Skip to main content
SpringerLink
Log in
Book cover

Advances in Intelligent Systems and Computing pp 129–148Cite as

Multi-modular Optimum Coding Systems Based on Remarkable Geometric Properties of Space

  • Chapter
  • First Online:

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 512))

Abstract

In this paper, we regard a new conceptual model of multi-modular optimum coding systems as multi-modular cyclic groups based on remarkable geometric properties of space, namely useful rotational symmetry and asymmetry relationships law. Moreover, the optimization embedded in the models. Proposed methodology provides the development of new directions in fundamental and applied research in systems engineering for improving the quality indices of engineering devices or systems (e.g. 3D space coordinates control system) with respect to redundancy, and embody reliability. These design techniques make it possible to configure systems with fewer elements than at present, while maintaining or improving on resolving ability, structural redundancy and security of the system. Examples of optimum vector codes over multimodular toroidal coordinate systems presented.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Toroidal Space. http://harmonicresolution.com/Toroidal%20Space.htm

  2. Manifold. https://en.wikipedia.org/wiki/Manifold

  3. Singer, J.: A theorem in finite projective geometry and some applications to number theory. Trans. Am. Math. Soc. 43(3), 377–385 (1938)

    Article  MathSciNet  MATH  Google Scholar 

  4. Hall Jr., M.: Combinatorial Theory, p. 470. Blaisell, New York (1967)

    Google Scholar 

  5. Riznyk, V.: Synthesis of Optimum Combinatorial Systems. Lviv, p. 165. High school (1989) (in Ukrainian)

    Google Scholar 

  6. Golomb, S., Osmera, P., Riznyk, V.: Combinatorial sequencing theory for optimization of signal data vector converting and signal processing. In: Workshop on Design Methodologies for Signal Processing, pp. 43–44. Zakopane (1996)

    Google Scholar 

  7. Riznyk, V.: Multidimensional Systems: Problems and Solutions, pp. 5/1–5/5. IEE, Savoy Place, London (1998)

    Google Scholar 

  8. Riznyk, V.: Multidimensional combinatorial systems based on gold ring bundles design approach. In: International Symposium on Combinatorial Optimization, p. 188. Universitet de Libre, Brussels (1998)

    Google Scholar 

  9. Riznyk, V.: Perfect distribution phenomenon in combinatorics and systems theory. In: 7th Zittau Fuzzy Colloquium, pp. 194–197. Germany (1999)

    Google Scholar 

  10. Riznyk, M., Riznyk, V.: Manufacturing systems based on perfect distribution phenomenon: intelligent systems in design and manufacturing III. In: Proceedings of SPIE, vol. 4192, pp. 364–367. Published by SPIE, Boston (2000)

    Google Scholar 

  11. Riznyk, V.: Applications of the combinatorial sequencing theory for innovative design based on diagrammatics. Mach. Gr. Vis. Int. J. 12(1), 83–98 (2003)

    Google Scholar 

  12. Riznyk, V.: Combinatorial 3D sequencing theory and methods in applied mechanics. In: Euromech 406 Colloquium, pp. 189–191. Warsaw (1999)

    Google Scholar 

  13. Riznyk, V.: Application of the perfect distribution phenomena for innovative information technologies. In: 4th International Conference and the Fourth Irish Conference on the Mathematical Foundations of Computer Science and Information Technology, pp. 385–389. National University of Ireland, Cork (2006)

    Google Scholar 

  14. Riznyk, V., Bandyrska, O., Skrybajlo-Leskiv, D.: Application of the gold ring bundles for innovative non-redundant sonar systems. Arch. Acoust. Q. 31(4 Supplement), 379–384 (2006)

    Google Scholar 

  15. Riznyk, V., Bandyrska, O.: Application of the gold ring bundles for innovative non-redundant radar or sonar systems. Eur. Phys. J. Spec. Top. 154, 183–186 (2008)

