grant APVV-16-0073

Pravdepodobnostné, algebrické a kvantovo-mechanické aspekty neurčitosti
(Probabilistic, Algebraic and Quantum-Mechanical Aspects of Uncertainty)

Trvanie projektu:

07/2017 - 06/2021 (predĺžený do 12/2021)

Riešiteľské organizácie:

Základné informácie o grante

Ciele projektu:

Sústredíme sa na získavanie originálnych výsledkov popisu neurčitosti súvisiacej s kvantovými štruktúrami a na neurčitosť obsiahnutú v konvexnej šturktúre kvantovo-mechanických meraní. Akcent bude kladený na výskum parciálnych a totálnych algebier akými sú efektové algebry, synaptické algebry, MV-algebry a ich nekomutatívne zovšeobecnenia ako aj na popis kvantových kanálov, stavov, odhadovacích a testovacích úloh kvantovo-mechanických procesov, kategoriálnych vlastností a agregačných funkcií. Tieto výsledky budú slúžiť na prehĺbenie našich poznatkov a upevnenie prestížneho postavenia slovenskej školy kvantových štruktúr v celosvetovom kontexte.

Riešitelia grantu

MÚ SAV

Svf STU, Bratislava

Publikácie 2022

  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 42 (2022), 17–42.
    DOI: 10.1016/j.fss.2021.08.027
  3. R. Frič, Lukasiewicz logic and the divisible extension of probability theory, Tatra Mt. Math. Publ. 78 (2021), 119–128. (Dr. Frič zomrel začiatkom r. 2021, doplnok za rok 2021.)
    DOI: 10.2478/tmmp-2021-0008
  4. A. Bluhm, A. Jenčová, I. Nechita, Incompatibility in general probabilistic theories, generalized spectrahedra, and tensor norms, Communications in Mathematical Physics 393 (2022), 1125–1198.
    DOI: 10.1007/s00220-022-04379-w
  5. A. Mesiarová-Zemánková, Characterizing functions of n-uninorms with continuous underlying functions, IEEE Transactions on Fuzzy Systems 30(5), (2022), 1239–1247.
    DOI: 10.1109/TFUZZ.2021.3057231
  6. A. Mesiarová-Zemánková, Characterization of idempotent n-uninorms, Fuzzy Sets and Systems 427 (2022) 1–22.
    DOI: 10.1016/j.fss.2020.12.019
  7. A. Mesiarová-Zemánková, Commutative, associative and non-decreasing functions continuous around diagonal, Iranian Journal of Fuzzy Systems 19(2), (2022), 31–48.
    DOI: 10.22111/ijfs.2022.6786
  8. M. Papčo, Fruits of a categorical approach to probability theory, Acta Universitatis Matthiae Belii, series Mathematics 29 (2021), 39–61. Článok vyšiel v r. 2022.
    URL: https://actamath.savbb.sk/pdf/aumb2902.pdf

