Advertisement

Differential Calculus of Zeon Functions

  • G. Stacey StaplesEmail author
Article
  • 5 Downloads
Part of the following topical collections:
  1. Homage to Prof. W.A. Rodrigues Jr

Abstract

Analogous to real functions, zeon functions are defined as zeon-valued functions of a zeon variable. In this paper, formal criteria for continuity and differentiability of zeon functions are put on a rigorous footing and the “usual” differentiation rules are formally established. As special cases, zeon extensions of real functions and zeon functions of one real variable are considered.

Keywords

Zeons Clifford algebras Calculus 

Mathematics Subject Classification

15A66 81R05 

Notes

References

  1. 1.
    Dollar, L.M., Staples, G.S.: Zeon roots. Adv. Appl. Cliff. Algebras 27, 1133–1145 (2017).  https://doi.org/10.1007/s00006-016-0732-4 MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Haake, E., Staples, G.S.: Zeros of zeon polynomials and the zeon quadratic formula. Adv. Appl. Cliff. Algebras 29, 21 (2019)Google Scholar
  3. 3.
    Lindell, T., Staples, G.S.: Norm inequalities in zeon algebras. Adv. Appl. Cliff. Algebras 29, 13 (2019)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Neto, A.F.: Higher order derivatives of trigonometric functions, Stirling numbers of the second kind, and zeon algebra. J. Integer Seq. 17, 14 (2014)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Neto, A.F., dos Anjos, P.H.R.: Zeon algebra and combinatorial identities. SIAM Rev. 56, 353–370 (2014)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Salzberg, P.M.: A reflection principle for calculating the derivatives of a polynomial. Am. Math. Mon. 89, 305–307 (1982)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Schott, R., Staples, G.S.: Zeons, lattices of partitions, and free probability. Comm. Stoch. Anal. 4, 311–334 (2010)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Schott, R., Staples, G.S.: Operator Calculus on Graphs. Imperial College Press, London (2012)CrossRefGoogle Scholar
  9. 9.
    Staples, G.S.: CliffMath: Clifford algebra computations in Mathematica, 2008–2018. http://www.siue.edu/~sstaple/index_files/research.htm. Accessed 6 Feb 2019
  10. 10.
    Staples, G.S.: Hamiltonian cycle enumeration via fermion-zeon convolution. Int. J. Theor. Phys. 56, 3923–3934 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Staples, G.S., Weygandt, A.: Elementary functions and factorizations of zeons. Adv. Appl. Cliff. Algebras 28, 12 (2018)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSouthern Illinois University EdwardsvilleEdwardsvilleUSA

Personalised recommendations