Reaserch Papers

On Sums Related to Dirichlet Lambda Tails, Journal of Mathematical Analysis and Applications, Vol 555, Issue 2, (2026). doi:j.maa.2025.130099

Input-to-state stability of discrete-time, linear time-varying systems. With Sneha Sanjeevini, Brian Lai, Yuan Wang, and Dennis S. Bernstein. Automatica 177 (2025) 112331. doi:10.1016/j.automatica.2025.112331,

On Some Improper Integrals Involving The Cube Of The Tails Of Two Maclaurin Series. With Russell A. Gordon, Seán M. Stewart. Journal of Classical Analysis. Volume 25, Number 1 (2025), 1–25, doi: 10.7153/jca-2025-25-01, PDF. 

Self-Excited Dynamics of Discrete-Time Lur'e Systems with Affinely Constrained Piecewise-C1 Feedback Nonlinearities. With Juan Paredes and Dennis S. Bernstein. IEEE Open Journal of Control Systems, 3, 214-224 (2024), doi: 10.1109/OJCSYS.2024.3402050, view. 

On the Dynamics of a Bead Sliding on a Freely Rotating Slanted Wire. With Dennis, S. Bernstein, Journal of Nonlinear Science. (2024) 34:57, doi: 10.1007/s00332-024-10036-4

Applications of a Hypergeometric Identity and Ramanujan-like Series, Bull. Malays. Math. Sci. Soc. (2024) 47:26, doi: 10.1007/s40840-023-01627-7 , view

Binomial identities obtained from the Gegenbauer series expansion, Integral transforms and Special Functions (2023) 34(12), 947-964, doi: 10.1080/10652469.2023.2244648 

Deriving Euler’s Equation for Rigid-Body Rotation via Lagrangian Dynamics with Generalized Coordinates, with Dennis S. Bernstein and Ankit Goel. Mathematics (2023), 11(12), 2727, doi: 10.3390/math11122727

On a Combinatorial Identity of Gavrea and Ivan and Related Results, With Horst Alzer, Aequationes Mathematicae, (2022), doi: 10.1007/s00010-022-00923-0

A Chaundy-Bullard identity type involving the Pochhammer symbol, Indagationes Mathematicae, (2022), doi: 10.1016/j.indag.2022.10.009.

On a combinatorial identity of Chaundy and Bullard, With Horst Alzer, Preprint. doi: 10.48550/arXiv.2205.00480

An Introduction to Inertial Navigation From the Perspective of State Estimation [Focus on Education], with A. Goel, A. Ul Islam, A. Ansari, O. Kouba and D. S. Bernstein, IEEE Control Systems, vol. 41, no. 5, pp. 104-128, Oct. (2021). doi: 10.1109/MCS.2021.3092855. 

 Applications of the Formula of Faà di Bruno: Combinatorial Identities and Monotonic Functions, with Horst Alzer. Results Math 76, 166 (2021). doi: 10.1007/s00025-021-01448-9, Direct link.

The Dynamics of a Bead Sliding on a Freely Rotating Horizontal Wire: An Analytical Solution, with Dennis S. Bernstein. Differential Equations and Dynamical Systems (2021). doi: 10.1007/s12591-021-00574-8

Computation of several Hessenberg determinants, with Feng Qi and Issam Kaddoura. Mathematica Slovaca, Volume 70 Issue 6, December (2020) , pp 1521-1537. URL, doi:10.1515/ms-2017-0445, Preprint.

Combinatorial Identities and Inequalities for Trigonometric Sums, with Horst Alzer and Man Kam Kwong. In: Raigorodskii A.M., Rassias M.T. (eds) "Discrete Mathematics and Applications". Springer Optimization and Its Applications, vol 165. Springer, Cham (2020) . https://doi.org/10.1007/978-3-030-55857-4_2 

What is the Adjoint of a Linear System?, with Dennis S. Bernstein. IEEE Control Systems. Volume 40 Issue 3  (2020). Preprint, URL, doi: 10.1109/MCS.2020.2976389

A Discrete-Time, Time-Delayed Lur’e Model with Biased Self-Excited Oscillations, with Juan Paredes, Syed Aseem Ul Islam, and Dennis S. Bernstein, March 2020, Preprint

Weighted Inequalities for Trigonometric Sums, with Horst Alzer.  In: A. Raigorodskii, M. T. Rassias (eds.) "Trigonometric Sums and Their Applications", Springer, Cham, (2020). doi: 10.1007/978-3-030-37904-9_4

How slippery is viscous friction?  with Anna Prach and Dennis S. Bernstein. IEEE Control Systems. Volume 39 Issue 3  (2019). Preprint, URL, doi: 10.1109/MCS.2019.2900785

Counting colorful necklaces and bracelets in three colors. with Dennis S. Bernstein. Aequationes Mathematicae (2019) Volume 93 Issue 3. pp 1183-1202. doi:10.1007/s00010-019-00645-w, Direct link.

