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Department of Mathematics

 

  • Research

    AREA OF RESEARCH:

    • Scientific Computing, Numerical Analysis and Differential Equations
    • Distributed System
    • Finsler Geometry
    • Instability Analysis in Fluids, Numerical Analysis
    • Cosmology
    • Bio- Mathematics Modelling
    • Demography and Bio-Statistics
    • Instability analysis in Fluids, Nonlinear Dynamics
    • Nano fluids, Computational Fluid Dynamics
    • Mathematical Biology
    • Operation Research, Fuzzy Set Theory, Optimization Techniques

  • GROUP 1: FLUID DYNAMICS


    Members: Dr. Vinod Gupta, Dr. Jogendra Kumar

    Flow pattern and stability of a horizontal fluid layer heated from below and cooled from above is known as the Rayleigh-Benard convection. This convection mainly depends on the buoyancy force, caused by the temperature difference across the fluid layers; therefore it is also called the natural convection. The classical Rayleigh- Benard convection and its porous analog have been studied extensively due to its wide range of applications, such as in the prediction of ground water movement in aquifers, in the energy extraction process from geothermal reservoirs, petroleum industry, and underground diffusion of contaminants. Presently, we are working in the area of solutal convection, modulated boundaries, triple diffusion, Nanofluids, instability in cylinders.

  • GROUP 2: MATHEMATICAL MODELLING AND SCIENTIFIC COMPUTING


    Members: Prof. Naresh M. Chadha, Dr. Sandeep Sharma, Dr. Fateh Singh

    Mathematical modeling of infectious diseases is one of the most important research areas of the current time. An epidemic model enables us to understand and identify the conditions and parameters which are playing pivotal role in disease transmission. In recent past many realistic models pertaining to cancer, dengue, Ebola, SARS, HIV etc. has been formulated and analyzed. These epidemic models may consider a set of ordinary differential equations, partial differential equations, delay differential equations or stochastic differential equations. With the aid of computer algebra and theory of dynamical systems, these models provide key information about the disease dynamics which helps health agencies to reduce the burden of a particular epidemic.


  • GROUP 3: Fuzzy decision making and Statistical uncertainty management


    Members: Dr. Dheeraj Kumar Joshi, Dr. Nitin Kamboj

    Fuzzy decision-making environments provide appropriate methods to treat uncertainties in the form of ambiguity and vagueness. Ambiguity refers to the type of uncertainty in which the selection of multiple options among a set of alternatives is plausible. Uncertainties in decision making problems are by reason of either randomness or fuzziness, or by both and can be classified into stochastic and non-stochastic uncertainty. Fuzzy and probabilistic approach-based decision-making method process only either probabilistic or non-probabilistic uncertainty. One major limitation is not to handle both types of uncertainties concurrently. Comprehensive concurrence of stochastic and non-stochastic uncertainty in real world problems concerned researchers to incorporate theory of probability with fuzzy logic theory.


