Research Interest 

Publications:

1.  M.Mustafa, A.Sorbi. Positive undecidable numberings in the Ershov hierarchy, Algebra and logic ,Vol. 50, N6, pp. 512--525, 2012.https://doi.org/10.1007/s10469-012-9162-0  (Translated from Algebra and Logika, Vol. 50, No. 6, pp. 759-780, November-December, 2011.)

2.  S.Badaev, M.Mustafa, S.Andrea. Rogers semilattices of families of two embedded sets in the Ershov hierarchy, Mathematical Logic Quarterly. -Vol. 58, issue 4-5. -P.366-376. -2012 August. https://doi.org/10.1002/malq.201100114

3.  K.Abeshev, S.Badaev, M.Mustafa. Families Without Minimal Numberings. Algebra and  Logic 53, 271–286 (2014). https://doi.org/10.1007/s10469-014-9290-9. (Translated from Algebra and Logika, Vol. 53, No. 4, pp. 427-450, July-August, 2014.)

4.  S.Badaev, M.Mustafa, A.Sorbi. Friedberg numberings in the Ershov hierarchy. Arch. Math. Logic 54, 59–73 (2015). https://doi.org/10.1007/s00153-014-0402-y.

5.  M.Mustafa,Bazhenov.N, Stephan F, M.Yamaleev. Boolean algebras realized by c.e.equvivalence relations. Siberian electronic mathematical reports. V14, pp848-855. \\ DOI 10.17377/semi.2017.14.071,2017.

6.  T.Bekjan, M.Mustafa, On interpolation of noncommutative symmetric Hardy spaces.  Positivity 21, 1307–1317 (2017). https://doi.org/10.1007/s11117-017-0468-y.

7.  M. Zubaira, A.Alzaatreh, M. H. Tahir, M. Mansoora and M.Mustafa.  A generalisation of the exponential distribution and its applications on modelling skewed data, Statistical Theory and Related Fields, 2:1, 68-79, 2018.  https://doi.org/10.1080/24754269.2018.1466099.

8.  N.Bazhenov, M.Mustafa, M.Yamaleev.  Computable Isomorphisms of Distributive Lattices. In: Gopal T., Watada J. (eds) Theory and Applications of Models of Computation. TAMC 2019. Lecture Notes in Computer Science, vol 11436. Springer, Cham, https://doi.org/10.1007/978-3-030-14812-6_3.

9.  N.Bazhenov, M.Mustafa, S.Ospichev. Bounded Reducibility for Computable Numberings. In: Manea F., Martin B., Paulusma D., Primiero G. (eds) Computing with Foresight and Industry. CiE 2019. Lecture Notes in Computer Science, vol 11558.2019. Springer, Cham.  https://doi.org/10.1007/978-3-030-22996-2_9

10.  M.Mustafa, D.Suragan.  Green-type identities for Rockland operators on graded lie groups. Complex Anal. Oper. Theory 13, 959–966 (2019). https://doi.org/10.1007/s11785-018-0824-3.

11.  N.Bazhenov, M.Mustafa and M.Yamaleev. Elementary theories and hereditary undecidability for semilattices of numberings.   Arch. Math. Logic (2019) 58: 485--500. https://doi.org/10.1007/s00153-018-0647-y.

12.  I.Herbert, M.Mustafa, S.Jain, S, Lempp, F.Stephan. Reductions between Types of Numberings. Annals of Pure and Applied Logic.Volume 170, Issue 12, 2019,102716, https://doi.org/10.1016/j.apal.2019.102716 . 2019.

13.   M.Mustafa. Sixteenth Asian Logic Conference: an official meeting of the Association for Symbolic Logic, Nazarbayev University, Nur-Sultan, Kazakhstan. June 17–21, 2019. The Bulletin of Symbolic Logic, 25(4),2019. 456-478. doi:10.2307/26875667.

14.  Bazhenov N., Mustafa M., Ospichev S.  Semilattices of Punctual Numberings. In: Chen, J., Feng, Q., Xu, J. (eds) Theory and Applications of Models of Computation. TAMC 2020. Lecture Notes in Computer Science(), vol 12337. Springer, Cham. https://doi.org/10.1007/978-3-030-59267-7_1.

15.  N. Bazhenov, M. Mustafa, L.S.Mauro, M. Yamaleev. Minimal Equivalence Relations in Hyperarithmetical and Analytical Hierarchies. Lobachevskii J Math 41, 145–150 (2020). https://doi.org/10.1134/S199508022002002X.

16.  N. Bazhenov, M. Mustafa, L.S.Mauro, M. Yamaleev, and A. Sorbi. Classifying equivalence relations in the Ershov hierarchy. Arch. Math. Logic 59, 835–864 (2020). https://doi.org/10.1007/s00153-020-00710-1 

17.  A.O. Basheyeva, M. Mustafa, A.M.Nurakunov.  Properties not retained by pointed enrichments of finite lattices. Algebra Univers. 81, 56 (2020). https://doi.org/10.1007/s00012-020-00692-4.

18.  N.Bazhenov ,M. Mustafa, S.Ospichev  , M.Yamaleev. Numberings in the analytical hierarchy. Algebra Logic 59, 404–407 (2020). https://doi.org/10.1007/s10469-020-09613-9.

