Rehana Naz

Professor, Department of Mathematics & Statistical Sciences

Dr. Naz is a Professor of Mathematics at the Lahore School of Economics, Lahore, Pakistan. She received the M.Sc and M.Phil degrees in Applied Mathematics from Quaid-i-Azam University, Islamabad in 2002 and 2004 and the Ph.D. degree from the University of Witwatersrand, Johannesburg, South Africa in 2008. She was awarded a short-term Post-Doctoral Fellowship from the University of the Witwatersrand, South Africa. Dr. Naz is actively engaged in research, teaching, and academic service. She received the Research Productivity Award from Pakistan Council for Science and Technology in 2012 and was honored with the Best University Teacher Award by Higher Education Commission in Feb 2018.

Dr. Naz has made significant contributions to the subject, her peers and students, the department, the university, and academic and the research community. She has significantly contributed to the designing of several new courses at the Lahore School of Economics. Her teaching portfolio includes Linear Algebra, Calculus, Advanced Calculus, Real Analysis, Mathematical Economics I & II at the undergraduate level, and Mathematical Economics in the M. Phil Economics program. She actively contributed, along with other colleagues from the department, to the development of several minor programs in mathematics and data analytics, launched in 2020. Notably, she played a pivotal role in the development of the BS Double Major in Economics and Mathematics degree program, launched in 2021.

Dr. Naz served on the National Curriculum Revision Committee (NCRC) of the Higher Education Commission (HEC) for curriculum development of BS, MS, and Ph.D. Mathematics. She has been an active member of the Department’s curriculum committee, Board of Studies (BOS), Board of Faculties (BOF), and the academic committee of Lahore School of Economics since October 2009. Dr. Naz is tasked with attending peers' lectures and providing feedback on effective approaches to teaching mathematics. For the faculty at the Lahore school, she has led several training courses on using technology in the classroom, including Zoom, Maple, Python, Latex, Overleaf, Endnote, Mendeley, and the learning management system of the Lahore School of Economics. She is a reviewer of top Impact factor Journals including Journals published by Sciencedirect, Springer link, Taylor and Francis, IOP. Dr. Naz has worked as the guest editor of many international journals and is working as the Academic Editor of International Journal PLOS ONE. Dr. Naz has presented and worked as an organizer in the several national and international conferences. She was a member of organizing committee of the First Annual Conference on “Mathematical and Statistical Models in Economics, Finance and Applied Sciences” held on February 6-7, 2015 at the Main Campus of Lahore School of Economics. Dr. Naz has organized special sessions in International Conference on Dynamical systems, Differential equations and applications of American institute of Mathematical sciences, held in (Madrid, Spain 7-11 July 2014), (Orlando, Florida, USA 1-5 July 2016), (Taiwan, Taipe 5-9 July 2018) and ( Wilmington, NC USA, May 31 - June 4, 2023).

Dr. Naz has expertise in applying Lie group methods to optimal control theory, calculus of variations, and dynamical systems. She has applied these techniques to a variety of problems arising from physical, biological, and economic phenomena. In her PhD thesis she developed a new theory of constructing conserved quantities for jet flows using conservation laws which is cited by several authors. Most of her research papers have been published in top-ranked world-class journals. She has active research collaboration with professors at leading universities in the USA, UK, Germany, Canada, Italy, Spain, Brazil, Nigeria, and South Africa. Dr. Naz jointly with Dr. Azam Chaudhry and Dr. Fazal Mahomed developed a novel method known as the partial Hamiltonian method for the construction of first integrals for optimal control problems arising in economic growth theory. Closed-form solutions, analyses of the growth rates of capital and consumption, and discussions of saving rates are offered for many celebrated economic growth models to aid policymakers in developing policies. Dr. Naz has supervised several M.Phil Economics students jointly with the leading economist Dr. Azam Chaudhry.

CV

    Dr. Naz has published 62 papers in well-reputed international journals indexed in the Web of Science. Her recent publications include.

