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Department of Applied Mathematics

DR. Ashutosh Narayan

Professor and Head

Dr. Ashutosh Narayan was awarded CSIR fellowship: Junior Research fellow (1982-84) and Senior Research fellow (1984-86). He was awarded the Ph. D degree on the topic: "Nonlinear effect in the motion and stability of interconnected satellite system near circular orbits" in the year 1986, from Bihar University Muzaffarpur. Dr. Ashutosh Narayan has been selected as a member of American Mathematical Society, with effect from January 2018, on the basis of the points he has earned by revewing research papers published in various reputed journals for Mathematical Review.

DR. Ashutosh Narayan

Department Applied Mathematics
Designation Professor and Head
Educational Qualification Ph. D.
E-Mail ashutoshmaths.narayan@gmail.com, ashu.narayan@bitdurg.ac.in
Contact Number
Areas of Interest

Celestial Mechanics: Stability Theory

Publications

     

    Papers in Journals

    Conferences paper (Full length)

    Books

    Book chapter

    National

    International

    National

    International

    16

    48

    12

    03

    04

    00

    Total: 64

    Total: 15

     

     

    Research Papers Published (National/ International Journal)

    [1]

    Non-linear non-resonance oscillation of inter-connected satellites system under the Solar pressure about the position equilibrium for small eccentricity. Proc. Nat. Acad. Sci., India vol. 57(A), pp 427-437, 1987. India

    [2]

    Non-linear main resonance oscillation of the system of two inter connected Satellites under the influence of solar pressure about stable equilibrium for small eccentricity. Proc. Nat. Acad. Sci., India, vol. 60(A) pp. 307-315, 1990.India

    [3]

    Non-linear parametric resonance oscillation of the system of two inter-connected satellites under the influence of solar pressure about the stable position of equilibrium for small eccentricity.  Proc. Nat. Acad. Sci., India, vol. 62(A) part I 1992. India

    [4]

    Non-linear effects in the motion and stability of an inter-connected satellites system Orbiting around an oblate earth. Proc. Nat. Acad. Sci., India, vol. 71 part III, pp 225 235, 2001, India

    [5]

    Non-linear parametric resonance oscillation of the system of two inter-connected Satellites orbiting around an oblate earth. Proc. Nat. Acad. Sci., India, vol. 67(A),      pp. 45-55, 1997. India

    [6]

    Non-linear oscillation of inter connected satellite system under the combined influence of the solar radiation pressure and dissipative force of general nature. Bulletin of the Astronomical Society of India, Bangalore, vol. 29, 2001. India

    [7]

    Effect of solar radiation pressure on the motion and stability of Inter-connected Satellites system in orbit. Indian J. Pure Appl. Math., vol. 33(5), pp 609-623, 2002. India

    [8]

    Some non-linear effects of perturbing forces of general nature and solar radiation Pressure On the motion and stability of an inter connected satellites system in elliptical orbit. Bull. Cal. Math. Soc. 95(3), pp. 245-256, 2003. India.

    [9]

    Stability of planar oscillations of a satellite in elliptical orbit. Journal of Modelling (AMSE), vol. 73, no. 3, pp.51, 2004. France

    [10]

    Effects of Earth Magnetic field on the stability of cable connected satellites system In equatorial orbit Journal of Modeling (AMSE), vol. 73, no. 4, pp.45-60, 2004.France

    [11]

    Non-linear planar oscillation of a rigid satellite in elliptical orbit” Bull. Cal. Math Soc. 97(1), pp. 31-40, 2005. India

    [12]

    Stability of extensible cable connected satellite system in elliptical orbit. Journal of AMSE, France, vol.-74, no.-7, 2005. France

    [13]

    Effect of solar radiation pressure and Magnetic field of the earth on stability of Cable connected satellites system in equatorial orbit. Bull. Cal. Math. Soc. 97(6), pp. 417-432, 2005. India

    [14]

    Modelling and simulation of extensible cable-connected satellites system in low altitude orbit. Journal of AMSE, France, vol.-49, no.-2, pp. 61, 2006. France

    [15]

    Effect of the earth magnetic field and tidal force on oscillations of cable-connected satellites system in elliptical orbit. Journal of AMSE, vol. – 75, no. 3, pp. 19, 2006. France

    [16]

