PJM - tłumacz języka migowego

  1. B. Kwaśniewski, K. Li, A. Skalski
    The Haagerup property for twisted groupoid dynamical systems
    J. Funct. Anal. 283 (2022), no. 1, 1-43.
    DOI: 10.1016/j.jfa.2022.109484
  2. B. Kwaśniewski, R. Meyer
    Aperiodicity: the almost extension property and uniqueness of pseudo-expectations
    IMRN 2022 (2022), no. 18, 14384-14426.
    DOI: 10.1093/imrn/rnab098
  3. K. Bardadyn, B. Kwaśniewski
    Spectrum of weighted isometries: C*-algebras, transfer operators and topological pressure
    Israel J. Math. 246 (2021), no. 1, 149 - 210.
    DOI: 10.1007/s11856-021-2246-6
  4. B. Kwaśniewski, R. Meyer
    Essential crossed products for inverse semigroup actions: simplicity and pure infiniteness
    Doc. Math. 26 (2021), 271-335.
    DOI: 10.25537/dm.2021v26.271-335
  5. J. Makowska, A. Rybak
    Kreatywne kształcenie matematyczne w Centrum Kreatywnego Uczenia się Matematyki na Wydziale Matematyki Uniwersytetu w Białymstoku
    Uniwersytet w Białymstoku, 2021.
  6. A. McKee
    Weak amenability for dynamical systems
    Studia Math. 258 (2021), no. 1, 53-70.
    DOI: 10.4064/sm200227-20-7
  7. A. McKee, R. Pourshahami
    Amenable and inner amenable actions and approximation properties for crossed products by locally compact groups
    Canad. Math. Bull. (2021), (on-line first).
    DOI: 10.4153/S0008439521000333
  8. A. McKee, L. Turowska
    Exactness and SOAP of crossed products via Herz-Schur multipliers
    J. Math. Anal. Appl. 496 (2021), no. 2, 1-16.
    DOI: 10.1016/j.jmaa.2020.124812
  9. K. Zajkowski
    On the strong law of large numbers for φ-subgaussian random variables
    Ukrainian Math. J. 73 (2021), no. 3, 431-436.
    DOI: 10.37863/umzh.v73i3.197
  10. B. Kwaśniewski, A. Lebedev
    Variational principles for spectral radius of weighted endomorphisms of C(X,D)
    Trans. Amer. Math. Soc. 373 (2020), no. 4, 2659-2698.
    DOI: 10.1090/tran/7993
  11. B. Kwaśniewski, R. Meyer
    Noncommutative Cartan C*-subalgebras
    Trans. Amer. Math. Soc. 373 (2020), no. 12, 8697-8724.
    DOI: 10.1090/tran/8174
  12. B. Kwaśniewski, R. Meyer
    Stone duality and quasi-orbit spaces for generalised C*-inclusions
    Proc. London Math. Soc. 121 (2020), no. 4, 788-827.
    DOI: 10.1112/plms.12332
  13. K. Zajkowski
    Bounds on tail probabilities for quadratic forms in dependent sub-gaussian random variables
    Statistics & Probability Letters 167 (2020), 1-7.
    DOI: 10.1016/j.spl.2020.108898
  14. K. Zajkowski
    On norms in some class of exponential type Orlicz spaces of random variables
    Positivity 24 (2020), no. 5, 1231-1240.
    DOI: 10.1007/s11117-019-00729-6
  15. V. Bakhtin, A. Lebedev
    Entropy statistic theorem and variational principle for t-entropy are equivalent
    J. Math. Anal. Appl. 474 (2019), no. 1, 59-71.
    DOI: 10.1016/j.jmaa.2019.01.032
  16. K. Bardadyn, B. Kwaśniewski, K. S. Kurnosenko, A. Lebedev
    t-Entropy formulae for concrete classes of transfer operators
    J. Bela. St. Univ. (2019), no. 3, 122-128.
    DOI: 10.33581/2520-6508-2019-3-122-128
  17. T. Carlsen, B. Kwaśniewski, E. Ortega
    Topological freeness for C*-correspondences
    J. Math. Anal. Appl. 473 (2019), no. 2, 749-785.
    DOI: 10.1016/j.jmaa.2018.12.069
  18. B. Kwaśniewski
    Invitation to Hilbert C*-modules and Morita–Rieffel Equivalence
    Geometric Methods in Physics XXXVI, Workshop and Summer School, Białowieża, Poland, 2017, (P. Kielanowski, A. Odzijewicz, E. Previato Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2019, pp. 383-388.
