Department of mathematics

Faculty of Electrical Engineering

prof. RNDr. Pavel Pták, DrSc.

Professor
22435 5122
JP:B-520
 
Education: 1965-1970 The Charles University of Prague, Faculty
    of Mathematics and Physics,
    specialization - mathematical analysis
  1972 RNDr. degree in the theory of categories
    (thesis: The generalized algebraic categories,
    Charles University)
  1976 CSc. degree (= PhD.) in topology
    (thesis: Discreteness in uniform spaces,
    Charles University)
Professional career:    
  1971-1981 Lecturer and Senior Lecturer at

The Czech

    Technical University of Prague-El. Eng.
  1981-1996 Docent = Associate Professor (ibid)
    Habilitation
    (thesis: Quantum logics, Czech
    Technical University)
  1991 DrSc. in algebra
    (thesis: States on orthostructures
    and the axiomatics of quantum theories,
    Charles University)
  1996-present Professor (ibid)
    (thesis: Mathematical methods of quantum
    theories, Czech Technical University)

Pedagogical experience:

Basic courses of mathematics for engineers (differencial and

integral calculus, linear algebra, Fourier series), the Laplace

transform, mathematical logic, elementary probability theory, etc. The

author of 2 textbooks:

Calculus II'' and Introduction to Linear

Algebra".

Lecture of postgraduate courses: topology, algebra, linear algebra, functional

analysis (operators in Hilbert spaces).

Research:

Recent interest - algebra (orthomodular structures and quantum logics) and

(non-comutative)measure theory,

also topology (uniform spaces), functional analysis,

mathematical methods in image processing.

Scientific leader of research team ("Seminar on

orthomodular structures and ordered algebras") 1980-1997; supervisor of 6 PhD.

students.

Active participation at several international conferences. Five invited

lectures.


 

Publications:

Over 100 research papers and a monograph ("Orthomodular Structures as

Quantum Logics", Kluwer, Boston/Dordrecht/London, 1991 - coauthor

S. Pulmannová)


 

Professional visits abroad:

 

1977 - Great Britain (10 months - The British Council Scholarship,
  research fellow at The St. Andrews University)
1984 - Great Britain (4 months - an invitation by The British Royal Society,
  research cooperation with The University of Reading)
1990 - Poland (2 months - Czech-Polish cultural agreement, research
  cooperation with Warsaw Technical University
1992 - Italy (2 months research cooperation with The University
  of Naples Federico II'')
1994 - Italy (2 months research cooperation with The University
  of Naples Federico II'')
1996 - France (1 month research cooperation with The University of Lyon)
1996 - Italy (1 month research cooperation with The University
  of Naples Federico II'')
1998 - Austria (1 month research cooperation with the Vienna Technical
  University and the University of Linz)
1998 - USA (2 weeks research cooperation with the University of Las Cruses)
1998 - Italy (1 month research cooperation with the University
  of Naples Federico II'')
2000 - USA (1 week research cooperation with the University of Las Cruces)

 

Languages: English fluent, Russian fair, German fair, Italian

passive

 

Interests: Chess (national masterclass), languages and literature

 

Health: good

 