    1. R. Naz, M. Torrisi, The first integrals and closed-form solutions of a Susceptible-Exposed-Infectious epidemic model, Mathematical Models in the Applied Sciences, 46 (4), 4352-4362 (2023).
    2. R. Naz, M. Torrisi, Symmetry methods for a hyperbolic model for a class of populations. Applied Mathematics and Computation, 439, 127640 (2023).
    3. R. Naz, M. Torrisi,  The Transmission Dynamics of a Compartmental Epidemic Model for COVID-19 with the Asymptomatic Population via Closed-Form Solutions. Vaccines, 10(12), 2162 (2022)
    4. R. Naz, A current-value Hamiltonian approach to discrete-time optimal control problems in economic growth theory. Journal of Difference Equations and Applications, 28(1), 109-119 (2022).
    5. 5. R. Naz, M. Al-Raeei, Analysis of transmission dynamics of COVID-19 via closed-form solutions of a susceptible-infectious-quarantined-diseased model with a quarantine-adjusted incidence function, Mathematical Methods in the Applied Sciences 44(14), 11196-11210, (2021).
    6.  R. Naz, F. M. Mahomed, Hamiltonian symmetry classification, integrals, and exact solutions of a generalized Ermakov system, Mathematical Methods in the Applied Sciences 44 (6) 4467-4478 (2021).
    7.  A. F. Cheviakov, C. Lee,  R. Naz, Radial waves in fiber-reinforced axially symmetric hyperelastic media Communications in Nonlinear Science and Numerical Simulation 95, art. no. 105649 (2021)
    8.  R. Naz, Noether-type Hamiltonian symmetry classification, first integrals and exact solutions of two classes of the generalized Ermakov’s systems, The European Physical Journal Plus 135 (8), art. No 641 (2020)
    9. R. Naz, On Sufficiency issues, First integrals and Exact solutions of Uzawa-Lucas model with unskilled labor, Discrete & Continuous Dynamical Systems - Series S 13(10):  2813-2828 (2020)
    10. R. Naz, F. M. Mahomed, Approximate Hamiltonian symmetries and related first integrals, International Journal of Non-Linear Mechanics 125,103547 (2020)
    11. R. Naz, F. M. Mahomed and A. Chaudhry, First Integrals of Hamiltonian Systems: the Inverse Problem, Discrete & Continuous Dynamical Systems - Series S 13(10):  2829-2840 (2020)
    12. R. Naz, The closed-form solutions for finance-extended Lucas-Uzawa model, Computational and Applied Mathematics 39 (2), art. no. 101 (2020)
    13. R. Naz and I. Naeem, The exact solutions of Black-Scholes model with time-dependent parameters by utilizing potential symmetries, , Discrete & Continuous Dynamical Systems - Series S 13(10):  2841-2851 (2020)
    14. R. Naz and I. Naeem, The approximate Noether symmetries and approximate first integrals for the approximate Hamiltonian systems, Nonlinear dynamics, 96 (2019), 2225–2239
    15. R. Naz, A. Chaudhry, Closed-form solutions of Lucas–Uzawa model with externalities via partial Hamiltonian approach, Computational and Applied Mathematics, Comp. Appl. Math. (2018) 37:5146–5161
    16. R. Naz, F. M. Mahomed, Characterization of partial Hamiltonian operators and related first integrals Discrete & Continuous Dynamical Systems - Series S (DCDS-S) , 11(4) 2018, 741-752.
    17. R. Naz, Characterization of approximate Partial Hamiltonian operators and related approximate first integrals, International Journal of nonlinear mechanics, volume 105 (2018), 158-164
    18. R. Naz, A. G. Johnpillai, Exact solutions via invariant approach for Black-Scholes model with time-dependent parameters, Mathematical Methods in the Applied Sciences 41(12), (2018) 4417-4427
    19. R. Naz, I. Naeem, The Artificial Hamiltonian, First Integrals,and Closed-Form Solutions of Dynamical Systems for Epidemics, Zeitschrift für Naturforschung A, 73 (4) 2018, 323-330
    20. A. Chaudhry, R. Naz, Closed-form solutions for the Lucas-Uzawa Growth model with logarithmic utility preferences via the partial Hamiltonian approach, Discrete & Continuous Dynamical Systems - Series S (DCDS-S) , 11(4) 2018, 661-672.
    21. R. Naz, Potential systems and nonlocal conservation laws of Prandtl boundary layer equations on the surface of a sphere, Zeitschrift für Naturforschung A, 72 (2017), 351-357.
