grant APVV 0178-11

Neurčitosť z pohľadu pravdepodobnosti, algebry,
samoadjungovaných operátorov a kvantových štruktúr
(Uncertainty from the point of view of probability theory, algebra,
self-adjoint operators and quantum structures)

Trvanie projektu:

07/2012 - 12/2015

Riešiteľské organizácie:

Základné informácie o grante

Ciele projektu:

Získavanie originálnych výsledkov z teórie kvantových štruktúr a ich aplikácií vhodných na axiomatiku matematických základov kvantovej mechanikz ako aj kvantového komputingu. Dôraz bude kladený na efektové algebry, ortomodulárne zväzy, MV-algebry, BL-algebry, reziduované zväzy, l-grupy, samoadjungované agregačné operátory a kvantovú štatistiku. Tieto výsledky poslúžia na prehĺbenie našich poznatkov a upevnenie prestížneho postavenia slovenskej školy kvantových štruktúr v celosvetovom kontexte.

Riešitelia grantu

MÚ SAV

FEI STU, Bratislava

Svf STU, Bratislava

Výsledky za rok 2013

Publikácie SCI: 1.1

Výjdené
  1. A. Dvurečenskij, Y. Xie, Aili Yang, Discrete (n+1)-valued states and n-perfect pseudo-effect algebras, Soft Computing 17 (2013), 1537–1552. CC
  2. A. Dvurečenskij, Y. Xie, Atomic effect algebras with the Riesz decomposition property, Found. Phys. 47 (2012), 1078–1093. CC
  3. A. Dvurečenskij, Smearing of observables and spectral measures on quantum structures, Found. Phys. 43 (2013), 210–224. CC
  4. A. Dvurečenskij, J. Krňávek, The lexicographic product of po-groups and n-perfect pseudo effect algebras, Inter. J. Theor. Phys. 52 (2013), 2760–2772. CC
  5. A. Dvurečenskij, J. Janda, On bilinear forms from the point of view of generalized effect algebras, Found. Phys. 43 (2013), 1136–1152. CC
  6. A. Dvurečenskij, Kite pseudo effect algebras, Found. Phys. 43 (2013), 1314–1338. CC
  7. F. Chovanec, M. Jurečková, Fractal properties of MV-algebra pasting, Fuzzy Sets and Systems 232 (2013), 46–61. CC
  8. J. Jakubík, J. Lihová, Generalized Specker lattice-ordered groups and two types of distributivity. Math. Slovaca 63 (2013), 5–12. SCI
  9. J. Jakubík, Š. Černák, Weak relatively uniform converegence on MV-algebras. Math. Slovaca 63 (2013), 13–32. SCI
  10. D.J. Foulis, S. Pulmannová, Dimension theory for generalized effect algebras, Alg. Univers. 69 (2013), 357–386. SCI
  11. D.J. Foulis, S. Pulmannová, Type-decompositions of a synaptic algebra, Found. Phys. 43 (2013) 948–986. CC
  12. J. Paseka, S. Pulmannová, Z. Riečanová, Properties of quasi-hermitian operators inherited from self-adjoint operators, Inter. J. Theor. Phys. 52 (2013), 1994–2000. CC
  13. S. Pulmannová, Representations of MV-algebras by Hilbert-space effects, Inter. J. Theor. Phys. 52 (2013), 2163–2170. CC
  14. D.J. Foulis, S. Pulmannová, Hull determination and type decomposition for a generalized effect algebra, Alg. Univers. 69 (2013) 45–81. SCI
  15. J. Janda J., Riečanová, Z., Extensions of Ordering Sets of States from Effect algebras onto Their MacNeille Completions, Inter. J. Theor. Phys. 52 (2013) 2171–2180. CC
  16. G. Jenča, Congruences generated by ideals of the compatibility center of lattice effect algebras. Soft Computing 17 (2013), 45–47. CC
  17. A. Jenčová, Extremal generalized quantum measurements, Lin. Algebra Its Appl., 439 (2013), 4070–4079. CC
  18. J. Paseka, Z. Riečanová, Inherited properties of Effect Algebras Preserved by Isomorphism, Acta Polytechnica 53 (2013), 308–313 . SCOPUS
  19. Z. Riečanová, M. Zajac, Intervals in Generalized Effect algebras and Their Sub-generalized effect algebras, Acta Polytechnica 53 (2013), 314–316. SCOPUS
  20. Z. Riečanová, J. Janda, Maximal subsets of Pairwise summable melements Generalized Effect Algebras, Acta Polytechnica 53 (2013), 457–461. SCOPUS
  21. A. Mesiarová-Zemánková, K. Ahmad, Multi-polar Choquet integral, Fuzzy Sets and Systems 220 (2013), 1–20. CC
Prijaté do tlače
  1. A. Dvurečenskij, M. Kuková, Observables on quantum structures, Inf. Sci. DOI:10.1016/j.ins.2013.09.014 CC
  2. A. Dvurečenskij, T. Kowalski, Kites and pseudo BL-algebras, Algebra Universalis SCI
  3. A. Dvurečenskij, Y. Xie, n-perfect and Q-perfect pseudo effect algebras, Inter. J. Theor. Phys. DOI: 10.1007/s10773-013-1723-z CC
  4. A. Dvurečenskij, H-perfect pseudo MV-algebras and their representations, Math. Slovaca http://arxiv.org/abs/1304.0743 SCI
  5. A. Dvurečenskij, States on quantum and algebraic structures and their integral representation, Fuzzy Sets and Systems DOI 10.1016/j.fss.2013.11.005 CC
  6. R.A. Borzooei, A. Dvurečenskij, O. Zahiri, State BCK-algebras and state-morphism BCK-algebras, Fuzzy Sets and Systems DOI 10.1016/j.fss.2013.12.007 CC
  7. A. Dvurečenskij, W.Ch. Holland, Some remarks on kite pseudo effect algebras,DOI: 10.1007/s10773-013-1966-8 CC
  8. G. Jenča, P. Sarkoci, Linear extensions and order-preserving poset partitions, J. Comb. Theory, Series A, 122, 2014,
  9. A. Jenčová, Base norms and discrimination of generalized quantum channels, accepted in J.Math. Phys. CC
  10. J. Janda, Z. Riečanová, Intervals in Generalized Effect Algebras, Soft Computing, DOI 10.1007/s00500-013-10183-x CC
  11. Z. Riečanová, J. Janda, J. Wu, Blocks in Pairwise Summable Generalized Effect Algebras, Rep. Math. Phys. CC
  12. S. Pulmannová, Z. Riečanová, E. Vinceková, Representation of Concrete Logics and Concrete Generalized OMPs, Rep. Math. Phys. CC
  13. A. Mesiarová-Zemánková, K. Ahmad, Extended multi-polarity and multi-polar-valued fuzzy sets. Fuzzy Sets and Systems 234 (2014), CC
  14. A. Mesiarová-Zemánková, Multi-polar aggregation operators in reasoning methods for fuzzy rule-based classification systems, IEEE CC

