Antieigenvalue analysis for continuum mechanics, economics, and number theory

• Autorzy: Karl Gustafson
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Antieigenvalue; granular materials; investment theory; Pythagorean Triples

• Wydawca: De Gruyter Open
• Czasopismo: Special Matrices
• Rocznik: 2016
• Tom: 4
• Numer: 1
• Strony: 1-8

Daty

wydano

2016-01-01

otrzymano

2015-07-26

zaakceptowano

2015-10-19

online

2015-12-16

Twórcy

autor

Karl Gustafson

• Department of Mathematics, University of Colorado, Boulder, Colorado, 80309-0395, USA

Bibliografia

• [1] I. Aldridge, High Frequency Trading, John Wiley & Sons, Hoboken (2010).
• [2] T.G. Anderson, T. Bolerslev, F.X. Diebold and P. Labys, Modeling and forecasting realized volatility, Econometrica 71 (2003), 579–625.[Crossref]
• [3] J. Borewein and P. Borwein, Pi and the AGM, Wiley, New York (1987).
• [4] J. Estrada, Geometric mean maximization: an overlooked portfolio approach, J. of Investing 19 (4) (2010), 134–147.
• [5] I. Gialampoukidis, K. Gustafson and I. Antoniou, Financial Time Operator for random walk markets, Chaos, Solitons & Fractals 57 (2013), 63–72.[WoS]
• [6] I. Gialampoukidis, K. Gustafson and I. Antoniou, Time operator of Markov chains and mixing times. Applications to financial data, Physica A 415 (2014), 141–155[WoS]
• [7] R. Gordon-Wright and P.A. Gremand, Granular free surfaces, SIAM Review 55 (2013), 169–183.[WoS]
• [8] K. Gustafson, The geometrical meaning of the Kantorovich-Wielandt Inequalities, Lin. Alg. and Applic. 296 (1999), 143-151.
• [9] K. Gustafson, Antieigenvalue Analysis, with Applications to Numerical Analysis, Wavelets, Statistics, Quantum Mechanics, Finance and Optimization, World-Scientific, Singapore (2012).
• [10] K. Gustafson and I. Antoniou, Financial time operator and the complexity of time, Mind and Matter 11 (2) (2013), 83–100.
• [11] K. Gustafson, A new financial risk ratio, Journal of Statistical Computation and Simulation, 85 (13) (2015), 2682–2692.
• [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] E. Maor, The Pythagorean Theorem, Princeton University Press, Princeton, New Jersey (2007).
• [14] W.F. Sharpe, G.J. Alexander, J.V. Bailey, Investments, 6th Ed., Prentice Hall, New Jersey (1999).
• [15] A. Trautman, Pythagorean spinors and Penrose twistors. In: The Geometric Universe (eds. S.A. Huggett, L.J. Mason, K.P. Tod, S.T. Tsou, N.M.J. Woodhouse), Oxford University Press, Oxford, U.K. (1998) pp. 411–419.
• [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]

Identyfikatory

DOI

10.1515/spma-2016-0001