    DOI: 10.1007/978-3-030-01156-7_39
  19. B. Kwaśniewski, N. Larsen
    Nica-Toeplitz algebras associated with product systems over right LCM semigroups
    J. Math. Anal. Appl. 470 (2019), no. 1, 532-570.
    DOI: 10.1016/j.jmaa.2018.10.020
  20. B. Kwaśniewski, N. Larsen
    Nica-Toeplitz algebras associated with right tensor C*-precategories over right LCM semigroups
    Int. J. Math. 30 (2019), no. 2, 1950013_1-1950013_57.
    DOI: 10.1142/S0129167X19500137
  21. K. Zajkowski
    Norms of sub-exponential random vectors
    Statistics & Probability Letters (2019), no. 152, 147-152.
    DOI: 10.1016/j.spl.2019.05.002
  22. A. Antonevich, A. Glaz
    Quasi-periodic Algebras and Their Physical Automorphisms
    Geometric Methods in Physics XXXV, Workshop and Summer School, Białowieża, Poland, June 26 - July 2, 2016, (P. Kielanowski, A. Odzijewicz, E. Previato Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2018, pp. 9-15.
    DOI: 10.1007/978-3-319-63594-1_2
  23. B. Kwaśniewski, R. Meyer
    Aperiodicity, topological freeness and pure outerness: from group actions to Fell bundles
    Studia Math. 241 (2018), 257-302.
    DOI: 10.4064/sm8762-5-2017
  24. A. Antonevich, A. N. Buzulutskaya (Glaz)
    Almost-Periodic Algebras and Their Automorphisms
    Mat. Zametki 102 (2017), no. 5, 657-672.
    DOI: 10.4213/mzm11738
  25. V. Bakhtin, A. Lebedev
    A new definition of t-entropy for transfer operators
    Entropy 19 (2017), no. 11, 1-6.
    DOI: 10.3390/e19110573
  26. B. Kwaśniewski
    Exel's crossed product and crossed products by completely positive maps
    Houston J. Math. 43 (2017), no. 2, 509-567.
  27. B. Kwaśniewski, W. Szymański
    Pure infiniteness and ideal structure of C*-algebras associated to Fell bundles
    J. Math. Anal. Appl. 445 (2017), no. 1, 898-943.
    DOI: 10.1016/j.jmaa.2016.07.044
  28. A. Lebedev, P. P. Zabreiko
    Banach geometry of financial markets models
    Dokl. Akad. Nauk. 95 (2017), no. 2, 164-167.
  29. K. Zajkowski
    A variational formula on the Cramér function of series of independent random variables
    Positivity 21 (2017), no. 1, 273-282.
    DOI: 10.1007/s11117-016-0419-z
  30. K. Zajkowski
    On the Azuma inequality in spaces of subgaussian of rank p random variables
    arXiv.org (2017), (on-line first).
  31. A. Antonevich, E. V. Panteleeva
    Well-posed boundary-value problems, right hyperbolicity, and exponential dichotomy
    Mat. Zametki 100 (2016), no. 1, 13-29.
    DOI: 10.4213/mzm11125
  32. B. Kwaśniewski
    Crossed products by endomorphisms of C_0(X)-algebras
    J. Funct. Anal. 270 (2016), no. 6, 2268-2335.
    DOI: 10.1016/j.jfa.2016.01.015
  33. B. Kwaśniewski, W. Szymański
    Topological aperiodicity for product systems over semigroups of Ore type
    J. Funct. Anal. 270 (2016), no. 9, 3453-3504.
    DOI: 10.1016/j.jfa.2016.02.014
  34. R. Meyer, S. Roy, S. L. Woronowicz
    Quantum group-twisted tensor products of C^*-algebras. II
    J. Noncommut. Geom. 10 (2016), no. 3, 859-888.
    DOI: 10.4171/JNCG/250
  35. A. Akhmatova, A. Antonevich, J. Makowska
    Maps with separable dynamics and spectral properties of the corresponding operators
    Mat. Sb. 206 (2015), no. 3, 3-34.