    Article  Google Scholar 

  16. Riznyk, V.: Application of the golden numerical rings for configure acoustic systems of fine resolution. Acta Phys. Polonica A 119(6-A), 1046–1049 (2011)

    Article  Google Scholar 

  17. Riznyk, V.: Perfect information systems concept based on remarkable space-time properties. In: Information Systems Architecture and Technology, pp. 19–26, Wroclaw (2008)

    Google Scholar 

  18. Riznyk, V.: Application of the symmetrical and non-symmetrical models for innovative coded design of signals. In: 9th International Conference on Modern Problems of Radio Engineering Telecommunications and Computer Science (TCSET), p. 70. Lviv Polytechnic, Lviv (2012)

    Google Scholar 

  19. Riznyk, V.: Multidimensional systems optimization developed from perfect torus groups. Int. J. Appl. Math. Inf. 9, 50–54 (2015)

    Google Scholar 

  20. Riznyk, V.: The concept of the embody reliability in design of cyber-physical systems. In: 11th International Conference on Perspective Technologies and Methods in MEMS Design, pp. 75–77. Lviv Polytechnic (2015)

    Google Scholar 

  21. Riznyk, V.: Advanced 3D information technologies based on symmetry and non-symmetry complementary ensembles. In: 8th International Science and Technical Conference, p. 115. Publishing Lviv Polytechnic, Lviv (2013)

    Google Scholar 

  22. Riznyk, V.: Combinatorial optimization of systems based on symmetric and asymmetric structure usage. Electr. Tech. J. Electrotech. Comput. Syst. 13(89), 40–45 (2014). (in Ukrainian)

    Google Scholar 

  23. Riznyk, V.: Application of perfect distribution phenomenon for acoustics and music. In: WSES International Conference on Acoustics and Music Theory, and Applications, pp. 581–585. Montego Bag, Jamajca (2000)

    Google Scholar 

  24. Riznyk, V.: Perfect distribution phenomenon and remarkable spacetime property. In: 9th Zittau Fuzzy Colloquium, pp. 238–241. Germany (2001)

    Google Scholar 

  25. Riznyk, V.: Perfecr distribution phenomenon and the origin of the spacetime harmony. https://www.generativeart.com/on/cic/ga2001_PDF/riznyk.pdf

  26. Riznyk, V.: A new vision of symmetry based on the ideal ring bundles theory. In: 9th International Conference on Generative Art, Milano Polytechnico, Italy. https://www.generativeart.com (2006)

  27. Wigner, P.: Symmetries and Reflections. Indiana University Press, Bloomington (1970)

    Google Scholar 

  28. Spacetime_symmetries. https://en.wikipedia.org/wiki/Spacetime_symmetries

  29. Euclidean_group. https://en.wikipedia.org/wiki/Euclidean_group

  30. Singleton_(mathematics). https://en.wikipedia.org/wiki/Singleton_(mathematics)

Download references

Acknowledgments

Author thanks to University Professor S. Golomb from University of Southern California for his acceptance of the proposal “Research and Applications of the Combinatorial Configurations for Innovative Devices and Process Engineering” for Cooperative Grants Program from CRDF (U.S. 1996).

Author information

Authors and Affiliations

  1. Institute of Computer Sciences and Information Technologies, Lviv Polytechnic National University, Lviv, Ukraine

    Volodymyr Riznyk

Authors
  1. Volodymyr Riznyk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Volodymyr Riznyk .

Editor information

Editors and Affiliations

  1. Lviv Polytechnic National University , Lviv, Ukraine

    Natalya Shakhovska

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Riznyk, V. (2017). Multi-modular Optimum Coding Systems Based on Remarkable Geometric Properties of Space. In: Shakhovska, N. (eds) Advances in Intelligent Systems and Computing. Advances in Intelligent Systems and Computing, vol 512. Springer, Cham. https://doi.org/10.1007/978-3-319-45991-2_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-45991-2_9

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45990-5

  • Online ISBN: 978-3-319-45991-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation