Pavel Pták, curriculum vitae

Personal data: Pavel P t á k , Prof., RNDr., DrSc.
  born June 17th, 1947
Home address: K Lucinam 13, 13000 - Praha 3, Czech Republic
Work address: Czech Technical University, Faculty of Electrical
  Engineering, Department of Mathematics,
  Technická 2, 16627 - Prague 6, Czech Republik
  e-mail address: ptak@math.feld.cvut.cz
  fax: +420 233 339 238, phone: +420 224 353 565


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 $\sigma $-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

Prof. RNDr. Pavel Pták, DrSc.