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DEPARTMENT OF MATHEMATICS
RESEARCH THRUST AREAS/ ACTIVE RESEARCH GROUPS
Department of Mathematics believe in developing good teaching and learning methods along
with research activities in areas which are relevant to the present day needs of Science,
Engineering and Technology. The Department is involved in the following research thrust
areas of Mathematics which are a good blend of pure and applied mathematics of
contemporary importance:
(a) Fractals & Chaos and Mathematical Analysis
(b) Numerical Analysis and Computational Continuum Mechanics
(c) Statistics, Fuzzy, Information Theory and Operations Research
(a) Fractals & Chaos and Mathematical Analysis
Fractals and chaos are new frontiers of science and important emerging interdisciplinary
areas of research nowadays. Wavelets and fractals have significant contributions in the
fields of image and signal processing, image compression, data compression and other
various approximations. Almost all branches of sciences and engineering are benefiting
from the new insights provided by them. Many shapes found in nature which are highly
rough and complex at different scales, fractal interpolation methods are popularly
accepted approximation tools in such cases. Mathematical analysis provides the
foundation for further development in these areas. The applications of explorations in
these areas encompasses various disciplines of sciences, engineering, medicine, business,
weather forecasting and several other areas of human activities.
Number of faculty members: 03 Number of publications: 41 (2014-18)
Number of Ph. D. awarded: 06 Number of Ph. D. ongoing: 01
(b) Numerical Analysis and Computational Continuum Mechanics
The numerical solutions of the problems occurring in Computational Continuum
Mechanics are of great practical importance. The governing simultaneous ordinary and
partial differential equations remain highly nonlinear and therefore, cannot be solved
analytically. These equations can be solved numerically by using numerical methods
such as finite element, finite difference, quasi-linearization, mesh free methods.
Number of faculty members: 09 Number of Publications: 123 (2014-18)
Number of Ph. D. awarded: 10 Number of Ph. D. ongoing: 13
(c) Statistics, Fuzzy, Information Theory and Operations Research
In this age of information revolution the role of statistics, fuzzy sets, information theory
2
and operations research is of prime importance. The statistical data are not always
precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy.
Also the results of measurements of such data can be best described by using fuzzy
numbers and fuzzy vectors. Statistical analysis methods have to be adapted for the
analysis of fuzzy data. Information theory deals with the study of problems concerning
information processing, information storage, information retrieval and decision-
making. This includes the study of uncertainty measures and various practical and
economical methods of coding information for transmission. Operations research is
required to deal with wide range of problem-solving techniques applied in the pursuit of
improved decision-making and efficiency, such as simulation, mathematical
optimization, queueing theory and other stochastic-process models.
Number of faculty members: 09 Number of Publications: 52 (2014-18)
Number of Ph. D. awarded: 08 Number of Ph. D. ongoing: 10
3
DEPARTMENT OF MATHEMATICS
Activities in Research Thrust Areas
Thrust Area Number of
Publications
Number of PhD’s
supervised
Number of
students
supervised for
M. Tech. thesis
(Completed)
Courses Offered
(2014-2018) Completed Ongoing
Fractals & Chaos
and Mathematical
Analysis
41 06 01 03
Fractals and Chaos,
Wavelets and Applications,
Integral Transforms.
Numerical
Analysis and
Computational
Continuum
Mechanics
123 10 13 02
Advanced Numerical Techniques,
Advanced Differential Equations,
Computational Fluid Dynamics,
Computer Programming and
Simulation,
Calculus of Variations and Finite
Element Method.
Statistics, Fuzzy,
Information
Theory and
Operations
Research
52 08 10 06
Advanced Operations Research,
Linear Statistical Models,
Fuzzy Calculus & Possibility
Theory,
Automata and Theory of
Computation,
Advanced Optimization
Techniques.
4
DEPARTMENT OF MATHEMATICS
Research Thrust Areas/ Active Research Groups
Publications (2014-18)
(a) Fractals & Chaos and Mathematical Analysis
A. Publications in International Journals:
1. Prasad, Bhagwati and K. Katiyar, "Multi Fuzzy Fractal Theorems in Fuzzy Metric
Spaces", Fuzzy Information and Engineering, vol. 9, pp. 225-236, 2017. [Indexed in
Scopus/ESCI] [Cited by Google-1, Cited by Scopus- 1, SNIP- 0.335, SJR- 0.855, JCR
Impact Factor-NIL H-Index-6]. 17KMSGMAIJ01
2. Singh, Akhilesh K., “Outer Measure on Effect Algebras”, Mathematica Slovaca, vol.
67 (4), 811-818, 2017. [Indexed in SCI] [Cited by Google-1, Cited by Scopus- 1, SNIP-
0.845, SJR- 0.339, JCR Impact Factor-0.314, H-Index-18]. 17ASOMMAIJ01
3. K. Mishra and Prasad, Bhagwati, "Classification of EEG Signals using Improved
Probabilistic Fractal Dimension", International Journal of Control Theory and
Applications, vol.10(6), pp.587-593, 2017. [Indexed in Scopus] [Cited by Google-1,
Cited by Scopus- 1, SNIP- 0.097, SJR- 0.104, JCR Impact Factor-NIL, H-Index-13].
17KMCOMAIJ01
4. Mishra, K. and Prasad, Bhagwati, “Some Generalized IFS in Fuzzy Metric Spaces”,
Advances in Fuzzy Mathematics, vol. 12(2), pp. 297-308, 2017. [Indexed in ICI]
[Cited by Google-1, Cited by Scopus- 0, SNIP- NIL, SJR- NIL, JCR Impact Factor-
NIL H-Index-NIL]. 17KMSGMAIJ01
5. Goyal, K. and Prasad, Bhagwati, “Approximate Fixed Points and Summable Almost
Stability”, Global Journal of Pure and Applied Mathematics, vol. 13, Number 9, pp.
6029-6040, 2017. [Cited by Google-NIL, Cited by Scopus- NIL, SNIP- NIL, SJR- NIL,
JCR Impact Factor-NIL, H-Index-NIL]
6. Prasad, Bhagwati and K. Katiyar, “The attractors of fuzzy super iterated function
systems”, Indian Journal of Science and Technology, vol. 10 (28), pp. 1-8, 2017.
[Indexed in Scopus] [Cited by Google-NIL, Cited by Scopus- NIL, SNIP- 1.270, SJR-
0.160, JCR Impact Factor- NIL, H-Index- 41].
5
7. Singhal, C. and Srivastava, G.S., On the logarithmic proximate order of analytic
functions of slow growth represented by Laplace-Stieltjes transformations, Journal of
Classical Analysis,10(2),119-129, 2017. . [Cited by Google-NIL, Cited by Scopus-
NIL, SNIP- NIL, SJR- NIL, JCR Impact Factor-NIL, H-Index-NIL]17CSOTMAIJ01
8. Srivastava, G.S., and Singhal, C., On the order and lower order of Laplace-Stieltjes
transformations with index pair (p,q), Italian J. Pure Appl. Math. 36 , 975-986,2016.
[Indexed in SCOPUS] [Cited by Google-0, Cited by Scopus-0, SNIP-0.459, SJR-0.216,
H-Index-8] 16GSOTMAIJ01
9. Srivastava G.S. and Kumar S., “Approximation and generalized growth of solutions to
a class of elliptic partial differential equations”, Funct. Approx. Comment. Math, Vol.
54, Issue 1, pp. 95-113, 2016. [Indexed in SCOPUS] [Cited by Google-0, Cited by
Scopus-0, SNIP-0.093, SJR-0.118, JCR Impact Factor-0, H-Index-2].16GSAAMAIJ01
10. Prasad, Bhagwati and Goyal K., "Stability of iteration for some general operators in
b-metric spaces", International Journal of Computer & Mathematical Sciences, vol. 5,
Issue 4, pp.78-83, 2016. [Cited by Google-1, Cited by Scopus- NIL, SNIP- NIL, IPP-
NIL, SJR- NIL, JCR Impact Factor-NIL H-Index-NIL]. 16BPSOMAIC02
11. Prasad, Bhagwati and Goyal K., "Stability Result of Iterative Procedure in Normed
Space", International Journal of Control Theory and Applications, Vol. 9(20), pp.
9465-9474, 2016. [Indexed in Scopus] [Cited by Google-2, Cited by Scopus- 1, SNIP-
0.097, IPP- NIL, SJR- 0.104, JCR Impact Factor-NIL H-Index-13].16BPSRMAIC01
12. Prasad, Bhagwati and Goyal, K., "Simple Comparison of Convergence of General
Iterations and Effect of Variation in Various Parameters", GRENZE International
Journal of Engineering and Technology, vol.5, pp. 200-206, 2016. [Cited by Google-2,
Cited by Scopus- 0, SNIP- NIL, IPP- NIL, SJR- NIL, JCR Impact Factor-NIL H-
Index-NIL].16BPSCMAIC01.
13. Prasad, Bhagwati and Goyal K., “Stability of Jungck-Noor iteration in b-metric
space”, International Journal of Control Theory and Applications, 9(41) 2016, pp.
1069-1079, 2016. [Indexed in Scopus] [Cited by Google-2, Cited by Scopus- 1, SNIP-
0.097, IPP- NIL, SJR- 0.104, JCR Impact Factor-NIL H-Index-13]. 16BPSOMAIJ01.
14. Shukla S. K., Pandey P. N., Saxena S., “Lagrange spaces with generalized $(\gamma,
\beta)$-metric”, Facta Universitatis (Nis) ¡ Ser. Math. Inform., Vol. 31, no.1, pp. 201-
6
212, 2016. [Cited by Google-NIL, Cited by Scopus- NIL, SNIP- NIL, SJR- NIL, JCR
Impact Factor-NIL, H-Index-NIL]
15. Singhal C. and Srivastava G.S., “On the approximation of an analytic function
presented by Laplace-Stieltje’s transformation”, Anal. Theory Appl., Vol. 31, Issue 4,
pp. 407- 420, 2015. [Cited by Google-4, Cited by Scopus-0, H-Index-8].
15CSOTMAIJ01
16. Srivastava G.S. and Kumar S., “Approximation and generalized lower order of entire
functions of several complex variables”, New Zealand Journal of Mathematics, Vol. 45,
pp. 11-17, 2015. [Cited by Google-0, Cited by Scopus-0]. 15GSAAMAIJ01
17. Sharma A. and Srivastava G. S., “Spaces of entire functions represented by vector
valued Dirichlet series of two complex variables”, Acta et. Univ.Tartuensis dr Math.,
Vol. 19, Issue 2, pp. 67-73, 2015. [Cited by Google-0, Cited by Scopus-0, SNIP-0.386,
SJR-0.143, H-Index-2]. 15ASSOMAIJ01
18. Akanksha and Srivastava G. S., “Multipliers on spaces of vector valued entire
Dirichlet series of two complex variables”, Italian J. Pure Appl. Math., Vol. 35, pp.