List of publications

Pavel Pták

1. "On equalizers in generalized algebraic categories". Comment. Math. Univ. Carolin. 13 (1972), 351-357.
2. "On the categorial extent of Johnson's theorem" (Czech). Kniznice odb. a tech. spisu, VUT Brno, 1974, 8-37.
3. "Intrinsic characterization of distal spaces". Seminar Uniform Spaces 1973-74, Publ. Math. Inst. of the Czechoslovak Acad. Sci., Prague, 1975, 217-231 (coauthor M. Kosina).
4. "Tietze-Urysohn theorem for functors" (Czech). RNDr. Dissertation,Charles University, Prague, 1974.
5. "A note on normal topological functors and extensions of transformations". Comment. Math. Univ. Carolin. 17 (1976), 567-574.
6. "Limits in generalized algebraic categories -- contravariant case". Acta Univ. Carolin. - Math. Phys. 18 (1977), 43-53 (coauthor V. Koubek).
7. "Big and small dimension agree for metric fine spaces". Proc. Conf. Tech. Univ. Prague, 1977, 62-64.
8. "Freckle refinement of uniform spaces". Seminar Uniform Spaces 1975-76, Publ. Math. Inst. of the Czechoslovak Acad. Sci., Prague, 1977, 115-120 (coauthor J. Pelant).
9. "Injectivity of polyedra". Seminar Uniform Spaces 1975-76, Publ. Math. Inst. of the Czechoslovak Acad. Sci., Prague, 1977, 121-122 (coauthor J. Pelant).
10. "Discreteness in uniform spaces" (Czech). CSc. Dissertation, Charles Univ., Prague, 1977.
11. "On extensions of uniformly continuous Banach-space-valued mappings". Comment. Math. Univ. Carolin. 20 (1979), 101-105.
12. "On the integration on -classes" (preliminary announcement). Comment. Math. Univ. Carolin. 21 (1980), 627 (coauthor M. Navara).
13. "Realcompactness and the notion of observable". J. London Math. Soc. (2) 23 (1981), 534-536.
14. "On states on the product of logics". Int. J. Theor. Physics 20 (1981), 451-457 (coauthor V. Manasová).
15. "Concerning the notion of -class - on three questions motivated by quantum system theories". Acta Polytechnica - Math. IV 10 (1981), 27-37 (coauthors V. Manasová and M. Navara).
16. "G-logic of a quantum system". Habilitation, Czech Technical University, Prague, 1981.
17. "The complexity of -discretely decomposable families in uniform spaces". Comment. Math. Univ. Carolin. 22 (1981), 317-326 (coauthor J. Pelant).
18. "On compatibility in quantum logics". Found. Phys. 12 (1982), 207-212 (coauthor J. Brabec).
19. "Concrete logic of a quantum system". Acta Polytechnica - Math. III 4 (1982), 65-67.
20. "Weak dispersion-free states and the hidden variables hypothesis". J. Math. Phys. 24 (1983), 839-840.
21. "Two-valued measures on -classes". Cas. Pest. Mat. 108 (1983), 225-229 (coauthor M. Navara).
22. "Logics with given centres and state spaces". Proc. Amer. Math. Soc. 88 (1983), 106-109.
23. "Regularly full logics and the uniqueness problem for observables". Ann. Inst. H. Poincaré 38 (1983), 69-74 (coauthor V. Rogalewicz).
24. "On the Radon-Nikodym property for -classes". J. Math. Phys. 24 (1983), 1450 (coauthor M. Navara).
25. "Measures on orthomodular partially ordered sets". J. Pure Appl. Algebra 28 (1983), 75-80 (coauthor V. Rogalewicz).
26. "Spaces of observables". Czechoslovak Math. J. 34 (109) (1984), 552-561.
27. "A note on centers and state spaces of a logic". Circolo Mat. di Palermo, Ser. II, Num. 3 (1984), 225-229.
28. "Quantum logics with Jauch-Piron states". Quart. J. Math. Oxford (2) 36 (1985), 261-271 (coauthors L.J. Bunce, M. Navara and J.D.M. Wright).
29. "Categories of orthomodular posets". Math. Slovaca 35 (1985), 59-65.
30. "Extensions of states on logics". Bull. Acad. Polon. Sci. Sér. Math. 33 (1985), 493-497.
31. "On the concreteness of quantum logics". Aplikace Mat. 30 (1985), 274-285 (coauthor J.D.M. Wright).
32. "A note on Jauch-Piron states". Rep. Math. Physics 23 (1986), 155-159.
33. "Summing of Boolean algebras and logics". Demonstratio Math. 19 (1986), 349-358.
