Tři nejdůležitější odborné publikace vydané během druhého období (do 30. září 2019). Seznam všech publikací výzkumného programu THEORY vydaných v rámci projektu CAAS najdete na zvláštní stránce, seznam nejdůležitějších publikací za první období pak zde.
On the Pointwise Bishop–Phelps–Bollobás Property for Operators,
Sheldon Dantas, Vladimir Kadets, Sun Kwang Kim, Han Ju Lee, Miguel Martin
Canad. J. Math., to appear
First online: 17.10.2018
We study approximation of operators between Banach spaces X and Y that nearly attain their norms in a given point by operators that attain their norms at the same point. When such approximations exist, we say that the pair (X,Y) has the pointwise Bishop–Phelps–Bollobás property (pointwise BPB property for short). In this paper we mostly concentrate on those X, called universal pointwise BPB domain spaces, such that (X,Y) possesses pointwise BPB property for every Y, and on those Y, called universal pointwise BPB range spaces, such that enjoys pointwise BPB property for every uniformly smooth X. We show that every universal pointwise BPB domain space is uniformly convex and that L_p(𝜇) spaces fail to have this property when p>2. No universal pointwise BPB range space can be simultaneously uniformly convex and uniformly smooth unless its dimension is one. We also discuss a version of the pointwise BPB property for compact operators.
Damage model for plastic materials at finite strains
David Melching, Riccardo Scala, Jan Zeman
ZAMM – Zeitschrift fuer Angewandte Mathematik und Mechanik
First online: 3.7.2019
We introduce a model for elastoplasticity at finite strains coupled with damage. The internal energy of the deformed elastoplastic body depends on the deformation, the plastic strain, and the unidirectional isotropic damage. The main novelty is a dissipation distance allowing the description of coupled dissipative behavior of damage and plastic strain. Moving from time‐discretization, we prove the existence of energetic solutions to the quasistatic evolution problem.
Constant slope, entropy, and horseshoes for a map on a tame graph
Adam Bartoš, Jozef Bobok, Pavel Pyrih, Benjamin Vejnar
Ergodic Theory and Dynamical Systems, to appear
First online: 22.4.2019
We study continuous countably (strictly) monotone maps defined on a tame graph, i.e. a special Peano continuum for which the set containing branch points and end points has countable closure. In our investigation we confine ourselves to the countable Markov case. We show a necessary and sufficient condition under which a locally eventually onto, countably Markov map f of a tame graph G is conjugate to a map of constant slope g. In particular, we show that in the case of a Markov map f that corresponds to a recurrent transition matrix, the condition is satisfied for a constant slope e^h_to(f), where h_to(f) is the topological entropy of f. Moreover, we show that in our class the topological entropy h_to(f)is achievable through horseshoes of the map f.