Alex Kasman's Publications
Most of the articles listed below are available online as PDF files or
on the arXiv of math/physics preprints. If you would like a printed copy
of any of these articles, please write to me at the address
above and I would be happy to send you one.
Bispectral KP Solutions and Linearization of Calogero-Moser Particle
Systems was published in Communications in Mathematical Physics
Orthogonal Polynomials and Finite Toda Lattices appeared
in The Journal of Mathematical Physics, 38 (1) 1997 pp. 247-254.
Bispectral Darboux Transformations: the Generalized Airy Case
by Mitchell Rothstein and myself was published in Physica D 102
(1997), no. 3-4 pp. 159-176.
Darboux Transformations from n-KdV to KP appeared in Acta
Applicandae Mathematicae 49 no. 2 (1997) pp. 179-197.
The Bispectral Involution as a Linearizing Map in "Caloger-Moser-Sutherland-Models",
Series in Mathematical Physics, JF van Diejen and L Vinet, eds. Springer
(2000) pp. 221--230.
Darboux Transformations and the Bispectral Problem in CRM
Proceedings and Lecture Notes 14 American Mathematical Society
Integrable Systems with Singular Rational Spectral Varieties
was my talk at the Workshop on Supersymmetry and Integrable Models, University
of Illinois - Chicago, April 1997. Published as Lecture Notes in Physics502
Springer-Verlag (1998) pp. 77-90
D-modules and Darboux Transformations written jointly with
Yuri Berest appeared in Letters in Mathematical Physics 43 (1998)
Duality and Construction of Quantum Integrable Systems (with
Trends in mathematical physics (Knoxville, TN, 1998),
289--297, AMS/IP Stud. Adv. Math., 13, Amer. Math. Soc., Providence, RI,
Spectral Difference Equations Satisfied by KP Soliton Wavefunctions
was published as Inverse Problems 14 (1998) pp.1481-1487.
Kernel Inspired Factorizations of Partial Differential Operators appeared as The
Journal of Mathematical Analysis and Applications 234/2 (1999) pp.
Grassmannians, Nonlinear Waves and Generalized Schur Functions was published in Contemporary
Mathematics 246 (1999) pp. 163-174.
Note: I liked my first draft of this article better than the one which
was published. That version was longer and did a better job of introducing
ideas (like Grasmmannian manifolds) which were cut out of the final version
at the editor's request. It is available from the arXiv as http://arXiv.org/abs/math-ph/9811008v2.
Darboux Transformations of Bispectral Quantum Integrable Systems
written jointly with Emil Horozov, was published as
Letters in Mathematical
Physics 49: 131-143, 1999.
Finite Canonical Commutation Relations and Rational Nested Bethe
Ansatz was published as Regular and Chaotic Dynamics 6 (2), 211-214 (2001).
arXiv or journal.
Commutative Partial Differential Operators written with Emma
Previato was published as Physica D 152-153 (2001) 66-77
Solitons and Almost-Intertwining Matrices with Michael Gekhtman
appeared in the Journal of Mathematical Physics 42 8 (2001) 3540-3553.
On the Quantization of a Self-Dual Integrable System was published as Journal of Physics A 23 (2001) 6307-6312.
- Overcoming the Phage Replication Threshold: A mathematical model
with implications for phage therapy with Laura M. Kasman, Caroline
Westwater, Joseph Dolan, Michael G. Schmidt, and James S. Norris was
published in The Journal of Virology.
76 11, (2002) 557-5564.
Systems and Rank One Conditions for Rectangular Matrices with
Michael Gekhtman was published as Theoretical and Mathematical
Physics 133(2): 1498-1503 (2002) [and in Russian as
Teoreticheskaya i Matematicheskaya Fizika Vol. 133 No. 2
pp. 211-217, November 2002].
arXiv or PDF
(Funny Note: I wrote this paper in English and submitted it to this
Russian journal which translated it into Russian for the original
edition of the journal. Interestingly, when the American Mathematical
Society summarized the paper in Math Reviews, they translated the Russian title back into English and ended up with something just slightly different than our original title!)
- On KP Generators and the Geometry of the HBDE with
Michael Gekhtman was published in The Journal of Geometry and
Physics 56 (2006) 282-309.
- On Decompositions of the KdV 2-Soliton with Nicholas Benes and Kevin Young was published as The Journal of Nonlinear Science Volume 16 Number 2 (2006) pages 179-200.
PDF or Journal or Slides from a Talk
- When is negativity not a problem for the ultra-discrete limit? with Stéphane Lafortune was published as Journal of Mathematical Physics 47, 103510 (2006).
Journal or arXiv
- Tau-Functions, Grassmannians and Rank One
Conditions with Michael Gekhtman was published as The
Journal of Computational and Applied Mathematics 202 (2007) 80--87.