    Non-linear effects of solar radiation pressure and magnetic field of the earth on the stability of cable connected satellites system in elliptical orbit. Bull. Cal. Math. Soc. 93(3), pp. 209-222, 2007 India

    [17]

    Non-linear stability of cable connected satellites system under the combined effects Of the solar radiation pressure and the magnetic field of the earth. Journal of AMSE, vol. 76, no. 1, pp. 73, 2007. France

    [18]

    Non-linear oscillation of extensible cable connected satellites system in elliptical orbit. Journal of AMSE, vol. – 76, no. 4, pp. 19-38, 2007. France

    [19]

    Effect of earth magnetic field and the solar radiation pressure on stability of extensible cable-connected satellites system in orbit. Bull. Cal. Math. Soc. 100(5), pp 427 –446, 2008. India

    [20]

    Non-linear oscillation of extensible cable connected satellites system in circular orbit. Bull. Cal. Math. Soc. 100(4), 2008 India

    [21]

    Stability of Triangular points in the generalized oblate elliptical restricted three body problem. Vol-77 no-2  ex- Modeling B  pp 1-19 , 2008  France

    [22]

    Resonance   Stability of Triangular points of the Planar elliptical restricted three Body Problem in which both of the primaries are oblate spheroid. Vol. 77 no-2 ex Modeling B pp. 55-73, 2008, France.

    [23]

    Stability of extensible cable connected satellites system under environmental Perturbation forces. Vol.  77 no-6 ex-Modeling B, pp35-54,2008, France

    [24]

    Non linear parametric resonance stability of cable connected satellites system under the combined  effects of the solar radiation pressure and magnetic field of the earth Vol. 77, no -5 , ex Modeling, B pp44-59, 2008. France

    [25]

    Non linear effects of the earth magnetic field and periodic forces on cable connected satellites system in elliptical orbit. Bull. Cal. Math Soc., 102,(3) 227-240 (2010)

    [26]

    Condition of free and constrained motion of cable connected satellites system in low altitude orbit. IJPAM, Vol. 63 no.1  ,107-127,2010 , Bulgaria

    [27]

    Stability of cable connected satellites system in low altitude equatorial orbit. Journal of AMSE ,France, Vol. 79, 2010

    [28]

    Non linear oscillations of extensible cable connected satellites system under environmental forces in elliptical orbit. Journal of AMSE ,France, Vol. 79, 2010

    [29]

    Condition of non linear stability of dumbell satellite in elliptical orbit.   IJPAM, Vol.72  no. 2  , 173, 194, 2011, Bulgaria.

    [30]

    Stability of triangular equilibrium points in elliptical restricted three body problem under the effects of photogravitational and oblateness of primaries. IJPAM, Vol. 70, no. 5 , 735-754, 2011,Bulgaria.

    [31]

    Effects of photogravitational and oblateness on the triangular Lagrangian points in Elliptical restricted three body problem. IJPAM, Vol. 68,  no. 2 ,201-224, 2011, Bulgaria

    [32]

    Some non-linear resonance oscillations of dumbell satellite in elliptical orbit IJPAM, Vol. 78, no. 6, 931-944, 2012, Bulgaria .

    [33]

    Existence and  stability of collinear  equilibrium points in elliptical restricted three body problem under the effects of photogravitational and oblateness primaries. IJPAM , Vo.l 80,  no.4 ,477-494, 2012, Bulgaria .

    [34]

    Stability of Equilibrium Points in Elliptical Restricted Three Body Problem under The radiation and oblateness of Primaries. Int. J. of Mathematical Sciences Vol. 33, no.1, 1103 -1118, 2012.

    [35]

    Parametric Resonance Stability of Triangular Equilibrium Points of the Planar Elliptical Restricted Three Body Problem around the Primaries of Radiating and oblate Spheroid  Int. J. of Mathematical Sciences Vol. 32, no. 12 , pp 346-360, 2012

    [36]

    Effects of Oblateness and Radiation of Primaries on the Equilibrium Points in the Elliptical Restricted Three Body Problem Int. J. of Mathematical Sciences Vol. 32, no. 10 pp 330-345, 2012.

    [37]

    Pulsating Different Curves of Zero Velocity around Triangular Equilibrium Pointin Elliptical Restricted Three-Body Problem. Journal of Mathematics Volume 2013 (2013), Article ID 936859.