    DOI: 10.4213/sm8340
  36. P. Kasprzak, P. Sołtan, S. L. Woronowicz
    Quantum automorphism groups of finite quantum groups are classical
    J. Geom. Phys. 89 (2015), 32-37.
    DOI: 10.1016/j.geomphys.2014.12.006
  37. B. Kwaśniewski
    Extensions of C*-dynamical systems to systems with complete transfer operators
    Math. Notes 98 (2015), no. 3, 419-428.
    DOI: 10.1134/S0001434615090072
  38. B. Kwaśniewski
    Ideal structure of crossed products by endomorphisms via reversible extensions of C*-dynamical systems
    Int. J. Math. 26 (2015), no. 3, 1-45.
    DOI: 10.1142/S0129167X15500226
  39. K. Zajkowski
    Cramér transform of Rademacher series
    Positivity 19 (2015), no. 3, 529-537.
    DOI: 10.1007/s11117-014-0313-5
  40. A. Antonevich, E. Panteleeva
    Right-side hyperbolic operators
    SCIENTIFIC PUBLICATIONS OF THE STATE UNIV. OF NOVI PAZAR (A) 6 (2014), no. 1, 1-9.
  41. B. Kwaśniewski
    Crossed product of a C*-algebra by a semigroup of interactions
    Demonstratio Math. 47 (2014), no. 2, 350-370.
    DOI: 10.2478/dema-2014-0028
  42. B. Kwaśniewski
    Crossed products for interactions and graph algebras
    Integr. Equ. Oper. Theory 80 (2014), no. 3, 415-451.
    DOI: 10.1007/s00020-014-2166-5
  43. B. Kwaśniewski
    Topological freeness for Hilbert bimodules
    Israel J. Math. 199 (2014), no. 2, 641-650.
    DOI: 10.1007/s11856-013-0057-0
  44. A. Lebedev, P. P. Zabreiko
    Arbitrage free markets geometry
    arXiv.org (2014), (on-line first).
  45. A. Lebedev, P. P. Zabreiko
    Fundamental theorem of asset pricing: a strengthened version and p-summable markets
    arXiv.org (2014), (on-line first).
  46. R. Meyer, S. Roy, S. L. Woronowicz
    Quantum group-twisted tensor products of C*-algebras
    Int. J. Math. 25 (2014), no. 2, 1-37.
    DOI: 10.1142/S0129167X14500190
  47. U. Ostaszewska, K. Zajkowski
    Cramér transform and t-entropy
    Positivity 18 (2014), no. 2, 347-358.
    DOI: 10.1007/s11117-013-0247-3
  48. K. Zajkowski
    A note on the gambling team method
    Statistics & Probability Letters 85 (2014), 45-50.
    DOI: 10.1016/j.spl.2013.11.003
  49. K. Zajkowski
    Penney's game between many players
    Didactics of Mathematics 11(15) (2014), 75-83.
    DOI: 10.15611/dm.2014.11.07
  50. A. Akhmatova, A. Antonevich
    On Operators Generated by Maps with Separable Dynamics
    Geometric Methods in Physics, XXXI Workshop, Białowieża, Poland, (P. Kielanowski, S. T. Ali, A. Odesski, A. Odzijewicz, M. Schlichenmaier, Th. Voronov Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2013, pp. 171-178.
    DOI: 10.1007/978-3-0348-0645-9_15
  51. A. Antonevich, J. Makowska
    Operators generated by Morse-Smale mappings
    arXiv.org (2013), (on-line first).
  52. B. Kwaśniewski
    $C^*$-algebras generalizing both relative Cuntz-Pimsner and Doplicher-Roberts algebras
    Trans. Amer. Math. Soc. 365 (2013), no. 4, 1809-1873, (http://arxiv.org/abs/0906.4382).
    DOI: 10.1090/S0002-9947-2012-05748-5
  53. B. Kwaśniewski
    Uniqueness Property for C^*-algebras Given by Relations with Circular Symmetry
    Geometric Methods in Physics, XXX Workshop 2011, Białowieża, Poland, (P. Kielanowski, S. T. Ali, A. Odzijewicz, M. Schlichenmaier, Th. Voronov Ed(s).), Trends in Mathematics , (publ. by) Birkhauser Verlag, 2013, pp. 303-312, (http://arxiv.org/abs/1209.0087).