Publikácie 2021

  1. A. Dvurečenskij, O. Zahiri, A variety containing EMV-algebras and Pierce sheaves, Fuzzy Sets and Systems 418 (2021), 101–125.
    DOI: 10.1016/j.fss.2020.09.011
  2. A. Dvurečenskij, O. Zahiri, Locally sigma-complete and locally complete EMV-algebras, Soft Computing 25 (2021), 883–894.
    DOI: 10.1007/s00500-020-05486-3
  3. A. Di Nola, A. Dvurečenskij, S. Lapenta, An approach to stochastic processes via non-classical logic, Ann. Pure Appl. Logic. 172 (2021), Art. Num. 103012.
    DOI: 10.1016/j.apal.2021.103012
  4. A. Dvurečenskij, Sum of n-dimensional observables on MV-effect algebras, Soft Computing 25 (2021), 8073–8084.
    DOI: 10.1007/s00500-021-05911-1
  5. A. Dvurečenskij, O. Zahiri, Weak pseudo EMV-algebras. I. Basic properties, J. Appl. Logic — IfCoLog Journal of Logics and their Applications 8 (2021), 2365–2399.
    Link: ifcolog00052.pdf
  6. A. Dvurečenskij, O. Zahiri, Weak pseudo EMV-algebras. II. Representation and subvarieties, J. Appl. Logic — IfCoLog Journal of Logics and their Applications 8 (2021), 2401–2433.
    Link: ifcolog00052.pdf
  7. R. Halaš, Z. Kurač, J. Pócs, On the minimality of some generating sets of the aggregation clone on a finite chain, Information Sciences 564 (2021), 193–201.
    DOI: 10.1016/j.ins.2021.02.070
  8. J. Pócs, J. Pócsová, On bonds for generalized one-sided concept lattices, Mathematics 2021, 9 (3), Art. Num. 211, 12 pages.
    DOI: 10.3390/math9030211
  9. M. Girard, M. Plávala, J. Sikora, Jordan products of quantum channels and their compatibility, Nature Communications 12 (2021), Art. Num. 2129, 6 pages.
    DOI: 10.1038/s41467-021-22275-0
  10. G. Aubrun, L. Lami, C. Palazuelos, M. Plávala, Entangleability of cones, Geom. Funct. Anal. 31 (2021), 181–205.
    DOI: 10.1007/s00039-021-00565-5
  11. A. Mesiarová-Zemánková, Convex combinations of uninorms and triangular subnorms, Fuzzy Sets and Systems 423 (2021) 55–73.
    DOI: 10.1016/j.fss.2020.10.011
  12. A. Mesiarová-Zemánková, The n-uninorms with continuous underlying t-norms and t-conorms, International Journal of General Systems 50 (1) (2021) 92–116.
    DOI: 10.1080/03081079.2020.1863395
  13. A. Mesiarová-Zemánková, Characterization of n-uninorms with continuous underlying functions via z-ordinal sum construction, International Journal of Approximate Reasoning 133 (2021) 60–79.
    DOI: 10.1016/j.ijar.2021.03.006
  14. A. Mesiarová-Zemánková, Natural partial order induced by a commutative, associative and idempotent function, Information Sciences 545 (2021) 499–512.
    DOI: 10.1016/j.ins.2020.09.028
  15. A. Jenčová, Rényi relative entropies and noncommutative Lp-spaces II., Annales Henri Poincare, 22 (2021), 3235–3254.
    DOI: 10.1007/s00023-021-01074-9
  16. A. Jenčová, S. Pulmannová, Observables on synaptic algebras, Fuzzy Sets and Systems 406 (2021), 93–106.
    DOI: 10.1016/j.fss.2020.05.015
  17. A. Jenčová, A general theory of comparison of quantum channels (and beyond), IEEE Transactions on Information Theory 67 (2021), 3945–3964, Art. Num. 9391724.
    DOI: 10.1109/TIT.2021.3070120
  18. A. Jenčová, S. Pulmannová, Tensor product of dimension effect algebras, Order 38 (2021), 377–389.
    DOI: 10.1007/s11083-020-09546-z
  19. A. Jenčová, S. Pulmannová: Geometric and algebraic aspects of spectrality in order unit spaces: A comparison, Journal of Mathematical Analysis and Applications, 504 (2021), art. nr. 125360.
    DOI: 10.1016/j.jmaa.2021.125360
  20. S. Pulmannová, Synaptic algebras as models for quantum mechanics, International Journal of Theoretical Physics 60 (2021), 483–498.
    DOI: 10.1007/s10773-019-04045-3
  21. M. Papčo, I. Rodríguez-Martínez, J. Fumanal-Idocin, A. H. Altalhi, H. Bustince, A fusion method for multi-valued data, Information Fusion 71 (2021), 1–10.
    DOI: 10.1016/j.inffus.2021.01.001
  22. J. Fumanal-Idocin, C. Vidaurre, M. Gomez, A. Urio, H. Bustince, M. Papčo, G. P. Dimuro, Optimizing a weighted moderate deviation for motor imagery brain computer interfaces, 2021 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), (2021), 1–6.
    DOI: 10.1109/FUZZ45933.2021.9494492.

