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prof. RNDr. Josef Tkadlec, CSc.

Všechny publikace

Associativity and Distributivity-Like Properties in Generalized Effect Algebras

  • DOI: 10.1007/s10773-023-05371-3
  • Odkaz: https://doi.org/10.1007/s10773-023-05371-3
  • Pracoviště: Katedra matematiky
  • Anotace:
    We prove "large" associativity of the partial plus operation in generalized effect algebras and present an overview of distributivity-like properties of partial operations plus and minus in generalized effect algebras with respect to (possibly infinite) suprema and infima and vice versa. These results generalize previous results in various subclasses of generalized effect algebras.

Interpolations in Posets and Effect Algebras

  • DOI: 10.1007/s10773-019-04079-7
  • Odkaz: https://doi.org/10.1007/s10773-019-04079-7
  • Pracoviště: Katedra matematiky
  • Anotace:
    We study various types of the interpolation property in posets and effect algebras. We present connections to other properties of posets and effect algebras (completeness, orthocompleteness, maximality property) and a theorem about preserving compatibility to suprema and infima using an interpolation property.

Weakly Jauch-Piron States in Effect Algebras

  • DOI: 10.1007/s10773-020-04709-5
  • Odkaz: https://doi.org/10.1007/s10773-020-04709-5
  • Pracoviště: Katedra matematiky
  • Anotace:
    We study various types of weakly Jauch-Piron states and various types of state-space properties in effect algebras. We generalize several results of Tkadlec (Tatra Mt. Math. Publ. 10, 55-62 1997; Algebra Universalis 61, 187-194 2009) and of Matousek and Ptak (Internat. J. Theoret. Phys. 54, 4476-4481 2015). In particular, we show when an effect algebra is an orthomodular poset, when a unital set of states is strongly order determining, and we present some state space characterizations of Boolean algebras.

Properties of Effect Algebras Based on Sets of Upper Bounds

  • DOI: 10.1007/s10773-017-3522-4
  • Odkaz: https://doi.org/10.1007/s10773-017-3522-4
  • Pracoviště: Katedra matematiky
  • Anotace:
    We give an overview and clear up some relations between various properties of effect algebras based on properties of sets of upper bounds, e.g., completeness, orthocompleteness, weak orthocompleteness, maximality property, interpolation property.

Distributivity and associativity in effect algebras

  • DOI: 10.1016/j.fss.2015.06.0250165
  • Odkaz: https://doi.org/10.1016/j.fss.2015.06.0250165
  • Pracoviště: Katedra matematiky
  • Anotace:
    We prove "large associativity" of the partial sum in effect algebras and present an overview of distributivity-like properties of partial operations circle plus and circle minus in effect algebras with respect to ( possibly infinite) suprema and infima and vice versa generalizing several previous results. (C) 2015 Elsevier B.V. All rights reserved.

States on effect algebras, their products and horizontal sums

  • DOI: 10.1515/ms-2015-0200
  • Odkaz: https://doi.org/10.1515/ms-2015-0200
  • Pracoviště: Katedra matematiky
  • Anotace:
    We study states (two-valued, extremal, Jauch-Piron, resp.) and properties of the set of such states (empty, unital, order determining, strongly order determining) on products and horizontal sums of effect algebras.

Atomic effect algebras with compression bases

  • DOI: 10.1063/1.3533918
  • Odkaz: https://doi.org/10.1063/1.3533918
  • Pracoviště: Katedra matematiky
  • Anotace:
    Compression base effect algebras were recently introduced by Gudder [Demonstr. Math. 39, 43 (2006)]. They generalize sequential effect algebras [Rep. Math. Phys. 49, 87 (2002)] and compressible effect algebras [Rep. Math. Phys. 54, 93 (2004)]. The present paper focuses on atomic compression base effect algebras and the consequences of atoms being foci (so-called projections) of the compressions in the compression base. Part of our work generalizes results obtained in atomic sequential effect algebras by Tkadlec [Int. J. Theor. Phys. 47, 185 (2008)]. The notion of projection-atomicity is introduced and studied, and several conditions that force a compression base effect algebra or the set of its projections to be Boolean are found. Finally, we apply some of these results to sequential effect algebras and strengthen a previously established result concerning a sufficient condition for them to be Boolean. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3533918]