    • S.No. Name of research scholar Title of thesis Supervisor(s) University Year of award
      1 Pratibha Tyagi Study Commutative Rings Graded by Finitely Generated Abelian Group Dr. Rakesh Mohan DIT University 2019
      2 Seema Yadav Performance Evaluation of Distributed Processing System Using Soft Computing Techniques Dr. Rakesh Mohan DIT University 2021
      3 Shruti Tomar Numerical study of few Nonlinear Partial Differential Equations Emerging from plasma physics. Dr. Naresh M. Chadha DIT University Ongoing
      4 Pervinder Singh A Study of Weakly Non-Linear Stability Analysis on Newtonian and Non-Newtonian Fluids Dr. Vinod K Gupta DIT University Ongoing
      5 Soniya Gupta Study of Fuzzy Set Theory in Linguistic and Probabilistic Environment Dr. Dheeraj K. Joshi DIT University Ongoing
    • S.No. Peer Reviewed Articles (Since 2017)
      1 Mishra, R. K., & Mohan, R. (2017). A report on graded rings and graded modules. Global Journal of Pure and Applied Mathematics, 13(9), 6827-6853.
      2 Tripathi, P. K., Ranjan, R., Pant, R., & Upadhyay, S. K. (2017). An approximate Bayes analysis of ARMA model for Indian GDP growth rate data. Journal of Statistics and Management Systems, 20(3), 399-419.
      3 Gupta, V. K., Kumar, A., & Singh, A. K. (2017). Analytical study of weakly nonlinear mass transfer in rotating fluid layer under time-periodic concentration/gravity modulation. International Journal of Non-Linear Mechanics, 97, 22-29.
      4 Pratibha, R. K. M. R. M. GRADED FUZZY REPRESENTABLE MODULE AND GRADED FUZZY ATTACHED PRIMES.
      5 Keshri, O. P., Kumar, A., & Gupta, V. K. (2018). Magento-solutal convection in Newtonian fluid layer with solutal modulated boundaries. International Journal of Non-Linear Mechanics, 107, 86-93.
      6 Kumar, A., & Gupta, V. K. (2018). Study of heat and mass transport in Couple-Stress liquid under G-jitter effect. Ain Shams Engineering Journal, 9(4), 973-984.
      7 Gupta, V. K. (2018). Study of mass transport in rotating couple stress liquid under concentration modulation. Chinese journal of physics, 56(3), 911-921.
      8 Keshri, O. P., Gupta, V. K., & Kumar, A. (2019). Study of weakly nonlinear mass transport in Newtonian fluid with applied magnetic field under concentration/gravity modulation. Nonlinear Engineering, 8(1), 513-522.
      9 Vimala, A., Ranji, S. A., Jyosna, M. T., Chandran, V., Mathews, S. R., & Pappachan, J. M. (2009). The prevalence, risk factors and awareness of hypertension in an urban population of Kerala (South India). Saudi Journal of Kidney Diseases and Transplantation, 20(4), 685.
      10 Pradhan, A., Dixit, A., & Singhal, S. (2019). Anisotropic MHRDE model in BD theory of gravitation. International Journal of Geometric Methods in Modern Physics, 16(12), 1950185.
      11 Tripathi, P. K., & Upadhyay, S. K. (2019). Bayesian Analysis of Extended Auto Regressive Model with Stochastic Volatility. Journal of the Indian Society for Probability and Statistics, 20(1), 1-29.
      12 Keshri, O. P., Kumar, A., & Gupta, V. K. (2019). Effect of internal heat source on magneto-stationary convection of couple stress fluid under magnetic field modulation. Chinese journal of physics, 57, 105-115.
      13 N. Awasthi, D. K. Joshi and S. Sachdev, "Discrimination of noise channels on the basis of quantum memory," 2020 International Conference on Advances in Computing, Communication & Materials (ICACCM), 2020, pp. 278-282, doi: 10.1109/ICACCM50413.2020.9212818.
      14 Yadav, S., Mohan, R., & Yadav, P. K. (2019). Fuzzy based task allocation technique in distributed computing system. International Journal of Information Technology, 11(1), 13-20.
      15 Pratibha, R. K. M. R. M. Graded 2-absorbing primary fuzzy ideals and Graded Weakly 2-Absorbing Primary Fuzzy Ideals.
      16 Kumar, J. (2020). A novel two-step iterative scheme based on composite Simpson rule for solving nonlinear equations. J. Math. Comput. Sci., 10(5), 1867-1874.
      17 Kumar, A., Gupta, V. K., Meena, N., & Hashim, I. (2020). Effect of rotational speed modulation on the weakly nonlinear heat transfer in Walter-B viscoelastic fluid in the highly permeable porous medium. Mathematics, 8(9), 1448.