Prijaté do tlače 2021

  1. A. Dvurečenskij, D. Lachman, n-dimensional observables on k-perfect MV-algebras and effect algebras. I. Characteristic points, Fuzzy Sets and Systems
    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
    DOI: 10.1016/j.fss.2021.08.027

Popularizačné a príležitostné články 2021

  1. A. Dvurečenskij, Doc. Roman Frič, DrSc. passed away, Math. Slovaca 71 (2021), 5–10.
    DOI: 10.1515/ms-2017-0448
  2. N. Dilna, A. Dvurečenskij, Prof. RNDr. Michal Fečkan, DrSc. Sexagenarian? Math. Slovaca 71 (2021), 265–266.
    DOI: 10.1515/ms-2017-0465
  3. N. Dilna, A. Dvurečenskij, Michal Fečkan (on his 60th birthday), Nonlinear Oscillations 24 (2021), 141–144.
    Link: https://imath.kiev.ua/~nosc/web/show_article.php?article_id=1335&lang=en

Publikácie 2020

  1. A. Dvurečenskij, D. Lachman, Spectral resolutions and observables in n-perfect MV-algebras, Soft Computing 24 (2020), 843–860.
    DOI: 10.1007/s00500-019-04543-w CC
  2. A. Dvurecenskij, D. Lachman, Two-dimensional observables and spectral resolutions, Rep. Math. Phys. 85 (2020), 163–191.
    DOI: 10.1016/S0034-4877(20)30023-9 CC
  3. A. Dvurečenskij, D. Lachman, Spectral resolutions and quantum observables, Inter. J. Theor. Phys. 59 (2020), 2362–2383.
    DOI: 10.1007/s10773-020-04507-z CC
  4. A. Dvurečenskij, D. Lachman, Lifting, n-dimensional spectral resolutions, and n-dimensional observables, Algebra Universalis 34 (2020), Art. Num. 34.
    DOI: 10.1007/s00012-020-00664-8 SCI
  5. A. Dvurečenskij, States on wEMV-algebras, Boll. Unione Matem. Italiana 13 (2020), 515–527.
    DOI: 10.1007/s40574-020-00233-w SCI
  6. G. Jenča, Pseudo effect algebras are algebras over bounded posets, Fuzzy Sets and Systems 397 (2020), 179–185.
    DOI: 10.1016/j.fss.2019.07.003 CC
  7. R. Carbone, A. Jenčová, On period, cycles and fixed points of a quantum channel, Annales Henri Poincaré 21 (2020), 155–188.
    DOI: 10.1007/s00023-019-00861-9 CC
  8. A. Jenčová, M. Plávala, Structure of quantum and classical implementations of the Popescu-Rohrlich box, Physical Review A 102 (2020), art. nr. 42208.
    DOI: 10.1103/PhysRevA.102.042208 CC
  9. M. Plávala, M. Ziman, Popescu-Rohrlich box implementation in general probabilistic theory of processes, Physics Letters A 384 (2020), art. nr. 126323.
    DOI: 10.1016/j.physleta.2020.126323 CC
  10. P. Eliaš, R. Frič, Conditional probability on full Lukasiewicz tribes, Soft Comput. 24 (2020), 6521–6529.
    DOI: 10.1007/s00500-020-04762-6 CC
  11. R. Frič, P. Eliaš, M. Papčo, Divisible extension of probability, Math. Slovaca 70 (2020), 1445–1456.
    DOI: 10.1515/ms-2017-0441 SCI
  12. A. Dvurečenskij, O. Zahiri, What are pseudo EMV-algebras?, J. Algebraic Hyperstructures and Logical Algebras 1 (2020), 1–20.
    DOI: 10.29252/hatef.jahla.1.1.1

