Publications

1  Research Papers

• Semisimple elements of order 3 in finite Chevalley groups, Journal of Algebra, Vol. 56 (1979), 481-498.
• Structure constants of algebraic groups, Journal of Algebra, Vol. 75(1982), 209-222.
• Root groups, Journal of Algebra, Vol. 76(1982), 211-213.
• The Jacobi identity, Punjab University Journal of Mathematics, Vol. XVI (1983), 9-30. PDF
• Homogeneous CR manifolds (co-authors: A. Huckleberry and W. Richthofer), Journal fuer die Reine and Angewandte Mathematik, Vol. 358(1985), 126-154.
• Levi-curvature of manifolds with a Stein-rational fibration, Manuscripta Mathematica, Vol. 50(1985), 269-311.
• On a theorem of Kempf and Ness (co-author: J.J. Loeb), Indiana Univ. Math. Journal, Vol. 39(1) (1990), 61-65.
• On the structure of parabolic subgroups (co-authors: M.J. Barry and G.M. Seitz), Communications in Algebra, Vol. 18(2) (1990), 551-562.
• Plurisubharmonic functions and the Kempf-Ness theorem (co-author: J.J. Loeb), Bull. London Math. Soc. 25(1993), 162-168.
• Plurisubharmonic functions and Kaehlerian metrics on complex symmetric varieties (co-author: J.J. Loeb), Indagationes Mathematicae, N.S. 3(4) (1992), 365-375.
• Totally real orbits in affine quotients of reductive groups, (co-authors: J.J. Loeb and M.N. Qureshi), Nagoya Math. Journal, Vol. 139(1995).
• A remark on the moment map, Proc. Amer. Math. Soc., Vol. 12(4), (1994), 1295-1297.
• Spherically symmetric manifolds which admit five isometrics (co-author: M. Ziad), J. Math. Phyics, 36(1995), 1908-1911.
• Quasi-potentials and Kaehler-Einstein metrics on flag manifolds, (co-authors: M.N. Qureshi and R. Kobayashi),  Journal of Algebra, Vol. 126 (1997), 620-629.
• Some applications of plurisubharmonic functions to orbits of real reductive groups, (co-author: J.J. Loeb), Indagationes Mathematicae, NS., 10(4) (1999), 473-482. PDF
• Comments on the paper “Geometric phase, bundle classification and group representation” (co-authors: M.N. Qureshi, M. Ziad), J. Math. Physics, 40(1999), 3693-3696.
• Holomorphic principal bundles over a compact Kaehler  manifold (co-authors: B. Anchouche and I. Biswas), C. R.  Acad. Sci. Paris Ser. I Math., 330(2000), no. 2, 109-114.
• Homogeneous affine bundles, Comm. Algebra, 16(1988), no. 8, 1599-1603.
• On the third Betti number of some compact homogeneous manifolds, Studia Sci. Math. Hungar. 25(1990), no. 1-2, 1-2.
• On holomorphic principal bundles over a compact Riemann surface admitting a flat connection (co-author: I. Biswas), Math Annalen, 322(2002), 333-346.
• Harder-Narasimhan reduction for principal bundles over a compact Kaehler manifold (co-authors B. Anchouch and I. Biswas), Math Annalen, 323 (2002), 333-346.
• On holomorphic principal bundles over a compact Riemann surface admitting a flat connection II (co-author: I. Biswas), Bull. London Math. Soc (accepted).
• Quasi-potentials and Kaehler-Einstein metrics on flag manifolds II (co-author: I.Biswas), Journal of Algebra, 269 (2003), 480-491. PDF
• On principal bundles over a flag manifold, (coauthor I.Biswas), Journal of Lie Theory,14(2004), no.2, 569-581).
• Focusing Surfaces (Coauthors: A. Laradji, A. Qadir) , Math.Gazette 90 (2006), no.519, 404-411).  PDF
• Harmonic morphisms of warped product type from Einstein manifolds (coauthor M.T.Mustafa) Archiv der Mathematik, 88, 368-377 (2007).
• Symmetry Analysis of Wave Equation on Sphere (coauthor M.T. Mustafa) J. Math. Anal. Appl., 333, 1180-1188 (2007).
• Symplectic Geometry of Semisimple Orbits (coauthors,E.P.Van den Ban and  I. Biswas)  Indagationes Mathematicae 19(4), 507-533 (2008).
• A note on the symplectic geometry of semisimple groups (coauthor I. Biswas)  Bulletin des Sciences Mathematiques 133(4), 330-334 (2009).

• A note on the tangent bundle of  G/P (coauthor I.Biswas) Proc. Indian Acad. Sci. Math. Sci. 120(2010), no. 1, 69--71. 