The convergence of some weighted means of values of a function. Bolletino Dell’Unione Matematica Italiana 11 (2018),  pp. 541-555, doi: 10.1007/s40574-017-0151-z, URL, Direct link

Sharp two-parameter bounds for the identric mean. Journal of Inequalities and Applications 2018:322 (2018), 8 pages. doi: 10.1186/s13660-018-1917-2, Direct link, PMCID: PMC6267388

On certain new refinements of Finsler-Hadwiger inequalities.  Journal of Inequalities and Applications 2017:80 (2017), 13 pages. doi: 10.1186/s13660-017-1356-5,   URL, Direct link, PMCID: PMC5395604

Generalized Stieltjes constants and integrals involving the LOG–LOG function: Kummer’s theorem in action. Journal Of Classical Analysis, 9, Issue 2. (2016). pp 79-88. URL, PDF, doi:10.7153/jca-09-09

Inequalities for finite trigonometric sums. An interplay: with the sum of certain series related to harmonic numbers. Journal of Inequalities and Applications 2016:173 (2016), 15 pages. doi: 10.1186/s13660-016-1112-2. URL. Direct link

"Iterating a Square-Root Expression"  Wolfram Demonstrations Project Published: June 24, 2016.

Binomial identities with Harmonic Numbers, with A. Kotronis. MathProblems. 5, Issue 1, (2015), pp. 402-406. URL, PDF.

A Reverse Hilbert-like Optimal Inequality. Mathematical Inequalities and Applications,  Volume 18, Number 2 (2015), pp. 607-614.  doi: 10.7153/mia-18-45, URL

Influence of contact's width on the resistance measurement and resistivity anisotropy determination method for an anisotropic circular disk, with A. Nader. Journal of Applied Physics 115, (23) 234909 (2014). doi: 10.1063/1.4883764. URL 

Bounds for the Ratios of Differences of Power Means in Two Arguments. Mathematical Inequalities and Applications,  Volume 17, Number 3 (2014), pp. 913-928. doi: 10.7153/mia-17-66,  PDF

An Inequality For Bounded Functions. Mathematical Inequalities and Applications, Volume 17, Number 2 (2014), pp. 531-537. doi: 10.7153/mia-17-40, PDF

A Mixed Parseval-Plancherel Formula. Journal Of Classical Analysis, 4, Issue 2. (2014). pp 159-165. URL, PDF, doi:10.7153/jca-04-10

Lecture Notes, Bernoulli Polynomials and Applications. (2013) PDF, 

The Polar Decomposition Of a Gamma Related Function, Proposed Solution to OQ. 4498. Octogon Mathematical Magazine, 21, No 2. April (2013). URL, PDF

Proposed Solution to OQ. 4193. Octogon Mathematical Magazine, 21, No 1. April (2013). URL, PDF

Exact Evaluation of Some Highly Oscillatory Integrals. Journal of Classical Analysis, 3, Issue  1. (2013). pp. 45-57. URL, PDF, doi:10.7153/jca-03-04

An Optimal Inequality For the Tangent Function. MathProblems. 2, Issue 3, (2012), pp. 112-117. URL, PDF

Partial Fraction Expansions for Newton's and Halley's Iterations for Square Roots. KYUNGPOOK Math. J. 52, 3. (2012), pp. 347--357. URL, doi:10.5666/KMJ.2012.52.3.347

A Note on The Positivity of the Coefficients of Some Power Series Expansions.  (2011). PDF

On Certain Sums Related to the Largest Odd Divisor, (2011). PDF

The Sum of Certain Series Related to Harmonic Numbers. Octogon Mathematical Magazine, 19, No 1. April (2011). URL, PDF

Explicit form of the geometric factor for a thin disk's resistivity measurement, with A. Nader. Measurement. 43, 9, (2010), pp. 1192-1196. URL

Accelerated convergence for a normal state layered superconductor's transverse resistance expression, measured with strip contacts, with A. Nader. Measurement. 43, 7, (2010), pp. 975-982. URL

A Generalization of Riemann sums. Mathematical Reflections, Issue 1. (2010). Later appeared in the book: Mathematical Reflections: two more years (2010-2011) (ed. Titu Andreescu),  XYZ Press (2014),  pp.  379--384. URL, PDF, PDF

The Sum of the ``Harmonic Series'' Is Not Enough. SIAM, Problems and Solutions, Electronic. (2009). URL

A duality based proof of the Combinatorial Nullstellensatz. The electronic journal of combinatorics, 16,  N9, (2009). PDF

New Bounds For The Identric Mean Of Two Arguments. Journal of Inequalities in Pure and Applied Mathematics, 9, No. 3, (2008) Art. 71. URL

Inequalities related to the error function. (2006) PDF

Elementary evaluation of  the integral of  t ↦ sinpt/tq on (0,+∞) . (2004) PDF

On the interpolation of injective or projective tensor products of Banach spaces. Journal of Functional Analysis. 96, 1, Feb. (1991). URL

H1-projective spaces. Quaterly journal of Mathematics. Oxford (2), 41, (1990), 295-312. URL

Les espaces H1-projectifs, (French.)  Séminaire d'Analyse, Eds. (G. Choquet, G. Godefroy, M. Rogalski, J. Saint Raymond.) 95, 01/(1989).

Sur l'interpolation des produits tensoriels projectifs ou injectifs d'espaces de Banach, (French.) Comptes Rendus de l'Academie des Sciences, Paris,  t.309, Série I, (1989), 683-686.

L'application canonique  définie sur le produit tensoriel projectif H2(X) ⊗ H2(X) à valeurs  dans H1(X ⊗ X)  n'est pas surjective en général, (French.)  Comptes Rendus de l'Academie des Sciences, Paris, t.307, Série I, (1988), 949-953.