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Research |
| Research areas |
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Operator algebras: C*-algebras, Jordan algebras, states and weights (quantum
measure theory), subspace structures, independence of operator algebras,
group representations, applications to quantum field theory and mathematical
foundations of quantum theory.
(Jan Hamhalter)
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Orthomodular structures (quantum logics): orthomodular posets, effect
algebras, concrete (set-representable) logics, logics with a symmetric
difference, compatibility, states (measures), pastings of logics,
constructions of logics.
(Pavel Pták, Josef Tkadlec)
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Semigroups and groups: varieties of semigroups, various types of
universality (categorial universality, weak universality, Q-universality),
subdirectly irreducible semigroups in various varieties, partial
representations of groups, Hamming distances, Latin squares, Latin trades.
(Marie Demlová, Natalia Zhukavets)
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Algebras and superalgebras: Lie, alternative, Malcev and their
generalizations, Poisson and their deformations.
(Natalia Zhukavets)
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Geometry of Banach spaces: differentiability of Lipschitz functions and
mappings between Banach spaces, porous and directionally porous sets in
infinite dimensional spaces, asymptotic convexity and smoothness.
(Jaroslav Tišer)
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Measure theory: covering and differentiation theorems in Hilbert space.
(Jaroslav Tišer)
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Coalgebraic methods in computer science: coalgebras as recursive
specifications, iterative algebras and their generalizations, semantics of
infinite behaviour, algebras where every recursive equation admits a strict
solution, coequational presentations of coalgebras, process algebra.
(Marie Demlová, Jiří Velebil)
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Fuzzy logics: algebraic semantics, residuated lattices, structure of
MTL-algebras, complexity and decidability, standard completeness theorems,
fragments, formalization of mathematics in fuzzy class theory.
(Rostislav Horčík)
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Numerical methods: finite element method and its application to nonlinear
elliptic problems on nonpolygonal domains, discontinuous Galerkin finite
element method and its application to approximation of nonlinear
convection-diffusion problems, effect of numerical integration.
(Veronika Sobotíková)
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Difference equations: qualitative properties of their solutions, mainly for
the linear case, applications to multidimensional systems theory, to
numerical solutions of partial differential equations, and to various areas
of discrete mathematics.
(Jiří Gregor)
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