      18 Joshi, B. C., Mohan, R., & Pankaj, P. (2020). Generalized Invexity and Mathematical Programs. Yugoslav Journal of Operations Research, 31(4), 455-469.
      19 Srivastava, I., Singh, F., Kotia, A., & Ghosh, S. K. (2020). MWCNT and graphene nanoparticles additives for energy efficiency in engine oil with regression modeling. Journal of Thermal Analysis and Calorimetry, 1-21.
      20 Yadav, S., Mohan, R., & Yadav, P. K. (2020). Task Allocation Model for Optimal System Cost Using Fuzzy C-Means Clustering Technique in Distributed System. Ingénierie des Systèmes d Inf., 25(1), 59-68.
      21 Bhattacharyya, D., Singh, G. N., Jawa, T. M., Sayed-Ahmed, N., & Pandey, A. K. (2021). An Exponential-Cum-Sine-Type Hybrid Imputation Technique for Missing Data. Computational Intelligence and Neuroscience, 2021.
      22 Sharma, S., & Singh, F. (2021). Backward bifurcation in a cholera model with a general treatment function. SN Applied Sciences, 3(2), 1-8.
      23 Kumari, N., Kumar, S., Sharma, S., Singh, F., & Parshad, R. (2021). Basic reproduction number estimation and forecasting of COVID-19: A case study of India, Brazil and Peru. Communications on Pure and Applied Analysis.
      24 Sharma, S., & Singh, F. (2021). Bifurcation and stability analysis of a cholera model with vaccination and saturated treatment. Chaos, Solitons & Fractals, 146, 110912.
      25 Kumar, A., Hashim, I., Singh, A. K., Gupta, V. K., & Saini, N. (2021). COMBINED EFFECT OF INTERNAL HEATING AND G-JITTER ON WALTER-B VISCOELASTIC FLUID IN HIGHLY PERMEABLE POROUS MEDIUM. Journal of Porous Media, 24(3).
      26 Kumar, A., Hashim, I., Singh, A. K., Gupta, V. K., & Saini, N. (2021). COMBINED EFFECT OF INTERNAL HEATING AND G-JITTER ON WALTER-B VISCOELASTIC FLUID IN HIGHLY PERMEABLE POROUS MEDIUM. Journal of Porous Media, 24(3).
      27 Joshi, D. K., Awasthi, N., (2021). Probabilistic hesitant fuzzy set based MCDM method with applications in Portfolio selection process. IJFSA, 70-75.
      28 Bharadwaj, S., Dubey, A., Kamboj, N. K., Sahoo, A. K., Kang, S. G., & Yadava, U. (2021). Drug repurposing for ligand-induced rearrangement of Sirt2 active site-based inhibitors via molecular modeling and quantum mechanics calculations. Scientific reports, 11(1), 1-25.
      29 Gupta, V. K., Keshri, O. P., & Kumar, A. (2021). Effect of rotational speed modulation on weakly nonlinear magneto convective heat transfer with temperature-dependent viscosity. Chinese Journal of Physics, 72, 487-498.
      30 Kumar, A., Keshri, O. P., & Gupta, V. K. (2021). G-jitter effect on mass transport in electrically conducting Newtonian fluid. Chinese Journal of Physics, 71, 224-234.
      31 Dixit, A., SINGHAL, S., & ZEYAUDDIN, M. (2021). Model for Modified Holographic Ricci Dark Energy in Gravitation Theory of Branc Dicke. Walailak Journal of Science and Technology (WJST), 18(3), 6986-15.
      32 Sharma, S. (2021). Modeling the role of information on the spread of online shopping. Computational and Mathematical Methods, 3(5), e1182.
      33 Raut, S., Roy, A., Mondal, K. K., Chatterjee, P., & Chadha, N. M. (2021). Non-stationary Solitary Wave Solution for Damped Forced Kadomtsev–Petviashvili Equation in a Magnetized Dusty Plasma with q-Nonextensive Velocity Distributed Electron. International Journal of Applied and Computational Mathematics, 7(6), 1-20.
      34 Narla, V. K., Tripathi, D., Bhandari, D. S., & Kumar, J. Peristaltic Pumping of Maxwell Fluids in a Curved Channel: a Model for Intestinal Transport.
      35 Joshi, D. K., Awasthi, N., & Chaube, S. (2022). Probabilistic hesitant fuzzy set based MCDM method with applications in Portfolio selection process. Materials Today: Proceedings, 57, 2270-2275.
      36 Pandey, A. K., Singh, G. N., Bhattacharyya, D., Ali, A. Q., Al-Thubaiti, S., & Yakout, H. A. (2021). Some Classes of Logarithmic-Type Imputation Techniques for Handling Missing Data. Computational Intelligence and Neuroscience, 2021.
      37 Manickam, A., Kumar, P., Dasunaidu, K., Govindaraj, V., & Joshi, D. K. (2021). A stochastic SIR model for analysis of testosterone suppression of CRH-stimulated cortisol in men. International Journal of Modeling, Simulation, and Scientific Computing, 2250021.
