Mohd Ibrahim Sheikh

@spechyd.ac.in

H&S Department/Mathematics
Saint Peters Engineering College, Maisammagudda, Hyderabad

Mohd Ibrahim Sheikh


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https://researchid.co/ibrahimsheikh
Ibrahim was born and grew up in Goom Ahmad Pora, a beautiful village in northern Kashmir (Jammu and Kashmir), India. He did his schooling until 8th standard, from a local school, Govt. Boys Middle School, Goom Ahmad Pora and then afterwards studied at a nearby higher secondary school, Govt. Higher Secondary School, Magam (Budgam), where he finished his secondary and higher secondary education. He did his bachelors of science (BSCN) from Govt. Degree College, Bemina, Srinagar (University of Kashmir.

EDUCATION

Ph.D, MSc, B.Ed, BSc

RESEARCH, TEACHING, or OTHER INTERESTS

Geometry and Topology, Analysis, Algebra and Number Theory, Computational Mathematics
8

Scopus Publications

23

Scholar Citations

3

Scholar h-index

Scopus Publications

  • Oriented disingquandles and invariants of oriented dichromatic singular links
    Mohd Ibrahim Sheikh, Mohamed Elhamdadi, Danish Ali
    Journal of Knot Theory and Its Ramifications, 2026
    In this paper, we introduce and investigate oriented dichromatic singular links. We also introduce oriented disingquandles and use them to define counting invariants for oriented dichromatic singular links. We provide some examples to show that these invariants distinguish some oriented dichromatic singular links.
  • A new unknotting operation for classical and welded knots
    Danish Ali, Zhiqing Yang, Mohd Ibrahim Sheikh, Sidra Batool
    Boletin De La Sociedad Matematica Mexicana, 2025
  • Dibiquandle coloring invariants for dichromatic links and associated di(bi)quandles
    Jieon Kim, Sang Youl Lee, Mohd Ibrahim Sheikh
    Topology and Its Applications, 2025
  • Presentations of diquandles and diquandle coloring invariants for solid torus knots and links
    Jieon Kim, Sang Youl Lee, Mohd Ibrahim Sheikh
    Journal of Knot Theory and Its Ramifications, 2024
    A diquandle is a set equipped with two quandle operations interacting via a kind of distributive laws which come from Reidemeister moves on dichromatic links. This algebraic systems provide coloring invariants for dichromatic links. In this paper, we give explicit constructions of free diquandles and diquandle presentations, and then discuss Tietze transformations for the diquandle presentations. We also introduce the fundamental diquandles for dichromatic links. Particularly, we describe the fundamental diquandles and diquandle counting invariants for knots and links in the solid torus via annulus diagrams. We append the tables of diquandles and dikei’s of orders [Formula: see text].
  • Disingquandles and invariants of dichromatic singular links
    Mohd Ibrahim Sheikh, Mohamed Elhamdadi, Danish Ali
    Journal of Knot Theory and Its Ramifications, 2023
    We introduce and investigate dichromatic singular links. We also construct disingquandles and use them to define counting invariants for unoriented dichromatic singular links. We provide some examples to show that these invariants distinguish some dichromatic singular links.
  • The H (n) -move is an unknotting operation for virtual and welded links
    Danish Ali, Zhiqing Yang, Abid Hussain, Mohd Ibrahim Sheikh
    Journal of Knot Theory and Its Ramifications, 2023
    An unknotting operation is a local move such that any knot diagram can be transformed into a diagram of the trivial knot by a finite sequence of these operations plus some Reidemeister moves. It is known that for all [Formula: see text] the [Formula: see text]-move is an unknotting operation for classical knots and links. In this paper, we extend the classical unknotting operation [Formula: see text]-move to virtual knots and links. Virtualization and forbidden move are well-known unknotting operations for virtual knots and links. We also show that virtualization and forbidden move can be realized by a finite sequence of generalized Reidemeister moves and [Formula: see text]-moves.
  • Diquandles and invariants for oriented dichromatic links
    Sang Youl Lee, Mohd Ibrahim Sheikh
    Journal of Knot Theory and Its Ramifications, 2021
    In this paper, we introduce an algebraic structure called a diquandle which is a set equipped with two quandle operations satisfying the right distributive laws. We discuss various examples and some properties of diquandles and also show that a diquandle enables us to distinguish oriented dichromatic links by telling that their coloring sets are different when their arcs are colored by elements of the diquandle.
  • Some Upper Bound Estimates for the Maximal Modulus of the Polar Derivative of a Polynomial
    A. Mir, M. Ibrahim Sheikh
    Journal of Contemporary Mathematical Analysis, 2020
    This paper deals with the problem of finding some upper bound estimates for the maximal modulus of the polar derivative of a complex polynomial on a disk under certain constraints on the zeros and on the functions involved. A variety of interesting results follow as special cases from our results.