• Analytic solutions of initial-boundary-value problems of transient conduction using symmetries (coauthors: A.F.M.Arif, M.T.Mustafa). Appl. Math. Comput. 215 (2010), no. 12, 4132--4140.

• Group Classification, optimal system and optimal reductions of a class of Klein Gordon equations (coauthor M.T. Mustafa, M. Ziad) Communications in Nonlinear Science and Numerical Simulation, 15 (5), 1132-1147 (2010) Preprint.
• Polynomial solutions of differential equations (coauthors A. Laradji, M. T. Mustafa), Advances in Difference Equations Article Number: 58 DOI: 10.1186/1687-1847-2011-58 ( 2011) Preprint
• On the Conjugacy of maximal unipotent subgroups of real semisimple groups (coauthor I.Biswas), Journal of Lie Theory, Vol.22,No.3,2012.
• On the maximal solvable subgroups of semisimple algebraic groups (coauthors I.Biswas and P.Chatterjee), Journal of Lie Theory, Vol.22,No.4,2012.
• Polynomial solutions of certain differential equations arising in physics (coauthors A. Laradji, M. T. Mustafa), Mathematical Methods in Applied Sciences. 36 (2013), 1615-1624. Appendix.
•  Symmetry analysis of wave equation on static spherically symmetric spacetimes with higher symmetries (coauthors A. Y. Al-Dweik, R. A. Ghanam, M. T. Mustafa), Journal of Mathematical Physics, 54 (2013), 063509.
• On computing joint invariants of Lie algebras (coauthors I. Biswas, R.A.Ghanam,M.T.Mustafa), Journal of Geometry and Physics(2015).
• Invariants of third-order ordinary differential equations  via point transformations,  ( coauthors Ahmad Y. Al-Dweik, M. T. Mustafa, and F. M. Mahomed), Mathematical Methods in Applied Sciences b(2015).
• A note on real algebraic groups , H. Azad & Indranil Biswas ,  Forum Mathematicum (2016) Forum Mathematicum , 2016  Volume 28 ,Issue 3.
• A point symmetry based method for transforming ODEs with three-dimensional symmetry algebras to their canonical forms ( coauthors:Ahmad Y. Al-Dweik, F. M. Mahomed, M. T. Mustafa) , Applied Mathematics and Computation (2016).
• Higher order self-adjoint operators with polynomial coefficients, H. Azad, A. Laradji and M.T.Mustafa, (Electronic Journal of Differential Equations, Vol. 2016 (2016), No. 22, pp. 1–21. ISSN: 1072-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.unt.edu  )

•  Embedding algorithms and applications to differential equations (coauthors Sajid Ali, Indranil Biswas, Ryad Ghanam, Tahir Mustafa)  to appear : Journal of Symbolic Computation (2017)

• Equality of the Algebraic and Geometric ranks of Cartans Subalgebras and Applications to Linearization of a System of Ordinary Differential Equations https://arxiv.org/abs/1612.08535
• A note on the Jordan normal form Preprint
• Orbits of Real Algebraic Groups. Preprint

 

2  Papers on Education

• On a theorem of Clay (co-author: A. Laradji), College Math. Journal, Vol. 31, No. 5, Nov. 2000, p. 405.
• The projection Method in Evaluating Multiple Integrals, Intl. J. of Math. Ed. in Sc. and Tech. (UK) 2001, Vol. 32, 444-466.
• On the Definition of the Cross Product (IJMEST) (UK), 2001, Vol. 32, # 4, 585-587.
• An equality for certain exponential sums (coauthor: A. Laradji), Math. Gazette, Vol.87, No.510, (2003).p.525-527.
• Some impossible constructions in elementary geometry (coauthor: A. Laradji), Math. Gazette, Vol.88, No.513 (2004), 548-551.
• Why do certain limacons have a dimple (coauthor T.Mustafa), Teaching Mathematics and its Applications, Oxford Univ. Press. Advance Access published on March 29, 2006. (doi:10.1093/teamat/hrl003).
• Technology and Calculus Sequence (coauthor M. T. Mustafa).

3  Books

• Algebraic Groups by T.A. Springer, Birkhauser Verlag (1981). I wrote the first draft.
• Post-Modern Analysis by J. Jost, Springer Verlag, 1998. I translated the German MS into English.

4  Essays

• Mathematics as a Profession: Essay written for the Mathematics Awareness Committee of KFUPM.
• Letter from a Mathematician, Plus Magazine, March 2003, Millenium Mathematics Project, Cambridge University.
• Mathematics Around Us: Essay written for Mathematics Awareness Committee.
• Mathematics Arts and Real Life: Reflections on Teaching Mathematics.
• Group Theory: What is it good for.

 

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