      38 Dhar, B., Kumar Gupta, P., & Yildirim, A. (2022). Dynamical behaviour of a tumor-immune model focusing on the dosage of targeted chemotherapeutic drug. International Journal of Computer Mathematics, (just-accepted).
      39 Awasthi, N., Joshi, D. K., & Sachdev, S. (2022). Dynamics of Quantum Speed Limit Time for Correlated and Uncorrelated Noise Channels. International Journal of Theoretical Physics, 61(4), 1-11.
      40 Dhar, B., Gupta, P. K., & Sajid, M. (2022). Solution of a dynamical memory effect COVID-19 infection system with leaky vaccination efficacy by non-singular kernel fractional derivatives. Math. Biosci. Eng, 19, 4341-4367.
      41 Awasthi, N., Joshi, D. K., & Sachdev, S. (2022). Study of correlated Markov noise channels and its effect on quantum speed limit. Materials Today: Proceedings, 57, 2334-2337.
      42 Awasthi, N., Kumar, J. D., & Sachdev, S. (2022). Variation of quantum speed limit under Markovian and non-Markovian noisy environment. Laser Physics Letters, 19(3), 035201.
      S.No. Book Chapters (Since 2017)
      1 Singh, P., Sharma, A., Sharma, S., & Narula, P. (2022). Estimation of Reproduction Number of COVID-19 for the Northeastern States of India Using SIR Model. In Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy (pp. 181-189). Springer, Singapore.
      2 Chadha, N. M., Raut, S., Mondal, K., & Tomar, S. (2022). Analytical Solution of a Time-Fractional Damped Gardner Equation Arising from a Collisional Effect on Dust-ion-acoustic Waves in a Dusty Plasma with Bi-Maxwellian Electrons. In Handbook of Fractional Calculus for Engineering and Science (pp. 121-149). Chapman and Hall/CRC.
      3 Analysis of Modified Factional Epidemiological Model for Computer Viruses, Jogendra Kumar.
      4 Oyakhire, F. I., Louis, O., & Kumar, J. A New High-Order Compact Finite Difference Scheme for One-Dimensional Helmholtz Equation using Dirichlet Boundary Conditions. In Computing and Simulation for Engineers (pp. 37-55). CRC Press.
      5 Sharma, S., Sharma, A., & Singh, F. (2021, February). Did the COVID-19 Lockdown in India Succeed? A Mathematical Study. In International Conference on mathematical Modelling and Computational Intelligence Techniques (pp. 21-38). Springer, Singapore.
      6 Kamboj, N. K., Sharma, S., & Sharma, S. (2021). Modelling and Sensitivity Analysis of COVID-19 Under the Influence of Environmental Pollution. In Mathematical Analysis for Transmission of COVID-19 (pp. 309-323). Springer, Singapore.
      7 Role of Applied Statistical Techniques in Interdisciplinary Research, N. K. Kamboj, Jabrinder Singh, ISBN 978-981-33-6264-2 (eBook)"
      8 Singh, H., Singh, J., Purohit, S. D., & Kumar, D. (Eds.). (2021). Advanced Numerical Methods for Differential Equations: Applications in Science and Engineering. CRC Press.
      9 "Programming In MATLAB" with Applied Numerical Mehtods for Engineers & Scientists, Notion Press, ISBN: 978-1637812693
      10 Kumar, S., Sharma, S., Singh, F., Bhatnagar, P. S., & Kumari, N. (2021). A mathematical model for COVID-19 in Italy with possible control strategies. In Mathematical analysis for transmission of COVID-19 (pp. 101-124). Springer, Singapore.
      11 An exponential Fourier series for the multi-variable I-Function and a general class of polynomials, Rubicon Publications, London, 9781913482527.
      12 Yadav, S., Mohan, R., Yadav, P. K., & Verma, G. (2019, February). Analytical Literature Survey on Existing Task Allocation Techniques in Distributed System. In Proceedings of 2nd International Conference on Advanced Computing and Software Engineering (ICACSE).
      13 Awasthi, N., Joshi, D. K., & Sachdev, S. (2020, August). Discrimination of noise channels on the basis of quantum memory. In 2020 International Conference on Advances in Computing, Communication & Materials (ICACCM) (pp. 278-282). IEEE.
      S.No. Patents
      1 An intelligent home automation system, 20 2022 100 120.0, Dr. Dheeraj Kumar Joshi, German-Deutsche Patent, https://register.dpma.de/DPMAregister/pat/register?AKZ=2020221001200