- Universality of Rank 6 Plücker Relations and Grassmann
Cone Preserving Maps with Takahiro Shiota, Kathryn Pedings and Amy
Reiszl was published as The Proceedings of the American Mathematical Society 136 (2008) 77-87.
- Spin Calogero Particles and Bispectral Solutions of the Matrix KP Hierarchy with Maarten Bergvelt and Michael Gekhtman was published as Mathematical Physics, Analysis and Geometry 12 (2009) 181-200.
arXiv or Journal
- Factorization and Resultants of Partial Differential Operators with Emma Previato was published as Mathematics in Computer Science 4 (2010) 169-184.
(The Mathematica notebook containing the commands for multiplying, conjugating and taking resultants of partial differential operators described in the paper is available here for download.)
- Duality and Collisions of Harmonically Constrained Calogero Particles was published as Contemporary Mathematics (2013) 593 pp. 109--123.
- Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity
was published as SIGMA 11 (2015), 087, 22 pages
Journal or arXiv
- Factorization of a Matrix Differential Operator Using Functions in its Kernel was published as The American Mathematical Monthly Vol. 123, No. 7 (August-September 2016), pp. 704-709
- Recurrence Relations for Exceptional Hermite Polynomials with D. Gomez-Ullate, A. Kuijlaars and R. Milson The Journal of Approximation Theory (2016), pp. 1-16
- On Factoring an Operator Using Elements of its Kernel Communications in Algebra (2017) 45 pp. 1443-1451.
- The Duplexing of the Genetic Code and Sequence-Dependent DNA Geometry Bulletin of Mathematical Biology 80 (10), 2734-2760 (2018).
Journal or Downloadable Mathematica Notebook or Springer Nature Sharing
- Quaternion-Valued Breather Soliton, Rational, and Periodic KdV Solutions (with John Cobb, Albert Serna, and Monique Sparkman) The Journal of Nonlinear Mathematical Physics 27:3, 429-452 (2020).
arXiv or Journal
- Did Sequence Dependent Geometry Influence the Evolution of the Genetic Code? (with Brenton LeMesurier) Contemporary Mathematics 746 pp.41-56 (2020).
arXiv or Journal
- The Adelic Grassmannian and Exceptional Hermite Polynomials (with Robert Milson) (submitted for publication)
Other Mathematics Related Publications:
Student Answer Manual to accompany "Calculus" by Hughes-Hallett,
Gleason, et al. John Wiley & Sons, 1993 (with S.A. Mallozzi,
A.H. Wang and G. Zhang).
Book Review: Imaginary
Numbers in the Notices of the AMS, Volume 47 Number 7, August 2000.
Book Review: Cryptonomicon
in the Notices of the AMS, Volume 46 Number 11, December 1999.
Letter to the Editor
in the Notices of the AMS, Volume 44 Number 6. (On Calculus Education.)
Letter to the Editor
in the Notices of the AMS, Volume 42 Number 10. (On typesetting preferences
Letter to the Editor
in the Notices of the AMS, Volume 43 Number 5. (On the need for mathematical
exposition to non-mathematicians.)
- Letter to
the Editor in the Notices of the AMS, Volume 49 Number 6. (On the
connection between mathematics and insanity implicit in works of fiction
such as the film A Beautiful Mind.)
Effectiveness, a short story was published in Math Horizons
- "Mathematics in Fiction: An Interdisciplinary Course" appeared in
PRIMUS Volume XIII Number 1, March 2003, Pages 1-16.
- Book Review: "It Must Be Beautiful" in the American Mathematical
Monthly, October 2003.
- Book Review: "After Math, The Fractal Murders and Other
Mathematical Murder Mysteries" in the AMS Notices, October 2003,
- "Mathematics in Science Fiction" in Math Horizons, April 2004,
- Book Review: "PopCo" published in the AMS Notices, February 2006.
- DNA Solitons and Codon Bias: A PDF copy of a poster that I presented at Mathematics of DNA Structure, Function and Interactions (Institute of Mathematics and its Applications, September 2007).
- Book Review: "Pythagorean Crimes" published in the AMS Notices, January 2009.
- My short story On the Quantum Theoretic Implications of Newton's Alchemy has been published in Analog (October 2007), Esli (February 2008) and the book The Shape of Content (AK Peters Publishing, 2008).
- Book Review: "After Genius" in the December 2010 issue of the Mathematical Intelligencer.
- My essay "Fictional Women in Mathematics" appeared in the January 2011 newletter of the AWM.
- Bispectrality and Duality: A PDF copy of the talk I gave at the 2012 Joint Mathematics Meeting in Boston reviewing progress on my "research program" aiming to demonstrate a correspondence between the action-angle duality of integrable particle systems and the bispectral property. The talk mentions a bit about the quantum correspondence, but focuses especially on the classical case.
- "A Survey of Fictional Mathematics in Literature" in Mathematics and Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media (Sklar and Sklar, Eds.), McFarland 2012.
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