381-388, 2015. [Cited by Google-0, Cited by Scopus-0, SNIP-0.523, SJR-0.211, JCR
Impact Factor-0, H-Index-8]. 15AKMOMAIJ01
19. Sharma A. and Srivastava G.S., “Spaces of analytic functions represented by vector
valued Dirichlet series in a half plane”, Int. Bull. Math. Res., Vol. 2, Issue 1, pp. 65-74,
2015. . [Indexed in SCOPUS]. [Cited by Google-0, Cited by Scopus-0, SNIP-Nil, SJR-
Nil, JCR Impact Factor-Nil, H-Index- Nil] 15ASSOMANC01
20. Singhal C. and Srivastava G.S., “On the (p,q)- order and (p,q)-type of entire matrix
functions in complete Reinhardt domain”, Int. Bull. Math. Res., Vol.2, Issue 1, pp. 75-
82, 2015. . [Indexed in SCOPUS]. [Cited by Google-0, Cited by Scopus-0, SNIP-Nil,
SJR-Nil, JCR Impact Factor-Nil, H-Index- Nil]. 15CSOTMANC01
21. Prasad, Bhagwati and K. Mishra, “Classification of diabetic and non diabetic retinal
images using generalized fractal dimension”, International Journal of Advanced
Research & Engineering, Vol. 4(11), pp. 250-254, 2015. [Cited by Google-0, Cited by
Scopus- 0, SNIP-NIL, IPP-NIL, SJR- NIL, JCR Impact Factor-NIL. H-Index-NIL].
15BPCOMAIJ01.
7
22. Prasad, Bhagwati and Mishra,K.,“Harmonic Extension on an LB-Fractal,”
International Journal of Hybrid Information Technology, vol. 8 (9), pp, 89-94, 2015.
[Indexed in Scopus][Cited by Google-1, Cited by Scopus- NIL, SNIP- 0.028 NIL, IPP-
NIL, SJR- NIL, JCR Impact Factor-NIL H-Index-NIL]. 15BPHEMAIJ01
23. Goyal, K. and Prasad, Bhagwati, "Some Fixed Point Results in Ordered G-Metric
Spaces", Journal of Basic and Applied Engineering Research, vol. 2(12), pp. 1006-
1008, 2015. [Cited by Google-2, Cited by Scopus- 0, SNIP- NIL, IPP- NIL, SJR- NIL,
JCR Impact Factor-NIL H-Index-NIL]. 15KGSFMAIJ01
24. Prasad, Bhagwati, Singh, Bani and Katiyar, Kuldip, "Trigonometric quadratic fractal
interpolation functions", International Journal of Applied Engineering Research, vol.
10(16), pp. 37290-37302, 2015. [Indexed in Scopus] [Cited by Google-3, Cited by
Scopus- 3, SNIP- NIL, IPP- NIL, SJR- NIL, JCR Impact Factor-NIL H-Index-NIL].
15BPTQMAIJ01
25. Prasad, Bhagwati and K. Katiyar, "Stability and Lyapunov exponents of a q-deformed
map", International Journal of Pure and Applied Mathematics, vol. 104 (4), pp. 509-
516, 2015. [Indexed in Scopus][Cited by Google-1, Cited by Scopus- NIL, SNIP- NIL,
IPP- NIL, SJR- NIL, JCR Impact Factor-NIL H-Index-NIL]. 15BPSAMAIJ01
26. Akanksha and Srivastava G.S., Multipliers on Spaces of vector Valued Entire Dirichlet
Series, J. Classical Anal. 4(1) (2014), 89-95. [Indexed in SCOPUS]. [Cited by Google-
0, Cited by Scopus-0, SNIP-Nil, SJR-Nil, JCR Impact Factor-Nil, H-Index- Nil]
14AKMOMAIJ01
27. Prasad, Bhagwati and Katiyar, Kuldip, "A stability analysis of logistic model",
International Journal of Nonlinear Sciences, vol. 17(1), pp. 71-79, 2014. [Indexed in
Scopus] [Cited by Google-3 Cited by Scopus- 0, SNIP- NIL, IPP- NIL, SJR- NIL, JCR
Impact Factor-NIL H-Index-NIL]. 14BPASMAIJ01
28. Prasad, Bhagwati and Katiyar, K., "Stability and fractal patterns of complex logistic
map", Cybernetics and Information Technologies, vol. 14, no. 3, pp.14–24, 2014.
[Indexed in Scopus] [Cited by Google-1, Cited by Scopus- 1, SNIP- 0.397, IPP- NIL,
SJR- 0.204, JCR Impact Factor-NIL H-Index-9]. 14BPSAMAIJ01
29. Prasad, Bhagwati and Sahni, Ritu, "A novel variant of N-R method and its
convergence", Applied Mathematical Sciences, vol. 8, , no. 141, pp. 7025 – 7029,
8
2014.[Indexed in Scopus][Cited by Google-NIL, Cited by Scopus- NIL, SNIP- 0.836,
IPP- NIL, SJR- 0.153, JCR Impact Factor-NIL H-Index-27]. 14BPANMAIJ01
30. Prasad, Bhagwati, Singh, Bani and Katiyar, Kuldip, "Modeling curves via fractal
interpolation with VSFF", International Journal of Computer Applications, vol.
ICACEA1(1), pp. 191-194, 2014. [Cited by Google-5, Cited by Scopus- 0, SNIP- NIL,
IPP- NIL, SJR- NIL, JCR Impact Factor-NIL H-Index-NIL]. 14BPMCMAIJ01
B. Publications in National Journals: NIL
C. Publications in International Conferences:
31. Katiyar, K. and Prasad, Bhagwati, "Shape preserving trigonometric fractal
interpolation", AIP Conference Proceedings 1802 (1), 020007, 2017. [Indexed in
Scopus] [Cited by Google-1, Cited by Scopus- 1, SNIP-0.300, IPP- NIL, SJR- 0.165,
JCR Impact Factor-NIL H-Index-54]. 17KKSPMAIC01
32. Goyal, K. and Prasad, Bhagwati,"Some fixed point theorems in Gb-cone metric
space", AIP Conference Proceedings 1802 (1), 020004, 2017. [Indexed in Scopus]
[Cited by Google-1, Cited by Scopus- 1, SNIP-0.300, IPP- NIL, SJR- 0.165, JCR
Impact Factor-NIL H-Index-54]. 17KGSFMAIC01
33. Goyal, K. and Prasad, Bhagwati, "Dynamics of iterative schemes for quadratic
polynomial", AIP Conference Proceedings 1897(1), 020031:1-8, 2017. [Indexed in
Scopus] [Cited by Google-1, Cited by Scopus- 1, SNIP-0.300, IPP- NIL, SJR- 0.165,
JCR Impact Factor-NIL H-Index-54]. 17KGDOMAIC01
34. Mishra, K. and Prasad, Bhagwati, "Iterated function systems in G b-metric space",
AIP Conference Proceedings 1897(1), pp.020035:1-8 (2017. [Indexed in Scopus]
[Cited by Google-1, Cited by Scopus- 1, SNIP-0.300, IPP- NIL, SJR- 0.165, JCR
Impact Factor-NIL, H-Index-54].17KMIFMAIC01
35. Katiyar, K. and Prasad, Bhagwati, “Construction of RFIF using VVSFs with
application”, AIP Conference Proceedings 1897(1), 020027 (2017); pp. 020027:1-8,
2017. [Indexed in Scopus] [Cited by Google-1, Cited by Scopus- 1, SNIP-0.300, IPP-
NIL, SJR- 0.165, JCR Impact Factor-NIL H-Index-54]. 17KKCOMAIC01
36. Akhilesh Kumar Singh, Functions of bounded variation on effect algebras, AIP
Conference Proceedings 1897, 020022 (2017); doi: 10.1063/1.5008701 [Indexed in
9
Scopus] [Cited by Google-0, Cited by Scopus- 0, SJR-0.165, H-Index-54].
17ASFOMAIC01
37. Saxena S., Pandey P. N. and Shukla S. K., “Geometric objects recurrent in a direction
and directionally recurrent Finsler spaces”, AIP Conference Proceedings, 2017, vol.
1897, p.020025. [Cited by Google-NIL, Cited by Scopus- NIL, SNIP- NIL, SJR- NIL,
JCR Impact Factor-NIL, H-Index-NIL]
38. Prasad, Bhagwati and Mishra, K., “Fractals in V-variable intutionistic fuzzy metric
spaces,” Proc. International Conference on Applications of Fractals and Wavelets,
Coimbatore, India, January 2015, pp. 67-77, 2015. [Cited by Google-1, Cited by
Scopus- NIL, SNIP- NIL, IPP- NIL, SJR- NIL, JCR Impact Factor-NIL H-Index-NIL].
15BPFIMAIC01
39. Prasad, Bhagwati, Singh, B. and Katiyar, K., “Superfractal Interpolation function with
VSFF,” Proc. International Conference on Applications of Fractals and Wavelets,
Coimbatore, India, January 2015, pp. 59–65, 2015. [Cited by Google-1, Cited by
Scopus- NIL, SNIP- NIL, IPP- NIL, SJR- NIL, JCR Impact Factor-NIL H-Index-NIL].
15BPSIMAIC01
40. Prasad, Bhagwati and Mishra, Kunti, "The graphics of some non quadratic rational
maps" International Conference on Innovative Trends in Applied Physical, Chemical,
Mathematical Science and Emerging Energy Technology for Sustainable Development
(APCMET-2014), New Delhi, India 19-20 April 2014, pp. 187-197, 2014. [Cited by
Google-NIL, Cited by Scopus- NIL, SNIP- NIL, IPP- NIL, SJR- NIL, JCR Impact
Factor-NIL H-Index-NIL].14BPTGMAIC01
D. Publications in National Conferences:
41. Prasad, Bhagwati, "On some remarkable contributions of Bhaskaracharya",
Mathematics and Reality (AISSQ2018), Bhubaneswar, India. October 2018, pp. 396-
408, 2018. [Cited by Google-NIL, Cited by Scopus- NIL, SNIP- NIL, SJR- NIL, JCR
Impact Factor-NIL, H-Index-NIL]
10
(b) Numerical Analysis and Computational Continuum Mechanics
A. Publications in International Journals:
1. Mittal, R. C. & Rohila, R., "Travelling and Shock Wave Simulations in a Viscous
Burgers'Equation with Periodic Boundary Conditions" Int J. Computational and
Applied Mathematics, vol. 4, No. 16 , pp. 150, 2018. [Cited by Google-NIL, Cited by
Scopus- NIL, SNIP- NIL, SJR- NIL, JCR Impact Factor-NIL, H-Index-NIL]
18RCTAMAIJ01
2. Aggarwal, A.K. and Dixit, D., “Effect of Suspended Particles on Thermosolutal
Convection of Rivlin-Ericksen Fluid in Porous Medium with Variable Gravity” Int. J.
of Applied Mechanics and Engineering, vol.23, No.3, pp.813-820, DOI: 10.2478/ijame-
2018-0045, 2018 [Indexed in Scopus] [Cited by Google-0, Cited by Scopus-0, SNIP-
0.0.331, SJR-0.0.153, JCR impact factor-NIL, H-index- 3]. 14AAEOMAIJ01
3. Sharma S., Panchal R., "Creep stresses in functionally graded rotating orthotropic
cylinder with varying thickness and density under internal and external pressure",
Structural Integrity and Life, Vol.18, No.2, pp. 111-119, 2018. [Indexed in Scopus,
ESCI] [Cited by Google-0, Cited by Scopus-0, SNIP-0.647, SJR-0.237, JCR impact
factor-NIL, H-index-3]. 18SSCSMAIJ01
4. Sharma S., Panchal R., "Elastic-Plastic Transition of Pressurized Functionally Graded
Orthotropic Cylinder using Seth’s Transition Theory", Journal of Solid Mechanics, Vol.
