Antieigenvalue analysis for continuum mechanics, economics, and number theory

Karl Gustafson

Special Matrices (2016)

  • Volume: 4, Issue: 1, page 1-8
  • ISSN: 2300-7451

Abstract

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My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly my matrix maximum turning angle of the stress tensor of the material. The important Sharpe ratio of the Capital Asset Pricing Model is now seen in terms of my antieigenvalue theory. Euclid’s Formula for Pythagorean triples becomes a special case of my operator trigonometry.

How to cite

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Karl Gustafson. "Antieigenvalue analysis for continuum mechanics, economics, and number theory." Special Matrices 4.1 (2016): 1-8. <http://eudml.org/doc/276822>.

@article{KarlGustafson2016,
abstract = {My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly my matrix maximum turning angle of the stress tensor of the material. The important Sharpe ratio of the Capital Asset Pricing Model is now seen in terms of my antieigenvalue theory. Euclid’s Formula for Pythagorean triples becomes a special case of my operator trigonometry.},
author = {Karl Gustafson},
journal = {Special Matrices},
keywords = {Antieigenvalue; granular materials; investment theory; Pythagorean Triples; antieigenvalue; Pythagorean triples},
language = {eng},
number = {1},
pages = {1-8},
title = {Antieigenvalue analysis for continuum mechanics, economics, and number theory},
url = {http://eudml.org/doc/276822},
volume = {4},
year = {2016},
}

TY - JOUR
AU - Karl Gustafson
TI - Antieigenvalue analysis for continuum mechanics, economics, and number theory
JO - Special Matrices
PY - 2016
VL - 4
IS - 1
SP - 1
EP - 8
AB - My recent book Antieigenvalue Analysis, World-Scientific, 2012, presented the theory of antieigenvalues from its inception in 1966 up to 2010, and its applications within those forty-five years to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance, and Optimization. Here I am able to offer three further areas of application: Continuum Mechanics, Economics, and Number Theory. In particular, the critical angle of repose in a continuum model of granular materials is shown to be exactly my matrix maximum turning angle of the stress tensor of the material. The important Sharpe ratio of the Capital Asset Pricing Model is now seen in terms of my antieigenvalue theory. Euclid’s Formula for Pythagorean triples becomes a special case of my operator trigonometry.
LA - eng
KW - Antieigenvalue; granular materials; investment theory; Pythagorean Triples; antieigenvalue; Pythagorean triples
UR - http://eudml.org/doc/276822
ER -

References

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  12. [12] K. Gustafson, Antieigenvalue analysis, new applications: continuum mechanics, economics, number theory, Extended Abstracts 24th IWMS, Haikou, China, May 25-28 (2015). Also arXiv: 1505.03678. 
  13. [13] E. Maor, The Pythagorean Theorem, Princeton University Press, Princeton, New Jersey (2007). Zbl1124.01002
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  16. [16] D. Yang and Q. Zhang, Drift independent volatility estimation based on high, low, open and close prices, J. of Business 73 (2000), 477–491.[Crossref] 

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