grant APVV-20-0069

Pravdepodobnostné, algebrické a kvantovo-mechanické metódy určovania neurčitosti
(Probabilistic, Algebraic and Quantum Mechanical Methods of Uncertainty Determination)

Trvanie projektu:

07/2021 - 06/2025

Riešiteľské organizácie:

Základné informácie o grante

Ciele projektu:

Použitím najmodernejších metód kvantových štruktúr budeme študovať matematické základy kvantovej mechaniky a neurčitosti. Prehĺbime naše poznatky o parciálnych a totálnych algebrách ako sú efektové algebry, MV-algebry, synaptické algebry, ortomodulárne zväzy, BL-algebry, EMV-algebry, wEMV-algebry, reziduované zväzy a ich nekomutatívne zovšeobecnenia a stavy na nich v súvislosti s čiastočne usporiadanými grupami. Kategoriálne postupy ozrejmia špecifické vlastnosti kvantových štruktúr. Pomocou agregačných metód sa budeme snažiť o kombináciu vybraných hodnôt merania do jednej agregačnej funkcie. Neurčitosť obsiahnutá v kvantových meraniach sa bude analyzovať z pohľadu stavov a kvantových kanálov so zameraním na aplikácie v kvantovej mechanike, kvantovej teórii informácie a popise mier nekompatibility.

Riešitelia grantu

MÚ SAV

Svf STU, Bratislava

Publikácie 2023

  1. A. Dvurečenskij, Representation of perfect and n-perfect pseudo effect algebras. Fuzzy Sets and Systems 455 (2023), 19–34. DOI: 10.1016/j.fss.2022.08.015
  2. A. Dvurečenskij, g-States on unital weak pseudo EMV-algebras. Soft Computing, 27 (2023), 4353–4368. ISSN 1432-7643. DOI: 10.1007/s00500-023-07850-5
  3. A. Dvurečenskij, O. Zahiri, On EMV-algebras with square roots. J. Math. Anal. Appl. 524 (2023), Art. Num. 127113. ISSN 0022-247X https://doi.org/10.1016/j.jmaa.2023.127113
  4. A. Dvurečenskij, O. Zahiri, Some results on pseudo MV-algebras with square roots. Fuzzy Sets and Systems 465 (2023), Art. Num. 108527. ISSN 0165-0114. DOI: 10.1016/j.fss.2023.108527
  5. A. Jenčová, S. Pulmannová, Spectrality in Convex Sequential Effect Algebras, International Journal of Theoretical Physics, 62 (2023), Art. Num. 193. DOI: 10.1007/s10773-023-05431-8
  6. T. Heinosaari, A. Jenčová, M. Plávala, Dispensing of quantum information beyond no-broadcasting theorem—is it possible to broadcast anything genuinely quantum?, Journal of Physics A: Mathematical and Theoretical, 56 (2023), Art. Num. 135301. DOI: 10.1088/1751-8121/acbc5b
  7. A. Jenčová, S. Pulmannová, Spectral order unit spaces and JB-algebras, Journal of Mathematical Analysis and Applications, 520 (2023), Art. Num. 126911. DOI: 10.1016/j.jmaa.2022.126911
  8. G. Jenča, Orthogonality Spaces Associated with Posets, Order, 40 (2023), 575-588, Order (2023) 40:575–588. DOI: 10.1007/s11083-022-09623-5
  9. G. Jenča, B. Lindenhovius: Quantum Suplattices, Electronic Proceedings in Theoretical Computer Science, EPTCS, 384 (2023), 58–74. DOI: 10.4204/EPTCS.384.4
  10. G. Jenča, Voltage lifts of graphs from a category theory viewpoint, Mathematica Slovaca, 73 (2023), 275–288. DOI: 10.1515/ms-2023-0023
  11. R. Halaš, R. Mesiar, J. Pócs, On the number of aggregation functions on finite chains as a generalization of Dedekind numbers, Fuzzy Sets and Systems 466 (2023), Art. Num. 108441. DOI: 10.1016/j.fss.2022.11.012
  12. R. Halaš, J. Pócs, J. Pócsová, On Join Dense Subsets of Certain Families of Aggregation Functions, Mathematics 2023, 11(1), 14. DOI: 10.3390/math11010014
  13. A. Mesiarová-Zemánková, Representation of non-commutative, idempotent, associative functions by pair-orders, Fuzzy Sets and Systems 475, (2024), Art. Num. 108759. DOI: 10.1016/j.fss.2023.108759
  14. A. Mesiarová-Zemánková, Uninorms internal on one or more non-trivial cuts, Information Sciences 653, (2024), Art. Num. 119793. DOI: 10.1016/j.ins.2023.119793
  15. Y. Su, A. Mesiarová-Zemánková, R. Mesiar, Idempotent uninorms on a bounded chain, Fuzzy Sets and Systems 471, (2023), Art. Num. 108671. DOI: 10.1016/j.fss.2023.108671
  16. A. Mesiarová-Zemánková, Decomposition of idempotent pseudo-uninorms via ordinal sum, Information Sciences 648, (2023), Art. Num. 119519. DOI: 10.1016/j.ins.2023.119519
  17. A. Mesiarová-Zemánková, J. Kalafut, Pseudo-uninorms with continuous Archimedean underlying functions, Fuzzy Sets and Systems 471, (2023), Art. Num. 108674. DOI: 10.1016/j.fss.2023.108674
  18. A. Mesiarová-Zemánková, On the monotonicity of functions constructed via z-ordinal sum construction, Fuzzy Sets and Systems 466, (2023), Art. Num. 108471. DOI:
  19. A. Mesiarová-Zemánková, On the monotonicity of functions constructed via ordinal sum construction, Fuzzy Sets and Systems, 466, (2023), Art. Num. 108473. DOI: 10.1016/j.fss.2023.01.008
  20. R. Fernandez-Peralta, S. Massanet, A. Mesiarová-Zemánková, A. Mir, Determination of the continuous completions of conditionally cancellative pre-t-norms associated with the characterization of (S,N)-implications: Part I, Fuzzy Sets and Systems 468, (2023), Art. Num. 108614. DOI: 10.1016/j.fss.2023.108614
  21. O. Krídlo, D. López-Rodríguez, Ľ. Antoni, P. Eliaš, S. Krajči, M. Ojeda-Aciego, Connecting concept lattices with bonds induced by external information. Information Sciences, 648, November 2023, Art. Num. 119498. DOI: 10.1016/j.ins.2023.119498
  22. Ľ. Antoni, P. Eliaš, T. Horváth, S. Krajči, O. Krídlo, C. Török, Squared Symmetric Formal Contexts and Their Connections with Correlation Matrices. In: Ojeda-Aciego, M., Sauerwald, K., Jäschke, R. (eds) Graph-Based Representation and Reasoning. ICCS 2023. Lecture Notes in Computer Science (LNAI 14133). Springer, Cham. DOI: 10.1007/978-3-031-40960-8_2

