Mathematics Genealogy Project

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

  1. 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.
  2. M. A. Mohd Azahari, M. A. K. Ahmad, Depressed cubic equation over domain Z2*, AIP Conference Proceedings, 2905(1), 2024
  3. M. Saburov, M. A. K. Ahmad, M. Alp, The study on general cubic equations over p-adic fields, Filomat, 35(4), 1115-1131 2021.
  4. 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.
  5. 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.
  6. 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.
  7. M. Saburov and M. A. K. Ahmad, On solvability of general cubic equations over Zp*, ScienceAsia, 41S, 1–8, 2017.
  8. 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.
  9. 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.
  10. 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.
  11. 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.
  12. M. Saburov and M. A. K. Ahmad, The number of solutions of cubic equations over Q3, Sains Malaysiana 44(5), 765–769, 2015.
  13. M. Saburov and M. A. K. Ahmad, Solvability of cubic equations over Q3, Sains Malaysiana 44(4), 635–641, 2015.
  14. 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

  1. Periodic p-adic Gibbs measures of q-states Potts model on Cayley trees II (with Shilei Fan, Lingmin Liao, and Mansoor Saburov)
  2. p-Adic Ising-Vannimenus model on Cayley tree of order three (with Farrukh Mukhamedov)
  3. Describing the 2-adic valuation trees generated by depressed cubic polynomial (with Murat Alp, Jane Long, Olena Kozhushkina, Mansoor Saburov, and Justin Trulen)
  4. 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)

Ong Ren Chin, Clique Polynomials of the Coprime Graph for Generalized Quaternion Group, ongoing (6/10/2024 – )

Master by Research

Muhammad Azim bin Mohd Azahari, Potts model and Polynomial Equations over p-Adic Fields, ongoing (1/5/2021 – )