Research Areas
p-Adic Potts Model, p-Adic Dynamical Systems
Thesis
p-Adic Gibbs Measures on Cayley Trees and related p-Adic Dynamical Systems, defended on 29 August 2019
Selected Publications
- M. A. K. Ahmad, M. Alp, M. A. Mohd Azahari, A. F. Embong, Classification of Fixed Points of Potts–Bethe Mapping of Degree Four on Q_5, Journal of Quality Measurement and Analysis, 20(2), 2024, 105-110.
- M. A. Mohd Azahari, M. A. K. Ahmad, Depressed cubic equation over domain Z2*, AIP Conference Proceedings, 2905(1), 2024
- M. Saburov, M. A. K. Ahmad, M. Alp, The study on general cubic equations over p-adic fields, Filomat, 35(4), 1115-1131 2021.
- M. A. K. Ahmad, C. H. Pah and M. Saburov, Dynamics of Potts–Bethe mapping of degree four on Q5, AIP Conference Proceedings, 2184, 020001-1–8, 2019.
- M. A. K. Ahmad, L. Liao and M. Saburov, Periodic p-adic Gibbs measures of q-states Potts model on Cayley trees I: The chaos implies the vastness of the set of p-adic Gibbs measures, Journal of Statistical Physics, 171(6), 1000–1034, 2018.
- M. Saburov, M. A. K. Ahmad, Local descriptions of roots of cubic equations over p-adic fields, Bulletin of the Malaysian Mathematical Sciences Society, 41(2), 965–984, 2018.
- M. Saburov and M. A. K. Ahmad, On solvability of general cubic equations over Zp*, ScienceAsia, 41S, 1–8, 2017.
- M. Saburov and M. A. K. Ahmad, The dynamics of Potts–Bethe mapping over Qp: The case p = 2 (mod 3), Journal of Physics: Conferences Series, 819(1), 2017.
- M. Saburov and M. A. K. Ahmad, Solvability and number of roots of bi-quadratic equations over p-adic fields, Malaysian Journal of Mathematical Sciences, 10(S), 15–35, 2016.
- M. Saburov and M. A. K. Ahmad, Quadratic equations over p-adic fields and their application in statistical mechanics, ScienceAsia, 41(3), 209–215, 2015.
- M. Saburov and M. A. K. Ahmad, On descriptions of all translation invariant p-adic Gibbs measures for Potts model on Cayley tree of order three, Mathematical Physics, Analysis, and Geometry 18(26), 1–33, 2015.
- M. Saburov and M. A. K. Ahmad, The number of solutions of cubic equations over Q3, Sains Malaysiana 44(5), 765–769, 2015.
- M. Saburov and M. A. K. Ahmad, Solvability of cubic equations over Q3, Sains Malaysiana 44(4), 635–641, 2015.
- M. Saburov and M. A. K. Ahmad, Solvability criteria for cubic equations over Z2*, AIP Conference Proceedings 1602, 792–797, 2014.
Submitted Articles and Preprints
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Ongoing Projects
- Periodic p-adic Gibbs measures of q-states Potts model on Cayley trees II (with Shilei Fan, Lingmin Liao, and Mansoor Saburov)
- p-Adic Ising-Vannimenus model on Cayley tree of order three (with Farrukh Mukhamedov)
- Describing the 2-adic valuation trees generated by depressed cubic polynomial (with Murat Alp, Jane Long, Olena Kozhushkina, Mansoor Saburov, and Justin Trulen)
- Cubic stochastics operators on 1D simplex (with Ahmad Fadillah Embong)
Collaborators
Lingmin LIAO, PAH Chin Hee, Mansoor SABUROV
Thesis Supervision
Doctor of Philosophy
Tan Li Xian, Ergodicity for p-Adic Dynamical Systems in Terms of Coordinate Functions, withdraw (1/4/2022-26/6/2022)
Master by Research
Muhammad Azim bin Mohd Azahari, Potts model and Polynomial Equations over p-Adic Fields, ongoing (1/5/2021-)