Publikácie 2019

  1. A. Dvurečenskij, O. Zahiri, On EMV-algebras, Fuzzy Sets and Systems 373 (2019), 116–148.
    DOI: 10.1016/j.fss.2019.02.013 CC
  2. A. Dvurečenskij, O. Zahiri, The Loomis–Sikorski theorem for EMV-algebras, J. Austral. Math. Soc. 106 (2019), 200–234.
    DOI: 10.1017/S1446788718000101 CC
  3. A. Dvurečenskij, O. Zahiri, Generalized pseudo-EMV-effect algebras, Soft Computing 23 (2019), 9807–9819.
    DOI: 10.1007/s00500-019-03880-0 CC
  4. A. Di Nola, A. Dvurečenskij, G. Lenzi, Observables on perfect MV-algebras, Fuzzy Sets and Systems 369 (2019), 57–81.
    DOI: 10.1016/j.fss.2018.11.018 CC
  5. A. Dvurečenskij, Perfect effect algebras and spectral resolutions of observables, Found. Phys. 49 (2019), 607–628.
    DOI: 10.1007/s10701-019-00238-2 CC
  6. A. Dvurečenskij, O. Zahiri, EMV-pairs, Inter. J. General Systems 48 (2019), 382–405.
    DOI: 10.1080/03081079.2019.1584893 CC
  7. A. Dvurečenskij, Observables on lexicographic MV-algebras, Inter. J. General Systems 48 (2019), 738–774.
    DOI: 10.1080/03081079.2019.1643338 CC
  8. A. Dvurečenskij, O. Zahiri, States on EMV-algebras, Soft Computing 23 (2019), 7513 7536.
    DOI: 10.1007/s00500-018-03738-x CC
  9. A. Dvurečenskij, O. Zahiri, Pseudo EMV-algebras. I. Basic properties, J. Appl. Logic 6 (7) (2019), 1285–1327.
    ISBN: 978-1-84890-320-3 SCI
  10. A. Dvurečenskij, O. Zahiri, Pseudo EMV-algebras. II. Representation and states, J. Appl. Logic 6 (7) (2019), 1329–1372.
    ISBN: 978-1-84890-320-3 SCI
  11. A. Dvurečenskij, D. Lachman, Observables on lexicographic effect algebras, Algebra Universalis 80 (2019), Art. 49.
    DOI: 10.1007/s00012-019-0628-y CC
  12. R. Halaš, R. Mesiar, J. Pócs, On generating sets of the clone of aggregation functions on finite lattices, Information Sciences 476 (2019), pp. 38–47.
    DOI: 10.1016/j.ins.2018.09.070
  13. R. Halaš, R. Mesiar, J. Pócs, On generation of aggregation functions on infinite lattices, Soft Computing 23 (2019), 7279–7286.
    DOI: 10.1007/s00500-018-3375-7 CC
  14. G. Jenča, Two monads on the category of graphs, Math. Slovaca 69 (2019), 257–266.
    DOI: 10.1515/ms-2017-0220
  15. A. Jenčová, M. Plávala, On the properties of spectral effect algebras, Quantum 3 (2019), 148.
    DOI: 10.22331/q-2019-06-03-148 (ADM)
  16. T. Heinosaari, L. Leppäjärvi, M. Plávala, No-free-information principle in general probabilistic theories, Quantum 3 (2019), 157.
    DOI: 10.22331/q-2019-07-08-157
  17. D. J. Foulis, S. Pulmannová, Spectral order on a synaptic algebra, Order 36 (2019), 1–17.
    DOI: 10.1007/s11083-018-9451-x
  18. S. Pulmannová, Congruences and ideals in generalized pseudoeffect algebras revisited, Soft Comput. 23 (2019), 735–745.
    DOI: 10.1007/s00500-018-3107-z CC

Články prijaté CC

  1. G. Jenča, Pseudo effect algebras are algebras over bounded posets, Fuzzy Sets and Systems, (2020)
    DOI: 10.1016/j.fss.2019.07.003
  2. R. Carbone, A. Jenčová, On period, cycles and fixed points of a quantum channel, Ann. Henri Poincaré, (2019)
    DOI: 10.1007/s00023-019-00861-9

