Automation and Remote Control

, Volume 72, Issue 11, pp 2402–2407 | Cite as

Discreteness versus continuity in information technologies: Quantum calculus and its alternatives

  • S. L. Blyumin
Control Systems and Information Technologies

Abstract

In the paper, we discuss a role of quantum calculus, “differential calculus without taking limits” as a discrete analog of continuous mathematical analysis oriented on information technologies. We studied distinctive calculi that are alternative to quantum calculus and relate finite discriminators of values of an argument with finite discriminators of values of a function at their different combinations.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Blyumin, S.L., Discreteness versus Continuity at System Modeling in Time and/or Space, Sist. Upravlen. Inform. Tekhn., 2004, no. 1(13), pp. 4–9.Google Scholar
  2. 2.
    Moiseev, N.N., Chelovek. Sreda. Obshchestvo (Person. Environment. Society), Moscow: Nauka, 1982.Google Scholar
  3. 3.
    Fikhtengol’ts, G.M., Kurs differentsial’nogo i integral’nogo ischisleniya (A Course in Differential and Integral Calculus), St. Petersburg: Lan’, 1997.Google Scholar
  4. 4.
    Kac, V. and Cheung, P., Quantum Calculus, New York: Springer, 2002.MATHCrossRefGoogle Scholar
  5. 5.
    Obshchaya algebra (General Algebra), Skornyakov, L.A., Ed., Moscow: Nauka, 1991.MATHGoogle Scholar
  6. 6.
    Nechepurenko, M.I., Iteratsii veshchestvennykh funktsii i funktsional’nye uravneniya (Iterations of Real Functions and Functional Equations), Novosibirsk: Inst. Vychisl. Mat. Mat. Geofis., 1997.Google Scholar
  7. 7.
    Bashirov, A., Kurpinar E., and Özyapici, A., Multiplicative Calculus and Its Applications, J. Math. Anal. Appl., 2008, no. 337, pp. 36–48.Google Scholar
  8. 8.
    Blyumin, S.L., Alternative Mathematical Analysis: Quotients instead of Differences, Nov. Tekhn. Obrazovan., 2002, no. 5, pp. 31–32.Google Scholar
  9. 9.
    Carroll, M., The Natural Chain of Binary Arithmetic Operations and Generalized Derivatives, arXiv.org/math.HO/0112050.Google Scholar
  10. 10.
    Bauman, Y., Quantum Microeconomics with Calculus, 2009; smallparty.org/yoram/quantum.
  11. 11.
    Blyumin, S.L., Sukhanov, V.F., and Chebotarev, C.V., Ekonomicheskii faktornyi analiz (Economic Factor Analysis), Lipetsk: Lipetsk. Ekologo-Gumanitarn. Inst., 2004.Google Scholar
  12. 12.
    Arnol’d, I.V., Teoreticheskaya arifmetika (Theoretical Arithmetic), Moscow: GUPI, 1938.Google Scholar
  13. 13.
    Grossman, M. and Katz, R., Non-Newtonian Calculus, Pigeon Cove: Lee Press, 1972.MATHGoogle Scholar
  14. 14.
    Gel’fond, A.O., Ischislenie konechnykh raznostei (Calculus of Finite Differences), Moscow: Nauka, 1967.Google Scholar
  15. 15.
    Kitaev, A., Shen’, A, and Vyalyi, M., Klassicheskie i kvantovye vychisleniya (Classical and Quantum Calculi), Moscow: MTsNMO, 1999.Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2011

Authors and Affiliations

  • S. L. Blyumin
    • 1
  1. 1.Lipetsk State Technical UniversityLipetskRussia

Personalised recommendations