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From the Desk of the Vice Chancellor

Greetings!

As the Vice Chancellor of this premier university, I am extremely pleased to share this space to converse with all of you. The University of Madras is a post- sesquicentennial institution which has forged a glorious path for itself and has been the site for significant scientific discoveries as well as the beacon for national and regional societal transformation. It has successfully managed to hold aloft its tradition even while keeping up with the emerging trends. One reason for this is the way in which the university has kept alive its interactions with all the stakeholders.

The COVID 19 pandemic has introduced a ‘new normal’ and its impact is felt in the workings of the university as well. The students have been attending the lectures online. While online learning has the advantage of being anytime and anywhere, it has taken away the peer group interaction and peer learning which are integral aspects of the university experience. We look forward to welcoming you to the campus very soon. Meanwhile, our faculty and administration will continue to bring the best to the virtual classrooms. As students, you need to view the restrictions posed by the pandemic as a temporary deterrent. Your focus should be to gain the competencies to conduct application oriented research in order to evolve as useful citizens of our society.

Our university boasts of faculty with a high degree of knowledge and commitment to offer the best in teaching and research. Given the context of the pandemic, we need to redefine our teaching-learning processes to offer the best pedagogic experience to our students. Similarly, the post-pandemic era demands that we hone the employment potential and entrepreneurial capacity of our learners. This necessitates that we focus on sponsored research in cutting edge areas.

Our administrative staff have been the backbone of the university. While we move towards a transparent and complete e-governance model, we need more support from you. When the teaching-learning process at our university – from admission to certification -- is moving into the digital era, your skills and competencies need to keep pace.

At our university, we are gearing up for the final round of NAAC re-accreditation. This has offered us an opportunity to assess our Strengths, Weaknesses, Opportunities and Challenges. Further, it has made us more determined to reiterate our quality benchmarks in teaching, research and extension activities. We are aware of this responsibility and fully prepared for it because, our university has always encouraged individual thinking within the established frameworks. This is echoed in the words of Tim Burners Lee, who initiated the World Wide Web: “We are forming cells within a global brain and we are excited that we might start to think collectively. What becomes of us still hangs crucially on how we think individually.” Let us unite to make the educational experience at the University of Madras a synergy of the best minds and best thoughts.

Prof.Dr.S.Gowri

Vice-Chancellor
University of Madras

Dr. M. PitchaimaniM.Sc., M. Phil., Ph.D

Associate Professor and Head i/c
Department of Ramanujan Institute for Advanced Study in Mathematics
3

Awards

59

Publications

18

Seminars / Conference

2

Projects

2

Ph.D Awarded

0

Ph.D Present

Publications

Articles (Total Articles: 55)