    [38]

    Some non-linear parametric resonance oscillations of dumbell satellite in elliptical orbit. IJAMR Vol.02, No. 02,  pp 200-212, 2013.

    [39]

    Effects of radiation and triaxiality of primaries on triangular equilibrium points in Elliptic restricted three body problem. Journal of Astrophysics and Space Science vol. 349 (1) pp 151-164, 2014.

    [40]

    Parametric resonance stability of triangular equilibrium points of the planar  elliptical restricted three-body problem around the primaries of oblate spheroid. Journal of AMSE, France, Vol. 78, issue 4, 2009.

    [41]

    Motion and stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries. Astrophysics and Space Science, DOI 10.1007/s10509-014-1903-1, 2014

    [42]

    Existence and stability of collinear equilibrium points in elliptical restricted three body problem under the radiating primaries. Astrophysics and Space Science, DOI 10.1007/s10509-014-2094-5, 2014

    [43]

    Resonance stability of triangular equilibrium points in elliptical restricted three body problem under the radiating primaries. Astrophysics and Space Science, DOI 10.1007/s10509-014-2085-6, 2014

    [44]

    Stability of triangular lagrangian points in elliptical restricted three body problem under the radiating binary systems. Astrophysics and Space Science, DOI 10.1007/s10509-014-2014-8, 2014

    [45]

    Stability of triangular equilibrium points in the elliptic restricted problem of three bodies with radiating and triaxial primaries. Astrophysics and Space Science, DOI 10.1007/s10509-014-1818-X, 2014

    [46]

    Existence of resonance stability of triangular equilibrium points in circular case of the planar elliptical restricted three body problem under the oblate and radiating primaries around the binary system. Advances in Astronomy, DOI.org/10.1155/2014/287174, 2014

    [47]

    Non-linear parametric resonance driven oscillations of dumbbell satellite in elliptical orbit under the combined effects of magnetic field of the earth and oblateness of the earth. International Journal of Advanced Astronomy, Vol. 03, pp  1-7, 2015.

    [48]

    Characteristic exponents of the triangular solution in the elliptical restricted three body problems under the radiation and oblateness of primaries. International Journal of Advanced Astronomy, Vol. 03, pp 8-16, 2015.

    [49]

     Higher order resonance stability of triangular libration points for radiating primaries in ER3BP. International Journal of Advanced Astronomy, Vol. 03, pp 26 -39, 2015.

    [50]    

    Non linear stability of triangular libration points in circular restricted three body           under radiating and oblate primaries in presence of resonance. International Journal of        Advanced Astronomy, Vol. 03 (2) 58-68

    [51]     

    Effects of radiation and triaxility of triangular equilibrium points in elliptical restricted three body problem International Journal of Advanced Astronomy, vol. 3 (2) (2015)

    [52]    

    Trajectories of the infinitesimal mass around the triangular equilibrium points in           elliptical restricted three bodies problem under oblate and radiating primaries for           the binary systems. International Journal of Advanced  Astronomy, vol. 3 (2)            (2015).

    [53]

    Non linear stability of  triangular equilibrium points in ER3BP under radiating primaries in presence of resonance. Diff. Eq.  and Dyn. System. DOI10.1007/s12591-015-0260-z.

    [54]

    Nonlinear stability of the triangular libration points for radiating and oblate primaries in  CR3BP in non-resonance  condition. Vol. 2015, Article ID 850252

    [55]

    Linear stability and resonance of triangular equilibrium points in elliptic restricted  three body problem with radiating primary and triaxial secondary. International           Journal of Advanced Astronomy, vol. 4 No.  (2) (2016) pp 82-89.

    [56]

           Existance and stability of collinear points in elliptic restricted three body problem   With raditiang and oblate primaries. International Journal of Advanced          Astronomy, vol. 4 No. (2) ,  (2016) pp 95-104.

    [57]

       Analysis of nonlinear stability of the triangular libration points for radiating and          oblate primaries in ER3BP. International journal of Advanced Astronomy Vol. 5,         No. (1)  PP 50-60.

    [58]

    Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial  rigid body of triangular equilibrium points in elliptical restricted tree body         problem International journal of  Advanced Astronomy Vol.5, No. (1) PP 29-37

    [59]

    Characteristics exponents of the triangular solution in the elliptical restricted three         body problem under radiating and triaxial primaries International Journal of                Advance  Astronomy Vol. 5, No. (1)  PP 12-18

    [60]

    Bifurcation analysis of stability of triangular equilibrium points in the elliptic restricted problem of  three bodies.  IJPAM,   Vol. 115,  No.02  PP 271-284.

