Dr. Mahenthiram Arunmaran

Arunmaran

Dr. Mahenthiram Arunmaran

BSc [Hons] (Jaffna), PhD (UniSA, Australia)

 

  • Lecturer in Mathematics
  • marunmaran03@gmail.com
  • 0094-755913640
Google Scholar
  • B.Sc (Hons) in Mathematics (University of Jaffna, Sri Lanka, 2017).
  • PhD in Mathematics (University of South Australia, Australia, 2023) 
  • Member of Australian Mathematical Society (2020 to date)

Professor Chellapah Suntharalingam Gold Medal in Mathematics.

  • Awarded for the best performance in Mathematics course units at the Special degree examination in Science for the years 2014 and 2015.

Sir Arunachalam Mahadeva Memorial Prize in Mathematics.

  • Awarded for the best performance in Mathematics in the Special Degree Examination in Science in 2015.

University Prizes.

  • Awarded for the best performance in physical science at the General Degree Examination in Science Level-2G, 2013.

Awarded Pradeepan Jeganathan Memorial Scholarship for the best performance in Math- ematics course units for Level-1G and Level-2G for the academic year 2013/2014.

Oral presentations 

  • New ℎ-functions and 𝑔-functions of simply connected regions, 66th Annual Conference of the Australian Mathematical Society, UNSW Sydney (2022).
  • Harmonic-measure distribution functions (ℎ-functions) of polygonal regions, 𝑔-functions, UniSA STEM graduate research day, University of South Australia (2022).
  • The harmonic-measure distribution functions of multiply connected regions, 65th Annual Conference of the Australian Mathematical Society, University of Newcastle (2021). 
  • The harmonic-measure distribution functions (ℎ-functions) of regions with many holes, UniSA STEM graduate research day, University of South Australia (2021).
  • Discussion on the relationships between semicontinuity in bitopological spaces and topological spaces, WinC-2018, Wayamba University of Sri Lanka. 
  •  Results related with semi compactness in Bitopological Spaces, VIRC-2018, University of Jaffna, Sri Lanka. 
  •  Results of τ1τ2 ´ δ semi compactness in bitopological spaces, iPURSE-2017, University of Per- adeniya, Sri Lanka. 
  •  Study on τ1τ2 ´ δ semi connectedness in bitopological spaces, IntSym-2017, South Eastern Uni- versity of Sri Lanka. 
  • PMM303G3 – Discrete and Combinatorial Mathematics (2023)
  • MMT407M3 – Numerical Solutions of Differential Equations (2023)
  • Limit Process (2019) 
  • Discrete and Combinatorial Mathematics (2023,2024,2025,2026) 
  • Foundations of Mathematics (2024,2025) 
  • Classical Mechanics (2024,2025) 
  • Numerical Differential Equations (2023,2024,2025) 
  • Topology II (2024,2025)
  • Topology I (2025)
  • Linear Algebra (2025)

  • Conference Organiser:

    An organiser of the MATRIX Applied and Computational Complex Analysis Workshop (24—28 August 2026)

  • Abstracts in Conference Proceedings:

     

    1.     P. Piriyalucksan and M. Arunmaran, Fuzzy semi-h-open sets in fuzzy
    topological spaces and their properties, (Ristcon 2026), Ruhuna University of
    Sri Lanka.

     

    2.     M. Arunmaran, S. Umadevi and K. Kannan, A study on fuzzy pre β-continuous
    functions in Fuzzy Topological Spaces, (Ristcon 2026), Ruhuna University of Sri
    Lanka.

     

    3.     M. Arunmaran  and P. Piriyalucksan, Computing h-function of the complement of a slit via parallel-slit mapping and validation via different
    methods    , (ICMME 2025), University of Peradeniya, Sri Lanka.

     

    4.     M. Arunmaran, P. Sachivathanan and K. Kannan, RESULTS ON VARIOUS CLOSED SETS IN BI-GENERALISED TOPOLOGICAL SPACES, (ICMME 2025), University of
    Peradeniya, Sri Lanka.

     

    5.     M. Arunmaran and P. Piriyalucksan, Investigating harmonic-measure distribution function of the exterior of a wedge domain with a deleted ray, (TASME 2025), University of Toronto, Canada.

     

    6.     M. Arunmaran and P. Piriyalucksan, Some properties of fuzzy h-open sets in
    fuzzy topological spaces, (iPURSE 2025), University of Peradeniya, Sri Lanka.