Characterizations of Spectral Automorphisms and a Stone-Type Theorem in Orthomodular Lattices

  • Autoři: Caragheorgheopol, D., prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: International Journal of Theoretical Physics. 2011, 50(12), 3750-3760. ISSN 0020-7748.
  • Rok: 2011
  • DOI: 10.1007/s10773-011-0738-6
  • Odkaz: https://doi.org/10.1007/s10773-011-0738-6
  • Pracoviště: Katedra matematiky
  • Anotace:
    The notion of spectral automorphism of an orthomodular lattice was introduced by Ivanov and Caragheorgheopol (Int. J. Theor. Phys. 49(12):3146-3152, 2010) to create an analogue of the Hilbert space spectral theory in the abstract framework of orthomodular lattices. We develop the theory of spectral automorphisms finding previously missing characterizations of spectral automorphisms, discussing several examples and the possibility to construct such automorphisms in direct products or horizontal sums of lattices. A factorization of the spectrum of a spectral automorphism is found. The last part of the paper addresses the problem of the unitary time evolution of a system from the point of view of the spectral automorphisms theory. An analogue of the Stone theorem concerning strongly continuous one-parameter unitary groups is given.

Commutative bounded integral residuated orthomodular lattices are Boolean algebras

  • DOI: 10.1007/s00500-010-0572-4
  • Odkaz: https://doi.org/10.1007/s00500-010-0572-4
  • Pracoviště: Katedra matematiky
  • Anotace:
    We show that a commutative bounded integral orthomodular lattice is residuated iff it is a Boolean algebra. This result is a consequence of (Ward, Dilworth in Trans Am Math Soc 45, 336-354, 1939, Theorem 7.31); however, out proof is independent and uses other instruments.

Note on Generalizations of Orthocomplete and Lattice Effect Algebras

Common generalizations of orthocomplete and lattice effect algebras

Classes of Effect Algebras

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Abstracts of the International Conference Quantum Structures 2009. Bratislava: Vydavatel'stvo STU, 2009. pp. 72. ISBN 978-80-227-3175-1.
  • Rok: 2009
  • Pracoviště: Katedra matematiky
  • Anotace:
    Various generalizations of orthocomplete and lattice effect algebras and the relations between them are presented.

Effect Algebras with the Maximality Property

  • DOI: 10.1007/s00012-009-0013-3
  • Odkaz: https://doi.org/10.1007/s00012-009-0013-3
  • Pracoviště: Katedra matematiky
  • Anotace:
    We show that the maximality property generalizes various conditions used in the theory of effect algebras. Some consequences are presented, (especially for Jauch-Piron states).

On the Solution of Trivalent Decision Problems by Quantum State Identification

Atomic Sequential Effect Algebras

Atomistic and Orthoatomistic Effect Algebras

  • DOI: 10.1063/1.2912228
  • Odkaz: https://doi.org/10.1063/1.2912228
  • Pracoviště: Katedra matematiky
  • Anotace:
    We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete

Opakování operací a relací při zlomu řádku

  • Pracoviště: Katedra matematiky
  • Anotace:
    Jsou uvedena řešení pro opakování operací a relací při zlomu řádku v TeXu.

Central elements of atomic effect algebras

Central elements of effect algebras

  • Pracoviště: Katedra matematiky
  • Anotace:
    Central elements of an effect algebra are characterized by means of a weak form of distributivity and of a maximality property. Examples of effect algebras fulfilling these conditions are presented.