19.  N.Bazhenov, M.Mustafa, S.Ospichev, On the universal pairs in the Ershov hierarchy.  Siberian Mathematical Journal, 62, 23-31 (2021). https://doi.org/10.1134/S0037446621010031.

20.  A.Kashkynbayev, M.Mustafa.  Basic Theory of Impulsive Quaternion-Valued Linear Systems. In: Ashyralyev, A., Kalmenov, T.S., Ruzhansky, M.V., Sadybekov, M.A., Suragan, D. (eds) Functional Analysis in Interdisciplinary Applications—II. ICAAM 2018. Springer Proceedings in Mathematics  Statistics, vol 351.(2021), Springer, Cham. https://doi.org/10.1007/978-3-030-69292-6_21.

21.  M.Mustafa, D.Suragan. Hardy type inequalities for quaternion-valued functions.V18, N1. Page 338-344 (2021) DOI 10.33048/semi.2021.18.023.

22.  N.Bazhenov, M.Mustafa, S.Ospichev, L.S.Mauro. Approximating Approximate Reasoning: Fuzzy Sets and the Ershov Hierarchy. In: Ghosh, S., Icard, T. (eds) Logic, Rationality, and Interaction. LORI 2021. Lecture Notes in Computer Science, vol 13039. Springer, Cham. https://doi.org/ 10.1007/978-3-030-88708-7_1.

23.  N.Bazhenov, , M.Mustafa, Z.Tleuliyeva. Theories of Rogers Semilattices of Analytical Numberings. Lobachevskii J Math 42, 701–708 (2021). https://doi.org/10.1134/S1995080221040065.

24.  S.A.Badaev, B.S.Kalmurzaev, N.Mukash, M.Mustafa,. One-Element Rogers Semilattices in the Ershov Hierarchy. Algebra Logic 60, 284–287 (2021). https://doi.org/10.1007/s10469-021-09653-9.(Translated from Algebra i Logika, Vol. 60, No. 4, pp. 433-437, July-August, 2021. Russian DOI: https://doi.org/10.33048/alglog.2021.60.404.)

25.  N.Bazhenov, M.Mustafa,  S.Ospichev. Rogers semilattices of punctual numberings. Mathematical Structures in Computer Science, 1-25.(2022)  doi:10.1017/S0960129522000093.

26.  N.Ismailov, I.Kaygorodov, M.Mustafa. The algebraic and geometric classification of nilpotent right alternative algebras, Period Math Hung 84, 18–30 (2022). https://doi.org/10.1007/s10998-021-00386-x.

27.  U.Andrews, S.Lempp, M.Mustafa, N.D.Schweber. The first-order theory of the computably enumerable equivalence relations in the uncountable setting, Journal of Logic and Computation,  Journal of Logic and Computation, Volume 32, Issue 1, January 2022, Pages 98–114, https://doi.org/10.1093/logcom/exab045.

28.  A.O.Basheyeva, M.Mustafa,   A.M.Nurakunov. Identities and Quasi-Identities of Pointed Algebras. Sib Math J 63, 197–205 (2022). https://doi.org/10.1134/S003744662202001X.

29.  N.Bazhenov, M.Mustafa, and Z.Tleuliyeva. Rogers semilattices of limitwise monotonic numberings. Math. Log. Quart., 68: 213-226. https://doi.org/10.1002/malq.202100077.

30.  N.Bazhenov, M.Mustafa.Computable embeddability for algebraic structures. Asian-European Journal of Mathematics. Volume No. 15, Issue No. 07, Article No. 2250126, Year 2022. https://doi.org/10.1142/S1793557122501261, World Scientific Publishing Co.

31.  N.Bazhenov, M.Mustafa. Rogers semilattices in the analytical hierarchy: the case of finite families. Accepted to XVI ALC. proceedings.

32.  N. Bazhenov, M. Mustafa, A.M. Nurakunov, On Two Types of Concept Lattices in the Theory of Numberings. In: Du, DZ., Du, D., Wu, C., Xu, D. (eds) Theory and Applications of Models of Computation. TAMC 2022. Lecture Notes in Computer Science, vol 13571. Springer, Cham. https://doi.org/10.1007/978-3-031-20350-3_8  

33. N.Bazhenov, M.Mustafa, S.Ospichev, L.S.Mauro. How to approximate fuzzy sets: mind-changes and the Ershov Hierarchy. Synthese 201, 55 (2023). https://doi.org/10.1007/s11229-023-04056-y  

34. Bekjan, T.N., Mustafa, M. Dominated convergence theorems in Haagerup noncommutative Lp-spaces. Adv. Oper. Theory 8, 34 (2023). https://doi.org/10.1007/s43036-023-00261-1

35. A.A. Mikhalev, M.Mustafa, U.Umirbaev,Representations via differential algebras and equa- tionally Noetherian algebras, Journal of Algebra,Volume 633,2023,Pages 814-830,ISSN 0021- 8693,https://doi.org/10.1016/j.jalgebra.2023.07.008.

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3. Scopus.

4.Web of Science™

Research Grants: 

1. NU Social policy Grant. 2015-2016

2. NU Faculty Development Competitive Research Grants  2018-2020.

3. NU Faculty Development Competitive Research Grants  2021-2023.