     

    7.     M. Arunmaran, S. Umadevi and K. Kannan, Study on 𝛽-Open Sets in Fuzzy Topological Spaces, (iPURSE 2025), University of Peradeniya, Sri Lanka.

     

    8.     M. Arunmaran and P. Piriyalucksan, New types of fuzzy open sets in bi-fuzzy topological spaces, (ICAPS 2025), University of Kaleniya, Sri Lanka.

     

    9.     M. Arunmaran, P.Sachivathanan and K.Kannan, Different Types of (m,n)-Open Sets in bi-Generalised Topological Spaces, (ARS 2025), Eastern University of Sri Lanka.

     

    10.  M. Arunmaran and P. Piriyalucksan, TWO TYPES OF BI-FUZZY OPEN SETS IN BI-FUZZY TOPOLOGICAL SPACES AND THEIR PROPERTIES, (RESCON 2025), University of Peradeniya, Sri Lanka.

     

    11.  P. Piriyalucksan and M. Arunmaran, ∆-OPEN SETS AND δ-SEMI CLOSED SETS IN FUZZY TOPOLOGICAL SPACES, (IRCOUSL 2025), Open University of Sri Lanka.

     

    12.  P. Piriyalucksan and M. Arunmaran, Computing h-function of the plane with a deleted line segment, with and without using the prime function, (IRCOUSL 2025), Open University of Sri Lanka.

     

    13.  M. Arunmaran, Computing ℎ-function of a doubly connected unbounded region formed by  deleting double slits from the right halfplane, Proceedings of International Conference on  multidisciplanary research (ICMR 2024), Eastern University of Sri Lanka, Sri Lanka, 23rd  January 2024.

     

    14.  M. Arunmaran, Computing the harmonic-measure distribution function of two unequal discs connected with a common line segment, Proceedings of Young Scientists Conference on Multidisciplinary Research (YSCMR 2024), National
    Institute of Fundamental Studies,     Kandy, Sri Lanka, 27th November 2024.

     

    15.  M. Arunmaran, Agreement of h-functions obtained via different conformal
    maps,  Proceedings of Faculty Annual Research Session 2024, Faculty of Applied Science (FARS 2024), University of Vavuniya, Sri Lanka, 30th October 2024.

     

    16.  M. Arunmaran, Computing ℎ-function of doubly connected region formed by deleting a slit from the unit disc, Proceedings of International Conference on Mathematics and Mathematics Education (ICMME 2023), Postgraduate Institute of Science, University of Peradeniya, Sri Lanka, 5th July 2023.

     

    17.  M. Arunmaran, Study on ℎ-function of a bounded simply connected region: Disc with deleted double slits, Proceedings of Research Congress (RESCON 2023), Postgraduate Institute of Science, University of Peradeniya, Sri Lanka, 4th November 2023.

     

    18.  M. Arunmaran, Computing ℎ-function of doubly connected unbounded region formed by  deleting a lollipop along with a slit in the complex plane, Proceedings of International  Conference of Sabragamuwa University (ICSUSL 2023), Sabaragamuwa University of Sri  Lanka, Sri Lanka, 6-8 December 2023.

     

    19.  M. Arunmaran, New ℎ-functions and g-functions of simply connected regions, Proceedings of 66th Annual Conference of the Australian Mathematical Society, UNSW Sydney (2022), 5-9 Dec 2022.

     

    20.  M. Arunmaran, The harmonic-measure distribution functions of multiply connected regions, Proceedings of 65th Annual Conference of the Australian
    Mathematical Society    , University of Newcastle (2021), 6-9 Dec 2021. 

  • Full paper in Conference Proceedings:

     1.     M.Arunmaran and P. Piriyalucksan, Cross-check the harmonic-measure distribution function of the plane with a deleted line segment via radial-slit mapping and Joukowski mapping, (ICAPS 2025), University of Kaleniya, Sri Lanka.

     2.     P.Piriyalucksan and M. Arunmaran, g-function and h-function of the
    complement of a slit, (ICAS 2025), Vavuniya University of Sri Lanka.

     3.     P.Piriyalucksan and M. Arunmaran, Computing h-function of the plane with a deleted line segment, with and without using the prime function, (IRCOUSL 2025), Open University of Sri Lanka.