RECENT SCHOLAR PUBLICATIONS

  • Oriented Disingquandles and Invariants of Oriented Dichromatic Singular Links
    MI Sheikh, M Elhamdadi, D Ali
    Journal of Knot Theory and Its Ramifications , 2026
    2026
  • A new unknotting operation for classical and welded knots: D. Ali et al.
    D Ali, Z Yang, MI Sheikh, S Batool
    Boletín de la Sociedad Matemática Mexicana 31 (3), 134 , 2025
    2025
  • Dibiquandle coloring invariants for dichromatic links and associated di (bi) quandles
    J Kim, SY Lee, MI Sheikh
    Topology and its Applications 371, 109358 , 2025
    2025
    Citations: 3
  • A new unknotting operation for classical and welded knots
    D Ali, Z Yang, MI Sheikh, S Batool
    Boletín de la Sociedad Matemática Mexicana: Tercera Serie 31 (3), 40 , 2025
    2025
  • Presentations of diquandles and diquandle coloring invariants for solid torus knots and links
    J Kim, SY Lee, MI Sheikh
    Journal of Knot Theory and Its Ramifications 33 (02), 2350102 , 2024
    2024
    Citations: 3
  • Disingquandles and invariants of dichromatic singular links
    MI Sheikh, M Elhamdadi, D Ali
    Journal of Knot Theory and Its Ramifications 32 (12), 2350076 , 2023
    2023
    Citations: 2
  • The -move is an unknotting operation for virtual and welded links
    D Ali, Z Yang, A Hussain, MI Sheikh
    Journal of Knot Theory and Its Ramifications 32 (09), 2350061 , 2023
    2023
    Citations: 3
  • A G-Family of Singquandles and Invariants of Dichromatic Singular links
    MI Sheikh, M Elhamdadi, D Ali
    arXiv preprint arXiv:2301.03792 , 2023
    2023
  • A G-Family of Singquandles and Invariants of Dichromatic Singular links
    DA Mohd Ibrahim Sheikh, Mohamed Elhamdadi
    arXiv preprint arXiv:2301.03792 , 2023
    2023
  • A new unknotting operation for classical and welded links
    D Ali, Z Yang, MI Sheikh
    arXiv preprint arXiv:2208.08761 , 2022
    2022
    Citations: 1
  • Diquandles and invariants for oriented dichromatic links
    SY Lee, MI Sheikh
    Journal of Knot Theory and Its Ramifications 30 (07), 2150049 , 2021
    2021
    Citations: 9
  • Some upper bound estimates for the maximal modulus of the polar derivative of a polynomial
    A Mir, M Ibrahim Sheikh
    Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences … , 2020
    2020
    Citations: 2
  • On The Maximum Modulus of a Polynomial
    BI Dar, M Abdullah, QM Dawood, MI Shiekh, MA Ali
    Chitkara University Publications , 2015
    2015

MOST CITED SCHOLAR PUBLICATIONS

  • Diquandles and invariants for oriented dichromatic links
    SY Lee, MI Sheikh
    Journal of Knot Theory and Its Ramifications 30 (07), 2150049 , 2021
    2021
    Citations: 9
  • Dibiquandle coloring invariants for dichromatic links and associated di (bi) quandles
    J Kim, SY Lee, MI Sheikh
    Topology and its Applications 371, 109358 , 2025
    2025
    Citations: 3
  • Presentations of diquandles and diquandle coloring invariants for solid torus knots and links
    J Kim, SY Lee, MI Sheikh
    Journal of Knot Theory and Its Ramifications 33 (02), 2350102 , 2024
    2024
    Citations: 3
  • The -move is an unknotting operation for virtual and welded links
    D Ali, Z Yang, A Hussain, MI Sheikh
    Journal of Knot Theory and Its Ramifications 32 (09), 2350061 , 2023
    2023
    Citations: 3
  • Disingquandles and invariants of dichromatic singular links
    MI Sheikh, M Elhamdadi, D Ali
    Journal of Knot Theory and Its Ramifications 32 (12), 2350076 , 2023
    2023
    Citations: 2
  • Some upper bound estimates for the maximal modulus of the polar derivative of a polynomial
    A Mir, M Ibrahim Sheikh
    Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences … , 2020
    2020
    Citations: 2
  • A new unknotting operation for classical and welded links
    D Ali, Z Yang, MI Sheikh
    arXiv preprint arXiv:2208.08761 , 2022
    2022
    Citations: 1
  • Oriented Disingquandles and Invariants of Oriented Dichromatic Singular Links
    MI Sheikh, M Elhamdadi, D Ali
    Journal of Knot Theory and Its Ramifications , 2026
    2026
  • A new unknotting operation for classical and welded knots: D. Ali et al.
    D Ali, Z Yang, MI Sheikh, S Batool
    Boletín de la Sociedad Matemática Mexicana 31 (3), 134 , 2025
    2025
  • A new unknotting operation for classical and welded knots
    D Ali, Z Yang, MI Sheikh, S Batool
    Boletín de la Sociedad Matemática Mexicana: Tercera Serie 31 (3), 40 , 2025
    2025
  • A G-Family of Singquandles and Invariants of Dichromatic Singular links
    MI Sheikh, M Elhamdadi, D Ali
    arXiv preprint arXiv:2301.03792 , 2023
    2023
  • A G-Family of Singquandles and Invariants of Dichromatic Singular links
    DA Mohd Ibrahim Sheikh, Mohamed Elhamdadi
    arXiv preprint arXiv:2301.03792 , 2023
    2023
  • On The Maximum Modulus of a Polynomial
    BI Dar, M Abdullah, QM Dawood, MI Shiekh, MA Ali
    Chitkara University Publications , 2015
    2015