10, No. 2, pp. 450-463, 2018. [Indexed in Scopus] [Cited by Google-0, Cited by
Scopus-0, SNIP-0.302, SJR-0.237, JCR impact factor-NIL, H-index-10].
18SSEPMAIJ01
5. Sharma S., Yadav S., Sharma R., "Creep Torsion in Thick-Walled Circular Cylinder
under Internal and External Pressure", Structural Integrity and Life, Vol.18, No.2, pp.
89-97, 2018. [Indexed in Scopus, ESCI] [Cited by Google-0, Cited by Scopus-0,
SNIP-0.647, SJR-0.237, JCR impact factor-NIL, H-index-3]. 18SSCTMAIJ01
6. Yadav S., Sharma S., "Torsion in Microstructure Hollow Thick-walled Circular
Cylinder Made up of Orthotropic Material", Journal of Solid Mechanics, Vol. 10, No.
3, pp. 581-590, 2018. [Indexed in Scopus] [Cited by Google-0, Cited by Scopus-0,
SNIP-0.302, SJR-0.237, JCR impact factor-NIL, H-index-10]. 18SYTIMAIJ01
11
7. Sharma S., Yadav S., Radaković Z., "Finite Creep Deformation in Thick-Walled
Circular Cylinder with Varying Compressibility under External Pressure", Structural
Integrity and Life, Vol. 18, No 1, pp. 31–36, 2018. [Indexed in Scopus, ESCI] [Cited
by Google-0, Cited by Scopus-0, SNIP-0.647, SJR-0.237, JCR impact factor-NIL, H-
index-3]. 18SSFCMAIJ01
8. Sharma R., Sharma S., Radaković Z., "Thermal Creep Analysis of Pressurized Thick-
Walled Cylindrical Vessels”, Structural Integrity and Life, Vol. 18, No 1, pp. 7–14,
2018. [Indexed in Scopus, ESCI] [Cited by Google-0, Cited by Scopus-0, SNIP-0.647,
SJR-0.237, JCR impact factor-NIL, H-index-3]. 18RSTCMAIJ01
9. Sharma S., Sharma R., Panchal R., "Creep Transition in Transversely Isotropic
Composite Circular Cylinder Subjected to Internal Pressure", International Journal of
Pure and Applied Mathematics, Vol. 120, No. 1, pp. 87-96, 2018. [Indexed in Scopus]
[Cited by Google-0, Cited by Scopus-0, SNIP-0.394, SJR-0.139, JCR impact factor-
NIL, H-index-21]. 18SSCTMAIJ02
10. Swapna, G., Kumar, L., Rana, P., Kumari, A. and Singh, B. "Finite element study of
radiative double-diffusive mixed convection magneto-micropolar flow in a porous
medium with chemical reaction and convective condition," Alexandria Engineering
Journal, Vol. 57, pp. 107--120, 2018 [Indexed in Scopus/SCI] [Cited by Google-5,
Cited by Scopus-3, SNIP-1.497, SJR-0.604, JCR impact factor-NIL, H-index-25]
18GSFEMAIJ01
11. Gupta, D., Kumar, L., Bég, O.A. and Singh, B., “Finite element analysis of MHD flow
of micropolar fluid over a shrinking sheet with a convective surface boundary
condition”, Journal of Engineering Thermophysics, Vol. 27, No. 2, pp. 202–220 (2018).
[Indexed in Scopus/SCI] [Cited by Google-2, Cited by Scopus-2, SNIP-1.080, SJR-
0.435, JCR impact factor-0.767, H-index-15] 18DGFEMAIJ01
12. Kumari P., Modi C., Sharma V. K., “Dynamic response of normal moving load on a
transversely isotropic piezoelectric half-space with parabolic irregularity”, Waves in
Random and Complex Media, vol.28, pp. 601-623, 2018. [Indexed in SCI] [Cited by
Google-3, Cited by Scopus- 2, SNIP- 0.895, SJR- 0.453, JCR Impact Factor-2.540, H-
Index-39]. 18PKDRMAIJ01
13. V. Chauhan and Srivastava P. K., “Trio-Geometric mean-based three-stage Runge–
Kutta algorithm to solve initial value problem arising in autonomous systems,”
12
International Journal of Modeling, Simulation, and Scientific Computing, vol. 9, no. 04,
pp. 1850026, 2018. [Indexed in Scopus] [Cited by Google-NIL, Cited by Scopus- 1,
SNIP- 0.430, SJR- 0.2, H-Index- 11]. . 18VCTGMAIJ01.
14. Rana, P. and Shukla, N. "Entropy generation analysis for non-similar analytical study
of nanofluid flow and heat transfer under the influence of aligned magnetic field,"
Alexandria Engineering Journal, Vol. 57, pp. 3299--3310, 2018. [Indexed in
Scopus/SCI] [Cited by Google-NIL, Cited by Scopus-NIL, SNIP-1.497, SJR-0.604,
JCR impact factor-NIL, H-index-25] 16MUFEMAIJ01
15. Rana, P., Shukla, N., Beg, O. A., Kadir, A. and Singh, B. "Unsteady electromagnetic
radiative nanofluid stagnation-point flow from a stretching sheet with chemically
reactive nanoparticles, Stefan blowing effect and entropy generation," Proceedings of
the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials,
Nanoengineering and Nanosystems, Vol. 232, pp. 69--82, 2018. [Indexed in
Scopus/SCI] [Cited by Google-2, Cited by Scopus-3, SNIP-0.518, SJR-0.169, JCR
impact factor-NIL, H-index-12] 18PRUEMAIJ01
16. Kaur L., Wazwaz A. M., “Dynamical analysis of lump solutions for (3+ 1)
dimensional generalized KP-Boussinesq equation and its dimensionally reduced
equations”, Physica Scripta, Vol. 93, pp. 075203, 2018. [Indexed in Scopus/SCI/SCIE]
[Cited by Google-9, Cited by Scopus- 6, SNIP- 0.601, SJR- 0.376, JCR Impact Factor-
1.902, H-Index-66]. 18LKDAMAIJ01
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26. Sharma S., Thakur P., Sharma R., Bhardwaj R.K., Radaković Z., "Elastic-Plastic
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27. Sharma S., Panchal R., "Thermal Creep Deformation in Pressurized Thick-Walled
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28. Sahni M., Sharma S., "Elastic-Plastic Deformation of a Thin Rotating Solid Disk of
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29. Rana, P., Dhanai, R. and Kumar, L. "MHD slip flow and heat transfer of Al2O3-water
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30. Rana, P., Dhanai, R. and Kumar, L. "Radiative nanofluid flow and heat transfer over a
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31. Tiwari P.,Nagar P., “A survey on buckling Analysis of nanostructures via nonlocal
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33. Sheikhoslami, M., Rana, P. and Soheil, S. "Numerical study of MHD natural
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35. Rana, P., Uddin, M. J., Gupta, Y. and Ismail, A. I. M. "Slip effects on MHD Hiemenz
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39. Dhanai, R., Rana, P. and Kumar, L. "Multiple solutions in MHD flow and heat transfer
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40. Dhanai, R., Rana, P. and Kumar, L. "Critical values in slip flow and heat transfer
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42. Dhanai, R., Rana, P. and Kumar, L. "MHD mixed convection nanofluid flow and heat
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43. Kumari P., Sharma V. K. and Modi C., “Reflection/refraction pattern of quasi-(P/SV)
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44. Kumari P., Sharma V.K., Modi C., “Modeling of magnetoelastic shear waves due to
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45. Kumari P., Modi C.,Sharma V.K., “Torsional waves in a magneto-viscoelastic layer
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46. Modi C., Kumari P., Sharma V.K., “Reflection/refraction of qP/qSV wave in layered
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51. Sheikholeslami, M., Gorji-Bandpy, M., Ganji, D. D., Rana, P. and Soleimani, S.
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52. Agarwal, S. and Rana, P. "Nonlinear convective analysis of a rotating Oldroyd-B
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53. Khurana, M., Rana, P. and Srivastava, S. "Influence of the combined effect of
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56. Sheikholeslami, M., Ashorynejad, H. R. and Rana, P. "Lattice Boltzmann simulation
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57. Dhanai, R., Rana, P. and Kumar, L. "Multiple solutions of MHD boundary layer flow
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58. Gupta, D., Kumar, L., Bég, O.A. and Singh, B., “Finite element simulation of nonlinear
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72. Agarwal, S. and Rana, P. "Convective transport in a binary nanofluid saturated porous
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78. Aggarwal A. K., Sharma R., Sharma S., "Collapse Pressure Analysis of Transversely
Isotropic Thick-walled Cylinder using Lebesgue Strain Measure and Transition
Theory", The Scientific World Journal, Vol. 2014, pp. 1-10, 2014. [Indexed in
22
Scopus] [Cited by Google-4, Cited by Scopus-6, SNIP-0.87, SJR-0.375, JCR impact
factor-0, H-index-62]. 14AACPMAIJ01
79. Sharma R., Aggarwal A. K., Sharma S., Sahni M., "Thermo Creep Transition in
Functionally Graded Thick-Walled Circular Cylinder under External Pressure", Annals
of the Faculty of Engineering Hunedoara, Vol. 12, No. 4, pp. 335-342, 2014. [Indexed
in Google Scholar] [Cited by Google-2, Cited by Scopus-0, SNIP-0, SJR-0, JCR
impact factor-NIL, H-index-0]. 14RSTCMAIJ01
80. Makhija, S., Aggarwal, A. K. “Effect of Suspended Particles, Rotation and Magnetic
Field on Thermosolutal Convection in Rivlin-Ericksen Fluid with Varying Gravity
Field in Porous Medium” Annals of the Faculty of Engineering Hunedoara, vol. 12, No.