Iné práce

Výjdené
  1. D.J. Foulis, S. Pulmannová, E. Vinceková, The exocenter and type decompositions of a generalized pseudo-effect algebra, Discuss. Math. General Algebra Appl. 33 (2013), 13–47.
  2. M. Papčo, Fuzzification of probabilistic objects. In: Advances in Intelligent Systems Research, EUSFLAT-13, Proceedings of the 8th conference of the European Society for Fuzzy Logic and Technology, Milan, Sept 10-13, 2013, Italy, Atlantis Press, ISBN 9781629932194, pp. 67–71.

Vedecké monografie

  1. F. Chovanec, Diferenčné posety a ich grafická reprezentácia. ISBN 978-80-8040-479-6, AOS gen. M.R. Štefánika, L. Mikuláš 2013. (in Slovak).

Výsledky za rok 2012

Publikácie SCI: 1.1

Výjdené
  1. S. Pulmannová, A note on ideals in synaptic algebras, Math. Slovaca 62 (2012), 1091–110.
  2. G. Jenča, Compatibility support mappings in effect algebras, Math. Slovaca, 62 (2012) 363-378.
Prijaté do tlače
  1. A. Dvurečenskij, Smearing of observables and spectral measures on quantum structures, Found. Phys. (2013) to appear. DOI: http://arxiv.org/abs/1204.6486
  2. A. Dvurečenskij, Y. Xie, Aili Yang, Discrete (n+1)-valued states and n-perfect pseudo-effect algebras, Soft Computing, to appear.
  3. J. Jakubík, J. Lihová, Generalized Specker lattice-ordered groups and two types of distributitivity. Math. Slovaca 63 (2013) to appear.
  4. Š. Černák, J. Jakubík, Weak relatively uniform converegences on MV-algebras. Math. Slovaca (2013), to appear.
  5. A. Mesiarová-Zemánkova, K. Ahmad, Multi-polar Choquet integral, Fuzzy Sets and Systems, to appear.
  6. J. Paseka, S. Pulmannová, Z. Riečanová, Properties of quasi-Hermitian operators inherited from self-adjoint operators, Int. J. Theor. Phys., DOI: 10.1007/s10773-012-1403 , to appear.
  7. G. Jenča: Congruences generated by ideals of the compatibility center of lattice effect algebras, Soft Computing, to appear.

Iné práce

Výjdené
  1. A. Mesiarová-Zemánkova, K. Ahmad, Multi-polar Aggregation. In Proc. IPMU 2012, Part 3, Catania, Italy, pp. 379–387.
Prijaté do tlače
  1. D. J. Foulis, S. Pulmannová, E. Vinceková, The exocenter and type decompositions of a generalized pseudoeffect algebra, Discussiones Mathematicae – General Algebra and Applications, prijaté.
  2. Z. Riečanová, M. Zajac, Intervals in generalized effect algebras and their sub-generalized effect algebras, Acta Polytechnica , to appear.
  3. J.Paseka, Z.Riečanová, Inherited properties of effect algebras preserved by isomorphism, Acta Polytechnica, to appear.