BROAD AREA(S) OF INTERESTFLUID MECHANICS, ANALYTIC NUMBER THEORY, TOPOLOGY
MathScinet author ID 778677 Research AccomplishmentHydrodynamic stabilityMy specialization is in numerical computing in Hydrodynamical systems, such as temperaturemodulated RayleighBenard convection(TMRBC), TaylorCouette flow in ferrofluids, Dean instability in ferrofluids etc. We explored TMRBC for bicritical states using FourierFloquet analysis. Some nonlinear calculations on patterns of TMRBC have also been done using FEM by modeling the problem in a finite rectangular box of aspect ratio 10[ See Kaur and Singh]. Energy stability analysis of transient convection in ferrofluids has also been done by us. Currently, we are exploring on temperaturemodulated convection in a vertical fluid layer for bicritical states, using the methods developed for dealing with the TMRBC. Analytic Number TheoryMotivated by the marvelous work of the Mathematical incarnate Leonhard Euler during the eighteenth century, I have worked on investigating the properties of Power Sums of integers via defining them in a more general setting. The motivation behind this work is the following simple identity $1+2+\ldots=\frac{n(n+1)}{2}$. Some new interesting analytical results are obtained. Some power sums of the Euler Phi function are also studied. Besides, we have contributed in General Mathematics, on new proofs of well known fundamental theorems such as binomial theorem, de Moivre's formula, Cauchy type product, subgroups of real line etc.
ContributionsA. Hydrodynamic stability
 Puneet Kaur and Jitender Singh. Heat transfer in a thermally modulated fluid layer. Inter. Jour. Ther. Sci. (Elsevier), 114C (2017), 3543. Link
 Puneet Kaur, Jitender Singh, Renu bajaj. “RayleighB\'enard convection with two frequency temperature modulation”, Phys. Rev. E, 93, (2016), 043111.
 Jitender Singh and Renu Bajaj. “Dean Instabilityin ferrofluids”, Meccanica, 51 (2016), 835847
 Jitender Singh and Renu Bajaj. Bicritical states in temperature modulated Rayleigh Benard convection. Phys. Rev. E, 92 (2015), 013005.
 Jitender Singh and S. S. Singh. Instability in modulated Rotating RayleighBenard convection. Fluid Dyn. Res.(IOP) 46(1) (2014), 015504.
 Jitender Singh. A nonlinear shooting method and its application to nonlinear RayleighB\'enard convection, ISRN Mathematical Physics (2013), 65020819.
 Singh, S. S. and Jitender Singh. Effect of Corrugation on Incident qSVwaves in prestressed elastic halfspaces, International Journal of Applied Mathematics and Mechanics, 9(9), (2013), 92106
 Jitender Singh, E. L. Hines, and Daciana Iliescu. Global stability results for temperature modulated convection in ferrofluids. Appl. Math. Comp. 219 (2013), 62046211.
 Jitender Singh and Renu Bajaj. Convective instability in a ferrofluid layer with temperature modulated rigid boundaries. Fluid Dyn. Res. (IOP), 43, (2011), 025502. IF2010~1.089, SCI indexed Journal; MathSciNet Link Cited in: EPJ, Microgravity Sci. Tech, IOSR Journal of Applied Physics
 Jitender Singh. Energyrelaxation for transient convection in ferrofluids, Phys. Rev. E (APS), 82, 2 (2010), 0263119. IF2009~2.400, IF2010~2.352 SCI indexed Journal Cited in: Proc. of Royal Soc. A (2012) , Phys. Rev. E (2012)
 Jitender Singh and Renu Bajaj. Temperature Modulation in Ferrofluid Convection, Phys. Fluids (AIP), 21, 6, (2009), 06410516. SCI indexed Journal Cited in:JMMM, Transp. Por. Med., Acta Mech., Mincrogravity Sci. Tech.,Phys. Fluids, Int. Jour. of Heat and Mass Transfer., Ph.D.Thesis , JMMM, Aerospace Sci. and Tech., Phys. Rev. E, Microgravity Sci. Tech, Aerospace Sci. Tech., IOSR Journal of Applied Physics
 Jitender Singh and Renu Bajaj. Thermal modulation in RayleighBenard convection, The ANZIAM J. (Cambridge University Press), 50, 2, (2008), 231245. IF2008~0.380, IF2009~0.286, IF2010~0.414. MathSciNet Link
 Jitender Singh and Renu Bajaj. Parametric modulation in the TaylorCouette ferrofluid flow, Fluid Dyn. Res.(IOP), 40, (2008), 737752. MathSciNet Link SCI indexed Journal (Poster: ICIAM 2007). Cited in: Physics Prodcedia
 Jitender Singh and Renu Bajaj. Nonaxisymmetric modes of CouetteTaylor instability in ferrofluids with radial flow, Magnetohydrodynamics, 42, (2006), 5768. IF~0.457
 Jitender Singh and Renu Bajaj. Stability of ferrofluid flow in rotating porous cylinders with radial flow, Magnetohydrodynamics, 42, (2006), 4156. IF~0.457
 Jitender Singh and Renu Bajaj. Stability of nonaxisymmetric ferrofluid flow in rotating cylinders with magnetic field, Int. J. Math. Math. Sci., 23 (2005) 37273737. MathSciNet Link; Cited in: Phys. Rev. (2009); Phys. Rev. (2010)
 Jitender Singh and Renu Bajaj. Couette flow in ferrofluids with magnetic field, J. Magn. Magn. Mat., 294 (2005), 5362 IF2008~1.283, IF2009~1.204, IF2010~1.689 SCI indexed Journal Cited in: Phys. Rev E (2009) ; Phys. Rev. E (2010) ; Physics Prodcedia (2010), Physical Review E (2013), Open Journal of Fluid Dynamics
B. Analytic Number Theory
 Jitender Singh. Sums of products of power sums, J. Integer Sequences, 19 (2016) Article 16.1.2.