    22. R. Naz, Azam Chaudhry, Comparison of Closed-form Solutions for the Lucas-Uzawa model via the Partial Hamiltonian Approach and the Classical Approach, Mathematical Modelling and analysis, 22(4), 2017, 464–483
    23. A. F. Cheviakov, R. Naz, A recursion formula for the construction of local conservation laws of differential equations. Journal of Mathematical Analysis and Applications, 448 (2017), 198-212.
    24. R. Naz, M. Torrisi, I. L. Freire, and I. Naeem , Editorial board note on Qualitative and Quantitative Techniques for Differential Equations Arising in Mathematical Physics, Advances in Mathematical Physics, Volume 2017, Article ID 8592571
    25. R. Naz, I. Naeem, Generalization of approximate partial Noether approach in phase space, Nonlinear Dynamics, 88 (2017), 735–748.
    26. R. Naz and A. F. Cheviakov , Conservation Laws and Nonlocally Related Systems of Two-Dimensional Boundary Layer Models, Zeitschrift für Naturforschung A (ZNA), 72 (2017), 1031-1051.
    27. A. Chaudhry, H. Tanveer, R. Naz, Unique and multiple equilibria in a macroeconomic model with environmental quality: An analysis of local stability, Economic Modelling, 63 (2017), 206-214.
    28. R. Naz, K. S. Mahomed, I. Naeem, First integrals and exact solutions of the SIRI and Tuberculosis models, Mathematical Methods in the Applied Sciences, 39 (2016), 4654-4666.
    29. R. Naz, F. M. Mahomed and A. Chaudhry, A partial Lagrangian Method for Dynamical Systems, Nonlinear dynamics, 84 (2016) , 1783–1794.
    30. R. Naz, The applications of the partial Hamiltonian approach to mechanics and other areas, International Journal of Non-Linear Mechanics, 86 (2016), 1–6.
    31. R. Naz, Azam Chaudhry and F. M. Mahomed, Closed-form solutions for the Lucas-Uzawa model of Economic Growth via the partial Hamiltonian approach, Commun Nonlinear Sci Numer Simulat 30 (2016) 299–306.
    32. I. Naeem, R. Naz, M. D. Khan, Nonclassical Symmetry Analysis of Heated Two-Dimensional Flow Problems, Zeitschrift für Naturforschung A 70, Issue 12, 1031–1037, 2015.
    33. R. Naz and F. M. Mahomed, Dynamic Euler-Bernoulli Beam Equation: Classification and Reductions, Mathematical Problems in Engineering Volume 2015, Article ID 520491, 7 pages http://dx.doi.org/10.1155/2015/520491.
    34. R. Naz and F. M. Mahomed, A complex Noether approach for variational partial differential Equations, Commun Nonlinear Sci Numer Simulat 27 (2015) 120–135.
    35. R. Naz, I. Naeem and F. M. Mahomed, A Partial Lagrangian Approach to Mathematical Models of Epidemiology, Mathematical problems in Engineering, Volume 2015 (2015), Article ID 602915, 11 pages http://dx.doi.org/10.1155/2015/602915.
    36. R. Naz, I. L. Freire, I. Naeem , M. Torissi, Editorial: Mathematical Methods and Models in the Natural to the Life Sciences, Abstract and Applied analysis Volume 2014, http://dx.doi.org/10.1155/2014/706858 (2014).
    37. R. Naz and F. M. Mahomed Lie and Noether Symmetries of systems of complex ordinary differential equations and their split systems, Pramana journal of physics 83, (2014) 9-20.
    38. R. Naz, F. M. Mahomed and A. Chaudhry, A Partial Hamiltonian Approach for Current Value Hamiltonian Systems, Commu. Nonlinear. Sci. Numer. Simulat, 19 (2014) 3600–3610
    39. R. Naz, I. L. Freire, I. Naeem, Comparison of different approaches to construct first integrals for ordinary differential equations, Abstract and applied analysis, Volume (2014), http://dx.doi.org/10.1155/2014/978636 (2014).
    40. R. Naz , I.Naeem, M. D.Khan, Conservation laws of some physical models via symbolic package GeM, Mathematical problems in Engineering Volume 2013, http://dx.doi.org/10.1155/2013/897912 (2013).
    41. R. Naz, Z. Ali, I. Naeem, Reductions and new exact solutions of ZK, Gardner KP, and Modified KP equations via generalized double reduction theorem, Abstract and applied analysis, Volume 2013, http://dx.doi.org/10.1155/2013/340564 (2013).