34. "Hidden variables on concrete logics (extensions)". Comment. Math. Univ. Carolinae 28 (1987), 157-163.
35. "A completeness criterion for inner product spaces". Bull. London Math. Soc. 19 (1987), 259-263 (coauthor J. Hamhalter).
36. "Exotic logics". Colloquium Math. 54 (1987), 1-7.
37. "An observation on observables". Acta Polytechnica - Math. IV 10 (1987), 81-85.
38. "Enlargements of quantum logics". Pacific J. Math. 135 (1988), 361-369 (coauthors M. Navara and V. Rogalewicz).
39. "Quantum logics with the Radon-Nikodym property". Order 4 (1988), 387-395 (coauthor M. Navara).
40. "Almost Boolean orthomodular posets". J. Pure Appl. Algebra 60 (1989), 105-111 (coauthor M. Navara).
41. "A note on determinacy of measures". Casopis pest. mat. 113 (1988), 435-436 (coauthor J. Tkadlec).
42. "Enlargements of logics (-orthocomplete case)". Proc. Conf. Topology and Measure V, Greifswald, 109-115, 1988 (coauthor M. Navara).
43. "FAT CAT (in the state space of quantum logics)". Proc. 1st Winter School on Measure Theory, Liptovský Ján, 113-118, 1988.
44. "A representation of orthomodular lattices". Acta Univ. Carolin. - Math. Phys. 31 (1990), 21-26 (coauthor J. Binder).
45. "Quantum Logics" (Slovak). Veda, Bratislava, 1989 (coauthor S. Pulmannová).
46. "Measure-determined enlargements of Boolean -algebras". Comment. Math. Univ. Carolinae 31 (1990), 105-107.
47. "Hilbert-space-valued measures on Boolean algebras (extensions)". Acta Math. Univ. Commenianae 60 (1991), 219-224 (coauthor J. Hamhalter).
48. "Hilbert-space-valued states on quantum logics". Applications Math. 37 (1992), 51-61 (coauthor J. Hamhalter).
49. "Measures on orthostructures and the axiomatics of quantum theory". DrSc. Thesis, Charles University, Prague, 1991.
50. "Orthomodular Structures as Quantum Logics". Kluwer Academic Publishers, Dordrecht/Boston/London, 1991 (coauthor S. Pulmannová).
51. "On the state space of soft fuzzy algebras". Bull. Sous-Ensembl. Flous Appl. 48 (1991), 55-63 (coauthor M. Navara).
52. "On the Radon-Nikodým property in quantum logics". In: Topology, Measures, and Fractals, C. Bandt, J. Flachsmeyer, H. Haase (eds.), Akademie Verlag, Berlin, 1992, 147-153 (coauthor M. Navara).
53. "Alternative probability models". Proc. Workshop 92, CTU Prague, 29-30, 1992 (coauthor M. Navara).
54. "Concrete quantum logics with covering properties". Int. J. Theor. Phys. 31 (1992), 843-854 (coauthors V. Müller and J. Tkadlec).
55. "States on soft fuzzy algebras -- finite and countable additivity". Tatra Mountains Math. Publ. 1 (1992), 125-134 (coauthor M. Navara).
56. "Quantum probability spaces that are nearly classical". Bull. Polish Acad. Sci. - Math. 40 (1992), 163-173 (coauthor P. de Lucia).
57. "A note on inner product spaces". Acta Polytechnica - Math., Vol. 34, No. 2, 1994, p. 35-37 (coauthor P. de Lucia).
58. "P-measures on soft fuzzy σ-algebras". Fuzzy Sets Syst. 56 (1993), No. 1, 123-126 (coauthor M. Navara).
59. "Calculus II (A Course for Engineers). Functions of Two or More Variables. Differencial Equations. The Laplace Transform." Textbook, Czech Technical University, Prague, 1994, 230 pp., ISBN 80-01-01207-7.
60. "Difference posets and orthoalgebras". Bulletin for Studies and Exchanges on Fuzziness and Its Appl. 69 (1997), 64-69 (coauthor M. Navara).
61. "States on orthoalgebras". Int. J. Theor. Physics 34 (1995), No. 8, 1439-1465. (coauthors J. Hamhalter and M. Navara).
62. "On the tensor product of Boolean algebras and orthoalgebras". Czechoslovak Math. J. 45 (120) (1995),117-126 (coauthor D. Foulis).
63. "On absolutely compatible elements and hidden variables in quantum logics". Ricerche di Matematica, Vol. XLIV, fasc. 1, (1995), 19-29 (coauthor D. Foulis).
64. "Orthomodular structures as quantum logics". Proc. Workshop 93, CTU Prague, 1993, 27-28.