4, pp. 63-72, 2014. [Cited by Google-2, Cited by Scopus-0, SNIP-0, SJR-0, JCR impact
factor-NIL, H-index-0]. 14SMEOMAIJ01
81. Sharma S., Sahai I., Kumar R., "Thermo Elastic-Plastic Transition of Transversely
Isotropic Thick-Walled Circular Cylinder under Internal and External Pressure",
Multidiscipline Modelling in Materials and Structures, Vol. 10, No. 2, pp 211-227,
2014. [Indexed in Scopus, ESCI] [Cited by Google-5, Cited by Scopus-6, SNIP-0.439,
SJR-0.191, JCR impact factor-NIL, H-index-16]. 14SSTEMAIJ01
82. Gupta, D., Kumar, L., Bég, O.A. and Singh, B., “Finite element analysis of transient
heat and mass transfer in microstructural boundary layer flow from a porous stretching
sheet”, Computational Thermal Sciences, Vol. 6 (2): 155–169 (2014). [Indexed in
Scopus/ ESCI] [Cited by Google-5, Cited by Scopus-5, SNIP-0.434, SJR-0.244, JCR
impact factor-NIL, H-index-11 ] - 14DGFEMAIJ01
83. Gupta, D., Kumar, L., Bég, O.A. and Singh, B., “Finite element simulation of mixed
convection flow of micropolar fluid over a shrinking sheet with thermal radiation”,
Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process
Mechanical Engineering, Vol. 228, 61-72 (2014). [Indexed in Scopus/SCI] [Cited by
Google-28, Cited by Scopus-23, SNIP-0.846, SJR-0.322, JCR impact factor-1.211, H-
index-24 ] - 14DGFEMAIJ02
84. Gupta, D., Kumar, L. and Singh, B., “Finite element solution of unsteady mixed
convection flow of micropolar fluid over a porous shrinking sheet”, The Scientific
World Journal, Vol. 2014, Article ID 362351, 11 pages (2014). [Indexed in Scopus]
23
[Cited by Google-11, Cited by Scopus-10, SNIP-0.870, SJR-0.375, JCR impact factor-
NIL, H-index-62 ] - 14DGFEMAIJ03
85. Saxena, P. and Kumar, L., “A study of the effect of magnetic field on the rotation of a
viscous fluid near a porous medium with a constant suction”, International Journal of
Engineering, Science and Technology, Vol. 6, No. 4, 64-76 (2014). [Indexed in NIL ]
[Cited by Google-1, Cited by Scopus-NIL, SNIP-NIL, SJR-NIL, JCR impact factor-
NIL, H-index-NIL] - 14PSASMAIJ01
86. Saxena, P. and Kumar, L., “Theoretical study of the effect of the magnetic field on
cardiovascular problems taking the approach of channel of varying gap bounded by a
porous medium”, Int. J. of Appl. Math and Mech., 10 (9): 76-95 (2014) [Indexed in the
Zentralblatt database] [Cited by Google-NIL, Cited by Scopus-NIL, SNIP- NIL, SJR-
NIL, JCR impact factor-NIL, H-index-NIL] - 14PSTSMAIJ01
87. Kumari P., Sharma V. K, “Propagation of torsional waves in a viscoelastic layer over
an inhomogeneous half space”, Acta Mechanica, vol. 225, pp. 1673-1684, 2014.
[Indexed in SCI] [Cited by Google-31, Cited by Scopus- 26, SNIP- 1.270, SJR- 1.040,
JCR Impact Factor-2.113, H-Index-61]. 14PKPOMAIJ01
88. Chattopadhyay A., Kumari P., Sharma V. K., “Reflection and transmission of three
dimensional qP wave through layered fluid medium between two distinct triclinic half-
spaces”, International Journal of Geomechanics (ASCE), vol. 14 (2), pp. 182-190,
2014. [Indexed in SCIE] [Cited by Google-14, Cited by Scopus- 12, SNIP- 1.270, SJR-
1.040, JCR Impact Factor-NIL, H-Index-44]. 14ACRAMAIJ01
89. Srivastava P. K., “Study of differential equations with their polynomial and
nonpolynomial spline based approximation,”Acta Tehnica Corviniensis – Bulletin of
Engineering, vol. 7, no. 3, pp. 139, 2014. [Indexed in Google Scholar] [Cited by
Google-6, Cited by Scopus- NIL, SNIP- NIL, SJR- NIL, H-Index-
NIL]. 14PSSOMAIJ01 .
B. Publications in National Journals:
90. Dhanai, R., Rana, P. and Kumar, L. "Dual solutions in MHD boundary layer nanofluid
flow and heat transfer with heat source/sink considering viscous dissipation," Research
Journal of Engineering and Technology, Vol. 6, pp. 142, 2015. [Cited by Google-2,
Cited by Scopus-NIL, SNIP-NIL, SJR-NIL, JCR impact factor-NIL, H-index-NIL] -
15RDDSMANJ01
24
C. Publications in International Conferences:
91. Verma P., Kaur L., "Analytic study of (3+ 1)-dimensional Kadomstev-Petviashvili-
Boussinesq equation: Painlevé analysis and exact solutions", AIP Conference
Proceedings, vol. 1975, pp.030022, 2018. [Indexed in Scopus] [Cited by Google-NIL,
Cited by Scopus- NIL, SNIP- 0.300, SJR- 0.165, JCR Impact Factor- NIL, H-Index-
54]. 18PVASMAIJ01
92. Aggarwal, A. K. and Makhija, S., “Hall Effect on Thermosolutal Convection of
Ferromagnetic Fluids in Porous Medium”, Advancement in Mathematical Sciences,
AIP Conference Proceedings, vol. 1897, Issue 1, pp. 020016-1–020016-11; 2017
[Indexed in Scopus] [Cited by Google-0, Cited by Scopus-0, SNIP-0.3, SJR-0.165,
JCR impact factor-NIL, H-index-54]. 17AAHEMAIC01.
93. Aggarwal, A. K. and Dixit, D. “ Thermosolutal instability of Rivlin-Ericksen fluid
under the effect of suspended particles and compressibility in porous medium”
Advancement in Mathematical Sciences, AIP Conference Proceedings, vol. 1897, Issue
1, pp. 020010-1-020010-7; 2017 [Indexed in Scopus] [Cited by Google-0, Cited by
Scopus-0, SNIP-0.3, SJR-0.165, JCR impact factor-NIL, H-index-54].
17AATIMAIC01.
94. Aggarwal, A. K. and Verma, A., “Effect of Hall currents on double diffusive
convection of compressible Rivlin-Ericksen fluid permeated with suspended particles
in porous medium” Mathematical Sciences and its Applications, AIP Conference
Proceedings, vol. 1802, Issue 1, pp. 020001-1-020001-9; ISSN 0094243, 2017
[Indexed in Scopus] [Cited by Google-2, Cited by Scopus-2, SNIP-0.3, SJR-0.165,
JCR impact factor-NIL, H-index-54]. 17AAEOMAIC01.
95. Sharma S., Panchal R., "Effect of Non-homogeneity on Orthotropic Creep Stresses in a
Pressurized Circular Cylinder", Advancement in Mathematical Sciences, American
Institute of Physics, 1897, 020002-1–020002-11; 2017. [Indexed in Scopus] [Cited by
Google-0, Cited by Scopus-0, SNIP-0.3, SJR-0.165, JCR impact factor-NIL, H-index-
54]. 17SSEOMAIC01
96. Sharma S., Sharma R., "Finite Deformations in Pressurized Thick-Walled Circular
Cylinder with Steady State Temperature", Advancement in Mathematical Sciences,
American Institute of Physics, 1897, 020004-1–020004-11; 2017. [Indexed in Scopus]
25
[Cited by Google-0, Cited by Scopus-0, SNIP-0.3, SJR-0.165, JCR impact factor-NIL,
H-index-54]. 17SSFDMAIC01
97. Sharma S., Sahani M., Sharma R., "Creep Deformation of a Non-homogeneous Thin
Rotating Disk of Exponentially Varying Thickness with Internal Pressure",
Advancement in Mathematical Sciences, American Institute of Physics, 1897,
020011-1–020011-15; 2017. [Indexed in Scopus] [Cited by Google-0, Cited by
Scopus-1, SNIP-0.3, SJR-0.165, JCR impact factor-NIL, H-index-54].
17SSCDMAIC01
98. Sharma S., Panchal R., Sahni M., Sharma R., "Finite Deformations of Functionally
Graded Shell under Outer Pressure with Steady State Temperature", Advancement in
Mathematical Sciences, American Institute of Physics, 1897, 020032-1–020032-9;
2017. [Indexed in Scopus] [Cited by Google-0, Cited by Scopus-0, SNIP-0.3, SJR-
0.165, JCR impact factor-NIL, H-index-54]. 17SSFDMAIC02
99. Sharma S., Sahni M., Kumar R., "Thermal Elastic-Plastic Transition of Non-
Homogeneous Thick-Walled Circular Cylinder under External Pressure",
Mathematical Sciences and its Applications, American Institute of Physics, 1802,
020013-1–020013-9; 2017. [Indexed in Scopus] [Cited by Google-2, Cited by
Scopus-2, SNIP-0.3, SJR-0.165, JCR impact factor-NIL, H-index-54].
17SSTEMAIC01
100. Sharma S., Yadav S., "Thermo Creep Analysis of Thick-Walled Functionally Graded
Cylinder under Internal and External Pressure", Mathematical Sciences and its
Applications, American Institute of Physics, 1802, 020014-1–020014-7; 2017.
[Indexed in Scopus] [Cited by Google-2, Cited by Scopus-2, SNIP-0.3, SJR-0.165,
JCR impact factor-NIL, H-index-54]. 17SSTCMAIC01
101. Gupta, D., Kumar, L., Bég, O.A., and Singh, B. “Numerical study of steady
dissipative mixed convection optically-thick micropolar flow with thermal radiation
effects”, AIP Conference Proceedings 1897, 020012 (2017). [Indexed in Scopus]
[Cited by Google-NIL, Cited by Scopus-NIL, SNIP-0.165, SJR-0.300, JCR impact
factor-NIL, H-index-54] -17DGNSMAIC01
102. Nagar P., Tiwari P., “Recursive differentiation method to study the nature of carbon
nanobeams: A numerical approach,” In AIP Conference Proceedings, 2017, vol. 1897,
26
p.020009. [Indexed in Scopus] [Cited by Google-NIL, Cited by Scopus-NIL, SNIP-
0.165, SJR-0.300, JCR impact factor-NIL, H-index-54]
103. Modi C., Kumari P., Sharma V.K., “Torsional surface wave propagation in
viscoelastic isotropic layer sandwiched between inhomogeneous half spaces”,
Mathematical Sciences and its Applications, AIP Conference Proceedings, vol. 1802,
Issue 1, pp. 020010, 2017. [Indexed in Scopus] [Cited by Google-0, Cited by Scopus-
0, SNIP- 0.300, SJR- 0.165, JCR Impact Factor-NIL, H-Index-54]. 17CMTSMAIC01
104. Kumari P., “Scattering of quasi seismic waves between self-reinforced and triclinic
media” Advancement in Mathematical Sciences, AIP Conference Proceedings, vol.
1897, Issue 1, pp. 020015, 2017. [Indexed in Scopus] [Cited by Google-0, Cited by
Scopus- 0, SNIP- 0.300, SJR- 0.165, JCR Impact Factor-NIL, H-Index-54].
