Academy, Springer, 91, 2025, 662–671. DOI: 10.1007/s43538-024-00348-0

14. K. Prasad, M. Kumari, R. Mohanty, H. Mahato: Spinor algebra of k-balancing and k-Lucas-balancing numbers, Journal of Algebra and Its Applications, World Scientific, 2024 (appear in 2025). DOI: 10.1142/S0219498825503670

15. M. Kumari, K. Prasad*, R. Mohanta: Algebra of quaternions and octonions associated with higher order Mersenne numbers, Proceedings of the Indian National Science Academy, Springer, 2024 (appear in 2025). DOI: 10.1007/s43538-024-00297-8 

16. [Book Chapter] M. Kumari,  R. Mohanta K. Prasad*, H. Mahato: On the Gaussian higher order Mersenne numbers, DeGruyter proceedings of 2nd ICRTMPCS 2023 on March 17-19, 2023 "Advances in Mathematical and Computational Sciences, Ch-26, 355-366, 2025. DOI: 10.1515/9783111313634-026

17. K. Prasad, M. Kumari, H. Mahato: A modified public key cryptography based on generalized Lucas matrices, Communications in Combinatorics and Optimization, 2024. DOI: 10.22049/CCO.2024.28022.1419  

18. M. Kumari, K. Prasad*, H. Mahato: On the k-Mersenne and k-Mersenne-Lucas Octonions. TWMS J. App. & Eng. Math., Vol. 14(3), 1218-1230, 2024.  (Article link: Read here)

19. K. Prasad, H. Mahato, M. Kumari: On the norms of r-Circulant matrices involving balancing and Lucas-balancing numbers. TWMS J. App. & Eng. Math. Vol. 14(2),  672-683, 2024. (Article link: Read here)

20. K. Prasad,  M. Kumari, J. Tanti: Octonions and hyperbolic octonions with the k-balancing and k-Lucas balancing Numbers, The Journal of Analysis, 2024.  DOI: 10.1007/s41478-023-00716-x 

21. M. Kumari, K. Prasad*, J. Tanti: On the generalization of Mersenne and Gaussian Mersenne polynomials, The Journal of Analysis, Vol. 32, 931–947, 2024. DOI: 10.1007/s41478-023-00666-4

2023

22. K. Prasad,  M. Kumari, J. Tanti: Generalized k-balancing and k-Lucas balancing numbers and associated polynomials, Kyungpook Mathematical Journal, Vol.: 63(4), 539-550, 2023. DOI: 10.5666/KMJ.2023.63.4.539 

23. K. Prasad, H. Mahato*: On Some New Identities of Lucas Numbers and Generalized Fibonacci Trace Sequences, Palestine Journal of Mathematics, Vol. 12 (2), 2023. (Article link: Click here)

24. K. Prasad, R. Mohanty, M. Kumari, H. Mahato: Some new families of generalized k-Leonardo and Gaussian Leonardo numbers. Communications in Combinatorics and Optimization. 2023. DOI: 10.22049/CCO.2023.28236.1485

25. 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

26. K. Prasad, H. Mahato, M. Kumari*: Some properties of r-Circulant Matrices with k-Balancing and k-Lucas Balancing Numbers. Boletín de la Sociedad Matematica Mexicana, Springer. DOI: 10.1007/s40590-023-00510-6 

27. K. Prasad, H. Mahato*: On the generalized Fibonacci-like sequences and matrices. Annales Mathematicae et Informaticae, Vol. 59: 102–116,  2023. DOI: 10.33039/ami.2023.05.001

28. 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

29. [Book Chapter] 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. Ch - 12, 196 - 210, 2023. DOI: 10.1201/9781003460169 

30. 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),  244-260, 2023. DOI: 10.55016/ojs/cdm.v18i2.74415 

31. 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

32. M. Kumari, K. Prasad, E. Ozkan*, Jagmohan 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 

33. 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

34. 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

35. R. Frontczak, K. Prasad*: Balancing polynomials, Fibonacci numbers and some new series for π, Mediterranean Journal of Mathematics, Vol.: 20, Article number: 207, 2023. DOI: 10.1007/s00009-023-02413-2

2022

36. 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

37. 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

38. [Book Chapter] 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

2021

39. K. Prasad, H. Mahato: Cryptography using generalized Fibonacci matrices with Affine-Hill cipher, Journal of Discrete Mathematical Sciences and Cryptography (Taylor & Francis), Vol. 25(8), 2341-2352, 2022. DOI: 10.1080/09720529.2020.1838744

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