Skip to main content
SpringerLink
Log in

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

  • Control Systems and Information Technologies
  • Published:
Automation and Remote Control Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  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.

  2. Moiseev, N.N., Chelovek. Sreda. Obshchestvo (Person. Environment. Society), Moscow: Nauka, 1982.

    Google Scholar 

  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. Kac, V. and Cheung, P., Quantum Calculus, New York: Springer, 2002.

    Book  MATH  Google Scholar 

  5. Obshchaya algebra (General Algebra), Skornyakov, L.A., Ed., Moscow: Nauka, 1991.

    MATH  Google Scholar 

  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. Bashirov, A., Kurpinar E., and Özyapici, A., Multiplicative Calculus and Its Applications, J. Math. Anal. Appl., 2008, no. 337, pp. 36–48.

  8. Blyumin, S.L., Alternative Mathematical Analysis: Quotients instead of Differences, Nov. Tekhn. Obrazovan., 2002, no. 5, pp. 31–32.

  9. Carroll, M., The Natural Chain of Binary Arithmetic Operations and Generalized Derivatives, arXiv.org/math.HO/0112050.

  10. Bauman, Y., Quantum Microeconomics with Calculus, 2009; smallparty.org/yoram/quantum.

  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. Arnol’d, I.V., Teoreticheskaya arifmetika (Theoretical Arithmetic), Moscow: GUPI, 1938.

    Google Scholar 

  13. Grossman, M. and Katz, R., Non-Newtonian Calculus, Pigeon Cove: Lee Press, 1972.

    MATH  Google Scholar 

  14. Gel’fond, A.O., Ischislenie konechnykh raznostei (Calculus of Finite Differences), Moscow: Nauka, 1967.

    Google Scholar 

  15. Kitaev, A., Shen’, A, and Vyalyi, M., Klassicheskie i kvantovye vychisleniya (Classical and Quantum Calculi), Moscow: MTsNMO, 1999.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lipetsk State Technical University, Lipetsk, Russia

    S. L. Blyumin

Authors
  1. S. L. Blyumin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Original Russian Text © S.L. Blyumin, 2008, published in Sistemy Upravleniya i Informatsionnye Tekhnologii, 2008, No. 1, pp. 217–221.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blyumin, S.L. Discreteness versus continuity in information technologies: Quantum calculus and its alternatives. Autom Remote Control 72, 2402–2407 (2011). https://doi.org/10.1134/S0005117911110142

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0005117911110142

Keywords

Search

Navigation