17PKSOMAIC01
105. Chaurasia A., Srivastava P. C., Gupta Y., “Solution of higher order boundary value
problems by spline methods” , Published in AIP Conference Proceedings 1897 (1),
020018 (2017). [Indexed in Scopus] [Cited by Google-NIL, Cited by Scopus-NIL,
SNIP-0.165, SJR-0.300, JCR impact factor-NIL, H-index-54] 17ACSOMAIC01
106. Gupta Y., “Numerical solution of system of boundary value problems using B-spline
with free parameter”, Published in AIP Conference Proceedings 1802, 020006 (2017).
[Indexed in Scopus] [Cited by Google-NIL, Cited by Scopus-NIL, SNIP-0.165, SJR-
0.300, JCR impact factor-NIL, H-index-54] 17YGNSMAIC01
107. Agarwal, S. and Rana, P. "Influence of g–jitter on the Rayleigh-Benard convection in
nanofluids with internal heat source" Advancement in Mathematical Science, AIP
Conference Proceedings, Vol. 1897, pp. 020013, 2017. [Indexed in Scopus/SCI]
[Cited by Google-NIL, Cited by Scopus-NIL, SNIP-0.300, SJR-0.165, JCR impact
factor-NIL, H-index-54] 17NSEOMAIC01
108. Rana, P., Khurana, M. and Srivastava, S. "Linear stability analysis on the onset of
MHD non-Newtonian viscoelastic rotating nanofluid layer with heat generation"
Advancement in Mathematical Science, AIP Conference Proceedings, Vol. 1897, pp.
020030, 2017. [Indexed in Scopus/SCI] [Cited by Google-NIL, Cited by Scopus-1,
SNIP-0.300, SJR-0.165, JCR impact factor-NIL, H-index-54] 17NSUMMAIC01
109. Shukla, N. and Rana, P. "Unsteady MHD nanofluid flow past a stretching sheet with
Stefan blowing effect: HAM solution"Advancement in Mathematical Science, AIP
27
Conference Proceedings, Vol. 1897, pp. 020037, 2017. [Indexed in Scopus/SCI]
[Cited by Google-2, Cited by Scopus-2, SNIP-0.300, SJR-0.165, JCR impact factor-
NIL, H-index-54] 17GVCTMAIC01
110. Shukla, N., Rana, P., Beg, O. A. and Singh, B. "Effect of chemical reaction and
viscous dissipation on MHD nanofluid flow over a horizontal cylinder: Analytical
solution", Advancement in Mathematical Science, AIP conference proceedings, Vol.
1802, pp. 020015, 2017. [Indexed in Scopus] [Cited by Google-9, Cited by Scopus-7,
SNIP-0.300, SJR-0.165, JCR impact factor-NIL, H-index-54] 17PRLSMAIC01
111. Verma, G. and Rana, P. "Creep stresses in a spherical shell under steady state
temperature" Advancement in Mathematical Science, AIP Conference Proceedings,
Vol. 1897, pp. 020033, 2017. [Indexed in Scopus] [Cited by Google-NIL, Cited by
Scopus-NIL, SNIP-0.300, SJR-0.165, JCR impact factor-NIL, H-index-54]
17SAIOMAIC01
112. Verma, G., Rana, P., Pathania, D. S. and Thakur, P. "Creep transition in the rotating
spherical shell under the effect of density variable by Seth’s transition theory",
Advancement in Mathematical Science, AIP Conference Proceedings, Vol. 1802, pp.
020020, 2017. [Indexed in Scopus] [Cited by Google-3, Cited by Scopus-1, SNIP-
0.300, SJR-0.165, JCR impact factor-NIL, H-index-54] 17GVCSMAIC01
113. Sahni M., Sharma S., "Elastic-Plastic Deformation of a Rotating Solid Disk of
Exponentially Varying Thickness and Exponentially Varying Density", Proceedings
of the International Multi Conference of Engineers and Computer Scientists 2016, Vol
II, IMECS 2016, March 16 - 18, 2016, Hong Kong. [Indexed in NO] [Cited by
Google-0, Cited by Scopus-0, SNIP-0, SJR-0, JCR impact factor-NIL, H-index-0].
16MSEPMAIC01
114. Sahni M., Sharma S., "Study of Creep Behaviour in Bending of Rotating Rectangular
Plates", 7th International Conference on Creep, Fatigue and Creep-Fatigue Interaction
(CF-7), Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu, India.
January 19-22, 2016, pp. 491-496. [Indexed in NO] [Cited by Google-0, Cited by
Scopus-0, SNIP-0, SJR-0, JCR impact factor-NIL, H-index-0]. 16MSSOMAIC01
115. Sharma R., Aggarwal A. K., Sharma S., "Collapse Pressure Analysis in Torsion of a
Functionally Graded Thick-Walled Circular Cylinder under External Pressure", First
International Conference on Structural Integrity (ICONS-2014), Kalpakkam, India,
28
723–730, February 4-7, 2014. [Cited by Google-0, Cited by Scopus-0, SNIP-0, SJR-
0, JCR impact factor-NIL, H-index-0]. 14RSCPMAIC01
116. Sharma R., Aggarwal A. K., Sharma S., "Collapse Pressure Analysis in Torsion of a
Functionally Graded Thick-Walled Circular Cylinder under External Pressure",
Procedia Engineering, Vol. 86, pp. 738-747, 2014. [Indexed in Scopus] [Cited by
Google-4, Cited by Scopus-5, SNIP-0.783, SJR-0.282, JCR impact factor-NIL, H-
index-40]. 14RSCPMAIC02
117. Aggarwal, A. K. and Sharma, R., “Safety factors in Thermal Creep Transition of
Thick-walled Circular Cylinder under External Pressure using Lebesgue Strain
Measure and Transition Theory”, Proceedings of First International Conference on
Structural Integrity (ICONS-2014), Kalpakkam, India, pp. 707–714, February, 2014.
[Cited by Google-0, Cited by Scopus-0, SNIP-0, SJR-0, JCR impact factor-NIL, H-
index-0]. 14AASFMAIC01
118. Sahni M., Sharma S., "Analysis of Safety Measures in Creep Transversely Isotropic
Thick-walled Rotating Cylinder by Finitesimal Deformation under External Pressure",
3rd International Conference on Reliability, Infocom Technologies and Optimization
(ICRITO), Amity, Noida, India, 685-689, October 8-10, 2014. [Indexed in NO]
[Cited by Google-0, Cited by Scopus-0, SNIP-0, SJR-0, JCR impact factor-NIL, H-
index-0]. 14MSAOMAIC01
119. Sharma S., Yadav S., "Thermo Elastic-Plastic Analysis of Thick-Walled Cylinder
Made of Non-Homogeneous Stainless Steel Composite Material Under Internal and
External Pressure using Shooting Method", First International Conference on
Structural Integrity (ICONS-2014), Kalpakkam, India, 1534–1541, February 4-7,
2014. [Indexed in NO] [Cited by Google-0, Cited by Scopus-0, SNIP-0, SJR-0, JCR
impact factor-NIL, H-index-0]. 14SSTEMAIC01
120. Sharma S., Sahni M., Panchal R., "Elastic-Plastic Transition of Non-Homogeneous
Isotropic Thick-Walled Spherical Shell under Pressure with Steady State
Temperature", First International Conference on Structural Integrity (ICONS-2014),
Kalpakkam, India, 731–738, February 4-7, 2014. [Indexed in NO] [Cited by Google-
0, Cited by Scopus-0, SNIP-0, SJR-0, JCR impact factor-NIL, H-index-0].
14SSEPMAIC01
29
121. Rana, P. and Kumar, L. "Effect of Uncertainties in Physical Properties on Mixed
Convection Along a Rotating Vertical Slender Cylinder With Nanofluids" ASME
2014 International Mechanical Engineering Congress and Exposition, American
Society of Mechanical Engineers, pp. V08BT10A090, 2014. [Indexed in Scopus]
[Cited by Google-NIL, Cited by Scopus-NIL, SNIP-0.115, SJR-0.192, JCR impact
factor-NIL, H-index-24] -14SAHRMAIC01
122. Agarwal, S. and Rana, P. "Horton-Rogers-Lapwood Convection in a Binary
Nanofluid Saturated Rotating Porous Layer", ASME 2014 International Mechanical
Engineering Congress and Exposition, American Society of Mechanical Engineers,
pp. V08BT10A046(1--10), 2014, [Indexed in Scopus] [Cited by Google-NIL, Cited
by Scopus-1, SNIP-0.192, SJR-0.115, JCR impact factor-NIL, H-index-24]
14PREOMAIC01
F. Abstract Published in National Conferences: NIL
G. Book Chapter:
123. Pughat A., Tiwari P., Sharma, V. And Singh N., “Communication, Localization,
Coverage, Error and Control, Time Synchronization, Naming and Addressing, and
Cross Layer issues,” in Energy Efficient Wireless Sensor Networks, CRC Press
(Taylor & Francis) pp.27, 2017. [Cited by Google-NIL, Cited by Scopus- NIL , SNIP-
NIL, SJR- NIL, JCR impact factor-NIL, H-index- NIL] 14APCLMABC01
30
(c) Statistics, Fuzzy, Information Theory and Operations Research
A. Publications in International Journals:
1. N. Mathur, Srivastava P. K., and A. Paul, “Algorithms for solving fuzzy transportation
problem,” International Journal of Mathematics in Operational Research, vol. 12, no. 2,
pp. 190–219, 2018. [Indexed in Scopus] [Cited by Google-7, Cited by Scopus-3, SNIP-
0.698, SJR- 0.322, H-Index-]. 18NMAFMAIJ01.
2. Srivastava P. K. and Bisht D. C., “Dichotomized Incenter Fuzzy Triangular Ranking
Approach to Optimize Interval Data Based Transportation Problem,” Cybern. Inf.
Technol., vol. 18, no. 4, pp. 111–119, 2018. [Indexed in Scopus] [Cited by Google-
NIL, Cited by Scopus- NIL, SNIP- 0.397, SJR- 0.204, H-Index-9]. 18PSDIMAIJ01.
3. Jain S., Bisht D. C., and Mathpal P. C., “Particle swarm optimised fuzzy method for
prediction of water table elevation fluctuation,” Int. J. Data Anal. Tech. Strateg., vol.
10, no. 2, pp. 99–110, 2018. [Indexed in Scopus] [Cited by Google-1, Cited by Scopus-
1, SNIP- 0.533, SJR- 0.23, H-Index-12]. 18SJPSMAIJ01
4. Jain S., Mathpal P. C., Bisht D., and Singh P., “A unique computational method for
constructing intervals in fuzzy time series forecasting,” Cybern. Inf. Technol., vol. 18,
no. 1, pp. 3–10, 2018. [Indexed in Scopus] [Cited by Google-2, Cited by Scopus- 2,
SNIP- 0.397, SJR- 0.204, H-Index-9]. 18SJAUMAIJ01
5. Bhardwaj A., Verma V. S. and Jha R. K., "Robust video watermarking using
significant frame selection based on coefficient difference of lifting wavelet transform",
Multimedia Tools and Applications, vol. 77, no. 15, pp. 19659-19678, 2018. [Indexed
in Scopus/SCI] [Cited by Google-5, Cited by Scopus- 3, SNIP- 0.881, SJR- 0.287, JCR
Impact Factor-1.541, H-Index-45]. 18ABRVMAIJ01
6. Garg, H., Agarwal, N., Tripathi, A., "Choquet Integral-Based Information Aggregation
Operators under the interval-valued intuitionistic fuzzy set and its applications to
Decision-Making Process", International Journal for Uncertainty Quantification, vol. 7,
no. 3, pp. 249 - 269, 2017. [Indexed in Scopus/SCI] [Cited by Google-9, Cited by
Scopus- 9, SNIP- 0.8, SJR- 0.531, JCR Impact Factor-1.019, H-Index-8].