    DOI: 10.1007/978-3-0348-0448-6_25
  54. B. Kwaśniewski, A. Lebedev
    Crossed products by endomorphisms and reduction of relations in relative Cuntz-Pimsner algebras
    J. Funct. Anal. 264 (2013), no. 8, 1806-1847, (http://arxiv.org/abs/1208.5232).
    DOI: 10.1016/j.jfa.2013.01.018
  55. B. Kwaśniewski, W. Szymański
    Topological aperiodicity for product systems over semigroups of Ore type
    arXiv.org (2013), (on-line first).
  56. J. Makowska
    Dyskretne operatory przesunięcia z wagą
    Publikacje naukowe stypendystów (M. Proniewski Ed(s).), Podlaski Fundusz Stypendialny vol. 2, Uniwersytet w Białymstoku, 2013, pp. 167-172.
  57. J. Makowska
    Operatory przesunięcia z wagą generowanie przez odwzorowanie afiniczne typu Morse'a-Smale'a
    Publikacje naukowe stypendystów (M. Proniewski Ed(s).), Podlaski Fundusz Stypendialny vol. 1, Uniwersytet w Białymstoku, 2013, pp. 302-313.
  58. R. Meyer, S. Roy, S. L. Woronowicz
    Quantum group-twisted tensor products of C*-algebras
    arXiv.org (2013), (on-line first).
  59. K. Zajkowski
    Convex conjugates of analytic functions of logarithmically convex functionals
    J. Convex Anal. 20 (2013), no. 1, 243-252.
  60. A. Antonevich, V. I. Bakhtin, A. Lebedev
    A road to the spectral radius of transfer operators
    Dynamical Systems and Group Actions (L. Bowen, R. Grigorchuk, Y. Vorobets Ed(s).), Contemp. Math. vol. 567, American Mathematical Society, Providence, RI, USA, 2012, pp. 17-52.
  61. A. Antonevich, C. B. Dolicanin
    Dynamical systems generated by linear maps
    State University of Novi Pazar, 2012.
  62. B. Kwaśniewski
    C*-algebras associated with reversible extensions of logistic maps
    Mat. Sb. 203 (2012), no. 10, 71-116.
    DOI: 10.4213/sm7819
  63. B. Kwaśniewski
    On transfer operators for $C^*$-dynamical systems
    Rocky Mountain J. Math. 42 (2012), no. 3, 919-936.
    DOI: 10.1216/RMJ-2012-42-3-919
  64. A. Antonevich
    On certain high-order partial differential expressions with δ-potential
    Integral Transforms Spec. Funct. 22 (2011), no. 4-5, 255-261.
    DOI: 10.1080/10652469.2010.541035
  65. A. Antonevich, V. I. Bakhtin, A. Lebedev
    Crossed product of $C^*$-algebra by an endomorphism, coefficient algebras and transfer operators
    Mat. Sb. 202 (2011), no. 9, 3-34.
    DOI: 10.4213/sm7703
  66. A. Antonevich, V. I. Bakhtin, A. Lebedev
    On t-entropy and variational principle for the spectral radii of transfer and weighted shift operators
    Ergodic Theory Dynam. Systems 31 (2011), no. 4, 995-1042.
    DOI: 10.1017/S0143385710000210
  67. A. Antonevich, S. A. Lo
    Polufredgol'movye zadači o periodičeskih rešeniâh funkcional'no-differencial'nyh uravnenij nejtral'nogo tipa
    Differ. Uravn. 47 (2011), no. 10, 1371-1382.
  68. A. Antonevich, T. Romanchuk
    Schrödinger operator of the form $−\Delta u+a\delta u+b\part\delta/\part x_1 u$
    Rend. Semin. Mat. Univ. Politec. Torino 69 (2011), no. 4, 319-330.
  69. U. Ostaszewska, K. Zajkowski
    Legendre-Fenchel transform of the spectral exponent of analytic functions of weighted composition operators
    J. Convex Anal. 18 (2011), no. 2, 367-377.
  70. A. Antonevich
    On Differential Expressions with delta-Potential: Exceptional Case d = 2l
    XXIX Workshop on Geometric Methods in Physics, Białowieża 2010, Poland, (P. Kielanowski, V. Buchstaber, A. Odzijewicz, M. Schlichenmaier, Ed(s).), AIP Conf. Proc. vol. 1307, (publ. by) American Institute of Physics, , , 2010, pp. 1-6.