    [61]

    Non-linear stability of the triangular equilibrium points in the ellptic restricted three     body problem  Asian journal of Mathematics and computer research Vol. 16 No.(1)     PP 46-62.

    [62]

    Existence and stability of triangular equilibrium points in the ER3BP with oblate, radiating and triaxial primaries Journal of Applied physical science international Vol.  8, No. (1) PP 7-12.

    [63]

    Influence of poynting Robertson drag and oblateness on existence and stability of        collinear points in elliptic restricted three body problem.  Journal of Applied                  physical science international Vol. 8,  No.  (1), PP 23-35

    [64]

    Evolutional and non evolutional motion of dumbell satellite near resonance oscillation. Journal  of  AMSE Vol. 83, No. (1) PP 63-84.

    [65]

    Existence and stability of collinear equilibrium points in elliptic restricted three body problem with radiating primary and triaxial secondary. Modelling, Measurement and Control A, 19(1), 1-8, 2018. (SCOPUS indexed Journal)

    T usha and A Narayan

    [66]

    Dynamics of Oblate Test Particle under the Influence of Oblate and Radiating Primaries in Elliptic Restricted Three Body Problem. J. of Informatics and Mathl. Sciences, 10(1), 73-92, 2018. (ESCI indexed Journal)

    A. Narayan, A. Chakraborty, A. Dewangan

    [67]

    Influence of Poynting-Robertson Drag and Oblateness on Existence and Stability of Out of Plane Equilibrium Points in Spatial Elliptic restricted three body problem. J. of Informatics and Mathl. Sciences, 10(1), 55-72, 2018. (ESCI indexed Journal)

    A. Chakraborty, A. Narayan

    [68]

    Effect of the oblateness of the infinitesimal on existence and stability of out of plane equilibrium points in spatial elliptic restricted three body. Int. J of Pure and Appl. Math., 119(1), 609-626, 2018. (SCOPUS indexed Journal)

    A. Narayan, A. Chakraborty, A. Dewangan

    [69]

    Pulsating Zero Velocity Surfaces and Fractal Basin of Oblate Infinitesimal in the Elliptic Restricted Three Body Problem. Few Body System, 59(3), 43-56, 2018. Doi:10.1007/s00601-018-1368-9. (SCI indexed Journal)

    A. Narayan, A. Chakraborty, A. Dewangan

    [70]

    Existence of Resonance Stability of Triangular Equilibrium Points for an Oblate Infinitesimal in Elliptical Restricted Three Body Problem with Radiating Oblate Primaries. Modelling, Measurement and Control B, 86(3), 609-626, 2018. (SCOPUS indexed Journal)

    A. Narayan, A. Chakraborty, A. Dewangan

    [71]

    Existence of Resonance Stability of Triangular Equilibrium Points for an Oblate Infinitesimal in Elliptical Restricted Three Body Problem with Radiating Oblate Primaries. Modelling, Measurement and Control B, 86(3), 609-626, 2018. (SCOPUS indexed Journal)

    A. Narayan, A. Chakraborty, A. Dewangan

    [72]

    Effect of Stellar Wind and Poynting–Robertson Drag on Photogravitational Elliptic Restricted Three Body Problem, Solar System Research, 52(2), 2018. Doi: 168-179, 10.1134/S0038094618020016. (SCI(E) indexed Journal)

    A. Chakraborty, A. Narayan

     

     

     Full length paper in proc. of International / National Conferences

    [1.] Non-linear effects on the motion and stability of inter connected satellite system in Elliptic orbit under the influence of Solar radiation pressure; Solar-Terrestrial Prediction Workshop; Hitachi, Japan.

    [2] Stability of an extensible cable-connected satellite system in elliptical orbit; International conference on Modeling and Simulation Vallasolid; 22-24 Sep 2004, Spain.

    [3] Effects of Solar radiation pressure with Earth shadow on the oscillations of Inter Connected Satellite system in elliptical orbit; International Conference on Modeling & Simulation Vallasolid; 22-24 Sep 2004; Spain.