17HGCIMAIJ01.
7. Garg, H., Agarwal, N., Tripathi, A., "Some improved interactive aggregation operators
under interval-valued intuitionistic fuzzy environment and their application to decision
31
making process", Scientia Iranica. Transaction E, Industrial Engineering, vol. 24 , no. 5,
pp. 2581-2604, 2017. [Indexed in Scopus/SCI] [Cited by Google-10, Cited by Scopus-
8, SNIP- 0.309, SJR- 0.189, JCR Impact Factor-1.025, H-Index-34]. 17HGSIMAIJ01.
8. Garg, H.,Agarwal, N., Tripathi, A., "A novel generalized parametric directed
divergence measure of intuitionistic fuzzy sets with its application", Annals of fuzzy
Mathematics and Informatics, vol. 13, no. 6, pp. 703-727, 2017. [Indexed in
Mathematical Reviews (MathSciNet, USA), Zentralblatt MATH (zbMATH, Germany)]
[Cited by Google-2, Cited by Scopus- NIL, SNIP- NIL, SJR- NIL, JCR Impact Factor-
NIL, H-Index- NIL]. 17HGANMAIJ01.
9. Ravi, K.M., Tripathi A., "Myhill-Nerode Theorem for Intuitionistic Fuzzy Regular
Language", International Journal of Computer & Mathematical Sciences, vol.3, no. 2,
pp.34-37, 2017.(ISSN:2347-8527). . [Indexed in Google Scholar] [Cited by Google-
NIL, Cited by Scopus- NIL, SNIP- NIL, SJR- NIL, JCR Impact Factor- NIL, H-Index-
NIL]. 17KRMNMAIJ01
10. Tyagi K., Tripathi A., “Rough Fuzzy Automata and Rough Fuzzy Grammar”,
International Journal of Fuzzy System and Applications, vol. 6, no. 1, pp. 36-55, 2017.
[Indexed in Scopus] [Cited by Google-4, Cited by Scopus- 2, SNIP- 0.267, SJR- 0.265,
JCR Impact Factor- NIL, H-Index- NIL]. 17KTRFMAIJ01.
11. Garg, H.,Agarwal, N., Tripathi, A., “Generalized intuitionistic fuzzy entropy measure
of order alpha and degree beta and its applications to multi-criteria decision making
problem”, International Journal of Fuzzy System Applications (IJFSA), vol. 6, no. 1,
pp. 59-107, 2017. [Indexed in Scopus] [Cited by Google-21, Cited by Scopus- 14,
SNIP- 0.267, SJR- 0.265, JCR Impact Factor- NIL, H-Index- NIL]. 17HGGIMAIJ01.
12. Goyal M., Yadav D., Tripathi A., "An Intuitionistic fuzzy approach to classify the user
based on assessment of learner’s knowledge level in e-learning decision
making”, Journal of information processing system, Vol.13, No. 1,pp. 57-67,2017.
[Indexed in Scopus] [Cited by Google-5, Cited by Scopus- 6, SNIP- 1.238, SJR- 0.265,
JCR Impact Factor- NIL, H-Index- 17]. 17MGAIMAIJ01.
13. Srivastava A. & Maheshwari, S. , “Some New Properties of negation of a probability
distribution”, International Journal of Intelligent systems, 33(6), pp. 1133-1145, 2017.
(indexed in Scopus/SCI, Cited by Google -3 , Cited by Scopus -3, SNIP -1.07 ,IPP-,
SJR-1.177, JCR IMPACT FACTOR - 3.363, H - index - 66] 18ASSNMAIJ01.
32
14. Singh V., Joshi G. C., and Bisht D., “Energy Dispersive X-Ray Fluorescent Analysis of
Soil in the Vicinity of Industrial Areas and Heavy Metal Pollution Assessment,” J.
Appl. Spectrosc., vol. 84, no. 2, pp. 306–311, 2017. [Indexed in Scopus/SCI] [Cited by
Google-2, Cited by Scopus- 3, SNIP- 0.381, SJR- 0.179, H-Index-
20]. 17VSEDMAIJ01
15. Tripathi, A., Panwar K., "Modified CURE algorithm with enhancement to identify
number of clusters", International Journal of Artificial Intelligence and Soft
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16. Garg, H.,Agarwal, N., Tripathi, A., "Fuzzy Number Intuitionistic fuzzy soft sets and
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17. Goyal M., Tripathi A., and Yadav D., “Intuitionistic Group Decision Making to
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18. Goyal, M., Tripathi (Choubey), A., and Yadav, D., “Aggregating evaluation using
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19. Maheshwari, S. & Srivastava A. (2016), “Study on divergence measure for
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20. Srivastava A. & Maheshwari, S. (2016), “Decision making in medical investigations
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33
Systems, pp. 13(1), 25-44. (indexed in Scopus/SCI, Cited by Google -11 , Cited by
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21. N. Mathur, Srivastava P. K., and A. Paul, “Trapezoidal fuzzy model to optimize
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22. Garg, H.,Agarwal, N., Tripathi, A., "Entropy based multi-criteria decision making
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23. Maheshwari, S.& Srivastava A. (2015) “Some New Results on Information
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24. Jain S. and Bisht D., “Genetic Algorithms Based Fuzzy Time Series Prediction for
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23, 2015. [Cited by Google-5, Cited by Scopus- 0, SNIP- NIL, SJR- NIL, H-Index-
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25. Khanna V., Das B. K., Bisht D., and Singh P. K., “A three diode model for industrial
solar cells and estimation of solar cell parameters using PSO algorithm,” Renew.
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26. Tripathi A., Tyagi K., "A note on rough sets", International Journal of Mathematical
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27. Ravi K. M., Choubey (Tripathi) A., Tripathi K. K., "Intuitionistic Fuzzy Automata for
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34
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14KRIFMAJ01
28. Tripathi A.,Tyagi K., “Approximate equalities using topological space”, International
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2014. . [Indexed in DBLP] [Cited by Google-4, Cited by Scopus- NIL, SNIP- NIL,
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29. Raju M. M., Kumar A., Bisht D., and Rao D. B., “Stochastic Analysis of Wind Energy
for Wind Pump Irrigation in Coastal Andhra Pradesh, India,” J. Inst. Eng. India Ser. A,
vol. 95, no. 3, pp. 157–168, 2014. [Indexed in Scopus] [Cited by Google-2, Cited by
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30. Singh B. and Bhardwaj A., “Wavelet optimized finite difference mesh for MHD flow
in a circular duct”, Computers & Mathematics with Applications, vol. 67, no. 8, pp.
1582-1594, 2014. [Indexed in SCI/SCIE] [Cited by Google-NIL, Cited by Scopus- NIL,
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B. Publications in National Journals:
31. Tripathi, A., Tyagi, K. "Generalization of Rough Topology", Indian Journal of
Science and Technology, vol. 9(20), pp. 1-10 , 2016. [Indexed in Scopus] [Cited by
Google-3, Cited by Scopus- 1, SNIP- 1.270, SJR- 0.160, JCR Impact Factor- NIL, H-
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32. Goyal, M., Yadav, D., and Tripathi, A., “Intuitionistic fuzzy genetic weighted
averaging operator and its application for multiple attribute decision making in E-
learning”, Indian Journal of Science and Technology, Vol. 9, Issue 1, pp. 1-15, 2016.
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C. Publications in International Conferences:
33. Tripathi, A., Tyagi, K., "Approximate equalities using generalized topological spaces",
Advancement in Mathematical Sciences and its applications, AIP Conf. Proc., vol.
1897, Issue 1, pp. 020034, 2017. [Indexed in Scopus] [Cited by Google-0, Cited by
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17ATAEMAIC01
34. Tyagi, K., Tripathi, A., "Equalities based on rough intuitionistic fuzzy topology",
Advancement in Mathematical Sciences and its Applications, AIP Conf. Proc., vol.
1802, Issue 1, pp. 020033, 2017. [Indexed in Scopus] [Cited by Google-0, Cited by
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17KTEBMAIC01
36. Verma, D., Aggarwal, A.K. and Agarwal, H., “Watermarking Scheme based on
Singular Value Decomposition and Homomorphic Transform”, Advancement in
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17DVWSMAIC01
37. Srivastava, A. (2017), “Parameterization of f - divergences and Associated Information
Inequalities”, Advancement in Mathematical Sciences, AIP Conf. Proc., vol. 1897,
Issue 1, pp. 020024-1-020024-5. (indexed in Scopus, Cited by Google -0 , Cited by
Scopus -0, SNIP -0.715 ,IPP-, SJR-0.16, JCR IMPACT FACTOR-NONE, H - index -
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38. Bisht, D., and Srivastava, P. K., “A unique conversion approach clubbed with a new
ranking technique to optimize fuzzy transportation cost,” in AIP Conference
Proceedings, vol. 1897, p. 020023., 2017 [Indexed in Scopus] [Cited by Google-3,
Cited by Scopus- 3, SNIP- 0.619, SJR- 0.472, H-Index-44]. 17DBAUMAIC01.
39. Jain S., Bisht D. C., Singh P., and Mathpal P. C., “Real coded genetic algorithm for
fuzzy time series prediction,” In AIP Conference Proceedings, 2017, vol. 1897, p.
020021. [Indexed in Scopus] [Cited by Google-1, Cited by Scopus- 1, SNIP- 0.619,
SJR- 0.472, H-Index-44]. 17SJRCMAIC01.
40. Bhardwaj A., Verma D. and Verma V. S., "A robust watermarking scheme using
lifting wavelet transform and singular value decomposition", In AIP Conference
Proceedings, 1802, Noida, India, Jan. 2017. [Indexed in Scopus] [Cited by Google-4,
Cited by Scopus- NIL, SNIP-0.3, SJR- 0.165, H-Index-54]. 17ABARMAIC01
41. Sharma R., Gupta A. K., Singh D., Singh V. S. and Bhardwaj A., "A robust image
watermarking in contourlet transform domain", In AIP Conference Proceedings, 1897,
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Noida, India, Oct. 2017. [Indexed in Scopus] [Cited by Google-2, Cited by Scopus-
NIL, SNIP-0.3, SJR- 0.165 , H-Index-54]. 17RSARMAIC01
42. Agarwal, H., Raman, B., Atrey, P. K., Kankanhalli, M., "Analysis of comparators for
binary watermarks", in Proceedings of International Conference on Computer Vision
and image Processing, Advances in Intelligent Systems and Computing, vol 460
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Scopus-1, SNIP- 0.338, SJR- NIL, JCR Impact Factor-NIL, H-Index-19].
