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

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