Compatibility and States in Quantum Structures

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Proceedings of the Quantum Structures 2004. New Mexico: New Mexico State University, 2004. pp. 33.
  • Rok: 2004
  • Pracoviště: Katedra matematiky
  • Anotace:
    Some recent results concerning compatibility and state properties in quantum structures and their consequences to the axiomatics are presented

Formal Aspects of a multiple-rule classifier

  • Autoři: prof. RNDr. Josef Tkadlec, CSc., Bruha, I.
  • Publikace: International Journal of Pattern Recognition and Artificial Intelligence. 2003,(17), 581-600. ISSN 0218-0014.
  • Rok: 2003
  • Pracoviště: Katedra matematiky
  • Anotace:
    The problem gives a common background for the multiple-rule problem which arises when several decision rules match.

Rule Quality for Multiple-rule Classifier: Empirical Expertise and Theoretical Methodology

  • Pracoviště: Katedra matematiky
  • Anotace:
    The paper surveys empirical and statistical formulas of the rule quality and compaire their characteristics.

Textové mezery v TeXu

  • Pracoviště: Katedra matematiky
  • Anotace:
    Článek podává přehled typografických pravidel pro psaní mezer v textu a možnosti jejich implementace v sázecím programu TeX.

Representations of Orthomodular Structures

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Algebra, Logic and Applied 16. Amsterdam: Gordon and Breach Science Publishers, 2001. p. 153-158. ISBN 90-5699-325-9.
  • Rok: 2001
  • Pracoviště: Katedra matematiky
  • Anotace:
    Various types of representations of orthomodular structures are presented: topological, orthogonality diagrams, Greechie Diagrams and dual diagrams.

Diagrams of Kochen-Specker Type Constructions

  • Pracoviště: Katedra matematiky
  • Anotace:
    Orthogonality diagrams of the so-called Kochen-Specker type constructions (quantum logics without any two-valued state) are presemnted.

Mathematical Models of Uncertainty

Triangular Norms with Non-continuous Generators

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Abstracts of 5th Int. Conf. Fuzzy Sets Theory Appl. Liptovský Mikuláš: Vojenská akadémia, 2000. pp. 171-172.
  • Rok: 2000

Representations of Orthomodular Structures

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Proceedings of Workshop 99. Praha: České vysoké učení technické v Praze, 1999. pp. 48.
  • Rok: 1999
  • Pracoviště: Katedra matematiky
  • Anotace:
    Various attempts how to represent orthomodular structures are presented.

Triangular Norms with Continuous Diagonals

  • Pracoviště: Katedra matematiky
  • Anotace:
    Some properties of triangular norms wit continuous diagonals are given.

Concrete Quantum Logics with Generalized Compantibility

  • Pracoviště: Katedra matematiky
  • Anotace:
    Several results stating when a concrete logic with covering properties are Boolean algebras are presented.

Dual Diagrams and Kochen-Specker Type Constructions

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Abstracts of Quantum Structures 98. Liptovský Mikuláš: Vojenská akadémia, 1998. pp. 93.
  • Rok: 1998
  • Pracoviště: Katedra matematiky
  • Anotace:
    Dual Diagrams and Kochen-Specker Type Constructions

Greechie Diagrams of Small Quantum Logics with Small State Spaces

  • Pracoviště: Katedra matematiky
  • Anotace:
    Greechie diagrams of several small quantum logics with a small state space are presented.

Representations of Orthomodular Structures

State Spaces of Quantum Logics

Triangular Norms with Continuous Diagonals

Classes of Orthomodular Posets

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Abstracts of IQSA's Conference '97. Atlanta: Georgia Institute of Technology, 1997. pp. 10.
  • Rok: 1997

Conditions that Force an Orthomodular Poset to Be a Boolean Algebra

  • Pracoviště: Katedra matematiky
  • Anotace:
    Simple conditions forcing an orthomodular poset to be a Boolean algebra are given

The Solution to a Problem Posed by P. Konopka

Bell-type inequalities in orthomodular lattices. I: Inequalities of order

Bell-type inequalities in orthomodular lattices. II: Onequalities of higher order

Greechie Diagrams, Nonexistence of Measures and Kochen-Specker Type Constructions

  • Pracoviště: Katedra matematiky
  • Anotace:
    We use Greechie diagrams to construct finite orthomodular lattices realizable in a three-dimensional Hilbert space with not large set of measures and discuss te number of their elements and their (ortho)generators.