 Jitender Singh. On an arithmetic convolution, J. Integer Sequences, 17 (2014) Article 17.6.7.
 Jitender Singh. Sums of products involving power sums of $\varphi(n)$ integers. J. numbers (2014) pp 16.
 Jitender Singh. Defining Power sums of n and φ(n) Integers, Int. Jour. Num. Th., 5, (1), (2009), 4153. MathSciNet Link. ZENTRABLATMath Link, IF2008~0.473, IF2010~0.395 (Presented in the International Congress of Mathematicians (ICM2010) held in Hyderabad (HICC) on August 21, 2010). Cited in: International Journal of Number theory(2012), The Ramanujan Journal (2012), arXive(2013), arXive2013 , Preprint(2013), arXiv:1306.5848v1 2013, Advances in Applied Mathematics(2013)
 Jitender Singh. Subgroups of the additive group of real line. arXiv1312.7067v1 (2013), pp 6.
 Jitender Singh, Sequence #A242225, The OnLine Encyclopedia of Integer Sequences.
 Jitender Singh, Sequence #A241885, The OnLine Encyclopedia of Integer Sequences.
C. General Mathematics
 (New)Jitender Singh. A Short Proof that Lebesgue Outer Measure of an Interval is Its Length. American Mathematical Monthly (2017) Accepted for publication
 (New)Jitender Singh. A Noninductive Proof of de Moivre's Formula. American Mathematical Monthly (2017) Accepted for publication
 Jitender Singh. Another Proof of the Binomial Theorem. American Mathematical Monthly, 124, (2017), 658.
 Jitender Singh and Harpreet K. Grover. Limit and Continuity revisited via Convergence (Unpublished)
Impact Factors of some Journals Journal  Impact factor 2014  Impact Factor 201516 
American Mathematical Monthly   0.349  International Journal of Number Theory  0.318  0.463  Journal of Integer Sequences   0.550 
Physical Review E  2.288  2.252  Physics of Fluids  2.031  2.017  Fluid Dynamics Research  0.990  0.846  Meccanica  1.949  1.982  Applied Mathematics and Computation  1.551  1.345  ANZIAM Journal  1.025  0.957  Journal of magnetism and magnetic materials  1.970  2.357  International Journal of Thermal Sciences  2.769  3.615 
Doing mathematics is a longterm thing. I've had graduate students
who said, "OK", I'm doing my PhD, and at the end of the four years, I'll
have learnt everything I need to know, and I'll be a leader in the
field". It doesn't work that way! You have to work through
undergraduate, and through graduate, and even after you finish, there is
still a lot more to learn. Mathematics is huge. You have to keep
pushing yourself and not be content with doing just one or two things
and sit in this niche of mathematics and never venture out of it, if you
want to really progress. I'd describe it as like running a marathon.
You can't just sprint right through it. You have to keep learning, and
really enjoy doing mathematics. If you don't enjoy it, you won't have
the stamina to keep at it. But it is very rewarding if you keep at it.
Terence Tao
Recommended readings
Here is a list of some of my favorite books/articles I often love to read:
 W. P. Johnson. The curious history of Faa di Bruno's Formula
 E. Bombier. Problem of the millennium: The Riemann Hypothesis.
 Jonathan. Sondow Ramanujan, Robin, Riemann Hypothesis and Recent Results
 W. Dunham. "Euler: The Master of Us All". (My Favorite Author!)
 W. Dunham. "The Calculus Gallery"
 W. Dunham."Touring the Calculus Gallery", AMM
 K. Janich. "Topology''
 N. Bourbaki, "Elements of MathematicsGeneral Topology"(English Translation)
 Armstrong, "Basic Topology"
 J. Conway. "Functional Analysis"
 Landau Lifshitz, "Fluid Dynamics"
 T. M. Apostol, "Introduction to Analytic Number Theory"
 Dummit and Foote, "Modern Algebra"
 J. Munkres, "Topology"
 J. Munkres, "Elements of Algebraic Topology"
 S. Morris, "Topology without Tears"
 W. Rudin, "Principles of Mathematical Analysis"
 Ahlfors, "Complex Analysis"
 J. Stillwell, "Mathematics and its History"
 K. S. Sarkaria,"Topological Work of Henri Poincare"
 K. S. Sarkaria, "A topological paradox of Motion"
 S. Chandraskhar, "Hydrodynamic and Hydromagnetic Stability"
 M. Spivak, "Calculus on Manifolds"
 L. S. Pontryagin, "Selected Works: Topological Groups Vol. 2"
 M. Farkas, "Periodic Motions"
 T. Tao, "Analysis I & II"
 M. Ahmed, "How many squares are there Mr. Franklin ?"
 W. H. Gustafson,"What is the probability that two group elements commute ?"
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