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. Mesiarová-Zemánková, Characterization of idempotent n-uninorms, Fuzzy Sets and Systems 427 (2022) 1–22.
    DOI: 10.1016/j.fss.2020.12.019

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