Quantum logics with small state spaces (Kochen-Specker type construction)

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Book of ABSTRACTS QUANTUM STRUCTURES 96. Berlin: Technische Universität, 1996. pp. 90-91.
  • Rok: 1996
  • Pracoviště: Katedra matematiky
  • Anotace:
    Quantum Logics with Small State Spaces (Kochen-Specker Type Construction)

Strong law of large numbers in D-posets

The Dog-and-Rabbit Chase Revisited

  • Pracoviště: Katedra matematiky
  • Anotace:
    For the dog-and-rabbit-chase problem we find an explicit description of the dog's path and the duration of the chase.

Typografie a počítače

A Relationship Between Intersection Conditions and Porosity Conditions for Local Systems

Abacus Logic: the Lattice of Quantum Propositions as the Poset of a Theory

Difference Posets, Effects, and Quantum Measurements

Kernel Logics

Orthosummable Orthoalgebras

Subadditivity of States on Quantum Logics

  • Pracoviště: Katedra matematiky
  • Anotace:
    Various concepts of subadditivity are compared. Several results when a quantum logic with sufficiently many properly subadditive states has to be a Boolean algebra are presented.

Boolean Orthoposets - Concreteness and Orthocompleteness

  • Pracoviště: Katedra matematiky
  • Anotace:
    It is shown that a Boolean orthoposet is concrete and that an orthocomplete Boolean orthoposet is a Boolean algebra.

Noncommutative Probability Theory and Its Applications

  • Pracoviště: Katedra matematiky
  • Anotace:
    Various results illustrating the difference between classical and noncommutative probability theory are presented.

Subadditive measures on orthoposets

  • Autoři: prof. RNDr. Josef Tkadlec, CSc.,
  • Publikace: Abstracts Quantum Structures 94. Praha: České vysoké učení technické v Praze, 1994. pp. 23.
  • Rok: 1994

An Ergodic Theorem in General Ordered Systems

Boolean Orthoposets and Two-valued Jauch-Piron States

Partially Additive Measures and Set Representations of Orthoposets

  • Pracoviště: Katedra matematiky
  • Anotace:
    Partially Additive Measures and Set Representations of Orthoposets

Properties of Boolean Orthoposets

Řešení úloh Co takhle vážení, Vážení

The Solution to a Problem Posed by V. Palko

Boolean orthoposets and two-valued states on them

Concrete Quantum Logics With Covering Properties

Automorphisms of Concrete Logics

  • Autoři: prof. RNDr. Josef Tkadlec, CSc., Navara, M.
  • Publikace: Commentationes Mathematicae Universitatis Carolinae. 1991, 32(1), 15-25. ISSN 0010-2628.
  • Rok: 1991

Automorphisms of concrete logics

Partially Additive States on Orthomodular Posets

  • Pracoviště: Katedra matematiky
  • Anotace:
    Partially additive states on orthomodular posets are studied and a set representation of an orthomodular poset is constructed such that for a given Boolean subalgebra the Stone representation is obtained.

Constructions of a Finite Borel Measure with Sigma-Porous Sets as Null Sets

  • Pracoviště: Katedra matematiky
  • Anotace:
    A finite Borel measure such that all sigma-porous sets are null sets is constructed.

Constructions of some non-sigma-porous sets on the real line

  • Pracoviště: Katedra matematiky
  • Anotace:
    Some non-sigma porous sets on the real line were constructed.

Za stránku zodpovídá: Ing. Mgr. Radovan Suk