    [4] Simulation of different Curves of zero velocity around triangular equilibrium points elliptical restricted three body problem; AICTE sponsored National Seminar on Applications of Mathematical Modeling in Science & Technology; 15-16 March 2013, BIT Durg.

    [5] Resonance Stability of Triangular equilibrium points of the planar elliptical restricted tree body problem in which both the primaries are oblate spheroids; AICTE sponsored National Seminar on Application of Mathematical Modeling in Science and Technology; 15-16 March 2013, BIT, Durg.

    [6] Non-linear resonance stability of cable-connected             satellite system under the combined effects of the solar radiation pressure and the magnetic field of the Earth; AICTE sponsored National Seminar on Application of Mathematical Modeling in Science and Technology; 15-16 March 2013, BIT, Durg.

    [7] Effects of Radiation and Triaxiality  of Triangular  equilibrium points in elliptical restricted three body problem; Proceedings of the National Conference on Applications of Mathematics in Science and Engineering; 10-11 March 2016 sponsored by C COST.

    [8] Existence and Stability of the  Triangular  equilibrium points in the dynamical system of elliptic restricted three body problem of three bodies with oblate, radiating and triaxial primaries; C COST sponsored National Conference on Application of  Mathematics in Science and Engineering; 10-11 March 2016.

    [9] Linear Resonance stability of Triangular equilibrium points in the elliptic restricted three body problem with radiating and triaxial primaries;  Proceedings of the National Conference on Applications of Mathematics in Science and Engineering; 10-11 March 2016 sponsored by C COST.

    [10] Linear Resonance stability of Triangular equilibrium points in the elliptic restricted three body problem under the radiating primaries around the binary systems; Proceedings of the National Conference on Applications of Mathematics in Science and Engineering; 10-11 March 2016 sponsored by C COST.

    [11] Non-linear stability of the triangular libration points in ERTBP for radiating and oblate primaries in non- resonance case; BITCON 2016 Emerging Trends in Science and Technology for National development.

    [12] Characteristic Exponents of the Triangular Solution in the Elliptic Restricted Three Body problem under Radiating and Triaxial primaries; BITCON 2017 , National Conference on Challenges in Mathematics for the development of Science and Technology, 28 March 2017

    [13] Existence and Stability of Triangular equiliubrium points in ERTBP with oblate infinitesimal mass; BITCON 2017 , National Conference on Challenges in Mathematics for the development of Science and Technology, 28 March 2017

    [14] Non-Linear Stability of the Equilibrium points in the Elliptic restricted three body problem; BITCON 2017, National Conference on Challenges in Mathematics for the development of Science and Technology, 28 March 2017.

    [15] Effects of Poynting Robertson drag and oblateness on the stability and position of Triangular equilibrium points in Elliptic Restricted Three body Problem; BITCON 2017, National Conference on Challenges in Mathematics for the development of Science and Technology, 28 March 2017.

     

Other Info.

Other Responsibilities:

    Experience of Administrative Responsibilities in Academic Institutions:

    From

    To

    Administrative Position

    Major responsibility

    01/02/2008

    Till date

    Head Of Department, Department of Mathematics

    To look after academic activity of faculty members.

    01/07/2008

    31/12/2014

    Dean (R&D ), Bhilai Instittue of Technology, Durg

    To monitor the research activities of the faculty members

     

    2008

    2010

    Chairman, Proctorial Board

    To look after administration of Hostel, monitor various activities of students.

    2009

    2011

    Chairman,  Board of Studies of Mathematics, Chhattisgarh Swami Vivekananda Technical University

     

    2009

    2011

    Worked as Dean Faculty of Sciences,  Chhattisgarh Swami Vivekananda Technical University

    To look after the Research activities of University

    2009

    2011

    Worked as member Executive Council as well as Academic Council of  Chhattisgarh Swami Vivekananda Technical University

     

    2009

    2010

    Center Superintendent of  Examination, BIT, DURG

    Administrator of Examination Cell

    2010

    2011

    Senior Center Superintendent of  Examination,  BIT, DURG

    Administrator of Examination Cell

    2008

    2015

    Dean (R & D),  BIT, DURG

     

    2016

    Till date

    Chairman,  Board of Studies of Mathematics, Chhattisgarh Swami Vivekananda Technical University

     

     

     

        

    Worked as Reviewer of following reputed journals :

    • Maths Reviewer: American Mathematical Society.
    • Astrophysics & Space Science, Springer Journal of high repute.
    • Advances of Space Research, Elsevier Journal.
    • Journal of AMSE, France.
    • Indian Journal of Physics , Springer Journal of high repute. 
    • Differential Equations & Dynamical Systems, Springer Journal of high repute.
    • Journal of New Astronomy, Elsevier Journal.