17HAAOMAIC01
43. Kumar P., "Improved DE algorithm with information utilization selection for
constrained optimization", AIP Conference Proceedings 1897, 020017 (2017) [Indexed
in Scopus] [Cited by Google-NIL, Cited by Scopus-NIL, SNIP-0.165, SJR-0.300, JCR
impact factor-NIL, H-index-54] 17PKIDMAIC01
44. Garg, H.,Agarwal, N., Tripathi, A., "Choquet integral-based intuitionistic fuzzy
bonferroni mean operator", Ninth International Conference on Contemporary
Computing (IC3), IEEE Xplore, Article No.7880259, 2016 . [Indexed in Scopus]
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45. Srivastava, A. & Sharma, M.(2016) “Evaluation of Channel Capacity of Very Noisy
Channels (VNCs) using the Weighted Generalization of Shannon Entropy and
Exponential Entropy” In Proceedings of 5th International Conference on Reliability,
Infocom Technologies and Optimization (ICRITO) (Trends and Future Directions),
Noida, India, pp. 292-295. (indexed in Scopus, Cited by Google -0 , Cited by Scopus -
0, SNIP - ,IPP-, SJR-, JCR IMPACT FACTOR- NIL, H-index - NIL ]
16ASEOMAIC01
46. Verma, V. S., Bhardwaj A., Jha R. K. and Ojha A., "Robust Image Watermarking
using Combined DSR-SVM with PCA based Feature Reduction", Sixth International
Symposium on Embedded Computing and System Design (ISED), IEEE, Patna, India,
pp. 323-327, 2016. [Indexed in Scopus] [Cited by Google-NIL, Cited by Scopus- NIL].
16VSRIMAIC01
47. Goyal, M., Yadav, D., Tripathi, A., "Fuzzy approach to detect learning style using
McCarthy model as a tool for e-learning system", 4th International Symposium on
37
Emerging Trends and Technologies in Libraries and Information Services, pp. 295-300,
Article No.,7048215,2015. [Indexed in Scopus] [Cited by Google-5, Cited by Scopus-
5, SNIP- 0.127, SJR-0.103, JCR Impact Factor- NIL, H-Index- 2]. 15MGFAMAIC01.
48. Goyal, M., Yadav, D., Tripathi, A., "Intuitionistic fuzzy approach for adaptive
presentation in an E-learning environment",IEEE International Conference on Research
in Computational Intelligence and Communication Networks (ICRCICN), PP . 108-
113, Article No. 7434219,2015. [Indexed in Scopus] [Cited by Google-1, Cited by
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15MGIFMAIC01
49. Maheshwari, S. and Srivastava A. " A new divergence measure for intuitionistic fuzzy
sets and its application in medical diagnosis", IEEE International Conference on Signal
Processing and Communication, 2015 organized by Jaypee Institute of Information
Technology, Noida from 16th March to 18th March, 2015.(Paper Published in
Conference Proceedings). (indexed in Scopus, Cited by Google -0 , Cited by Scopus -
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15SMANMAIC01.
50. Khanna V., Das B. K., Bisht D., and Singh P. K., “Estimation of photovoltaic cells
model parameters using particle swarm optimization,” in Physics of Semiconductor
Devices, Springer, pp. 391–394, 2014. [Indexed in Scopus] [Cited by Google-3, Cited
by Scopus- 3, SNIP- 0.619, SJR- 0.472, H-Index-44]. 14VKEOMAIC01.
F. Abstract Published in National Conferences: NIL
G. Book Chapter
51. Bisht, D. C., Srivastava, P. K. and Ram, M. “Role of Fuzzy Logic in Flexible
Manufacturing System,” in Diagnostic Techniques in Industrial Engineering, Springer,
pp. 233–243, 2017 [Not Indexed] [Cited by Google-2, Cited by Scopus- NIL, SNIP-
NIL, SJR- NIL, H-Index-NIL]. 17DBROMABC01.
52. Srivastava P. K., Bisht, D. and Ram, M., “Soft computing techniques and
applications,” in Advanced Mathematical Techniques in Engineering Sciences, Taylor
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Cited by Scopus- NIL, SNIP- NIL, SJR- NIL, H-Index-NIL]. 18PSSCMABC01.
38
RESEARCH THRUST AREAS/ ACTIVE RESEARCH GROUPS
Completed/ Ongoing Ph. D. Dissertations (Mathematics Department: JIIT)
Ph. D. Completed
Fractals & Chaos and Mathematical Analysis
1. Some Applications of Fixed Point Theorems
2. A study of Growth Properties and Spaces of Vector Valued Dirichlet Series
3. Growth and Approximation of Entire and Analytic Functions
4. A Study of Fractals and Fractal Interpolation
5. Some investigations in Fractal Theory
6. Studies on Fixed Point Theory for Various Maps in General Spaces
Numerical Analysis and Computational Continuum Mechanics
7. Numerical Studies of Stresses in Transversely Isotropic Materials
8. Some Stability Problems of Non-Newtonian Fluids
9. Some Thermal Stability Problems of Elastico-Viscous, Ferromagnetic and Nanofluids
10. Non-linear Problems in Micropolar Fluid Flow.
11. Non-Linear Stress Analysis of Thick- Walled Circular Cylinders.
12. Nonlinear MHD Flow Problems of Micropolar Fluids
13. Numerical Studies of Stresses in Materials
14. A Study of Seismic Wave Propagation in Different Anisotropic Media
15. Numerical Study of MHD Flow and Heat Transfer Problems in Nanofluids
16. Application of Homotopy Analysis Method to Transport Phenomena in Nanofluids
Statistics, Fuzzy, Information Theory and Operations Research
17. Performance Analysis of Some Queuing Models
18. Some Investigations in Fuzzy Automata
19. Some Special Classes of Efficient Multiple Bursts Codes
20. Information Measures and Aggregation Operators on Fuzzy/Intuitionistic Fuzzy Sets
with Applications in Decision Making
21. Efficient codes with class errors of SK-Metric and polynomial power product
composition for codes.
22. Generalized Measures of Information and Divergence and their Applications
23. Generalisation of Topology, Automata and Decision Theory Using Rough Fuzzy Sets
24. Methods for Solving Decision Making Problems Under Intuitionistic Fuzzy
Environment
39
Ph. D. Ongoing
Fractals & Chaos and Mathematical Analysis
1. Generalization of Contraction Maps and Its Applications
Numerical Analysis and Computational Continuum Mechanics
2. Safety Analysis of Anisotropic Materials
3. Solution of Differential Equations using Numerical and Emerging Computing
Techniques
4. Stability Problems of Fluid Dynamics
5. Solutions of Nonlinear Partial Differential Equations
6. Thermal Stability Analysis in Nanofluids
7. Numerical Solution of Some Problems in Nanofluid
8. Study of Seismic Wave in Propagation in Layered and Anisotropic Media
9. Elastic-Plastic and Creep Stress Analysis in Anisotropic Materials
10. Numerical Solution of Partial Differential Equation
11. Non-Linear Problems in Nanofluid Flows
12. Visualization and Classification of Fluids
13. Solutions of Differential equations
14. Numerical Methods for Differential Equations
Statistics, Fuzzy, Information Theory and Operations Research
15. Mathematical and Statistical Methods in Object Recognition
16. Optimal Solution of Pattern Matching Problems
17. Segmentation and Retrieval Problems in Image Processing
18. Fuzzy Optimization and Decision Making
19. Fuzzy Logic and Evolutionary Optimization
20. Some Investigations in Automata Theory and formal languages in Fuzzy Environment
21. Study of Uncertainty Measures in Crisp and Fuzzy Environments
22. Image Authentication and Copyright Protection
23. Study of Fuzzy Set Theory and Its Applications
24. Developments and Applications of Soft Computing
40
M. Tech. Dissertations (Mathematics Department; JIIT)
M. Tech (ACM) Dissertations (Completed)
Fractals & Chaos and Mathematical Analysis
1. Approximations by Wavelets
2. Fixed Point Theory in Fractals.
3. Iterated Function Systems and Chaotic Maps
Numerical Analysis and Computational Continuum Mechanics
4. Finite Element Solution of Magnetohydrodynamic Flow of Micropolar Fluid.
5. Mesh Free Methods for Boundary Value Problems
6. Nonlinear Differential Equations
7. Application of Evolutionary Computation Algorithms in Numerical Optimization
Problems
8. Numerical Solutions of Boundary Value Problems using Splines
Statistics, Fuzzy, Information Theory and Operations Research
9. Image Compression by using Fuzzy Techniques
10. Fuzzy Linear Programming
11. Face Recognition with Fuzzy C-Mean Algorithm using Principal Component Analysis
12. Multi-Objective Linear Programming Problems
13. Error Control Coding
14. Digital Signature Scheme Based on Error correcting Code
15. Cluster Analysis
M. Tech (ACM) Dissertations (Ongoing) NIL
41
Elective Courses Offered (Mathematics Department; JIIT)
Fractals & Chaos and Mathematical Analysis
1. Fractals and Chaos
2. Wavelets and Applications
3. Integral Transforms
Numerical Analysis and Computational Continuum Mechanics
1. Advanced Numerical Techniques
2. Advanced Differential Equations
3. Computer Programming and Simulation
4. Calculus of Variations and Finite Element Method
5. Computational Fluid Dynamics
Statistics, Fuzzy, Information Theory and Operations Research
1. Advanced Operations Research
2. Linear Statistical Models
3. Fuzzy Calculus & Possibility Theory
4. Automata and Theory of Computation
5. Advanced Optimization Techniques
42
Syllabi of Courses Offered
Fractals and Chaos
Metric Space: Review of metric spaces, complete metric space, compact metric space, contraction
mappings, Hutchinson operator, Banach contraction theorem, Hausdorff metric and the spaces of
fractals, iterated function systems (IFS), attractor of IFS.
Fractals: Introduction, fractals in nature, mathematical fractals, Koch curve, Koch snowflake, Cantor
set, Sirpinski triangle, Sierpinski gasket.
Fractal Dimensions: Box counting dimension, Hausdorff-Besicovitch dimension, dimensions of the
well known fractals, theoretical determination of fractal dimension.
Fractal Interpolation: Fractal interpolation, fractal interpolation functions, fractal dimension of
fractal interpolation functions.
Chaos: Dynamical systems, orbits, repelling and attracting fixed points, logistic map, bifurcations,
brief introduction about the Julia and the Mandelbrot sets.
Wavelets and Applications
Basics of linear algebra: Fourier series and Fourier transform. The problem of approximation of
functions in various spaces, Inner product, Norm, Orthogonality, Banach and Hilbert spaces. B-
splines.
Wavelet basics: Haar, Morlet, Meyer and Daubechies wavelets. Design of wavelets. Orthogonal and
biorthogonal bases. Wavelet Transforms.
Multiresolution analysis: Compactly supported wavelets. Cardinal spline wavelets. Numerical
algorithms.Discrete time bases, series expansions of discrete time signals, DWT.
Analysis and design of filter banks: Orthogonal and biorthogonal filter banks, Tree structured and
linear phase filter banks. Subband filtering.