    DOI: 10.1063/1.3527419
  71. J. Makowska
    One-side invertibility of the weighted shift operators
    XXIX Workshop on Geometric Methods in Physics, Białowieża 2010, Poland, (P. Kielanowski, V. Buchstaber, A. Odzijewicz, M. Schlichenmaier, Ed(s).), AIP Conf. Proc. vol. 1307, (publ. by) American Institute of Physics, , , 2010, pp. 101-105.
    DOI: 10.1063/1.3527404
  72. U. Ostaszewska, K. Zajkowski
    Legendre - Fenchel transform of the spectral exponent of polynomials of weighted composition operators
    Positivity 14 (2010), no. 3, 373-381.
    DOI: 10.1007/s11117-009-0023-6
  73. U. Ostaszewska, K. Zajkowski
    Variational principle for the spectral exponent of polynomials of weighted composition operators
    J. Math. Anal. Appl. 361 (2010), no. 1, 246-251.
    DOI: 10.1016/j.jmaa.2009.08.057
  74. K. Zajkowski
    Spectral radius of weighted composition operators in Lp-spaces
    Studia Math. 198 (2010), no. 3, 301-307.
    DOI: 10.4064/sm198-3-8
  75. A. Antonevich
    On Extensions of the Legendre Transform
    XXVIII Workshop on Geometrical Methods in Physics, Białowieża 2009, Poland, (P. Kielanowski, S. T. Ali, A. Odzijewicz, M. Schlichenmaier, T. Voronov Ed(s).), AIP Conf. Proc. vol. 1191, (publ. by) American Institute of Physics, , , 2009, pp. 1-6.
    DOI: 10.1063/1.3275593
  76. A. Antonevich
    Rasszirenie prostranstva C ( X ), svjazannoe s preobrazovaniem Leżandra
    Aktual'nye problemy sovremennogo analiza. Sbornik naucznych trudov (V. G. Krotov, Ja. V. Radno, Ju. M. Vuvunikjan Ed(s).), Grodnenskij Gosudarstvennyj Universitet, 2009, pp. 4-18.
  77. A. Antonevich, T. A. Romanchuk
    Equations with delta-shaped coefficients: the finite-dimensional perturbations approach
    Integral Transforms Spec. Funct. 20 (2009), no. 3-4, 239-246.
    DOI: 10.1080/10652460802564340
  78. V. I. Bakhtin, A. Lebedev
    A new definition of t-entropy for transfer operators
    arXiv.org (2009), (on-line first).
  79. B. Kwaśniewski, A. Lebedev
    Crossed Product of a C*- Algebra by a Semigroup of Endomorphisms Generated by Partial Isometries
    Integr. Equ. Oper. Theory 63 (2009), no. 3, 403-425.
    DOI: 10.1007/s00020-009-1665-2
  80. K. Zajkowski
    Covariance matrices of self-affine measures
    Statistics & Probability Letters 79 (2009), no. 8, 1021-1024.
    DOI: 10.1016/j.spl.2008.12.007
  81. A. Antonevich
    Ob odnostronney obratimosti operatorov vsvieshennogo sdviga
    Spectral Evol. Problems 18 (2008), 15-18.
  82. A. Antonevich, V. I. Bakhtin, A. Lebedev
    T-entropy and Variational Principle for the spectral radius of transfer and weighted shift operators
    arXiv.org (2008), (on-line first).
  83. A. Antonevich, J. Jakubowska
    A model example of a weighted shift operator generated by a mapping with a saddle point
    Proceedings of the Crimean Autumn Mathematical School-Symposium, KROMSH, Sep 17-29, 2008, Laspi-Batiliman, Crimea, Ukraine, Sovrem. Mat. Fundam. Napr. vol. 29, (publ. by) RUDN University, 2008, pp. 29-48.
  84. A. Antonevich, J. Makowska
    On spectral properties of weighted shift operators generated by mappings with saddle points
    Complex Anal. Oper. Theory 2 (2008), no. 2, 215-240.
