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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


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


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)



In this age of information revolution the role of statistics, fuzzy sets, information theory

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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)


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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.

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Research Thrust Areas/ Active Research Groups

Publications (2014-18)


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].

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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-

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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.

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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,

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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


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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

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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,”

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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

17. Kaur L., Wazwaz A. M., “Similarity solutions of field equations with an

electromagnetic stress tensor as source”, Romanian Reports in Physics, Vol. 70, pp.

1-12, 2018. [Indexed in Scopus/SCIE] [Cited by Google-6, Cited by Scopus- 5, SNIP-

0.689, SJR- 0.772, JCR Impact Factor-1.582, H-Index-25]. 18LKSSMAIJ01

18. Kumar V., Kaur L., Kumar A., Koksal M. E., "Lie symmetry based-analytical and

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33. Sheikhoslami, M., Rana, P. and Soheil, S. "Numerical study of MHD natural

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34. Rana, P., Bhargava, R., Beg, O. A. and Kadir, A. "Finite element analysis of

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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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41. Dhanai, R., Rana, P. and Kumar, L. "Lie group analysis for bioconvection MHD slip

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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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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


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]

https://scholar.google.com/scholar?oi=bibs&cluster=13537031999689650546&btnI=1&hl=en



23


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


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


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


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


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


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.


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]


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]


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]


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



1. N. Mathur, Srivastava P. K., and A. Paul, “Algorithms for solving fuzzy transportation

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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

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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

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4. Jain S., Mathpal P. C., Bisht D., and Singh P., “A unique computational method for

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5. Bhardwaj A., Verma V. S. and Jha R. K., "Robust video watermarking using

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8. Garg, H.,Agarwal, N., Tripathi, A., "A novel generalized parametric directed

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9. Ravi, K.M., Tripathi A., "Myhill-Nerode Theorem for Intuitionistic Fuzzy Regular

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10. Tyagi K., Tripathi A., “Rough Fuzzy Automata and Rough Fuzzy Grammar”,

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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

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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

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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-,

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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.

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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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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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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

transmission over noisy channels”. Demonstratio Mathematica, 48(3), 462-472.

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0.23, JCR IMPACT FACTOR-NONE, H - index - 7] 15SMSNMAIJ01.

24. Jain S. and Bisht D., “Genetic Algorithms Based Fuzzy Time Series Prediction for

Water Table Elevation Fluctuation,” Aloy J. Soft Comput. Appl., vol. 3, no. 1, pp. 14–

23, 2015. [Cited by Google-5, Cited by Scopus- 0, SNIP- NIL, SJR- NIL, H-Index-

NIL.] 15SJGAMAIJ01

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.

Energy, vol. 78, pp. 105–113, 2015. [Indexed in Scopus/SCI] [Cited by Google-79,

Cited by Scopus- 64, SNIP- 2.008, SJR- 1.847 H-Index-143]. 15VKETMAIJ01

26. Tripathi A., Tyagi K., "A note on rough sets", International Journal of Mathematical

sciences, Vol. 13. pp. 1-10, 2014. [Indexed in Google Scholar] [Cited by Google-NIL,

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14ATANMAIJ01.

27. Ravi K. M., Choubey (Tripathi) A., Tripathi K. K., "Intuitionistic Fuzzy Automata for

Approximate String Matching", International Journal of Fuzzy Information and

34

Engineering, Vol. 6, pp. 29-39, 2014. [Indexed in Elsevier] [Cited by Google-3, Cited

by Scopus- NIL, SNIP- NIL, SJR-NIL, JCR Impact Factor- NIL, H-Index- NIL].

14KRIFMAJ01

28. Tripathi A.,Tyagi K., “Approximate equalities using topological space”, International

Journal Granular Computing, Rough Sets and Intelligent Systems, Vol. 3, pp. 272-291,

2014. . [Indexed in DBLP] [Cited by Google-4, Cited by Scopus- NIL, SNIP- NIL,

SJR-NIL, JCR Impact Factor- NIL, H-Index- NIL]. 14ATAEMAIJ01

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

Scopus- NIL, SNIP- 0.393, SJR- 0.183, H-Index-5]. 14MRSAMAIJ01

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,

SNIP-1.152, SJR- 1.058, JCR Impact Factor-1.86, H-Index-98]. 14BSWOMAIJ01

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-

Index- 41]. 16ATGOMANJ01

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.


JCR Impact Factor- NIL, H-Index- 41]. 16MGIFMANJ01.


33. Tripathi, A., Tyagi, K., "Approximate equalities using generalized topological spaces",

Advancement in Mathematical Sciences and its applications, AIP Conf. Proc., vol.


35

Scopus- 0, SNIP- 0.300, SJR-0.165, JCR Impact Factor- NIL, H-Index- 54].

17ATAEMAIC01

34. Tyagi, K., Tripathi, A., "Equalities based on rough intuitionistic fuzzy topology",

Advancement in Mathematical Sciences and its Applications, AIP Conf. Proc., vol.


Scopus- 0, SNIP- 0.300, SJR-0.165, JCR Impact Factor- NIL, H-Index- 54].

17KTEBMAIC01

36. Verma, D., Aggarwal, A.K. and Agarwal, H., “Watermarking Scheme based on

Singular Value Decomposition and Homomorphic Transform”, Advancement in

Mathematical Sciences, AIP Conf. Proc., vol. 1897, Issue 1, pp. 020036-1–020036-9;

https://doi.org/10.1063/1.5008715, 2017 [Indexed in Scopus] [Cited by Google-NIL,

Cited by Scopus- NIL, SNIP- 0.715, SJR- 0.957, JCR Impact Factor-NIL, H-Index-54].

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 -

54] 17ASPOMAIC01.

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,

36

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

Springer, pp. 399--410, 2017. [Indexed in Scopus] [Cited by Google-1, Cited by

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]

[Cited by Google-NIL, Cited by Scopus- NIL, SNIP- NIL, SJR-NIL, JCR Impact

Factor- NIL, H-Index- 2]. 16HGCIMAIC01

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

Scopus-1, SNIP- NIL, SJR-NIL, JCR Impact Factor- NIL, H-Index- NIL].

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 -

0, SNIP -0.443 , SJR-0.23, JCR IMPACT FACTOR-NIL, H - index - 7]

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

& Francis Group, pp. 57-69, 2018. [Indexed in Google Scholar] [Cited by Google-NIL,

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


1. Generalization of Contraction Maps and Its Applications


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


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)


1. Approximations by Wavelets

2. Fixed Point Theory in Fractals.

3. Iterated Function Systems and Chaotic Maps


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


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)


1. Fractals and Chaos

2. Wavelets and Applications

3. Integral Transforms


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


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.

45

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.

46

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.

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