# Title Author Publisher Volume Year Page(s)
1 Approximation of common fixed points in 2-Banach spaces with applications. D. Ramesh Kumar, M. Pitchaimani Appl. Gen. Topology 1 2019 43 - 55
2 Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses. S.P. Rajesekar, M. Pitchaimani Chaos, Solitons and Fractals, Elsevier, 118 2019 207-221
3  Dynamic threshold probe of stochastic SIR model with saturated incidence rate and saturated treatment function. S.P. Rajesekar , M. Pitchaimani, Quanxin Zhu Physica A Elsevier, 535 2019 122300
4 Stability of Stochastic SIRS Model with Variable Diffusion Rates. R. Rajaji , M. Pitchaimani, W.H. Lim Nonlinear Functional Analysis and Applications 23(1) 2018 31-48
5  Approximation and stability of common fixed points of Presic mappings in ultrametric spaces. D. Ramesh Kumar, M. Pitchaimani J. Fixed Point Theory Appl. 20(1)-Springer 2018 1-21
6  New coupled fixed point theorems in cone metric spaces with applications to integral equations and Markov process. D. Ramesh Kumar, M. Pitchaimani Transactions of A. Razmadze Mathematical Institute Elsevier, DOI:org/10.1016/j.trmi.2018.01.006. 2018
7 An analysis of the delay-dependent HIV-1 protease inhibitor model. M. Divya , M. Pitchaimani International Journal of Biomathematics World Scientific, 11(3) 2018 1-22
8  Geometric Stability Switch Criteria in HIV-1 Infection Delay Model. C. Monica , M. Pitchaimani Journal of Nonlinear Science Springer, 1-19 2018 doi.org/10.1007/s00332-018-9481-y
9  Global Analysis of Stochastic SIR Model with Variable Diffusion Rates. M. Pitchaimani , S.P. Rajesekar Tamkang Journal of Mathematics 49(2) 2018 155-182
10 Effects of Randomness on Viral Infection Model with Application. M. Pitchaimani , M. Brasanna Devi IFAC Journal of Systems and Control Elsevier, 6 2018 53-69
11  Fixed Point Theorems for Multivalued Nonlinear Contraction Mapping in G-Metric Space. M. Pitchaimani ,Pavana Devassykutty, W.H. Lim Nonlinear Functional Analysis and Applications 23(4) 2018 723-742
12  Analysis of Stochastic Viral Infection Model with Immune Impairment M. Pitchaimani,R. Rajaji International Journal of Applied and Computational Mathematics Springer, DOI 10.1007/s40819017-0314-8 2017
13 Modeling and bifurcation analysis of a viral infection with time delay and immune impairment M. Pitchaimani , P. Krishnapriya Japan Journal of Industrial and Applied Mathematics Springer, DOI 10.1007/s13160-017-0240-5 2017
14  Set-valued contraction mappings of Pre?si´c-Reich type in ultrametric spaces M. Pitchaimani, D. Ramesh Kumar Asian-European Journal of Mathematics World Scienti?c, 10(4) (2017) 1750065(115) DOI: 10.1142/S1793557117500656. 2017
15  On Nadler type results in ultrametric spaces with application to well-posedness M. Pitchaimani, D. Ramesh Kumar Asian-European Journal of Mathematics World Scienti?c, 10(4) (2017) 1750073 (115) DOI: 10.1142/S1793557117500735 2017
16  Mathematical analysis of an in?uenza A epidemic model with discrete delay P. Krishnapriya, M. Pitchaimani, Tarynn M. Witten Journal of Computational and Applied Mathematics Elsevier, Volume 324 (11) (2017) (155 - 172) DOI: org/10.1016/j.cam.2017.04.030. 2017
17  Generalized Nadler type results in ultrametric spaces with application to well-posedness M. Pitchaimani, D. Ramesh Kumar Afr. Mat., Springer, 28 (2017) 957-970 2017
18 A generalization of set-valued Pre?si´c-Reich type contractions in ultrametric spaces with applications M. Pitchaimani, D. Ramesh Kumar J. Fixed Point Theory Appl. Springer, 19(3) (2017) 1871-1887 2017
19 Analysis of stability and Hopf bifurcation for HIV-1 dynamics with PI and three intracellular delays C. Monica and M. Pitchaimani Nonlinear Analysis: Real World Applications 27 2016 55-69
20 Optimal control of mixed immunotherapy and chemotherapy of tumours with discrete delay. P. Krishnapriya and M. Pitchaimani International Journal of Dynamics and Control, Springer-Verlag 2016
21  Common and coincidence ?xed point theorems for asymptotically regular mappings in 2-Banach spaces M. Pitchaimani, D. Ramesh Kumar Nonlinear Functional Analysis and Applications 21(1), 131-144 2016
22  On construction of ?xed point theory under implicit relation in Hilbert spaces M. Pitchaimani, D. Ramesh Kumar Nonlinear Functional Analysis and Applications 21(3), 513-522 2016
23  Stochastic Asymptotic Stability of Nowak-May Model with Variable Di?usion Rates M. Pitchaimani,R. Rajaji Methodology and Computing in Applied Probability Springer, 18(3), 901-910 2016
24  Analysis of time delay in viral infection model with immune impairment M. Pitchaimani , P. Krishnapriya Sohag Journal of Mathematics Natural Sciences Publishing, 3(3), 105-112 2016
25 A mathematical model of HIV-1 infection within host cell to cell viral transmissions with RTI and discrete delays M. C. Maheswari, P. Krishnapriya, K. Krishnan,M. Pitchaimani Journal of Applied Mathematics and Computing Springer, DOI 10.1007/s12190-0161066-z 2016
26  Analysis of HIV-1 Model: Within Host Cell to Cell Viral Transmission with ART M. Pitchaimani , P. Krishnapriya Nonlinear Functional Analysis and Applications 21(4), 597-612 2016
27 Analyzing on stability of HIV-PI model with general incidence rate M. Divya, M. Pitchaimani Journal of Applied Mathematics and Computing Springer, DOI 10.1007/s12190-016-1073-0 2016
28 Mathematical modeling of intra venous glucose tolerance test model with two discrete delays. M. Pitchaimani and P. Krishnapriya, C. Monica Journal of Biological Systems, World Scientific 23(4) 2015 631-660