Publikácie 2022

SCI

  1. A. Dvurečenskij, D. Lachman, n-dimensional observables on k-perfect MV-algebras and effect algebras. I. Characteristic points, Fuzzy Sets and Systems 442 (2022), 1–16.
    DOI: 10.1016/j.fss.2021.05.005
  2. A. Dvurečenskij, D. Lachman, n-dimensional observables on k-perfect MV-algebras and effect algebras. II. One-to-one correspondence, Fuzzy Sets and Systems 442 (2022), 17–42.
    DOI: 10.1016/j.fss.2021.08.027
  3. A. Dvurečenskij, D. Lachman, Homogeneous effect algebras and observables vs spectral resolutions, Inter. J. Theor. Phys. 61 (2022), Art. Num. 214.
    DOI: 10.1007/s10773-022-05185-9
  4. A. Dvurečenskij, O. Zahiri, Pierce sheaves of pseudo EMV-algebras, Soft Computing 26 (2022), 8351–8369.
    DOI: 10.1007/s00500-022-07271-w
  5. A. Dvurečenskij, States on weak pseudo EMV-algebras. I. States and states morphisms, Iranian J. Fuzzy Systems 19 (2022), 1–15.
    DOI: 10.22111/IJFS.2022.7082
  6. A. Dvurečenskij, States on weak pseudo EMV-algebras. II. Representations of states, Iranian J. Fuzzy Systems 19 (2022), 17–26.
    DOI: 10.22111/IJFS.2022.7083
  7. A. Jenčová, S. Pulmannová, Spectral resolutions in effect algebras, Quantum 6 (2022), Art. No. 849., pp. 31 pages
    DOI: 10.22331/q-2022-11-03-849
  8. A. Jenčová, Assemblages and steering in general probabilistic theories, J. Phys. A: Math. Theor. 55(43) (2022), Art. No. 434001, pp. 25 pages.
    DOI: 10.1088/1751-8121/ac97ce
  9. G. Jenča, Orthomodular posets are algebras over bounded posets with involution, Soft Computing 26 (2022), 491–498.
    DOI: 10.1007/s00500-021-06433-6
  10. R. Halaš, J. Pócs, J. Pócsová: Remarks on Sugeno integrals on bounded lattices, Mathematics 10(17) (2022), Art. No. 3078, pp. 9 pages.
    DOI: 10.3390/math10173078
  11. A. Mesiarová-Zemánková, A note on simplification of z-ordinal sum construction, Fuzzy Sets and Systems 451 (2022), 3–15.
    DOI: 10.1016/j.fss.2022.05.011

mimo SCI

  1. A. Dvurečenskij, A short note on categorical equivalences of proper weak pseudo EMV-algebras, J. Algebraic Hyperstructures and Logical Algebras 3 (2022), 35–44.
  2. M. Papčo, Fruits of a categorical approach to probability theory, Acta Universitatis Matthiae Belii, series Mathematics 29 (2021), 39–61.

Popularizačné a príležitostné články

  1. A.Dvurečenskij, Prof. Antonio Di Nola -- 3/4C?, J. Algebraic Hyperstructures and Logical Algebras 3 (2022), 1--3.
  2. A.Dvurečenskij, K. Nemoga, Odišiel prof. RNDr. Lev Bukovský, DrSc., Obzory matem., fyz. inform. 51 (1) (2022), 10--14.
  3. A.Dvurečenskij, Prof. RNDr. Pavol Brunovský, DrSc. - his life and opus, In EQUADIFF 15 : Conference on Differential Equations and Their Applications. - Brno, Czech Republic: Masaryk University Press, 2022, p. 22-24. ISBN 978-80-280-0082-0.
  4. A.Dvurečenskij, T. Macko, Prof. RNDr. Július Korbaš, CSc. passed away, Math. Slovaca 72 (2022), 1383--1386.