     4.     P.Piriyalucksan and M. Arunmaran, ∆-OPEN SETS AND δ-SEMI CLOSED SETS IN FUZZY TOPOLOGICAL SPACES, (IRCOUSL 2025), Open University of Sri Lanka. 

  • Manuscripts in-preparation:

    1.     C.C.Green, A. Mahenthiram, and L.A. Ward, Constructive solution of the inverse
    problem  for harmonic-measure distribution functions that are step functions. In preparation.

     2.     A.Mahenthiram, B.L. Walden, and L.A. Ward, Existence and Non-existence of Harmonic-measure distribution functions for  new planar simply connected regions. In preparation.

     3.     A.Mahenthiram, B.L. Walden, and L.A. Ward, Harmonic-measure distribution functions for  new planar simply connected regions, and behaviour of their derivatives. In preparation.

     4.     A.Mahenthiram, B.L. Walden, and L.A. Ward. Stephenson’s g-function
    for simply connected planar domains. In preparation. 


  • Journal Publications

    1. A. Mahenthiram and P. Paramesvarampillai, Study on special features of new ℎ-functions of some simply connected planar regions, Journal of Acta Mathematica Vietnamica, 2026.

    2.A. Mahenthiram and P. Paramesvarampillai, Computing new ℎ-functions of several unbounded planar regions and  validating the ℎ-functions via different methods, Journal of Ramanujan Mathematical  Society, 2026, 18pages.

    3.A. Mahenthiram. Computing harmonic-measure distribution functions of some multiply connected unbounded planar domains, Journal of Mathematical Analysis and Applications, 547(1), PaperID: 129291, 2025. https://doi.org/10.1016/j.jmaa.2025.129291.

     

    4.A. Mahenthiram and P. Parameswarampillai. Computing harmonic-measure distribution functions of some planar doubly connected regions, Annales Polonici
    Mathematici, 134(2)    :187-206, 2025 . DOI: 10.4064/ap240724-12-4

     

    5. A. Mahenthiram. New harmonic-measure distribution functions of some simply connected planar regions in the complex plane. Revista de la Unión Matemática Argentina, 68(2): 459-483, 2025. https://doi.org/10.33044/revuma.4038

     

    6. C. C. Green, A. Mahenthiram & L. A. Ward. Harmonic-measure distribution
    functions of multiply connected domains with various geometries. Proc. R. Soc. A., 481(2321), Paper No. 20240392, 2025. https://doi.org/10.1098/rspa.2024.0392

     

    7.A. Mahenthiram. Harmonic-measure distribution functions of simply connected and doubly connected polygonal domains, Journal of Mathematical Analysis and
    Applications    , 537(1), Paper ID: 128308, 2024. https://doi.org/10.1016/j.jmaa.2024.128308.

     

    8.A. Mahenthiram, Harmonic-measure Distribution Functions and Related Functions of Simply  Connected and Multiply Connected Two-Dimensional Regions, Bulletin of the Australian  Mathematical Society. 2024;109(1):163-164. doi:10.1017/S0004972723000990

     

    9. A. Mahenthiram. Computing h-functions of some planar simply connected
    two-dimensional regions, Taiwanese Journal of Mathematics, 27(5):931-952, 2023. DOI: 10.11650/tjm/230704.

     

    10.M. Arunmaran and K.Kannan. Semicontinuity, Semiconnected and Semicompactness in bitopological spaces, Communications in Mathematics and Applications, 13(3): 843-850, 2022. DOI: 10.26713/cma.v13i3.1859

     

    11. M.Arunmaran and K.Kannan. Some results of τ1τ2− δ semiconnectedness
    and compactness in bitopological spaces, Journal of Mathematics, 2018(1): Paper ID: 7863713, 2018.     https://doi.org/10.1155/2018/7863713

     

    12. M.Arunmaran and K.Kannan. Some results of τ1τ2− δ semiconnectedness
    and compactness in bitopological spaces, Journal of Mathematics, 2018(1): Paper ID: 7863713, 2018.     https://doi.org/10.1155/2018/7863713

     

     13. M. Arunmaran and K.Kannan. Some properties of τ1τ2 − δ semi open sets/ closed sets in 1τ2 – δ bitopological spaces, International Journal of Pure and Applied Mathematics, 115(4):759-769, 2017. 10.12732/ijpam.v115i4.9

     

    14. A. Mahenthiram and K. Kannan, Some results related with Fuzzy α-normed linear space,  Journal of Advances in Mathematical Sciences, Knowvel, UK, Volume 1(2019), 11-12.