Applications to Image and Video compression: solution of differential and integral equations.
Wavelet software- Matlab.
Integral Transforms
Laplace Transforms: Existence condition for the Laplace transform, differentiation and integration
of Laplace transform. Inverse Laplace transform, convolution theorem. Applications of Laplace
transform to ordinary differential equations and partial differential equations.
Fourier Transform: Definition of the Fourier transform and examples, basic properties of Fourier
transforms. Applications of Fourier transforms to ordinary differential equations and partial
differential equations,
Hankel Transforms: The Hankel transform, operational properties of Hankel transform. Application
of Hankel transform to partial differential equations.
Mellin Transforms: Definition of the Mellin transform, basic operational properties of Mellin
transforms. Applications of Mellin transforms to summation of series. Generalized Mellin transforms.
Hilbert Transforms: Definition of Hilbert transform, basic properties of Hilbert transforms, Hilbert
transforms in complex plane. Applications of Hilbert transforms, asymptotic expansion of one sided
Hilbert transforms.
Z Transform: Dynamic linear systems and impulse response, Definition of Z transform, basic
operational properties of Z transforms. The inverse Z transform. Applications of Z transforms to finite
difference equations, summation of infinite series.
Advanced Numerical Techniques
Solution of Nonlinear Equations: Newton-Raphson method for two or more variables, Muller’s
method, Graeffe’s root-squaring method, Lin-Bairstow’s method.
43
Interpolation and Approximation: Interpolation using divided differences, Hermite interpolation,
cubic splines. Method of least squares, orthogonal polynomials, Gram-Schmidt orthogonalization
process, Chebyshev polynimals, economization of power series, numerical integration, Romberg
integration, Newton-Cotes integration formulae, Gaussian quadrature.
Matrix and Linear System of Equations: Iterative methods for x = Ax + b, SOR method, Jacobi
method, Householder’s method for eigenvalues and vectors.
Numerical Solution of Differential Equations: Singel Step methods, multistep methods, Predictor-
Corrector methods for initial value problems. Finite difference methods for Elliptic (Laplace
equation), parabolic (Heat equation) and hyperbolic equations (Wave equation). Method of weighted
residuals, Rayleigh-Ritz method, finite element method for one dimensional problems.
Advanced Differential Equations
Ordinary Differential Equations: Review of linear and nonlinear ODEs. Initial and boundary value
problems, review of second order linear differential equations. Cauchy-Euler form. General method
for second order linear differential equations. Method of variation of parameters. Green’s function,
applications.
System of Linear Differential Equations: Operator method, basic theory of linear systems in normal
form. Homogeneous linear system with constant coefficients. Matrix method for homogeneous linear
systems with constant coefficients.
Oscillation Theory: Qualitative properties of solutions, Eigenvalues and eigenfunctions, Sturm-
Liouville problem.
Existence and Uniqueness Theory: Existence and uniqueness of the solutions of the IVP:
00 )(),,( yxyyxfy . Existence and uniqueness of system of equations and higher order
equations.
Nonlinear Differential Equations: First order nonlinear equations and their linearization, Abel’s
equation, exact linearization of nonlinear second order equation via factoring, Transformation of
nonlinear equation to nonlinear integrable forms, reducing nonlinear second order equation to first
order equation.
Partial Differential Equations: Linear equation of first order, Lagrange method, linear equation with
constant coefficients, Classification, method of separation of variables, special methods for Laplace
equation.
Computer Programming and Simulation
C/C++: Basic data types, constants and variables, Arithmetic operators, built-in mathematical
functions. Arithmetic expression.
Logical and relational operators. scanf ( ) and printf ( ) functions. I/O using cin and cout. Control of
flow. Use of break, return and exit.
Looping. Arrays and strings. Functions. Pointers. Call by reference. Structures, unions, enumerations
and type def.
Dynamic memory allocation in C. File I/O in C.
Random number generation. Random variates and their generation.
Monte-Carlo simulation. Case studies.
Calculus of Variations and Finite Element Method
Functional and Its Variation: Stationary values of a functional. Euler- Lagrange equations. Some
special cases. Brachisto chrone problem and its history. Examples. More general cases. Constraints
and Lagrange multipliers. Variable end points.
Sturm-Liouville problems. Vibration problems. Hamilton principle. Lagrange equations.
Method of Weighted Residuals (MWR): Collocation, Galerkin and Ritz methods.
44
Fredholm and Volterra Type of Integral Equations: Relationship with differential equations,
Green’s function, Fredholm equation with separable kernel, Iterative methods, Singular integral
equations, Abel’s equation.
Numerical Methods: The finite element method. One dimensional problems. Ritz and Galerkin’s
methods. Various type of elements and their shape functions. Stiffness matrix. Assembly of equations
. Handling of the boundary conditions.
Two Dimensional Problems: Triangular and rectangular elements. Stiffness matrices and assembly.
Some simple three dimensional elements. Comparison of FEM and FDM.
Computational Fluid Dynamics
Basics of Fluid Dynamics: Basics of Fluid Dynamics, Equation of continuity, Equation of Motion,
General Navier-Stokes (N-S) equations, various forms of N-S equations, dimensionless form, Energy
Equation.
Basic Numerical Methods: Applied numerical methods, numerical solution of ordinary differential
equations, Runge Kutta Method, Finite differences, Discretization, Consistency, Stability and
Fundamentals of Fluid Flow Modelling.
Applications of Finite Difference Method: Finite difference applications in heat conduction and
convection, discrete approximations, upwind corrected scheme, higher order methods, Hermitian
method and Mehrstellen methods, multidimensional equation, explicit schemes for the advection-
diffusion equations, ADI method, explicit schemes for a nonlinear equation in conservative form,
generalized ADI methods, Quasilinearization Method for nonlinear boundary value problems.
Finite Element Method: Incompressible viscous flow via FEM, artificial compressibility method,
pressure correction methods, SIMPLE, pressure implicit with splitting of operators, Marker and Cell
method (MAC).
Finite Volume Method Finite volume methods via FDM, 2-D problem, node centered control
volume, cell centered control volume, cell centered average scheme, three dimensional problems, 3-D
geometry structure, 3-D FVM equations; Illustrative problems.
Programming Aspects: Programming, testing and information processing of numerical methods.
Advanced Operations Research
Linear Programming Problems and Duality - Convex sets, graphical and simplex method,
artificial variable techniques, revised simplex method, Duality theory, dual simplex method.
Parametric and Sensitivity Analysis - Sensitivity analysis, parametric linear programming.
Inventory Controls – Introduction, Inventory models, Economic order quantity (EOQ), Deterministic
inventory problems with and without shortages.
Network Analysis – Shortest path problem, PERT/CPM, Simulation techniques.
Games and Strategies - Pure and mixed strategies, solution by graphical and linear programming
methods.
Multi-objective and Goal Programming Problems- Solution by graphical and simplex method.
Nonlinear Programming: Convex functions and their properties, Kuhn Tucker theory, convex
quadratic programming, Wolfe’s and Beale’s algorithm, Separable convex programming.
Linear Statistical Models
Random Vectors and Matrices: Mean vectors and covariance matrices for random vectors.
Correlations matrices, mean vectors and covariance matrices for partitioned random vectors. Linear
functions of random vectors.
Multivariate Normal Distribution: Univariate normal density function. multivariate normal density
function. moment-generating functions. Properties of the multivariate normal distribution. Partial
correlation.
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Distribution of Quadratic Forms in y: Mean and variance of quadratic forms. Noncentral Chi-
square, F- and t- distributions. Distributions of quadratic forms. Independence of linear forms and
quadratic Forms.
Simple Linear Regression: Estimation of 2
10 and ,, . Hypothesis test and confidence interval for
1 . Coefficient of determination.
Multiple Regression: Estimation: Estimation of 2 and . Geometry of least squares. Normal
model. Generalized least squares.
Multiple Regression: Tests of Hypotheses and Confidence Intervals: Test of overall regression.
Tests on a subset of the values. F-test in terms of 2R . The general linear hypothesis tests for
1C:H and 0C:H 00 . tests on a' and s'j. confidence region for .a' and , j
Multiple Regression: Random x’s: Multivariate normal regression model. estimation in multivariate
normal regression.
Analysis of Variance Models Non-full-rank models. estimation, estimators. reparameterizatio.
testing of hypothesis.
Fuzzy Calculus & Possibility Theory
Fuzzy sets, Zadeh’s extension principle. fuzzy calculus for fuzzy-set-valued functions, fundamental
theorem of calculus, fuzzy calculus for fuzzy bunches of functions,
Fuzzy differential equations with fuzzy derivatives, fuzzy initial value problem (FIVP), fuzzy
differential inclusions, autonomous FIVP with fuzzy initial condition, study of fuzzy differential
equations with different forms of fuzzy derivatives, main approaches to fuzzy control, stability of
fuzzy control systems, fuzzy controller design, fuzzy measures, evidence theory, necessity and belief
measures, probability measures vs possibility measures,
Fuzzy decision making, fuzzy relational inference, compositional rule of inference, efficiency of
inference with hierarchical models.
Automata and Theory of Computation
Introduction : Sets, relations, functions, recursive function, generating function, graphs and trees,
strings and their properties, principle of induction.
Finite Automata and Regular Languages : Finite automata, transition systems, determinism and
non determinism, properties of finite automata, regular expressions and finite automata, push-down
automata, context free grammars, pumping lemma, application of pumping lemma.
Computability:The standard turing machine model, multi-tape turing machines, nondeterministic
turing machines, representing restricted models of computation, universal turing machines, encoding
of strings and turing machines, limits on language acceptance, reducibility and unsolvability,
functions computed by turing machines.
Complexity Theory:Languages and problems, serial computational models, classification of decision
problems (space and time hierarchies, time-bounded complexity classes, space-bounded complexity
classes), complements of complexity classes, hard and complete problems, NP-complete problems,
the boundary between P and NP.
Advanced Optimization Techniques
Preliminaries of Linear programming Problems:- Mathematical formulation of LPP, graphical
solution, simplex method, big-m method and two phase simplex method.
Nonlinear Programming: Convex sets, convex functions, Kuhn-Tucker conditions, Lagrange’s
multipliers method, convex programming problem.
One-Dimensional Optimization: Unimodal functions, elimination methods- interval halving method,
Fibonacci method, Ggolden section method, interpolation method, direct root methods- Newton
method, Secant method.
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Unconstrained Optimization: Direct search techniques, indirect search techniques- Steepest descent,
Newton-Raphson method, Hooke’s and Jeev’s method, conjugate gradient method, quasi Newton
method.
Constrained Optimization: Direct methods- random search method, indirect methods- penalty and
barrier methods, cutting plane and dual methods.
Dynamic Programming: Characteristics of dynamic programming problems, deterministic dynamic
programming and probabilistic dynamic programming.
Fuzzy Linear Programming: Introduction to fuzzy sets, basic definitions, fuzzy linear programming,
multiobjective linear programming, multiobjective fuzzy linear programming, fuzzy dynamic
programming.