29  Some common fixed point theorems using implicit relation in 2-Banach spaces M. Pitchaimani, D. Ramesh Kumar Surveys in Mathematics and its Applications 10, 159-168 2015
30 Global stability analysis of HIV-1 infection model with three time delays. M. Pitchaimani, C. Monica Journal of Applied Mathematics and Computing 48(1-2) 2014 293-319
31 Unique Estimation of Solid Tumour Growth Gompertz Parameter and Its Sensitivity Behaviour. M. Pitchaimani, G. Somasundara Ori and Tim Eakin British Journal of Mathematics & Computer 4(8) 2014 2603-2617
32 Maximum life span predicitions using Gompertz tumour Growth Model. M. Pitchaimani, G. Somasundara Ori IOSR. Journal of Mathematics 10(6) 2014 55-62
33 Existence of a critical allometry model parameter and its asymptotic expression. M. Pitchaimani Journal of Applied Mathematics and Computing 41, No. 1-2, Springer 2013 133 – 152
34 Stability analysis for HIV infection delay model with protease inhibitor. M. Pitchaimani, C. Monica and M.Divya BioSystems 114 2013 118-124
35 Existence and Estimation of Negative critical allometry model parameter. M. Pitchaimani and R.Asokan, Int.J. Emer.Sci and Engg 1(11) 2013 78-86
36 Homotopy perturbation method for solving a model for HIV-1 Infection. M. Pitchaimani, M. Divya International journal of Mathematical Science Vol 11, No. 3-4 2012 411-421
37 Stability analysis for HIV-1 infection dynamics using the matrix Lambert W function. M. Pitchaimani, C. Monica International journal of Mathematical Science, Vol 11, No. 3-4 2012 411-421
38 Introduction to Estimation of Survival Model Parameters. M. Pitchaimani Mathematics Newsletter 20(3) 2011 33-44
39 E.S. Lakshminarayanan and M. Pitchaimani. Unique Estimation of Mortality rates in Gompertz survival model Parameters Appl. Math. Lett. Vol 16, No. 2, 211-219 (2003).
40 E.S. Lakshminarayanan and M. Pitchaimani. On Existence of Gom- pertz Parameters and its Asymptotic Formulae for a Large Population. Appl. Math. Lett. Vol 17, No. 2, 173-180 (2004)
41 E.S. Lakshminarayanan and M. Pitchaimani. A Note on Gompertz Survival Parameters: Estimation and Sensitivity. Advances in Applied Mathematics and Statistics,Eds., G. Arivarignan and A. Sundaram, MKU, pp: 143 - 146, (2003).
42 E.S. Lakshminarayanan and M. Pitchaimani. Existence of Critical Gompertz Parameter and Its Asymptotic Expression. Comp. and Math. with Appl. Vol 55,1302-1309, (2008).
43 E.S. Lakshminarayanan and M. Pitchaimani. Existence and Estimation of Negative Critical Gompertz Parameters. Comp. and Math. with Appl. Vol 55, 1686-1692, (2008).
44 M. Pitchaimani. Maximum Lifespan prediction from the Gompertz model and estimation of negative Gompertz parameter. Journal of Ap- plied Statistical Sciences (accepted for publications).
45 M. Pitchaimani. Estimation and Sensitivity of Gompertz parameter with mortality deceleration rate. Journal of Applied Mathematics and Computing. Vol. 18 No.1-2, 311-320 (2005).
46 M. Pitchaimani and Tim Eakin. Unique Estimation of Gompertz Pa- rameters with Mortality Deceleration Rate. Mathematical and Com- puter Modeling. Vol. 47, 104-114 (2008).
47 M. Pitchaimani and Tim Eakin. Existence and Estimation of Gompertz parameters with Mortality deceleration rate and their Asymptotic Formu- lae for a Large Population. Mathematical and Computer Modeling. Vol. 46, 1477-1486 (2007) .
48 M. Pitchaimani and Tim Eakin. Estimation and Sensitivity of Allom- etry Model Parameters. Int. J. Pure and Appl. Math. Vol. 38, 251-270 (2007).
49 M. Pitchaimani. Maximum Lifespan prediction from the Gompertz model. Int. J. Math. Game Theory and Algebra Vol. 17 No. 1/2 57-67
50 M. Pitchaimani. Gompertzian Model for Tumor Growth. Int. J. Pure and Appl. Math. Sci. (in press).
51 R. Asokan and M. Pitchaimani. Nonclassical Symmetries and Direct Similarity Analysis of a Nonlocal Gaseous Ignition Model. Int. J. Pure and Appl. Math. Vol.41, No.5,737-748(2007).
52 Auto-Backlund transformation, Lax pairs and Painleve property of ut + p(t)uux + q(t)uxxx + r(t)u = 0. Int.J. Math. Game Theory and Algebra (in press). R. Asokan, M. Pitchaimani.
53  Uniqueness of allometry model parameters. Journal of Applied Mathematics and Computing. Vol. 28, 485-5000 (2008). M. Pitchaimani.
54 Existence of allometry model parameters and their asymptotic formulae for a large population. Journal of Applied Mathematics and Computing.DOI 10.1007/s12190-009-0348-0 M. Pitchaimani
55  Stability of frailty model parameters. Journal of Applied Mathematics ( in press). M. Pitchaimani.

Papers (Total Papers: 3)

# Title Author Publisher Volume Year Page(s)
1 Sensitivity and Variational iteration method for solving tumour-immune system M. Pitchaimani and P. Krishnapriya Sacred Heart Journal of Science and Humanities 6(2) 2015 6-19
2 Stability analysis for the model of HIV infection dynamics. M. Pitchaimani and M.Divya Sacred Heart Journal of Science and Humanities 6(2) 2015 20-35
3 A new method for solving delay differential equations. M. Pitchaimani and P. Krishnapriya National Conference on Mathematical Modelling 2014 136-142

Books (Total Books: 1)

# Title Author Publisher Volume Year Page(s)
1 Proceedings of the Eighteenth Ramanujan Symposium on Recent Trends in Dynamical Systems and Mathematical Modeling M. Pitchaimani 2014 1-127
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