Felowship/Awards/Other recognitions:

    Sponsored Workshops/STTP Conducted/FDP (Conferences chair/ Convertor/Coordinator/Co-Coordinator):

    Sl. No.

    Topic/Title

    Dates

    No. of Days

    Organization/Place

    1

    Workshop for faculty  on Applied Mathematics I

    28-29 July 2012

    02

    CSVTU Bhilai

    2

    Workshop for faculty  on Applied Mathematics II

    9-10 Nov 2012

    02

    CSVTU Bhilai

     

     

     

     

     

     

    Sponsored National/International Conference/Seminar/Symposium conducted:

    Sl. No.

    Topic/Title

    Dates

    No. of Days

    Organization/Place

    1

    National Seminar on Applications of Mathematical Modeling in Science and Technology

    15-16 March 2013

    02

    BIT ,DURG, Sponsored by AICTE

    2

    National conference on Application of Mathematics in Science and Engineering

    10-11 March 2016

    02

    BIT,DURG, Sponsored by  CCOST, Raipur

     

     

     

     

     

     

     

     Ph.D. Supervision (Awarded/Ongoing):

    S. No.

    Scholar’s Name

    Year of Regn.

    Status(Ongoing/Completed)

    1

    Sanjay Sharma

    1997

    Completed

    2

    Shilpi Dewangan

    2006

    Completed

    3

    Sandip Shrivastava

    2006

    Completed

    4

    M D Pandey

    2009

    Completed

    5

    C Ramesh Kumar

    2009

    Completed

    6

    Anil Kumar Dubey

    2012

    Completed

    7

    Amit Shrivastava

    2012

    Completed

    8

    T. Usha

    2013

    Thesis Submitted

    9

    Nutan Singh

    2013

    Thesis Submitted

    10

    K K Pandey

    2013

    Ongoing

     Invited talk/ Guest lecture delivered

    No.

    Title of

    paper

    presented

     

    Title of

    conference/seminar

    etc.

     

    Date

    of

    event

     

    Organized

    by

     

    Whether

    International/National/State/

    Regional/University or

    College level

    1.

    Non-linear parametric resonance of Cable connected Satellite system under effects of Solar radiation pressure and Magnetic field of the Earth

    73rd Annual Conference of IMA

    27-30 Dec 2007

    Indian Mathematical Society

     

    2.

    Invited talk on- Environmental Optimization

    Staff Development Program on Environmental Monitoring for Sustainable Development

    28 Nov-12 Dec 2008

    Department of Civil Engineering , BIT, DURG

    AICTE, New Delhi

     Books Authored

    S. No.

    Name of Book

    Co-authors

    Publisher

    Year of Publication

    1

    Non-linear effects on extensible cable connected satellite system

    Shilpi Dewangan

    Scholar’s Press

    2014

    2

    Photo gravitational elliptical restricted three body problem

    C Ramesh Kumar

    Scholar’s Press

    2014

    3

    Some non-linear effect on the motion and stability of satellite system

    M D Pandey

    Lambert Academic Publication

    2014

    4

    Study of Fixed point theorems in TVS and application to fractal

    A K Dubey

    Lambert Academic Publication

    2014

    Research Project Undertaken/Going on

    S. No.

    Name of Research Project

    Co-Investigator

    Funding Agency/Amount

    Status

    1

    Stability of the oblate                               infinitesimal in the elliptic restricted three body problem with oblate radiating primaries

     

     

    CCOST

     

    Ongoing

    Membership

    • Life member of Indian Astronomical society, Banglore, India.
    • Life member’s of the Indian Society of theoretical and Applied Mechanics, I.I.T. Khargpur, India.
    •  Life Member of Indian Academy of Mathematics Indore, India.
    •  Life member of Indian Society of Technical Education.

    List of National/International Workshop/STTP/FDP Attended :  

     

    Title

    No. of Days

    Organization

    Duration

     

    Functional Analysis & Metric Spaces

    21 days

    Jabalpur University