    42. R. Naz , M. D.Khan, I.Naeem, Conservation laws and exact solutions of a class of non-linear regularized long wave equations via double reduction theory and Lie symmetries, Commu. Nonlinear. Sci. Numer. Simulat , 18 (2013) 826–834
    43. R. Naz, Conservation laws for some systems of nonlinear partial differential equations via multiplier approach, Journal of applied Mathematics , doi:10.1155/2012/871253 (2012)
    44. R. Naz, Conservation laws for some compacton equations using the multiplier approach, Applied Mathematics Letters, 25 (2012) 257-261.
    45. R. Naz , M. D. Khan, I.Naeem, Nonclassical symmetry analysis of boundary layer equations, Journal of applied Mathematics doi:10.1155/2012/938604 (2012)
    46. R. Naz, Conservation laws for laminar axisymmetric jet flows with weak swirl, Vol. 91, No. 5, May 2012, 1045–1052 Applicable analysis, (2012). |
    47. R. Naz, Group invariant solutions for two-dimensional free, wall and liquid jets having finite fluid velocity at orifice, Mathematical problems in engineering, Volume 2011, Article ID 615612, DOI: 10.1155/2011/615612 (2011).
    48. F. M. Mahomed and R. Naz, A note on the Lie symmetries of complex partial differential equations and their split real systems, Pramana journal of physics , 77 (2011) 483-491.
    49. R. Naz, Approximate partial Noether operators and first integrals for cubically coupled nonlinear Duffing oscillators subject to a periodically driven force, Journal of Mathematical analysis and application, 380 (2011) 289-298.
    50. R. Naz, D. P. Mason and I. Naeem, Group invariant solution for a liquid film on the surface of a sphere, Zeitschrift fuer Naturforschung A (2011) 66a 272-280.
    51. R. Naz, I. Naeem, F. M. Mahomed, First integrals for two linearly coupled nonlinear duffing oscillators, Mathematical problems in Engineering, Volume 2011, Article ID 831647, doi:10.1155/2011/831647.
    52. R. Naz, Group invariant solution for a free jet on a hemi-spherical shell, Applied Mathematics and Computations. 215 (2010) 3265–3270.
    53. R. Naz, F. M. Mahomed, T. Hayat, Conservation laws for third-order variant Boussinesq system, Applied Mathematics Letters 23 (2010) 883-886.
    54. R. Naz, I. Naeem, F. M. Mahomed, Conservation laws and conserved quantities for laminar radial jets with swirl, Mathematical and Computational applications 15 (2010) 742-761.
    55. R. Naz, Conservation laws for a complexly coupled KdV system, coupled Burgers’ system and Drinfeld-Sokolov-Wilson system via multiplier approach, Commun. Nonlinear. Sci. Numer. Simulat. 15 (2010) 1177-1182.
    56. R. Naz, I. Naeem and S. Abelman, Conservation laws for Camassa – Holm equation, Dullin-Gottwald-Holm equation and Generalized Dullin-Gottwald-Holm equation, Nonlinear Analysis: Real World Applications. 10 (2009) 3466-3471.
    57. R. Naz, D. P. Mason and F. M. Mahomed, Conservation laws and conserved quantities for laminar two-dimensional and radial jets, Nonlinear Analysis: Real World Applications. 10 (2009) 2641-2651.
    58. R. Naz, F. M. Mahomed and D. P. Mason, Conservation laws via the partial Lagrangian and group invariant solutions for radial and two-dimensional free jets, Nonlinear Analysis: Real World Applications. 10 (2009) 3457-3465.
    59. R. Naz and D. P. Mason, Conservation laws for heated laminar radial liquid and free jets, Journal of Nonlinear Mathematical Physics. 16 (2009) 299-309.
    60. R. Naz, F. M. Mahomed and D. P. Mason, Symmetry solutions of a third-order ordinary differential equation which arises from Prandtl boundary layer equations, Journal of Nonlinear Math. Phys. 15 supplement 1 (2008) 179-191.
    61. R. Naz, F. M. Mahomed and D. P. Mason, Comparison of different approaches to conservation laws for some partial differential equations in fluid mechanics, Applied Mathematics and Computations. 205 (2008) 212-230.
    62. T. Hayat, R. Naz and S. Asghar, Hall effects on unsteady duct flow of a non-Newtonian fluid in a porous medium, Applied Mathematics and Computations. 157 (2004) 103-114.