65. "Central envelopes of orthomodular lattices". Tatra Mountains Math. Publ. 2 (1993), 221-228.
66. "A measure-theoretic characterization of Boolean algebras among orthomodular lattices". Comment. Math. Univ. Carolinae, Vol. 35, No. 1 (1994), p. 205-208 (coauthor S. Pulmannová).
67. "Jauch-Piron property (everywhere!) in the logico-algebraic foundations of quantum theories". Int. J. Theor. Phys. 32 (1993), 1985-1990.
68. "The dog-and-rabbit chase revisited". Acta Polytechnica 36 (1996), 5-10 (coauthor J. Tkadlec).
69. "Enveloping classical and quantum logics (macroscopic measuring apparatuses and quantum events)". In Symposium on the Foundations of Modern Physics (Köln 1993), World Scientific Publ., Singapore, 1993, pp. 338-340.
70. "Mathematical methods of quantum theories". Workshop 94, Czech Technical Univ., Prague, 1994, 25-26.
71. "State space of an orthoalgebra". Workshop 95, Czech Technical Univ., Prague, 1995, 39-40.
72. "States on Orthomodular Posets (Recent Results on Orthostructures and Noncommutative Measure Theory)". Research Report, Czech Technical University -- El. Eng., 1995.
73. "States on orthomodular posets (recent results in noncommutative measure theory)". Rendiconti dell'Instituto di Matematica dell'Universitŕ di Trieste, Vol. XXVI, 1994, suppl., Workshop di Teoria della Misura e Analisi Reale, Grado (Italia), 19.9.-2.10. 1993.
74. "Almost Boolean algebras as quantum logics". Volume of Abstracts, 10th Int. Congress of Logic, Methodology and Philosophy of Science, August 19-25, Commune di Cesena - Assessorato alla Cultura - Centro di Epistamologia F. Enriques", Florence, Italy, 1995, 438.
75. "Types of uncertainty - types of dependence". Proc. 4th Workshop on Uncertainty Processing, University of Economics, Prague, 1997, 130-143 (coauthor M. Navara).
76. "Digital topologies revisited: an approach based on topological point - neighbourhood". Discrete Geometry for Computer Imagery, Springer Verlag - Lecture Notes in Computer Science, 1347, 7th International Workshop, Montpellier, France (1997), 151-163 (coauthors W. Kropatsch and H. Kofler).
77. "Introduction to Linear Algebra". Textbook, Czech Technical University, Prague 1997, 165 pp., ISBN 80-01-01678-1.
78. "Quantum logics with given centres and variable state spaces". International Journal of Theoretical Physics 37 (1998), No. 1, 139-145 (coauthor M. Navara).
79. "Considering Uncertainty and dependence in Boolean, quantum and fuzzy logics". Kybernetika 34 (1998), No. 1, 121-134 (coauthor M. Navara).
80. "Some nearly Boolean orthomodular posets". Proc. Amer. Math. Soc. 126 (1998), No. 7, 2039-2046.
81. "Types of uncertainty and the role of the Frank t-norms in classical and nonclassical logics". Non-Classical Measures and their Applications to Decision Making, D. Butnariu and E. P. Klement, eds., Linz 1998 (coauthor M. Navara).
82. "Two remarks on inner product spaces". Contributions to General Algebra 10, Proc. of the Klagenfurt Conference, May 29 to June 1, 1997, Verlag Joh. Heyn, Friedensgasse 23, A-9020 Klagenfurt, Austria (coauthor H. Weber).
83. "Orthomodular lattices with state-separated noncompatible pairs". Czechoslovak Math. J. 50 (125) (2000) (coauthor R. Mayet).
84. "The path-connectedness in Z2 and Z3 and classical topologies". Structural and Syntactic Pattern Recognition, Sydney 1998, to appear in Springer Verlag - Lecture Notes in Computer Science.
85. "Quasivarieties of orthomodular lattices determined by conditions on states". Algebra Universalis 42 (1999), 155-164 (coauthor R. Mayet).
86. "Lattice properties of subspace families in an inner product space". Proc. Amer. Math. Soc. 129 (2001), 2111-2117 (coauthor H. Weber).
87. "Quantum logics with classical state spaces". Colloquium Mathematicum 80 (1999), No. 1, 147-154 (coauthor P. de Lucia).
