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 2024

  1. A. Dvurečenskij, O. Zahiri, Representation and embedding of pseudo MV-algebras with square roots I. Strict square roots, J. Appl. Logic IfCoLog Journal of Logics and their Applications 11(4) (2024), 499–527. ISBN: 978-1-84890-461-3.
    URL: https://www.collegepublications.co.uk/ifcolog/?00066
  2. A. Dvurečenskij, O. Zahiri, Representation and embedding of pseudo MV-algebras with square roots II. Closures, J. Appl. Logic IfCoLog Journal of Logics and their Applications 11(4) (2024), 529–563. ISBN: 978-1-84890-461-3.
    URL: https://www.collegepublications.co.uk/ifcolog/?00066
  3. A. Dvurečenskij, O. Zahiri, M. Shenavaei, R. A. Borzooei, n-roots on MV-algebras, Fuzzy Sets and Systems 484 (2024), Art. Num. 108930.
    DOI: 10.1016/j.fss.2024.108930
  4. A. Dvurečenskij, O. Zahiri, MV-algebras and their corresponding Bézout domains, Comm. Algebra 52 (2024), 5165–5179.
    DOI: 10.1080/00927872.2024.2367165
  5. F. Hiai, A. Jenčová, α-z-Rényi divergences in von Neumann algebras: Data processing inequality, reversibility, and monotonicity properties in α,z, Communications in Mathematical Physics 405 (2024), art. nr. 271.
    DOI: 10.1007/s00220-024-05124-1
  6. A. Jenčová, Recoverability of quantum channels via hypothesis testing, Letters in Mathematical Physics 114 (2024), art. nr. 31.
    DOI: 10.1007/s11005-024-01775-2
  7. A. Jenčová, The exponential Orlicz space in quantum information geometry, Information Geometry, 7 (2024), 377–395.
    DOI: 10.1007/s41884-023-00097-x
  8. A. Mesiarová-Zemánková, M. Holčapek, Commutative, associative and monotone functions on horizontal sum of chains, Fuzzy Sets and Systems 479 (2024), art. nr. 108843.
    DOI: 10.1016/j.fss.2023.108843
  9. A. Mesiarová-Zemánková, Representation of non-commutative, idempotent, associative functions by pair-orders, Fuzzy Sets and Systems 475 (2024), art. nr. 108759.
    DOI: 10.1016/j.fss.2023.108759
  10. A. Mesiarová-Zemánková, Uninorms internal on one or more non-trivial cuts, Information Sciences 653 (2024), art. nr. 119793.
    DOI: 10.1016/j.ins.2023.119793
  11. Y. Su, Z. Wang, A. Mesiarová-Zemánková, R. Mesiar, Characterizing three classes of idempotent uninorms on a bounded lattice, Iranian Journal of Fuzzy Systems 20(5), (2023), 109–120.
    DOI: 10.22111/IJFS.2023.7685
  12. R. Halaš, J. Pócs, On zero-divisor graphs of infinite posets, Soft Computing 28 (2024), 12113–12118.
    DOI: 10.1007/s00500-024-09958-8
  13. Ľ. Antoni, P. Eliaš, J. Guniš, D. Kotlárová, S. Krajči, O. Krídlo, P. Sokol, Ľ. Šnajder, Bimorphisms and attribute implications in heterogeneous formal contexts, International Journal of Approximate Reasoning 172 (2024), art. nr. 109245.
    DOI: 10.1016/j.ijar.2024.109245
  14. T. Pitka, J. Bucko, S. Krajči, O. Krídlo, J. Guniš, Ľ. Šnajder, Ľ. Antoni, P. Eliaš, Time analysis of online consumer behavior by decision trees, GUHA association rules, and formal concept analysis, Journal of Marketing Analytics (2024).
    DOI: 10.1057/s41270-023-00274-y
  15. A.S. Monteiro, R. Santiago, M. Papčo, R. Mesiar, H. Bustince, On conditional monotonicities of interval-valued functions, Computational and Applied Mathematics 43 (2024), art. nr. 200.
    DOI: 10.1007/s40314-024-02715-5

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.