    DOI: 10.1007/s11785-008-0050-5
  85. A. B. Antonevich, I. Yu. Trubnikov
    Linear extensions associated with abstract functional operators
    Funktsional Anal. i Prilozhen. 42 (2008), no. 1, 78-82.
  86. B. Kwaśniewski, A. Lebedev
    Reversible extensions of irreversible dynamical systems: the $C^*-$method
    Mat. Sb. 199 (2008), no. 11, 45-74.
  87. J. Makowska
    On spectral properties of weighted shift operators generated by mappings with saddle points in Lp
    Geometric Methods in Physics, Proceedings of the XVII Workshop, 2008, Białowieża, Poland, (P. Kielanowski, A. Odzijewicz, M. Schlichenmaier, T. Voronov Ed(s).), AIP Conf. Proc. vol. 1079, (publ. by) American Institute of Physics, , , 2008, pp. 96-101.
    DOI: 10.1063/1.3043878
  88. A. B. Antonevich
    Ob usrednenii koefficientov funkcional'nych operatorov
    Spectral Evol. Problems 17 (2007), 5-10.
  89. U. Ostaszewska, K. Zajkowski
    Spectral Exponent of Finite Sums of Weighted Positive Operators in Lp-Spaces
    Positivity 11 (2007), no. 4, 549-562.
    DOI: 10.1007/s11117-007-2096-4
  90. A. Antonevich
    Coefficients averaging for functional operators generated by irrational rotations
    Modern Operator Theory and Applications, The Igor Borisovich Simonenko Anniversary Volume (I. Gohberg Ed(s).), Oper. Theory Adv. Appl. vol. 170, Springer, 2006, pp. 27-41.
    DOI: 10.1007/978-3-7643-7737-3_2
  91. A. Antonevich
    Variational principles for spectral radii of positive functional operators
    Differential and Functional-Differential Equations, 4th International Conference, Apr 14-21, 2005, Moscow, Russia, Sovrem. Mat. Fundam. Napr. vol. 15, (publ. by) RUDN University, 2006, pp. 5-18.
  92. A. Antonevich, J. Jakubowska
    The effect of saddle points on the fine spectral properties of weighted shift operators
    Vestn. Beloruss. Gos. Univ. Ser. 1 Fiz. Mat. Inform. 3 (2006), 86-93.
  93. A. Antonevich, K. Zajkowski
    Variational principles for the spectral radius of functional operators
    Mat. Sb. 197 (2006), no. 5, 3-50.
  94. A. B. Antonevich
    Coherent local hyperbolicity of a linear extension and the essential spectra of a weighted shift operator on a closed interval
    Funktsional Anal. i Prilozhen. 39 (2005), no. 1, 11-26.
  95. A. B. Antonevich, V. I. Bakhtin, A. V. Lebedev
    Spectra of operators associated with dynamical systems: from ergodicity to the duality principle
    Twenty years of Bialowieza: a mathematical anthology, Aspects of Differential Geometric Methods in Physics, XX Workshop, Jul 1-7, 2001, Białowieża, Poland, (S.T. Ali, G.G. Emch, A. Odzijewicz, M. Schlichenmaier, S.L. Woronowicz Ed(s).), World Scientific Monograph Series in Mathematics vol. 8, (publ. by) World Scientific, 2005, pp. 129-162.
    DOI: 10.1142/9789812701244_0007
  96. B. Kwaśniewski
    Covariance algebra of a partial dynamical system
    Cent. Eur. J. Math. 3 (2005), no. 4, 718-765, ( ).
    DOI: 10.2478/BF02475628
  97. B. Kwaśniewski
    Inverse limit systems associated with $F_2^n$ zero Schwarzian unimodal maps
    Bull. Soc. Sci. Lett. Łódź z Sér. Rech. Déform. 55 (2005), 83-109.
  98. A. V. Lebedev
    Topologically free partial actions and faithful representations of crossed products
    Funktsional Anal. i Prilozhen. 39 (2005), no. 3, 54-63.
  99. K. Zajkowski
    Spectral radius of operators associated with dynamical systems in the spaces C(X)
    Banach Center Publ. 67 (2005), 397-403.
    DOI: 10.4064/bc67-0-33
  100. A. Antonevich, K. Zajkowski
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