- → Strongly related to the subject.
- → Weakly related.
Apolloniana
Apollonian disk packings: geometry, number theory, physics.
- A note on unbounded Apollonian disk packings
[arXiv:1910.05924]
-
Tessellations and Descartes disk configurations
[ arXiv:1910.05919 ]
- Apollonian coronas and a new Zeta function (2019),
[ arXiv:1909.09941]
- Spinors and the Descartes configuration of circles (2019),
arXiv:1909.06994
- Coupled-ring resonance and unitary groups
(with M. Sayeh),
The Journal of the Optical Society of America B,
36 (3), 2019, 667-673.
[arXiv:1807.06773]
- Skein relations for spin networks, modified,
Journal of Knot Theory and Its Ramifications,
27 (7) 2018
[arXiv:1807.07244 ]
- The Koide Lepton Mass Formula and Geometry of Circle Configurations,
arXiv:1201.2067
- On a Diophantine equation that generates all integral Apollonian gaskets,
, ISRN Geometry. Article ID 348618, 19 pages, 2012. doi:10.5402/2012/348618.
[pdf]
- Golden Window [light matters] (2010),
Mathematics Magazine,
83 (5) 2010, no. 5, pp. 228-237.
[pdf]
- Lens sequences (2007),
arXiv:0710.3226.
- A theorem on circle configurations (2007).
arXiv:0706.0372,
- Clifford algebras and Euclid's parameterization of Pythagorean triples,
Advances in Applied Clifford Algebras (Mathematical Structures),
17 2007 pp. 71-93.
[pdf]
Relativity
- The loop of relativistic velocities as a deformation of the menhir loop
[arXiv:1910.06556]
- Making sense of relativistic composition of velocities
[arXiv:1910.06785]
- Cromlech, menhirs and celestial sphere: an unusual representation of the Lorentz group,
[ arXiv:1604.05698 ]
- Geometric diagram for relativistic addition of velocities,
Am. J. Phys. Aug 2012 80 (8) p. 737.
[pdf]
- A Porism Concerning Cyclic Quadrilaterals,
Geometry, Volume 2013 (Jun 2013), Article ID 483727.
[arXiv:1408.1493]
- Structure of matrix manifolds and a particle model
(with J. Rzewuski),
Journal of Mathematical Physics, 37 (2), 1996, pp. 1004-28.
[pdf]
- On projections of spinor spaces onto Minkowski space
(with J. Rzewuski),
in "Symmetries in Science II," (B. Gruber, ed.),
Plenum, New York, 1986.
Lie algebras and mathematical physics
- Casimir energy of Sierpinski triangles
(with K.V. Shajesh, P. Parashar, I. Cavero-Pelaez, and I. Brevik),
Phys. Rev. D, 96, Nov 2017, eid 105010
[arXiv:1709.06284]
- Krawtchouk matrices from the Feynman path integral and from the split quaternions,
Contemporary Mathematics, 668,
2016, pp . 131-164.
[arXiv:1604.00109]
- Canonical endomorphism field on a Lie algebra,
Journal of Generalized Lie Theory and Applications,
4 Oct 2010, article ID G100302.
[pdf]
- Traces, symmetric functions, and a raising operator:
Generating function for Cauchy's enumeration formula,
Proc. of the Fifth Intern. Workshop on Appl. Category Theory,
Graph-Operad-Logic, Merida, May 2006 (to appear)
[pdf]
- Krawtchouk polynomials and Krawtchouk matrices,
(with P. Feinsilver),
Recent Advances in Applied Probability, R. Baeza-Yates et al. (eds),
Springer Verlag, 2005, pp. 115-143.
[pdf],
[arXiv:quant-ph/0702073]
- Representations of the Schroedinger algebra and Appell systems
(with P. Feinsilver and R. Schott)
Fortschritte der Physik Vol. 52 (4) 2004, pp. 343-359.
[pdf]
- Berezin quantization of the Schroedinger algebra
(with P. Feinsilver and R. Schott)
Infinite-Dimensional Analysis: QP, 6 1, 2003, pp. 57-71.
[pdf]
- Krawtchouk matrices from classical and quantum walks
(with P. Feinsilver)
Contemporary Mathematics, 287 2002 , pp. 83-96.
[pdf].
- Canonical variables and analysis on so(n,2)
(with M. Giering and P. Feinsilver),
Journal of Physics: A Mathematical, 34 2001 pp 2367--2376.
[pdf]
- Duplex numbers, diffusion systems, and generalized quantum mechanics,
International Journal for Theoretical Physics, 38 (8) 1999 (Aug), pp. 2219-28.
[pdf]
- The geometry of elastic collisions and Heron's law,
American Journal of Physics, 67 (6) 1999, pp. 516-19.
[pdf]
- Representations and stochastic processes on groups of type H
(with P. Feinsilver and R. Schott),
Journal of Functional Analysis, 115, 1993, 146-165.
[pdf]
- Representation of the Heisenberg algebra, Riccati systems, and
associated geometric structures,
(with P. Feinsilver),
Proceedings of the Conference on Differential Geometric Methods in
Physics, Claustal, 1986.
- On geometry of phenomenological thermodynamics,
in "Symmetries in Science II," (B.Gruber, ed.), Plenum, New York, 1986.
[arXiv:1807.08908 [math-ph]]
Discrete math
- Harmonic evolutions on graphs,
Int. J. Math. and Comp. Sci.,
2 2007, no. 1, pp. 65-82.
[pdf]. [arXiv:1201.1355 [math.CO]}
- Mathematics of the English tense system,
Preprint of UIUC, 1998.
[pdf coming soon]
General math and creative contributions
- Disentangling a triangle [light maters] (with A. Solecki),
Am. Math. Monthly, 116 (3), March 2009, pp 228-237.
[pdf]
This paper received the Lester Ford Award
from the
Mathematical Association of America.
- Simpson's paradox: proof without words. [light matters]
Mathematics Magazine 74 2001 (Dec).
[pdf]
- On the Crossroads of Time, or Mismeasurement of Tense,
ToBe (Polish American Academic Quarterly),
Vol. 1, No 1, September 1993, pp. 18-24.
- Entries in the Online Encyclopedia of Integer Sequences: nid:A181106
- Two article-entries in the "Encyclopedia of Supersymmetry"
(1) Riemann Sphere, (2) Poisson Bracket. (J. Bagger, S. Duplij, W. Siegel, eds.), Kluwer, Dec 2003.
Other creative contributions