     

    15. A. Mahenthiram and K. Kannan, Discussion on Quotient bi-space and pairwise regular and  normal spaces in bitopological spaces, Journal of Advances in Mathematical Sciences, Knowvel, UK, Volume 1(2019), 13-15. 

  • Green, C.C., Mahenthiram, A. and Ward, L.A. Harmonic-measure distribution functions of multiply connected regions with various geometries. Manuscript in preparation.
  • Mahenthiram, A., Walden, B.L. and Ward, L.A. Discussing ℎ-functions of several planar simply connected regions. Manuscript in preparation.
  • Mahenthiram, A., Walden, B.L. and Ward, L.A. Results on Stephenson’s 𝑔-function. Manuscript in preparation.
  • Mahenthiram, A. Harmonic-measure distribution functions of simply connected and doubly connected polygonal regions. Manuscript in preparation.

2023

  • Mahenthiram, A. Computing ℎ-function of doubly connected region formed by deleting a slit from the unit disc, (Accepted) Proceedings of International Conference on Mathematics and Mathematics Education (ICMME 2023), PGIS, University of Peradeniya, Sri Lanka.
  • Mahenthiram, A. Computing ℎ-functions of some planar simply connected two-dimensional regions, Taiwanese Journal of Mathematics. (Submitted)
  • Mahenthiram, A. New harmonic-measure distribution functions of some simply connected planar regions, Journal of Revista de la Union Mathematica Argentina. (Submitted)
  • Mahenthiram, A. Study on ℎ-function of a bounded simply connected region: Disc with deleted double slits, (Submitted) (RESCON 2023), PGIS, University of Peradeniya, Sri Lanka.

2022

  • Mahenthiram, A. New ℎ-functions and 𝑔-functions of simply connected regions, Proceedings of 66th Annual Conference of the Australian Mathematical Society, UNSW Sydney (2022).

2021

  • Mahenthiram, A. The harmonic-measure distribution functions of multiply connected regions, Proceedings of 65th Annual Conference of the Australian Mathematical Society, University of Newcastle (2021).

2019

  • M.Arunmaran and K.Kannan, “Discussion on Quotient bi-space and on pairwise regular and normal spaces in Bitopological spaces, Journal of Advances in Mathematical Sciences, Knowvel Vol-01, pp.13-15, (2019).

  • M.Arunmaran and K.Kannan , “Some results related with Fuzzy α-normed linear space”, Journal of Advances in Mathematical Sciences, Knowvel Vol.1, pp.11-12, (2019).

2018

  • M.Arunmaran and K.Kannan, “Some results of τ1τ2 ´ δ semi connectedness and com- pactness in bitopological spaces”, Journal of Mathematics, (2018).

2017

  • M.Arunmaran and K.Kannan , “Some Properties of τ1τ2 ´ δ  Semi Open Sets/Closed Sets In Bitopological Spaces”, International Journal of Pure and Applied Mathematics, Vol 115, No. 4, pp. 759-770, (2017).
  • M.Arunmaran and K.Kannan, “Some results in Bitopological Spaces”, Mathematical Sci- ences International Research Journal , Vol 6, No. 2, pp.18-20, (2017).

Abstracts in Conference Proceedings.

2018

  • M.Arunmaran and K.Kannan, “Discussing the relationships between semicontinuity in bitopological spaces and topological spaces”, Proceddings of WinC-2018, Wayamba Uni- versity of Sri Lanka.
  • M.Arunmaran and K.Kannan, “Some Results related with semi compactness in Bitopo- logical Spaces”, Proceedings of VIRC-2018, University of Jaffna, Sri Lanka, p7.

2017

  • Some results of τ1τ2 ´δ semi compactness in bitopological spaces, Proceedings of iPURSE- 2017, University of Peradeniya, Sri Lanka.
  • τ1τ2 ´ δ semi connectedness in bitopological spaces, proceedings of IntSym-2017, South Eastern University of Sri Lanka, p25, (2017).

Commonwealth Funded Scholarship

  • Awarded Commonwealth funded Australian Government Research Training Program (RTP) Scholarship to follow PhD program at the University of South Australia in 2019.