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# Publications, talks, essays, monographs

Contact: jenskoeplinger@gmail.com -
last updated 28 March 2021

## Publications

J. A. Shuster, J. Köplinger,
Doubly nilpotent numbers in the 2D plane,
Appl. Math. Comput. **217** (2011), pp. 7295-7310 (personal version
PDF).

J. A. Shuster, J. Köplinger,
Elliptic complex numbers with dual multiplication,
Appl. Math. Comput. **216** (2010), pp. 3497-3514 (personal version
PDF,
PS.gz).

J. Köplinger,
Gravity and electromagnetism on conic sedenions,
Appl. Math. Comput. **188** (2007), pp. 948-953 (personal version
PDF,
PS).

J. Köplinger,
Hypernumbers and relativity,
Appl. Math. Comput. **188** (2007), pp. 954-969 (personal version
PDF,
PS).

J. Köplinger,
Signature of gravity in conic sedenions,
Appl. Math. Comput. **188** (2007), pp. 942-947 (personal version
PDF,
PS).

J. Köplinger,
Dirac equation on hyperbolic octonions,
Appl. Math. Comput. **182** (2006), pp. 443-446 (personal version
PDF,
PS);
**corrigendum PDF,
PS**.

J. Köplinger, G. Kasper, and S. Hunklinger,
Glass transition in chlorobenzene-decalin under pressure,
J. Chem. Phys. **113** (2000) 4701-4706 (issue 11).

## Select talks, essays, monographs

J. Köplinger, "The square root of Bayesian inference": Quantum states in one dimension from multivalued complex exponentiation,
draft talks (2019), PDF
#1,
#2,
#3.

J. Köplinger, Dirac equation with Euclidean-Minkowskian "gravity phase",
monograph (2019),
PDF.

J. Köplinger, Four dimensional Euclidean gravity and octonions,
talk at 4^{th} Mile High Conference on Nonassociative Mathematics (2017),
University of Denver, CO (PDF).

J. Köplinger, Introducing Burgin hypernumbers in one page,
monograph (2013),
PDF.

J. Köplinger, John A. Shuster, "1 + 1 = 2" A step in the wrong direction?,
essay (2012),
PDF.

J. Köplinger, V. Dzhunushaliev, and M. Gogberashvili, Emergent time from non-associative quantum theory,
essay (2008),
PDF.

J. Köplinger, Gravity on four dimensional Euclidean spacetime,
monograph (2005),
PDF.

## Current work in progress

Nothing to share at this point.

## All other

J. Köplinger, V. Dzhunushaliev, Nonassociative quantum theory, emergent probability, and coquasigroup symmetry,
arXiv:
0910.3347 (2011).

J. Köplinger, An analysis of Rick Lockyer's "octonion variance sieve"
arXiv:
1103.4748 (2011).

J. Köplinger, J. A. Shuster, Beyond the Complexes: Toward a lattice based number system,
talk at 3^{rd} Mile High Conference on Nonassociative Mathematics (2013),
University of Denver, CO (PDF).

J. Köplinger, Beyond complex number exponentiation: Two prototypes,
talk at AMS Spring Central Section Meeting (2013),
Iowa State University, Ames, IA (PDF).

J. Köplinger, V. Dzhunushaliev, Notes towards a nonassociative quantum theory,
talk at AMS Fall Central Section Meeting (2010),
University of Notre Dame, South Bend, IN (PDF,
PS).

J. Köplinger, Nonassociative quantum theory on octooctonion algebra,
J. Phys. Math. (defunct)
**1** (2009), S090501 (personal version PDF).

V. Dzhunushaliev, J. Köplinger, Hidden nonassociative structures in quantum mechanics,
talk at 2^{nd}
Mile High Conference on Nonassociative Mathematics (2009),
University of Denver, CO (PDF,
PS).

J. Köplinger, V. Dzhunushaliev, Non-associative decomposition of angular momentum operator using complex octonions,
talk at 75^{th} SESAPS meeting (2008),
SES08-2008-000089 (PDF,
PS.gz;
see also supplement with details and notation cross-reference:
PDF,
PS).

J. Köplinger, Quantum of area from gravitation on complex octonions,
arXiv:
0812.0212 (2008).

J. Köplinger, Proposed operator description of four dimensional Euclidean quantum gravity,
talk at 74^{th} SESAPS meeting (2007),
SES07-2007-000015 (PDF,
PS).

J. Köplinger, Remarks on four dimensional Euclidean gravity without Wick rotation,
arXiv:
hep-th/0605233 (2006).

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