Články výjdené nie CC

  1. R. Halaš, J. Pócs, Aggregation via Clone Theory Approach. In: Halaš R., Gagolewski M., Mesiar R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, 981 (2019), 244–254.
    DOI: 10.1007/978-3-030-19494-9_23
  2. P. Butka, J. Pócs, J. Pócsová, Isotone Galois Connections and Generalized One-Sided Concept Lattices. In: Choroś K., Kopel M., Kukla E., Siemiński A. (eds) Multimedia and Network Information Systems. MISSI 2018. Advances in Intelligent Systems and Computing, vol. 833 (2019), p. 151–160.
    DOI: 10.1007/978-3-319-98678-4_17
  3. P. Butka, J. Pócs, J. Pócsová, Note on Aggregation Functions and Concept Forming Operators. In: Halaš R., Gagolewski M., Mesiar R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol. 981 (2019), p. 279–288.
    DOI: 10.1007/978-3-030-19494-9_26
  4. D. Babicová, R. Frič, Real functions in stochastic dependence, Tatra Mt. Math. Publ. 74 (2019), 17–34.
    DOI: 10.2478/tmmp-2019-0016
  5. R. Frič, Product of measurable spaces and applications, Tatra Mt. Math. Publ. 74 (2019), 47–56.
    DOI: 10.2478/tmmp-2019-0018

Výsledky 2018

  1. A. Dvurečenskij, O. Zahiri, Morphisms on EMV-algebra and their applications. Soft Computing 22 (2018), 7519–7537.
    https://doi.org/10.1007/s00500-018-3039-7 CC
  2. M. Botur, A. Dvurečenskij, Kites and residuated lattices, Algebra Universalis 79 (2018), Art. 83. 26 p.
    DOI: 10.1007/s00012-018-0564-2 CC
  3. R.A. Borzooei, A. Dvurečenskij, A.H. Sharafi, Generalized EMV-effect algebras, Inter. J. Theor. Phys. 57 (2018), 2267–2279.
    DOI: 10.1007/s10773-018-3750-2 CC
  4. A. Dvurečenskij, Quantum observables and effect algebras, Inter. J. Theor. Phys. 57 (2018), 637–651.
    DOI: 10.1007/s10773-017-3594-1 CC
  5. A. Dvurečenskij, Riesz space-valued states on pseudo MV-algebras, Journal of Logics and their Applications 5 (2018), 1723–1764.
    ISBN: 978-1-84890-291-6 SCI
  6. A. Dvurečenskij, Prof. RNDr. Beloslav Riečan, DrSc., Dr.h.c., * Nov. 10, 1936 — † Aug. 13, 2018, Math. Slovaca 68 (2018), 951–956.
    DOI: 10.1515/ms-2017-0157 SCI
  7. G. Jenča, Effect algebras as presheaves on finite Boolean algebras, Order 35 (2018), 525–540.
    DOI: 10.1007/s11083-017-9447-y CC
  8. A. Jenčová, Rényi Relative Entropies and Noncommutative Lp-Spaces, Annales Henri Poincare 19 (2018), 2513–2542.
    DOI: 10.1007/s00023-018-0683-5 CC
  9. A. Jenčová, Incompatible measurements in a class of general probabilistic theories, Physical Review A 98 (2018), art. nr. 12133.
    DOI: 10.1103/PhysRevA.98.012133 CC
  10. R. Halaš, Z. Kurač, R. Mesiar, J. Pócs, Binary generating set of the clone of idempotent aggregation functions on bounded lattices, Information Sciences 462 (2018), 367–373.
    DOI: 10.1016/j.ins.2018.06.038 CC
  11. O. Hutník, J. Pócs, On *-associated comonotone functions, Kybernetika, 54 (2018), No. 2, 268–278.
    DOI: 10.14736/kyb-2018-2-0268 CC
  12. S. Pulmannová, Corrignedum to Banach synaptic algebras, Inter. J. Theore. Phys. 57 (2018), 3772–3775.
    DOI: 10.1007/s10773-018-3889-x CC
  13. D.J. Foulis, S. Pulmannová, Banach synaptic algebras, Inter. J. Theor. Phys. 57 (2018), 1103–1119.
    DOI: 10.1007/s10773-017-3641-y CC