88. "Observable in the logico-algebraic approach". In: Current Reserarch in Operational Quantum Logic, Kluwer Academic Publ., Dordrech, Boston, London (2000), 67-80.
89. "The Vitali-Hahn- Saks theorem for the product of quantum logics". Demonstratio Mathematica 35, 4 (2002), 717-725 (coauthors A. De Simone and M. Navara).
90. "On the de Morgan property of the standard Brouwer-Zadeh poset". Foundations of Physics 30 (10) (2001), 1801-1805 (coauthors G. Cattaneo and J. Hamhalter).
91. "Concrete quantum logics". International Journal of Theoretical Physics 39 (2000), 827-839.
92. "On interval homogeneous orthomodular lattices". Comm. Math. Univ. Carolinae, 42, 1 (2001), 23-30 (coauthors A. De Simone and M. Navara).
93. "On the set representation of an orthomodular poset". Coll. Math. 89, no. 1-2 (2001), 233-240 (coauthor J. Harding).
94. "Lattice properties of subspace families in an inner product space". Proc. Am. Math. Soc. 129, 7 (2001), 2111-2117 (coauthor H. Weber).
95. "On states on orthogonally closed sbspaces of an inner product space". Letters in Math. Physics 62 (2002), 63-70 (coauthor A. Dvurečenskij).
96. "Quantum Logics with the Riesz interpolation property". Math. Nachrichten 271 (2004), 10-14 (coauthor A. Dvurečenskij).
97. "For n>=5 there is no nontrivial Z(2)-measure on L(R-n)". Int. J. Ther. Physics 43, no. 7-8 (2004), 1595-1598 (coauthor M. Navara).
98. "Order properties of splitting subspaces in an inner product space". Math. Slovaca 54, 2 (2004), 119-126 (coautor H. Weber).
99. "On the (non)existence of states on orthogonally closed subspaces in an inner product space". Int. J. Theor.Physics 44, 7 (2005), 1023-1028 (coauthors K. Svozil and E. Chetcuti).
100. "Relatively additive states on quantm logics". Comm. Math. Univ. Carolinae 46, 2 (2005), 327-338 (coauthor H. Weber).
101. "Extending coarse-grained measures". Bull. Polish Acad. Sci. 54, no. 1 (2006), 1-11 (coauthor A.De Simone).
102. "Extending states on finite concrete logics". Int. J. Theor. Physics 46, n. 8 (2007), 2046-2052 (coauthors A. De Simone and M. Navara).
103. "Group-valued measures on coarse-grained quantum logics". Czech. Math. J. 57 (2007), 737-746 (coauthor A. De Simone).
104. "Symetric difference on orthomodular lattices and Z(2)-valued states ". Comment. Math. Carolin 50,4 (2009), 535-547 (coauthor M. Matoušek).
105. "Orthocomplemented Posets with a Symmetric Difference ". Order Vol. 26, No. 1 (2009), 1-21 (coauthor M. Matoušek).
106. "Measures on circle coarse--grained systems of sets ". Positivity Vol 14, n.2 (2010) 247-256 (coauthor A. De Simone).
107. "On identities in orthocomplemented difference lattices ". Math. Slovaca 60 No.5. (2010) 1-8 (coauthor M. Matoušek).
108. "Orthocomplemented difference lattices as associated with generalized rings ". Math. Slovaca 62 No.6. (2012) 1063-1068 (coauthor M. Matoušek).
109. "Orthomodular Posets Related to Z2-Valued States". Int. J. Theor. Physics 53, n. 10 (2014), 3323-3332 (coauthor M. Matoušek).
110. "States on systems of sets that are closed under symmetric difference". to appear in Math. Nachrichten (2015), (coauthor A. De Simone and M. Navara).
111. "Characterization of Boolean algebras in terms of states of Jauch-Piron type". to appear Int. J. Theor. Physics (2015), (coauthor M. Matoušek).
112. "States with values in the Łukasiewicz grupoid". to appear Math. Slovaca (2015), (coauthor M. Matoušek).
113. "On the Farkas lemma and the Horn-Tarski measure-extension theorem". to appear in Lin. Algebra and App. (2015), (coauthor A. De Simone).
114. "States on orthocomplemented posets (Extensions)". submited for publication, (coauthor M. Hroch).

April 2015

Prague, 2015

Responsible person: doc. RNDr. Martin Bohata, Ph.D.